CSE_E---1.7.THM-CRf.s

%------------------------------------------------------------------------------
% File     : CSE_E---1.7
% Problem  : SWW365+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 : n017.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 05:32:06 PM UTC 2026

% Result   : Theorem 38.70s 22.39s
% Output   : CNFRefutation 39.63s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_6069)

% Comments : 
%------------------------------------------------------------------------------
fof(fact_of__int__num,axiom,
    ! [X32,X10] :
      ( class_Rings_Oring__1(X10)
     => ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(X10),X32) = c_Groups_Ozero__class_Ozero(X10) )
        & ( X32 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X10),X32) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X32))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X10),X32) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X10,X10)),tc_fun(tc_Int_Oint,X10)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),X10),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X10,X10)),tc_fun(tc_Int_Oint,X10)),tc_Int_Oint),c_COMBB(tc_fun(X10,X10),X10,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_fun(X10,X10),X10),tc_Int_Oint),c_HOL_OLet(X10,X10)),c_Int_Oring__1__class_Oof__int(X10)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X10,X10),tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,X10)),tc_fun(tc_fun(X10,X10),tc_fun(X10,X10)),tc_Int_Oint),c_COMBS(X10,X10,X10)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X10,X10),tc_fun(X10,tc_fun(X10,X10))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,X10)),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_fun(X10,X10))),tc_Int_Oint),c_COMBB(X10,tc_fun(X10,X10),X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),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(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_COMBI(X10))))),hAPP(hAPP(c_COMBC(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Oplus__class_Oplus(X10)),hAPP(hAPP(c_COMBS(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_COMBI(X10)))),c_Groups_Oone__class_Oone(X10))))),c_Divides_Odivmod__int(X32,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,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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(X27),X34),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__power2__lt__zero) ).

fof(fact_power2__less__0,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__0) ).

fof(fact_zmod__number__of__Bit1,axiom,
    ! [X68,X92] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = 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),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))),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),X92)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = 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),X68)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))),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,
    ! [X92,X68] :
      ( 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),X68)))
     => ( ( 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),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = 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),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68))) )
        & ( ~ 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),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),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),X68)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__eqn__number__of) ).

fof(fact_negDivAlg__eqn__1__number__of,axiom,
    ! [X92] :
      ( 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),X92)))
     => ( ( 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),X92))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = 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),X92))) )
        & ( ~ 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),X92))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),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),X92)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).

fof(fact_posDivAlg__eqn__number__of,axiom,
    ! [X92,X68] :
      ( 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),X68)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = 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),X92)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),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),X68)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__eqn__number__of) ).

fof(fact_posDivAlg__eqn__1__number__of,axiom,
    ! [X92] :
      ( 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),X92)))
     => ( ( 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),X92)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = 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),X92)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),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),X92)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).

fof(fact_negDivAlg__eqn,axiom,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => ( ( 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),X37),X36)))
         => c_Divides_OnegDivAlg(X37,X36) = 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),X37),X36)) )
        & ( ~ 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),X37),X36)))
         => c_Divides_OnegDivAlg(X37,X36) = hAPP(c_Divides_Oadjust(X36),c_Divides_OnegDivAlg(X37,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)))),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__eqn) ).

fof(fact_posDivAlg__eqn,axiom,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),X36))
         => c_Divides_OposDivAlg(X37,X36) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),X36))
         => c_Divides_OposDivAlg(X37,X36) = hAPP(c_Divides_Oadjust(X36),c_Divides_OposDivAlg(X37,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)))),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__eqn) ).

fof(fact_hd__dropWhile,axiom,
    ! [X200,X42,X10] :
      ( c_List_OdropWhile(X10,X42,X200) != c_List_Olist_ONil(X10)
     => ~ hBOOL(hAPP(X42,hAPP(c_List_Ohd(X10),c_List_OdropWhile(X10,X42,X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__dropWhile) ).

fof(fact_power__number__of__odd__number__of,axiom,
    ! [X93,X90,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( ( 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),X90)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),hAPP(hAPP(c_COMBS(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)))),c_COMBI(X10))) )
        & ( ~ 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),X90)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = c_Groups_Oone__class_Oone(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__number__of__odd__number__of) ).

fof(fact_takeWhile__eq__filter,axiom,
    ! [X200,X42,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),c_List_OdropWhile(X10,X42,X200))))
         => ~ hBOOL(hAPP(X42,X3)) )
     => c_List_OtakeWhile(X10,X42,X200) = hAPP(c_List_Ofilter(X10,X42),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__filter) ).

fof(fact_power__number__of__odd,axiom,
    ! [X19,X90,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( ( 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),X90)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),hAPP(hAPP(c_COMBS(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Groups_Otimes__class_Otimes(X10),X19))),c_COMBI(X10))) )
        & ( ~ 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),X90)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = c_Groups_Oone__class_Oone(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__number__of__odd) ).

fof(fact_zpower__number__of__odd,axiom,
    ! [X19,X90] :
      ( ( 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),X90)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),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),X19))),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),X90)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = 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,
    ! [X11,X110,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X10,X10),X110)),c_Transitive__Closure_Ortrancl(X10,X110)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X11)),c_Transitive__Closure_Otrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).

fof(fact_dropWhile__append1,axiom,
    ! [X199,X42,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ( ~ hBOOL(hAPP(X42,X11))
       => c_List_OdropWhile(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),c_List_OdropWhile(X10,X42,X200)),X199) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__append1) ).

fof(fact_dvd_OatLeastatMost__psubset__iff,axiom,
    ! [X20,X6,X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X20)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14))
          | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X13))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X20))
            & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X13))
                & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X6)) )
              | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X20))
                & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X14)) ) ) ) )
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__psubset__iff) ).

fof(fact_acyclic__def,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Oacyclic(X10,X110)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),c_Transitive__Closure_Otrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__def) ).

fof(fact_zdiv__number__of__Bit1,axiom,
    ! [X68,X92] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X68))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X68))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = 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),X68)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit1) ).

fof(fact_acyclicI,axiom,
    ! [X110,X10] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),c_Transitive__Closure_Otrancl(X10,X110)))
     => c_Wellfounded_Oacyclic(X10,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicI) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [X200,X10,X11,X42] :
      ( ( hBOOL(hAPP(X42,X11))
       => c_List_OdropWhile(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = c_List_OdropWhile(X10,X42,X200) )
      & ( ~ hBOOL(hAPP(X42,X11))
       => c_List_OdropWhile(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_nat__number__of__Bit1,axiom,
    ! [X90] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__Bit1) ).

fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
    ! [X60,X61,X42] :
      ( c_List_Olist__ex(tc_Nat_Onat,X42,c_List_Oupt(X61,X60))
    <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X42),X61,X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__not__all__inverval__nat) ).

fof(fact_upt__rec__number__of,axiom,
    ! [X25,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__rec__number__of) ).

fof(fact_iszero__number__of__Bit1,axiom,
    ! [X92,X27] :
      ( ( class_Int_Onumber__ring(X27)
        & class_Int_Oring__char__0(X27) )
     => ~ c_Int_Oiszero(X27,hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).

fof(fact_dropWhile__eq__Cons__conv,axiom,
    ! [X199,X16,X200,X42,X10] :
      ( c_List_OdropWhile(X10,X42,X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199)
    <=> ( X200 = hAPP(hAPP(c_List_Oappend(X10),c_List_OtakeWhile(X10,X42,X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199))
        & ~ hBOOL(hAPP(X42,X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).

fof(fact_not__iszero__Numeral1,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => ~ c_Int_Oiszero(X27,hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).

fof(fact_removeAll__id,axiom,
    ! [X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => hAPP(c_List_OremoveAll(X10,X11),X200) = X200 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__id) ).

fof(fact_removeAll__filter__not,axiom,
    ! [X200,X10,X11,X42] :
      ( ~ hBOOL(hAPP(X42,X11))
     => hAPP(c_List_OremoveAll(X10,X11),hAPP(c_List_Ofilter(X10,X42),X200)) = hAPP(c_List_Ofilter(X10,X42),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__filter__not) ).

fof(fact_Suc__nat__number__of__add,axiom,
    ! [X25,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X68))),X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).

fof(fact_upt__Suc,axiom,
    ! [X43,X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
       => c_List_Oupt(X44,hAPP(c_Nat_OSuc,X43)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X44,X43)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X43),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
       => c_List_Oupt(X44,hAPP(c_Nat_OSuc,X43)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__Suc) ).

fof(fact_upt__rec,axiom,
    ! [X43,X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
       => c_List_Oupt(X44,X43) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X44),c_List_Oupt(hAPP(c_Nat_OSuc,X44),X43)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
       => c_List_Oupt(X44,X43) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__rec) ).

fof(fact_nat__number__of__add__1,axiom,
    ! [X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),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),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X68)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__1) ).

fof(fact_nat__number__of__diff__1,axiom,
    ! [X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),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),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X68)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__diff__1) ).

fof(fact_nat__1__add__number__of,axiom,
    ! [X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),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),X68)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),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),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X68)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__1__add__number__of) ).

fof(fact_Suc__nat__number__of,axiom,
    ! [X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X68)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).

fof(fact_member__rec_I2_J,axiom,
    ! [X34,X27] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X27),c_List_Olist_ONil(X27)),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I2_J) ).

fof(fact_adjust__def,axiom,
    ! [X14] : c_Divides_Oadjust(X14) = 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)),X14))))),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)),X14))))),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,
    ! [X33] : c_Int_Osucc(c_Int_OBit0(X33)) = c_Int_OBit1(X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit0) ).

fof(fact_Bit0__def,axiom,
    ! [X33] : c_Int_OBit0(X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).

fof(fact_diff__bin__simps_I2_J,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33),c_Int_OMin) = c_Int_Osucc(X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).

fof(fact_prod__fun__imageE,axiom,
    ! [X29,X1,X2,X102,X18,X6,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X6),hAPP(c_Set_Oimage(tc_prod(X18,X102),tc_prod(X10,X8),c_Product__Type_Omap__pair(X18,X10,X102,X8,X2,X1)),X29)))
     => ~ ! [X3,X51] :
            ( X6 = hAPP(hAPP(c_Product__Type_OPair(X10,X8),hAPP(X2,X3)),hAPP(X1,X51))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X102)),hAPP(hAPP(c_Product__Type_OPair(X18,X102),X3),X51)),X29)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__fun__imageE) ).

fof(fact_converse__rtranclE2,axiom,
    ! [X110,X263,X264,X265,X159,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X159),X265)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X264),X263))),c_Transitive__Closure_Ortrancl(tc_prod(X10,X8),X110)))
     => ( hAPP(hAPP(c_Product__Type_OPair(X10,X8),X159),X265) != hAPP(hAPP(c_Product__Type_OPair(X10,X8),X264),X263)
       => ~ ! [X46,X81] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X159),X265)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81))),X110))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X264),X263))),c_Transitive__Closure_Ortrancl(tc_prod(X10,X8),X110))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).

fof(fact_divmod__int__pdivmod,axiom,
    ! [X83,X32] :
      ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(X32,X83) = 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)) )
      & ( X32 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( X83 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X32,X83) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32) )
          & ( X83 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X32,X83) = 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,X83))),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)),X83)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X83),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X32,X83)),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),X83))))),c_Divides_Opdivmod(X32,X83)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__pdivmod) ).

fof(fact_apsnd__def,axiom,
    ! [X2,X10,X18,X8] : c_Product__Type_Oapsnd(X8,X18,X10,X2) = c_Product__Type_Omap__pair(X10,X10,X8,X18,c_Fun_Oid(X10),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__def) ).

fof(fact_divmod__int__code,axiom,
    ! [X83,X32] :
      ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(X32,X83) = 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)) )
      & ( X32 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( X83 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X32,X83) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32) )
          & ( X83 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(X32,X83) = 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,X83))),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,X32)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X83))),c_Divides_Opdivmod(X32,X83)),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),X83))))),c_Divides_Opdivmod(X32,X83)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__code) ).

fof(fact_Nitpick_Oplus__frac__def,axiom,
    ! [X110,X141,X10] : c_Nitpick_Oplus__frac(X10,X141,X110) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X10),X141),hAPP(c_Nitpick_Odenom(X10),X110))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X10),tc_Int_Oint),c_Nitpick_Ofrac(X10)),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(X10),X141))),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(X10),X141))))),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(X10),X110))),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(X10),X110)))))),c_COMBI(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oplus__frac__def) ).

fof(fact_Nitpick_Odenom__def,axiom,
    ! [X10] : c_Nitpick_Odenom(X10) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X10,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Odenom__def) ).

fof(fact_Nitpick_Onum__def,axiom,
    ! [X10] : c_Nitpick_Onum(X10) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X10,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Onum__def) ).

fof(fact_reflcl__set__eq,axiom,
    ! [X16,X11,X110,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X110)),c_fequal),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflcl__set__eq) ).

fof(fact_rtrancl__empty,axiom,
    ! [X10] : c_Transitive__Closure_Ortrancl(X10,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))) = c_Relation_OId(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__empty) ).

fof(fact_adjust__eq,axiom,
    ! [X110,X141,X14] : hAPP(c_Divides_Oadjust(X14),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X141),X110)) = 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),X110),X14)),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)))),X141)),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)))),X141)),X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_adjust__eq) ).

fof(fact_trancl__insert,axiom,
    ! [X110,X11,X16,X10] : c_Transitive__Closure_Otrancl(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X11)),X110)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X110)),hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10))),hAPP(hAPP(c_COMBC(X10,X10,tc_prod(X10,X10)),c_Product__Type_OPair(X10,X10)),X16))),c_Transitive__Closure_Ortrancl(X10,X110))))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10))),hAPP(c_Product__Type_OPair(X10,X10),X11))),c_Transitive__Closure_Ortrancl(X10,X110)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__insert) ).

fof(fact_trancl__unfold__left,axiom,
    ! [X110,X10] : c_Transitive__Closure_Otrancl(X10,X110) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X110),c_Transitive__Closure_Ortrancl(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).

fof(fact_SUP2__E,axiom,
    ! [X6,X14,X15,X12,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => ~ hBOOL(hAPP(hAPP(hAPP(X15,X3),X14),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__E) ).

fof(fact_sum__power2__le__zero__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),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(X10),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X10)))
      <=> ( X11 = c_Groups_Ozero__class_Ozero(X10)
          & X16 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__le__zero__iff) ).

fof(fact_transpose_Opsimps_I3_J,axiom,
    ! [X237,X200,X11,X10] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X10)),c_List_Otranspose__rel(X10)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),X237)))
     => c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),X237)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_Olist__case(tc_List_Olist(X10),X10,c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),c_COMBK(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10))))),X237)))),c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),X200),c_List_Oconcat(tc_List_Olist(X10),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X10)),X10,c_List_Olist_ONil(tc_List_Olist(X10)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_OCons(tc_List_Olist(X10))),c_List_Olist_ONil(tc_List_Olist(X10)))))),X237))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Opsimps_I3_J) ).

fof(fact_concat__conv__foldl,axiom,
    ! [X237,X10] : c_List_Oconcat(X10,X237) = hAPP(c_List_Ofoldl(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Oappend(X10),c_List_Olist_ONil(X10)),X237),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__conv__foldl) ).

fof(fact_transpose_Osimps_I3_J,axiom,
    ! [X237,X200,X11,X10] : c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),X237)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_Olist__case(tc_List_Olist(X10),X10,c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),c_COMBK(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10))))),X237)))),c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),X200),c_List_Oconcat(tc_List_Olist(X10),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X10)),X10,c_List_Olist_ONil(tc_List_Olist(X10)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_OCons(tc_List_Olist(X10))),c_List_Olist_ONil(tc_List_Olist(X10)))))),X237))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Osimps_I3_J) ).

fof(fact_odd__power__less__zero,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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)))),X25)))),c_Groups_Ozero__class_Ozero(X27))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__power__less__zero) ).

fof(fact_rel__compE,axiom,
    ! [X116,X110,X18,X197,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X197),hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X110),X116)))
     => ~ ! [X3,X51,X177] :
            ( X197 = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X3),X177)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X18)),hAPP(hAPP(c_Product__Type_OPair(X10,X18),X3),X51)),X110))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X8)),hAPP(hAPP(c_Product__Type_OPair(X18,X8),X51),X177)),X116)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compE) ).

fof(fact_odd__0__le__power__imp__0__le,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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)))),X25)))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).

fof(fact_Cons__eq__filter__iff,axiom,
    ! [X199,X42,X200,X11,X10] :
      ( hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) = hAPP(c_List_Ofilter(X10,X42),X199)
    <=> ? [X220,X225] :
          ( X199 = hAPP(hAPP(c_List_Oappend(X10),X220),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X225))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X220)))
             => ~ hBOOL(hAPP(X42,X3)) )
          & hBOOL(hAPP(X42,X11))
          & X200 = hAPP(c_List_Ofilter(X10,X42),X225) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__filter__iff) ).

fof(fact_filter__eq__Cons__iff,axiom,
    ! [X200,X11,X199,X42,X10] :
      ( hAPP(c_List_Ofilter(X10,X42),X199) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)
    <=> ? [X220,X225] :
          ( X199 = hAPP(hAPP(c_List_Oappend(X10),X220),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X225))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X220)))
             => ~ hBOOL(hAPP(X42,X3)) )
          & hBOOL(hAPP(X42,X11))
          & X200 = hAPP(c_List_Ofilter(X10,X42),X225) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__eq__Cons__iff) ).

fof(fact_power2__sum,axiom,
    ! [X34,X26,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),X34)),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(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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(X27),X34),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(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__sum) ).

fof(fact_power2__diff,axiom,
    ! [X34,X26,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X26),X34)),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(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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(X27),X34),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(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X26)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__diff) ).

fof(fact_dvd_OgreaterThan__iff,axiom,
    ! [X32,X61] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X61),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32)))
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X61))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X61),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThan__iff) ).

fof(fact_dvd_OlessThan__iff,axiom,
    ! [X32,X61] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X61),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32)))
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X61),X32))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OlessThan__iff) ).

fof(fact_Nitpick_Osetsum_H__def,axiom,
    ! [X2,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => c_Nitpick_Osetsum_H(X10,X8,X2,X12) = hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X10),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_List_Oset(X10))),X12))),c_List_Odistinct(X10))))) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => c_Nitpick_Osetsum_H(X10,X8,X2,X12) = c_Groups_Ozero__class_Ozero(X8) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).

fof(fact_sum__power2__gt__zero__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),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(X10),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      <=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
          | X16 != c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__gt__zero__iff) ).

fof(fact_transpose__aux__max,axiom,
    ! [X237,X8,X200,X10] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))),c_List_Ofoldr(tc_List_Olist(X8),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X8)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X8))),X237,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(X10)),X200)),c_List_Ofoldr(tc_List_Olist(X8),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X8)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X8),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X8)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X8)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X8),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X8)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X8),tc_List_Olist(X8),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X8)))),X237),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__max) ).

fof(fact_foldr__foldl,axiom,
    ! [X13,X200,X2,X10,X8] : c_List_Ofoldr(X8,X10,X2,X200,X13) = hAPP(c_List_Ofoldl(X10,X8,hAPP(c_COMBC(X8,X10,X10),X2),X13),hAPP(c_List_Orev(X8),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__foldl) ).

fof(fact_sublist__shift__lemma,axiom,
    ! [X61,X200,X12,X10] : hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10,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(X10,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X10,tc_Nat_Onat))),X12)),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X200),c_List_Oupt(X61,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10,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(X10,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X10,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(X10,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X10,tc_Nat_Onat))),X61))),X12)),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X200),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__shift__lemma) ).

fof(fact_sorted__list__of__set__range,axiom,
    ! [X30,X31] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30)) = c_List_Oupt(X31,X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).

fof(fact_Random_Osimps,axiom,
    ! [X243,X1,X10,X244] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X244),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X10,X1,X244,X243) = 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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X10)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X244),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X10,X1,X244,X243) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10,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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X243)),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(X10)))),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(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X10,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(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X10,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X244),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X243))),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(X10)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X10,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(X10)))),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(X10)))),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(X10))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),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(X10)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10))))),tc_prod(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X10)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),tc_prod(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X10)),c_Product__Type_Ofst(X10,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,
    ! [X68,X24] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = 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)))),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div__number__of) ).

fof(fact_Suc__div__eq__add3__div,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24)))),X25) = 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)))),X24)),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__div__eq__add3__div) ).

fof(fact_New__DSequence_Opos__not__seq__def,axiom,
    ! [X61,X232] : hAPP(c_New__DSequence_Opos__not__seq(X232),X61) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X232,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)))),X61))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).

fof(fact_mem__splitE,axiom,
    ! [X148,X6,X18,X8,X19,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X19),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,tc_fun(X10,tc_HOL_Obool)),X6),X148)))
     => ~ ! [X3,X51] :
            ( X148 = hAPP(hAPP(c_Product__Type_OPair(X8,X18),X3),X51)
           => ~ hBOOL(hAPP(hAPP(c_member(X10),X19),hAPP(hAPP(X6,X3),X51))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitE) ).

fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
    ! [X93,X12,X11,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),X93))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ~ ! [X51] :
                ( X93 = hAPP(hAPP(X2,X11),X51)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X51)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE) ).

fof(fact_int__of__code,axiom,
    ! [X33] :
      ( ( X33 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Code__Numeral_Oint__of,X33) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X33 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => ( ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X33,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,X33) = 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),X33),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,X33,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,X33) = 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),X33),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,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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(X27),X34),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,X8,X12,X10] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
            & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),hAPP(hAPP(c_COMBC(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole__infinite) ).

fof(fact_concat__eq__concat__iff,axiom,
    ! [X199,X200,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10))))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X3)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X199)
       => ( c_List_Oconcat(X10,X200) = c_List_Oconcat(X10,X199)
        <=> X200 = X199 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__eq__concat__iff) ).

fof(fact_concat__injective,axiom,
    ! [X199,X200,X10] :
      ( c_List_Oconcat(X10,X200) = c_List_Oconcat(X10,X199)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X199)
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),X3),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199))))
             => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10))))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X3)) )
         => X200 = X199 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__injective) ).

fof(fact_nat__rec__add__eq__if,axiom,
    ! [X30,X93,X2,X13,X10] : hAPP(c_Nat_Onat_Onat__rec(X10,X13,X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),X30)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X10,X13,X2),X30))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10,X10),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)),X30))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Int_Oint),c_Nat_Onat_Onat__rec(X10,X13,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)),X30))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__add__eq__if) ).

fof(fact_add__Min__right,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),c_Int_OMin) = c_Int_Opred(X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min__right) ).

fof(fact_neg__zmod__mult__2,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),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)))),X36)),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)))),X37)) = 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),X36),c_Groups_Oone__class_Oone(tc_Int_Oint)),X37))),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,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),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)))),X36))),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)))),X37)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X36),c_Groups_Oone__class_Oone(tc_Int_Oint))),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zdiv__mult__2) ).

fof(fact_pos__zdiv__mult__2,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
     => 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)))),X36))),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)))),X37)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zdiv__mult__2) ).

fof(fact_eq__number__of__Suc,axiom,
    ! [X30,X93] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93) = hAPP(c_Nat_OSuc,X30)
    <=> 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(X93))),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)),X30))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Suc) ).

fof(fact_Suc__eq__number__of,axiom,
    ! [X93,X30] :
      ( hAPP(c_Nat_OSuc,X30) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)
    <=> 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(X93))),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)),X30))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__number__of) ).

fof(fact_Nitpick_Ocard_H__def,axiom,
    ! [X12,X10] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Nitpick_Ocard_H(X10,X12) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_Hilbert__Choice_OEps(tc_List_Olist(X10),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_List_Oset(X10))),X12))),c_List_Odistinct(X10)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Nitpick_Ocard_H(X10,X12) = 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,
    ! [X61,X143] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X143))
     => 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)),X143))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X61)))) = 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)),X143))),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,X61))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less__Suc2) ).

fof(fact_power2__less__imp__less,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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(X27),X34),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(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__less__imp__less) ).

fof(fact_power2__le__imp__le,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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(X27),X34),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(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__le__imp__le) ).

fof(fact_vimage__if,axiom,
    ! [X15,X8,X20,X12,X6,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X20),X12))
           => hAPP(c_Set_Ovimage(X8,X10,hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBC(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))),X6)),X20)),X12) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X20),X12))
           => hAPP(c_Set_Ovimage(X8,X10,hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBC(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))),X6)),X20)),X12) = X15 ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X20),X12))
           => hAPP(c_Set_Ovimage(X8,X10,hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBC(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))),X6)),X20)),X12) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),X15) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X20),X12))
           => hAPP(c_Set_Ovimage(X8,X10,hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBC(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))),X6)),X20)),X12) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__if) ).

fof(fact_pos__zmod__mult__2,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
     => 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)))),X36)),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)))),X37)) = 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,X36,X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__zmod__mult__2) ).

fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
    ! [X68,X24] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = 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)))),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod__number__of) ).

fof(fact_zero__le__even__power_H,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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)))),X25)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__even__power_H) ).

fof(fact_Suc__mod__eq__add3__mod,axiom,
    ! [X25,X24] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24))),X25) = 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)))),X24),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mod__eq__add3__mod) ).

fof(fact_mod__Suc__eq__mod__add3,axiom,
    ! [X25,X24] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X25)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,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)))),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__mod__add3) ).

fof(fact_div__Suc__eq__div__add3,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X25)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),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)))),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__Suc__eq__div__add3) ).

fof(fact_trancl__Int__subset,axiom,
    ! [X116,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X110)),X116)),X110)),X116))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X110)),X116)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__Int__subset) ).

fof(fact_setprod__gen__delta,axiom,
    ! [X6,X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),X6)),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X14,X13)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X28)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),X6)),X28) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),hAPP(c_Finite__Set_Ocard(X10),X28)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__gen__delta) ).

fof(fact_setsum__delta,axiom,
    ! [X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),c_Groups_Ozero__class_Ozero(X8))),X28) = hAPP(X14,X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),c_Groups_Ozero__class_Ozero(X8))),X28) = c_Groups_Ozero__class_Ozero(X8) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__delta) ).

fof(fact_setprod__delta,axiom,
    ! [X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),c_Groups_Oone__class_Oone(X8))),X28) = hAPP(X14,X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),c_Groups_Oone__class_Oone(X8))),X28) = c_Groups_Oone__class_Oone(X8) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__delta) ).

fof(fact_less__Suc__number__of,axiom,
    ! [X93,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)))
    <=> 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(X93))),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),X30)),c_Int_Onat))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__number__of) ).

fof(fact_le__Suc__number__of,axiom,
    ! [X93,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)))
    <=> 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(X93))),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),X30)),c_Int_Onat))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__number__of) ).

fof(fact_apsnd__apfst__commute,axiom,
    ! [X148,X1,X102,X2,X10,X8,X18] : hAPP(c_Product__Type_Oapsnd(X18,X8,X10,X2),hAPP(c_Product__Type_Oapfst(X102,X10,X18,X1),X148)) = hAPP(c_Product__Type_Oapfst(X102,X10,X8,X1),hAPP(c_Product__Type_Oapsnd(X18,X8,X102,X2),X148)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__apfst__commute) ).

fof(fact_apfst__def,axiom,
    ! [X2,X8,X18,X10] : c_Product__Type_Oapfst(X10,X18,X8,X2) = c_Product__Type_Omap__pair(X10,X18,X8,X8,X2,c_Fun_Oid(X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__def) ).

fof(fact_lexord__append__leftD,axiom,
    ! [X110,X93,X77,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X11),X77)),hAPP(hAPP(c_List_Oappend(X10),X11),X93))),c_List_Olexord(X10,X110)))
     => ( ! [X46] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X46),X46)),X110))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X77),X93)),c_List_Olexord(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftD) ).

fof(fact_rel__pow__E2,axiom,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
     => ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X11 != X19 )
       => ~ ! [X51,X74] :
              ( X30 = hAPP(c_Nat_OSuc,X74)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),X29))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X74),X29))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__E2) ).

fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
    ! [X14,X13] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
    ! [X83,X32] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32,X83) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X83))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X83),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).

fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
    ! [X14,X13] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X13,X14)
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff2) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
    ! [X83,X32] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32,X83)
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X83))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X83),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).

fof(fact_dvd_Ostrict__monoD,axiom,
    ! [X16,X11,X2,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X10,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
       => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
            & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X11)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X11)),hAPP(X2,X16))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ostrict__monoD) ).

fof(fact_power__odd__eq,axiom,
    ! [X25,X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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)))),X25))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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_power__odd__eq) ).

fof(fact_takeWhile__neq__rev,axiom,
    ! [X11,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_OtakeWhile(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X11)),hAPP(c_List_Orev(X10),X200)) = hAPP(c_List_Orev(X10),hAPP(c_List_Otl(X10),c_List_OdropWhile(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X11)),X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__neq__rev) ).

fof(fact_dropWhile__eq__drop,axiom,
    ! [X200,X42,X10] : c_List_OdropWhile(X10,X42,X200) = hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200))),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__drop) ).

fof(fact_apsnd__compose,axiom,
    ! [X11,X1,X102,X2,X10,X8,X18] : hAPP(c_Product__Type_Oapsnd(X18,X8,X10,X2),hAPP(c_Product__Type_Oapsnd(X102,X18,X10,X1),X11)) = hAPP(c_Product__Type_Oapsnd(X102,X8,X10,hAPP(c_Fun_Ocomp(X18,X8,X102,X2),X1)),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__compose) ).

fof(fact_apfst__compose,axiom,
    ! [X11,X1,X102,X2,X8,X10,X18] : hAPP(c_Product__Type_Oapfst(X18,X10,X8,X2),hAPP(c_Product__Type_Oapfst(X102,X18,X8,X1),X11)) = hAPP(c_Product__Type_Oapfst(X102,X10,X8,hAPP(c_Fun_Ocomp(X18,X10,X102,X2),X1)),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__compose) ).

fof(fact_sum__power2__eq__zero__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),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(X10),X16),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X11 = c_Groups_Ozero__class_Ozero(X10)
          & X16 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__power2__eq__zero__iff) ).

fof(fact_transpose__rectangle,axiom,
    ! [X30,X10,X200] :
      ( ( X200 = c_List_Olist_ONil(tc_List_Olist(X10))
       => X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
     => ( ! [X91] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X200)))
           => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X200),X91)) = X30 )
       => c_List_Otranspose(X10,X200) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X10)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X10)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X10),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X10)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X10)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_Nat_Onat,X10),tc_Nat_Onat),c_List_Onth(X10)),hAPP(c_List_Onth(tc_List_Olist(X10)),X200))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X200)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__rectangle) ).

fof(fact_negDivAlg_Opinduct,axiom,
    ! [X42,X57,X152] :
      ( 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),X152),X57)))
     => ( ! [X46,X81] :
            ( 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),X46),X81)))
           => ( ( ~ ( 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),X46),X81)))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X81),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
               => hBOOL(hAPP(hAPP(X42,X46),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)))),X81))) )
             => hBOOL(hAPP(hAPP(X42,X46),X81)) ) )
       => hBOOL(hAPP(hAPP(X42,X152),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Opinduct) ).

fof(fact_setsum__delta_H,axiom,
    ! [X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(c_fequal,X13))),X14)),c_Groups_Ozero__class_Ozero(X8))),X28) = hAPP(X14,X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(c_fequal,X13))),X14)),c_Groups_Ozero__class_Ozero(X8))),X28) = c_Groups_Ozero__class_Ozero(X8) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__delta_H) ).

fof(fact_setprod__delta_H,axiom,
    ! [X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(c_fequal,X13))),X14)),c_Groups_Oone__class_Oone(X8))),X28) = hAPP(X14,X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(c_fequal,X13))),X14)),c_Groups_Oone__class_Oone(X8))),X28) = c_Groups_Oone__class_Oone(X8) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__delta_H) ).

fof(fact_posDivAlg_Opinduct,axiom,
    ! [X42,X57,X152] :
      ( 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),X152),X57)))
     => ( ! [X46,X81] :
            ( 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),X46),X81)))
           => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X46),X81))
                    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X81),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
               => hBOOL(hAPP(hAPP(X42,X46),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)))),X81))) )
             => hBOOL(hAPP(hAPP(X42,X46),X81)) ) )
       => hBOOL(hAPP(hAPP(X42,X152),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Opinduct) ).

fof(fact_listrel__Cons2,axiom,
    ! [X110,X199,X16,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199))),c_List_Olistrel(X10,X110)))
     => ~ ! [X3,X208] :
            ( X200 = hAPP(hAPP(c_List_Olist_OCons(X10),X3),X208)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X16)),X110))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X208),X199)),c_List_Olistrel(X10,X110))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons2) ).

fof(fact_rel__pow__Suc__E2,axiom,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30)),X29)))
     => ~ ! [X51] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),X29))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__E2) ).

fof(fact_Nitpick_Otimes__frac__def,axiom,
    ! [X80,X114,X27] : c_Nitpick_Otimes__frac(X27,X114,X80) = hAPP(hAPP(c_Nitpick_Ofrac(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X27),X114)),hAPP(c_Nitpick_Onum(X27),X80))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X27),X114)),hAPP(c_Nitpick_Odenom(X27),X80))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Otimes__frac__def) ).

fof(fact_rel__pow__E,axiom,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
     => ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X11 != X19 )
       => ~ ! [X51,X74] :
              ( X30 = hAPP(c_Nat_OSuc,X74)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X74),X29)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),X29)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__E) ).

fof(fact_rel__pow__Suc__E,axiom,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30)),X29)))
     => ~ ! [X51] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),X29)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__E) ).

fof(fact_negDivAlg_Opsimps,axiom,
    ! [X14,X13] :
      ( 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),X13),X14)))
     => ( ( ( 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),X13),X14)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OnegDivAlg(X13,X14) = 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),X13),X14)) )
        & ( ~ ( 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),X13),X14)))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OnegDivAlg(X13,X14) = hAPP(c_Divides_Oadjust(X14),c_Divides_OnegDivAlg(X13,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))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Opsimps) ).

fof(fact_posDivAlg_Opsimps,axiom,
    ! [X14,X13] :
      ( 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),X13),X14)))
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13),X14))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OposDivAlg(X13,X14) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13) )
        & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13),X14))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
         => c_Divides_OposDivAlg(X13,X14) = hAPP(c_Divides_Oadjust(X14),c_Divides_OposDivAlg(X13,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))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Opsimps) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
    ! [X25,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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)))),X25))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).

fof(fact_arith__series__int,axiom,
    ! [X30,X20,X13] : 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),X13)),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),X30))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),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),X30),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,
    ! [X30,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Nat_OSuc,X30)))
    <=> 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(X93))),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)),X30)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__Suc) ).

fof(fact_le__number__of__Suc,axiom,
    ! [X30,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Nat_OSuc,X30)))
    <=> 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(X93))),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)),X30)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__Suc) ).

fof(fact_of__nat__double,axiom,
    ! [X26,X27] :
      ( class_Rings_Osemiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),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)))),X26))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onat,X26))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onat,X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__double) ).

fof(fact_negDivAlg_Osimps,axiom,
    ! [X36,X37] :
      ( ( ( 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),X37),X36)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OnegDivAlg(X37,X36) = 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),X37),X36)) )
      & ( ~ ( 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),X37),X36)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OnegDivAlg(X37,X36) = hAPP(c_Divides_Oadjust(X36),c_Divides_OnegDivAlg(X37,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)))),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg_Osimps) ).

fof(fact_posDivAlg_Osimps,axiom,
    ! [X36,X37] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),X36))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OposDivAlg(X37,X36) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),X36))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
       => c_Divides_OposDivAlg(X37,X36) = hAPP(c_Divides_Oadjust(X36),c_Divides_OposDivAlg(X37,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)))),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg_Osimps) ).

fof(fact_power__minus1__odd,axiom,
    ! [X25,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27))),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)))),X25))) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__odd) ).

fof(fact_power__minus__even,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),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)))),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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)))),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus__even) ).

fof(fact_power__m1__odd,axiom,
    ! [X25,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),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)))),X25))) = hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__odd) ).

fof(fact_Suc3__eq__add__3,axiom,
    ! [X25] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X25))) = 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)))),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc3__eq__add__3) ).

fof(fact_ImageE,axiom,
    ! [X12,X110,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(c_Relation_OImage(X8,X10,X110),X12)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X3),X14)),X110))
           => ~ hBOOL(hAPP(hAPP(c_member(X8),X3),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ImageE) ).

fof(fact_n__lists_Osimps_I2_J,axiom,
    ! [X200,X30,X10] : c_Enum_On__lists(X10,hAPP(c_Nat_OSuc,X30),X200) = c_List_Oconcat(tc_List_Olist(X10),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),tc_List_Olist(X10)),c_List_Omap(X10,tc_List_Olist(X10))),hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)))),X200)),c_Enum_On__lists(X10,X30,X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists_Osimps_I2_J) ).

fof(fact_nat__case__add__eq__if,axiom,
    ! [X30,X93,X2,X13,X10] : c_Nat_Onat_Onat__case(X10,X13,X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),X30)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X10,X13,X2,X30))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X30)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__add__eq__if) ).

fof(fact_mod2__gr__0,axiom,
    ! [X31] :
      ( 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,X31,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,X31,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,X11,X2,X10,X8,X18] :
      ( hAPP(c_Product__Type_Oapsnd(X18,X8,X10,X2),X11) = hAPP(c_Product__Type_Oapsnd(X18,X8,X10,X1),X11)
    <=> hAPP(X2,hAPP(c_Product__Type_Osnd(X10,X18),X11)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X10,X18),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__eq__conv) ).

fof(fact_apfst__eq__conv,axiom,
    ! [X1,X11,X2,X8,X10,X18] :
      ( hAPP(c_Product__Type_Oapfst(X18,X10,X8,X2),X11) = hAPP(c_Product__Type_Oapfst(X18,X10,X8,X1),X11)
    <=> hAPP(X2,hAPP(c_Product__Type_Ofst(X18,X8),X11)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X18,X8),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__eq__conv) ).

fof(fact_Id__def,axiom,
    ! [X10] : c_Relation_OId(X10) = hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X10,X10)),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(tc_prod(X10,X10),tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_HOL_Obool)),tc_prod(X10,X10)),c_COMBB(tc_prod(X10,X10),tc_HOL_Obool,X10)),c_fequal)),hAPP(hAPP(c_COMBS(X10,X10,tc_prod(X10,X10)),c_Product__Type_OPair(X10,X10)),c_COMBI(X10))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__def) ).

fof(fact_apsnd__apfst,axiom,
    ! [X11,X1,X102,X2,X10,X8,X18] : hAPP(c_Product__Type_Oapsnd(X18,X8,X10,X2),hAPP(c_Product__Type_Oapfst(X102,X10,X18,X1),X11)) = hAPP(hAPP(c_Product__Type_OPair(X10,X8),hAPP(X1,hAPP(c_Product__Type_Ofst(X102,X18),X11))),hAPP(X2,hAPP(c_Product__Type_Osnd(X102,X18),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__apfst) ).

fof(fact_apfst__apsnd,axiom,
    ! [X11,X1,X102,X2,X8,X10,X18] : hAPP(c_Product__Type_Oapfst(X18,X10,X8,X2),hAPP(c_Product__Type_Oapsnd(X102,X8,X18,X1),X11)) = hAPP(hAPP(c_Product__Type_OPair(X10,X8),hAPP(X2,hAPP(c_Product__Type_Ofst(X18,X102),X11))),hAPP(X1,hAPP(c_Product__Type_Osnd(X18,X102),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__apsnd) ).

fof(fact_half__gt__zero__iff,axiom,
    ! [X110,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber__ring(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X110),hAPP(c_Int_Onumber__class_Onumber__of(X10),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_half__gt__zero__iff) ).

fof(fact_max__Suc__number__of,axiom,
    ! [X30,X93] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))),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,X30))),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)),X30)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc__number__of) ).

fof(fact_zero__less__power2,axiom,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> X13 != c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power2) ).

fof(fact_min__Suc__number__of,axiom,
    ! [X30,X93] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))),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)),X30)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc__number__of) ).

fof(fact_nat__rec__number__of,axiom,
    ! [X93,X2,X13,X10] : hAPP(c_Nat_Onat_Onat__rec(X10,X13,X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),c_Nat__Numeral_Oneg)),X13)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10,X10),tc_Int_Oint),X2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Int_Oint),c_Nat_Onat_Onat__rec(X10,X13,X2)),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__number__of) ).

fof(fact_transpose__aux__filter__head,axiom,
    ! [X237,X10] : c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_Olist__case(tc_List_Olist(X10),X10,c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),c_COMBK(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10))))),X237)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),X10),c_List_Ohd(X10)),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10)))),X237)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__filter__head) ).

fof(fact_transpose__aux__filter__tail,axiom,
    ! [X237,X10] : c_List_Oconcat(tc_List_Olist(X10),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X10)),X10,c_List_Olist_ONil(tc_List_Olist(X10)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10))),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),c_List_Olist_OCons(tc_List_Olist(X10))),c_List_Olist_ONil(tc_List_Olist(X10)))))),X237)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Otl(X10)),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10)))),X237)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__aux__filter__tail) ).

fof(fact_rtrancl__Int__subset,axiom,
    ! [X110,X116,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Relation_OId(X10)),X116))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X110)),X116)),X110)),X116))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X110)),X116)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Int__subset) ).

fof(fact_listrel__Cons1,axiom,
    ! [X110,X200,X199,X16,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199)),X200)),c_List_Olistrel(X10,X110)))
     => ~ ! [X51,X207] :
            ( X200 = hAPP(hAPP(c_List_Olist_OCons(X10),X51),X207)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X51)),X110))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X199),X207)),c_List_Olistrel(X10,X110))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons1) ).

fof(fact_power__even__eq,axiom,
    ! [X25,X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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)))),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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_power__even__eq) ).

fof(fact_sublist__def,axiom,
    ! [X12,X200,X10] : c_List_Osublist(X10,X200,X12) = hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X10,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(X10,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X10,tc_Nat_Onat))),X12)),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X200),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__def) ).

fof(fact_fold1Set_Oequations,axiom,
    ! [X64,X56,X57,X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X57),X56)),X64))
    <=> ? [X46,X52] :
          ( hAPP(hAPP(c_Set_Oinsert(X10),X57),X56) = hAPP(hAPP(c_Set_Oinsert(X10),X46),X52)
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X46,X52),X64))
          & ~ hBOOL(hAPP(hAPP(c_member(X10),X46),X52)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set_Oequations) ).

fof(fact_Nitpick_Ouminus__frac__def,axiom,
    ! [X114,X27] : c_Nitpick_Ouminus__frac(X27,X114) = c_Nitpick_OAbs__Frac(X27,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(X27),X114))),hAPP(c_Nitpick_Odenom(X27),X114))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).

fof(fact_snd__apsnd,axiom,
    ! [X11,X2,X18,X10,X8] : hAPP(c_Product__Type_Osnd(X8,X10),hAPP(c_Product__Type_Oapsnd(X18,X10,X8,X2),X11)) = hAPP(X2,hAPP(c_Product__Type_Osnd(X8,X18),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__apsnd) ).

fof(fact_fst__apfst,axiom,
    ! [X11,X2,X18,X8,X10] : hAPP(c_Product__Type_Ofst(X10,X8),hAPP(c_Product__Type_Oapfst(X18,X10,X8,X2),X11)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X18,X8),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__apfst) ).

fof(fact_fst__apsnd,axiom,
    ! [X11,X2,X18,X8,X10] : hAPP(c_Product__Type_Ofst(X10,X8),hAPP(c_Product__Type_Oapsnd(X18,X8,X10,X2),X11)) = hAPP(c_Product__Type_Ofst(X10,X18),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__apsnd) ).

fof(fact_snd__apfst,axiom,
    ! [X11,X2,X18,X10,X8] : hAPP(c_Product__Type_Osnd(X8,X10),hAPP(c_Product__Type_Oapfst(X18,X8,X10,X2),X11)) = hAPP(c_Product__Type_Osnd(X18,X10),X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__apfst) ).

fof(fact_nat__case__number__of,axiom,
    ! [X93,X2,X13,X10] : c_Nat_Onat_Onat__case(X10,X13,X2,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X10),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X10,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),c_Nat__Numeral_Oneg)),X13)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,
    ! [X93,X30] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))),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,X30))),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),X30)),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__number__of__Suc) ).

fof(fact_min__number__of__Suc,axiom,
    ! [X93,X30] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))),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),X30)),c_Int_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__number__of__Suc) ).

fof(fact_Suc__n__div__2__gt__zero,axiom,
    ! [X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => 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),X25),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,
    ! [X80,X27] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X27)
        & class_Int_Onumber__ring(X27) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X80))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X80),hAPP(c_Int_Onumber__class_Onumber__of(X27),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,
    ! [X25,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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)))),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(fact_div__2__gt__zero,axiom,
    ! [X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25))
     => 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),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_div__2__gt__zero) ).

fof(fact_power3__eq__cube,axiom,
    ! [X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X37)),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power3__eq__cube) ).

fof(fact_zero__le__power2,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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,
    ! [X25,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27))),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)))),X25)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus1__even) ).

fof(fact_power__m1__even,axiom,
    ! [X25,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),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)))),X25)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__m1__even) ).

fof(fact_diff__nat__number__of,axiom,
    ! [X93,X119] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)) = 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),X93),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X119)))),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,
    ! [X200,X2,X8,X42,X10] : c_List_OdropWhile(X10,X42,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_OdropWhile(X8,hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,X8,X42),X2),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__map) ).

fof(fact_diff__nat__eq__if,axiom,
    ! [X19,X137] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X137))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X19)),hAPP(c_Int_Onat,X137)) = hAPP(c_Int_Onat,X19) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X137))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X19)),hAPP(c_Int_Onat,X137)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X137)),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,
    ! [X11,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_OdropWhile(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X11)),hAPP(c_List_Orev(X10),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),hAPP(c_List_Orev(X10),c_List_OtakeWhile(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X11)),X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__neq__rev) ).

fof(fact_wf__weak__decr__stable,axiom,
    ! [X110,X2,X10] :
      ( ! [X91] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X2,hAPP(c_Nat_OSuc,X91))),hAPP(X2,X91))),c_Transitive__Closure_Ortrancl(X10,X110)))
     => ( c_Wellfounded_Owf(X10,c_Transitive__Closure_Otrancl(X10,X110))
       => ? [X91] :
          ! [X59] : hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X91),X59)) = hAPP(X2,X91) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__weak__decr__stable) ).

fof(fact_fold__graph__permute__diff,axiom,
    ! [X13,X11,X12,X14,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X14,X12),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X14),X12))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X13,hAPP(hAPP(c_Set_Oinsert(X10),X14),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X11)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__permute__diff) ).

fof(fact_concat__map__singleton,axiom,
    ! [X200,X2,X8,X10] : c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(X8,tc_List_Olist(X10)),hAPP(hAPP(c_COMBC(X8,tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X8),c_List_Olist_OCons(X10)),X2)),c_List_Olist_ONil(X10))),X200)) = hAPP(hAPP(c_List_Omap(X8,X10),X2),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__map__singleton) ).

fof(fact_Nitpick_Oless__eq__frac__def,axiom,
    ! [X110,X141,X10] :
      ( c_Nitpick_Oless__eq__frac(X10,X141,X110)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X10),c_Nitpick_Oplus__frac(X10,X141,c_Nitpick_Ouminus__frac(X10,X110)))),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,
    ! [X110,X141,X10] :
      ( c_Nitpick_Oless__frac(X10,X141,X110)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X10),c_Nitpick_Oplus__frac(X10,X141,c_Nitpick_Ouminus__frac(X10,X110)))),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,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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(X27),X34),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(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
           => X26 = X34 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__imp__eq) ).

fof(fact_less__2__cases,axiom,
    ! [X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
     => ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X25 = 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,
    ! [X24] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24))),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),X24),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,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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(X27),X37),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,
    ! [X114,X27,X10] :
      ( ( class_Rings_Oinverse(X10)
        & class_Rings_Oring__1(X10) )
     => c_Nitpick_Oof__frac(X27,X10,X114) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(c_Nitpick_Onum(X27),X114))),hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(c_Nitpick_Odenom(X27),X114))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oof__frac__def) ).

fof(fact_converseE,axiom,
    ! [X110,X198,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X198),hAPP(c_Relation_Oconverse(X8,X10),X110)))
     => ~ ! [X3,X51] :
            ( X198 = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X51),X3)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X3),X51)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseE) ).

fof(fact_setsum__natinterval__difff,axiom,
    ! [X2,X30,X31,X10] :
      ( class_Groups_Oab__group__add(X10)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X10)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,X31,X30)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(X2,X31)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X10)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,X31,X30)) = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__natinterval__difff) ).

fof(fact_fold__graph__insert__swap,axiom,
    ! [X19,X16,X12,X14,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X14,X12),X16))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X14),X12))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X19,hAPP(hAPP(c_Set_Oinsert(X10),X14),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X19),X16))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__insert__swap) ).

fof(fact_fold__graph_OinsertI,axiom,
    ! [X16,X19,X2,X8,X12,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X16))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),hAPP(hAPP(X2,X11),X16))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).

fof(fact_tranclD,axiom,
    ! [X29,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Otrancl(X10,X29)))
     => ? [X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X177)),X29))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X177),X16)),c_Transitive__Closure_Ortrancl(X10,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD) ).

fof(fact_tranclD2,axiom,
    ! [X29,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Otrancl(X10,X29)))
     => ? [X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X177)),c_Transitive__Closure_Ortrancl(X10,X29)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X177),X16)),X29)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tranclD2) ).

fof(fact_apfst__conv,axiom,
    ! [X16,X11,X2,X8,X10,X18] : hAPP(c_Product__Type_Oapfst(X18,X10,X8,X2),hAPP(hAPP(c_Product__Type_OPair(X18,X8),X11),X16)) = hAPP(hAPP(c_Product__Type_OPair(X10,X8),hAPP(X2,X11)),X16),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__conv) ).

fof(fact_apsnd__conv,axiom,
    ! [X16,X11,X2,X10,X8,X18] : hAPP(c_Product__Type_Oapsnd(X18,X8,X10,X2),hAPP(hAPP(c_Product__Type_OPair(X10,X18),X11),X16)) = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),hAPP(X2,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__conv) ).

fof(fact_list__ex1__simps_I2_J,axiom,
    ! [X200,X11,X42,X10] :
      ( c_List_Olist__ex1(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))
    <=> ( ( hBOOL(hAPP(X42,X11))
         => c_List_Olist__all(X10,hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X42))),hAPP(c_fequal,X11)),X200) )
        & ( ~ hBOOL(hAPP(X42,X11))
         => c_List_Olist__ex1(X10,X42,X200) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__simps_I2_J) ).

fof(fact_transpose__max__length,axiom,
    ! [X200,X10] : c_List_Ofoldr(tc_List_Olist(X10),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X10)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),c_List_Otranspose(X10,X200),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10)))),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__max__length) ).

fof(fact_dropWhile__nth,axiom,
    ! [X200,X42,X10,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OdropWhile(X10,X42,X200))))
     => hAPP(hAPP(c_List_Onth(X10),c_List_OdropWhile(X10,X42,X200)),X60) = hAPP(hAPP(c_List_Onth(X10),X200),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__nth) ).

fof(fact_zmod__number__of__Bit0,axiom,
    ! [X92,X68] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = 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),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__number__of__Bit0) ).

fof(fact_power2__abs,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),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(X27),X37),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,
    ! [X37,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),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(X27),X37),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,
    ! [X24] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X24)),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,X24,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,
    ! [X42,X12,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X9),X12))
       => ( hBOOL(hAPP(X42,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
         => ( ! [X46,X47] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X47))
               => ( hBOOL(hAPP(hAPP(c_member(X10),X46),X12))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X46),X47))
                   => ( hBOOL(hAPP(X42,X47))
                     => hBOOL(hAPP(X42,hAPP(hAPP(c_Set_Oinsert(X10),X46),X47))) ) ) ) )
           => hBOOL(hAPP(X42,X9)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset__induct) ).

fof(fact_mult__2,axiom,
    ! [X38,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X38) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X38),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2) ).

fof(fact_listsum__map__filter,axiom,
    ! [X2,X42,X200,X10,X8] :
      ( class_Groups_Omonoid__add(X8)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
           => ( ~ hBOOL(hAPP(X42,X3))
             => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X8) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),hAPP(c_List_Ofilter(X10,X42),X200))) = hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__map__filter) ).

fof(fact_nat__mult__2,axiom,
    ! [X38] : 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)))),X38) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X38),X38),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2) ).

fof(fact_add__2__eq__Suc,axiom,
    ! [X25] : 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)))),X25) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc) ).

fof(fact_length__dropWhile__le,axiom,
    ! [X200,X42,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OdropWhile(X10,X42,X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__dropWhile__le) ).

fof(fact_folding__image__simple_Oinsert,axiom,
    ! [X11,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X8),X11),X12))
         => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X8),X11),X12)) = hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X9,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).

fof(fact_RangeE,axiom,
    ! [X110,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(c_Relation_ORange(X8,X10),X110)))
     => ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X3),X14)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeE) ).

fof(fact_trancl__trans,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Otrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),c_Transitive__Closure_Otrancl(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Otrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__trans) ).

fof(fact_trancl__converseI,axiom,
    ! [X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Otrancl(X10,X110))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Otrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseI) ).

fof(fact_trancl__converseD,axiom,
    ! [X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Otrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X110))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Otrancl(X10,X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converseD) ).

fof(fact_fold1Set_Ointros,axiom,
    ! [X11,X12,X13,X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X13,X12),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set_Ointros) ).

fof(fact_power2__eq__1__iff,axiom,
    ! [X13,X10] :
      ( class_Rings_Oring__1__no__zero__divisors(X10)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X10)
      <=> ( X13 = c_Groups_Oone__class_Oone(X10)
          | X13 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Groups_Oone__class_Oone(X10)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__1__iff) ).

fof(fact_zero__eq__power2,axiom,
    ! [X13,X10] :
      ( class_Rings_Oring__1__no__zero__divisors(X10)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X10)
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__eq__power2) ).

fof(fact_removeAll__append,axiom,
    ! [X201,X202,X26,X27] : hAPP(c_List_OremoveAll(X27,X26),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(hAPP(c_List_Oappend(X27),hAPP(c_List_OremoveAll(X27,X26),X202)),hAPP(c_List_OremoveAll(X27,X26),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__append) ).

fof(fact_removeAll__filter__not__eq,axiom,
    ! [X11,X10] : c_List_OremoveAll(X10,X11) = c_List_Ofilter(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(c_fequal,X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll__filter__not__eq) ).

fof(fact_rotate__rev,axiom,
    ! [X202,X25,X27] : hAPP(c_List_Orotate(X27,X25),hAPP(c_List_Orev(X27),X202)) = hAPP(c_List_Orev(X27),hAPP(c_List_Orotate(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__rev) ).

fof(fact_rotate__def,axiom,
    ! [X30,X10] : c_List_Orotate(X10,X30) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X10),tc_List_Olist(X10)),X30),c_List_Orotate1(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__def) ).

fof(fact_rtrancl__trancl__trancl,axiom,
    ! [X19,X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X19)),c_Transitive__Closure_Otrancl(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),c_Transitive__Closure_Otrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).

fof(fact_trancl__rtrancl__trancl,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Otrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),c_Transitive__Closure_Ortrancl(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Otrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).

fof(fact_trancl__into__trancl2,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),c_Transitive__Closure_Otrancl(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Otrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).

fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Otrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),X110))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Otrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).

fof(fact_Collect__conv__if,axiom,
    ! [X10,X13,X42] :
      ( ( hBOOL(hAPP(X42,X13))
       => hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X42)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X42,X13))
       => hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X42)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__conv__if) ).

fof(fact_foldr__map,axiom,
    ! [X13,X200,X2,X18,X1,X10,X8] : c_List_Ofoldr(X8,X10,X1,hAPP(hAPP(c_List_Omap(X18,X8),X2),X200),X13) = c_List_Ofoldr(X18,X10,hAPP(c_Fun_Ocomp(X8,tc_fun(X10,X10),X18,X1),X2),X200,X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__map) ).

fof(fact_fun__upd__image,axiom,
    ! [X16,X2,X8,X12,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Set_Oimage(X10,X8,c_Fun_Ofun__upd(X10,X8,X2,X11,X16)),X12) = hAPP(hAPP(c_Set_Oinsert(X8),X16),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Set_Oimage(X10,X8,c_Fun_Ofun__upd(X10,X8,X2,X11,X16)),X12) = hAPP(c_Set_Oimage(X10,X8,X2),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__image) ).

fof(fact_trancl__subset__Sigma,axiom,
    ! [X12,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X110)),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Sigma) ).

fof(fact_norm__frac_Opsimps,axiom,
    ! [X14,X13] :
      ( 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),X13),X14)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(X13,X14) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ( X13 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X14 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X13,X14) = 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)) )
            & ( ~ ( X13 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | X14 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X13,X14) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X13),X14)),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),X13))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Opsimps) ).

fof(fact_foldr__append,axiom,
    ! [X13,X199,X200,X2,X10,X8] : c_List_Ofoldr(X8,X10,X2,hAPP(hAPP(c_List_Oappend(X8),X200),X199),X13) = c_List_Ofoldr(X8,X10,X2,X200,c_List_Ofoldr(X8,X10,X2,X199,X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__append) ).

fof(fact_psubset__insert__iff,axiom,
    ! [X15,X11,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),X15)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
         => ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X15)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__insert__iff) ).

fof(fact_lexord__irreflexive,axiom,
    ! [X16,X110,X10] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X110))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X16)),c_List_Olexord(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__irreflexive) ).

fof(fact_diff__bin__simps_I8_J,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OBit1(X45)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X33)),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I8_J) ).

fof(fact_inj__on__insert,axiom,
    ! [X12,X13,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12))
    <=> ( c_Fun_Oinj__on(X10,X8,X2,X12)
        & ~ hBOOL(hAPP(hAPP(c_member(X8),hAPP(X2,X13)),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__insert) ).

fof(fact_apfst__id,axiom,
    ! [X8,X10] : c_Product__Type_Oapfst(X10,X10,X8,c_Fun_Oid(X10)) = c_Fun_Oid(tc_prod(X10,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apfst__id) ).

fof(fact_apsnd__id,axiom,
    ! [X10,X8] : c_Product__Type_Oapsnd(X8,X8,X10,c_Fun_Oid(X8)) = c_Fun_Oid(tc_prod(X10,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_apsnd__id) ).

fof(fact_trancl__reflcl,axiom,
    ! [X110,X10] : c_Transitive__Closure_Otrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10))) = c_Transitive__Closure_Ortrancl(X10,X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__reflcl) ).

fof(fact_subset__insert__iff,axiom,
    ! [X15,X11,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),X15)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X15)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert__iff) ).

fof(fact_eq__special_I4_J,axiom,
    ! [X11,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X11) = c_Groups_Oone__class_Oone(X10)
      <=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),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,
    ! [X16,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( c_Groups_Oone__class_Oone(X10) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)
      <=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),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),X16)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I2_J) ).

fof(fact_norm__frac_Osimps,axiom,
    ! [X13,X14] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(X13,X14) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ( X13 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | X14 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X13,X14) = 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)) )
          & ( ~ ( X13 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X14 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X13,X14) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X13),X14)),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),X13))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).

fof(fact_rtrancl__into__trancl2,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),c_Transitive__Closure_Ortrancl(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Otrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).

fof(fact_rtrancl__into__trancl1,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),X110))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Otrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).

fof(fact_power2__eq__square__number__of,axiom,
    ! [X92,X10] :
      ( ( class_Groups_Omonoid__mult(X10)
        & class_Int_Onumber(X10) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X92)),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(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X92)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square__number__of) ).

fof(fact_r__r__into__trancl,axiom,
    ! [X6,X29,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X29))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),X29))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Otrancl(X10,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).

fof(fact_DomainE,axiom,
    ! [X110,X8,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Relation_ODomain(X10,X8),X110)))
     => ~ ! [X51] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X51)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainE) ).

fof(fact_add__self__div__2,axiom,
    ! [X24] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X24,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__self__div__2) ).

fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
    ! [X20,X6,X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X20)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14))
        | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X13))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__subset__iff) ).

fof(fact_mult__2__right,axiom,
    ! [X38,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X38),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__2__right) ).

fof(fact_power2__eq__square,axiom,
    ! [X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),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(X27),X37),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power2__eq__square) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X26) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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,
    ! [X13,X6,X14,X15,X12,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(X15,X13),X14),X6))
       => ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__E) ).

fof(fact_nat__mult__2__right,axiom,
    ! [X38] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X38),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),X38),X38),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__2__right) ).

fof(fact_add__2__eq__Suc_H,axiom,
    ! [X25] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),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,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__2__eq__Suc_H) ).

fof(fact_zero__power2,axiom,
    ! [X27] :
      ( class_Rings_Osemiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),c_Groups_Ozero__class_Ozero(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(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__power2) ).

fof(fact_one__power2,axiom,
    ! [X27] :
      ( class_Rings_Osemiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),c_Groups_Oone__class_Oone(X27)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__power2) ).

fof(fact_map__fun__upd,axiom,
    ! [X93,X2,X8,X200,X16,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X200)))
     => hAPP(hAPP(c_List_Omap(X10,X8),c_Fun_Ofun__upd(X10,X8,X2,X16,X93)),X200) = hAPP(hAPP(c_List_Omap(X10,X8),X2),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__fun__upd) ).

fof(fact_trancl__mono,axiom,
    ! [X116,X110,X148,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Transitive__Closure_Otrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Transitive__Closure_Otrancl(X10,X116))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__mono) ).

fof(fact_not__sum__squares__lt__zero,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__ring(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X34))),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__sum__squares__lt__zero) ).

fof(fact_trancl__subset__Field2,axiom,
    ! [X110,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X110)),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),hAPP(c_Relation_OField(X10),X110)),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_Relation_OField(X10),X110))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Field2) ).

fof(fact_sup2E,axiom,
    ! [X16,X11,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16))
     => ( ~ hBOOL(hAPP(hAPP(X12,X11),X16))
       => hBOOL(hAPP(hAPP(X15,X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2E) ).

fof(fact_rtrancl__eq__or__trancl,axiom,
    ! [X29,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X29)))
    <=> ( X11 = X16
        | ( X11 != X16
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Otrancl(X10,X29))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).

fof(fact_trancl__into__rtrancl,axiom,
    ! [X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Otrancl(X10,X110)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).

fof(fact_inf2E,axiom,
    ! [X16,X11,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16))
     => ~ ( hBOOL(hAPP(hAPP(X12,X11),X16))
         => ~ hBOOL(hAPP(hAPP(X15,X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2E) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [X121,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X122)),c_Int_OBit1(X121)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),X121)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I16_J) ).

fof(fact_rel__simps_I17_J,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X32)),c_Int_OBit1(X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [X121,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X122)),c_Int_OBit1(X121)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X122),X121)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_rel__simps_I34_J,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X32)),c_Int_OBit1(X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_distinct__removeAll,axiom,
    ! [X26,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => hBOOL(hAPP(c_List_Odistinct(X27),hAPP(c_List_OremoveAll(X27,X26),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__removeAll) ).

fof(fact_map__removeAll__inj__on,axiom,
    ! [X200,X11,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => hAPP(hAPP(c_List_Omap(X10,X8),X2),hAPP(c_List_OremoveAll(X10,X11),X200)) = hAPP(c_List_OremoveAll(X8,hAPP(X2,X11)),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__removeAll__inj__on) ).

fof(fact_dropWhile__append2,axiom,
    ! [X199,X42,X200,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,X3)) )
     => c_List_OdropWhile(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = c_List_OdropWhile(X10,X42,X199) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__append2) ).

fof(fact_map__removeAll__inj,axiom,
    ! [X200,X11,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(hAPP(c_List_Omap(X10,X8),X2),hAPP(c_List_OremoveAll(X10,X11),X200)) = hAPP(c_List_OremoveAll(X8,hAPP(X2,X11)),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__removeAll__inj) ).

fof(fact_nth__length__takeWhile,axiom,
    ! [X200,X42,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => ~ hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__length__takeWhile) ).

fof(fact_length__transpose,axiom,
    ! [X200,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X200)) = c_List_Ofoldr(tc_List_Olist(X10),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X10)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X200,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__transpose) ).

fof(fact_trancl__power,axiom,
    ! [X29,X148,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Transitive__Closure_Otrancl(X10,X29)))
    <=> ? [X123] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X123))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X123),X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__power) ).

fof(fact_concat__append,axiom,
    ! [X201,X202,X27] : c_List_Oconcat(X27,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X27)),X202),X201)) = hAPP(hAPP(c_List_Oappend(X27),c_List_Oconcat(X27,X202)),c_List_Oconcat(X27,X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__append) ).

fof(fact_distinct__list__update,axiom,
    ! [X61,X13,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(hAPP(c_Set_Oinsert(X10),hAPP(hAPP(c_List_Onth(X10),X200),X61)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olist__update(X10,X200),X61),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__list__update) ).

fof(fact_pigeonhole,axiom,
    ! [X12,X2,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_Oimage(X8,X10,X2),X12))),hAPP(c_Finite__Set_Ocard(X8),X12)))
     => ~ c_Fun_Oinj__on(X8,X10,X2,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pigeonhole) ).

fof(fact_rtranclD,axiom,
    ! [X29,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,X29)))
     => ( X13 = X14
        | ( X13 != X14
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Otrancl(X10,X29))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtranclD) ).

fof(fact_takeWhile__eq__take__P__nth,axiom,
    ! [X42,X200,X10,X30] :
      ( ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),X30))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
           => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X91))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
         => ~ hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X30))) )
       => c_List_OtakeWhile(X10,X42,X200) = hAPP(hAPP(c_List_Otake(X10),X30),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__take__P__nth) ).

fof(fact_trancl_Or__into__trancl,axiom,
    ! [X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Otrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).

fof(fact_divide__less__eq__number__of,axiom,
    ! [X90,X6,X14,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6)),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of) ).

fof(fact_divide__le__eq__number__of,axiom,
    ! [X90,X6,X14,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6)),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of) ).

fof(fact_less__divide__eq__number__of,axiom,
    ! [X6,X14,X90,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6)),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of) ).

fof(fact_le__divide__eq__number__of,axiom,
    ! [X6,X14,X90,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6)),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of) ).

fof(fact_inj__on__fun__updI,axiom,
    ! [X11,X16,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X8),X16),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => c_Fun_Oinj__on(X10,X8,c_Fun_Ofun__upd(X10,X8,X2,X11,X16),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__fun__updI) ).

fof(fact_distinct__concat,axiom,
    ! [X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X10)),X200))
     => ( ! [X207] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X207),hAPP(c_List_Oset(tc_List_Olist(X10)),X200)))
           => hBOOL(hAPP(c_List_Odistinct(X10),X207)) )
       => ( ! [X207] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X207),hAPP(c_List_Oset(tc_List_Olist(X10)),X200)))
             => ! [X240] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X240),hAPP(c_List_Oset(tc_List_Olist(X10)),X200)))
                 => ( X207 != X240
                   => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X207)),hAPP(c_List_Oset(X10),X240)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) )
         => hBOOL(hAPP(c_List_Odistinct(X10),c_List_Oconcat(X10,X200))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__concat) ).

fof(fact_Collect__conv__if2,axiom,
    ! [X10,X13,X42] :
      ( ( hBOOL(hAPP(X42,X13))
       => hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X13))),X42)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X42,X13))
       => hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X13))),X42)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__conv__if2) ).

fof(fact_rotate__drop__take,axiom,
    ! [X202,X25,X27] : hAPP(c_List_Orotate(X27,X25),X202) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Odrop(X27),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))),X202)),hAPP(hAPP(c_List_Otake(X27),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__drop__take) ).

fof(fact_in__set__zipE,axiom,
    ! [X199,X200,X16,X11,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),hAPP(c_List_Oset(tc_prod(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
         => ~ hBOOL(hAPP(hAPP(c_member(X8),X16),hAPP(c_List_Oset(X8),X199))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__zipE) ).

fof(fact_removeAll_Osimps_I2_J,axiom,
    ! [X202,X27,X34,X26] :
      ( ( X26 = X34
       => hAPP(c_List_OremoveAll(X27,X26),hAPP(hAPP(c_List_Olist_OCons(X27),X34),X202)) = hAPP(c_List_OremoveAll(X27,X26),X202) )
      & ( X26 != X34
       => hAPP(c_List_OremoveAll(X27,X26),hAPP(hAPP(c_List_Olist_OCons(X27),X34),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X34),hAPP(c_List_OremoveAll(X27,X26),X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll_Osimps_I2_J) ).

fof(fact_acyclic__insert,axiom,
    ! [X110,X11,X16,X10] :
      ( c_Wellfounded_Oacyclic(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X11)),X110))
    <=> ( c_Wellfounded_Oacyclic(X10,X110)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__insert) ).

fof(fact_wf__insert,axiom,
    ! [X110,X11,X16,X10] :
      ( c_Wellfounded_Owf(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X11)),X110))
    <=> ( c_Wellfounded_Owf(X10,X110)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__insert) ).

fof(fact_trancl__unfold,axiom,
    ! [X110,X10] : c_Transitive__Closure_Otrancl(X10,X110) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Otrancl(X10,X110)),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold) ).

fof(fact_wf__eq__minimal,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
    <=> ! [X195] :
          ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),X195))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X195))
              & ! [X51] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X3)),X110))
                 => ~ hBOOL(hAPP(hAPP(c_member(X10),X51),X195)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [X121,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X122)),c_Int_OBit0(X121)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),X121)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_rel__simps_I16_J,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X32)),c_Int_OBit0(X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [X121,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X122)),c_Int_OBit0(X121)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),X121)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_rel__simps_I33_J,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X32)),c_Int_OBit0(X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_Nitpick_Oint__lcm__def,axiom,
    ! [X34,X26] : c_Nitpick_Oint__lcm(X26,X34) = 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),X26)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X34)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).

fof(fact_Nitpick_Onat__lcm__def,axiom,
    ! [X34,X26] : c_Nitpick_Onat__lcm(X26,X34) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X34)),c_Nitpick_Onat__gcd(X26,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Onat__lcm__def) ).

fof(fact_foldr_Osimps_I2_J,axiom,
    ! [X13,X200,X11,X2,X10,X8] : c_List_Ofoldr(X8,X10,X2,hAPP(hAPP(c_List_Olist_OCons(X8),X11),X200),X13) = hAPP(hAPP(X2,X11),c_List_Ofoldr(X8,X10,X2,X200,X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr_Osimps_I2_J) ).

fof(fact_wf__not__sym,axiom,
    ! [X11,X13,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X11)),X110))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X13)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__sym) ).

fof(fact_wf__asym,axiom,
    ! [X11,X13,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X11)),X110))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X13)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__asym) ).

fof(fact_divmod__nat__rel__def,axiom,
    ! [X155,X30,X31] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X31,X30),X155))
    <=> ( X31 = 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),X155)),X30)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X155))
        & ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X155) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X30 != 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)),X30))
             => ( 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),X155)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X155)),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),X30),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X155)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X155)),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,
    ! [X13,X90,X14,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X13))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq__number__of1) ).

fof(fact_divide__le__eq__number__of1,axiom,
    ! [X13,X90,X14,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X13))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq__number__of1) ).

fof(fact_minus__Bit1,axiom,
    ! [X33] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X33)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit1) ).

fof(fact_small__lazy_H_Opinduct,axiom,
    ! [X42,X57,X152] :
      ( 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),X152),X57)))
     => ( ! [X75,X91] :
            ( 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),X75),X91)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X75),X91))
               => hBOOL(hAPP(hAPP(X42,X75),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X91),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(X42,X75),X91)) ) )
       => hBOOL(hAPP(hAPP(X42,X152),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy_H_Opinduct) ).

fof(fact_less__eq,axiom,
    ! [X30,X31] :
      ( 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),X31),X30)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq) ).

fof(fact_quotientE,axiom,
    ! [X110,X12,X48,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
     => ~ ! [X3] :
            ( X48 = hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotientE) ).

fof(fact_divmod__nat__if,axiom,
    ! [X31,X30] :
      ( ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) )
       => c_Divides_Odivmod__nat(X31,X30) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31) )
      & ( ~ ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) )
       => c_Divides_Odivmod__nat(X31,X30) = 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),X31),X30),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__if) ).

fof(fact_divmod__nat__def,axiom,
    ! [X30,X31] : c_Divides_Odivmod__nat(X31,X30) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X31,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__def) ).

fof(fact_bin__less__0__simps_I4_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I4_J) ).

fof(fact_append__eq__append__conv__if,axiom,
    ! [X226,X227,X228,X229,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X229),X228) = hAPP(hAPP(c_List_Oappend(X10),X227),X226)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X229)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X227)))
         => ( X229 = hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X229)),X227)
            & X228 = hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X229)),X227)),X226) ) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X229)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X227)))
         => ( hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X227)),X229) = X227
            & hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X227)),X229)),X228) = X226 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv__if) ).

fof(fact_rel__simps_I13_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X32)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I13_J) ).

fof(fact_rel__simps_I12_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X32)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I12_J) ).

fof(fact_rel__simps_I29_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X32)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_rel__simps_I30_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X32)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I30_J) ).

fof(fact_neg__number__of__Bit1,axiom,
    ! [X90] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X90))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Bit1) ).

fof(fact_length__remdups__concat,axiom,
    ! [X237,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremdups(X10,c_List_Oconcat(X10,X237))) = hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X10)),X237)),c_List_Oset(X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__concat) ).

fof(fact_less__special_I2_J,axiom,
    ! [X16,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_le__special_I2_J,axiom,
    ! [X16,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Oone__class_Oone(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_less__divide__eq__number__of1,axiom,
    ! [X90,X14,X13,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq__number__of1) ).

fof(fact_le__divide__eq__number__of1,axiom,
    ! [X90,X14,X13,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq__number__of1) ).

fof(fact_sup2CI,axiom,
    ! [X8,X10,X12,X16,X11,X15] :
      ( ( ~ hBOOL(hAPP(hAPP(X15,X11),X16))
       => hBOOL(hAPP(hAPP(X12,X11),X16)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2CI) ).

fof(fact_not__acc__down,axiom,
    ! [X29,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),c_Wellfounded_Oacc(X10,X29)))
     => ~ ! [X177] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X177),X11)),X29))
           => hBOOL(hAPP(hAPP(c_member(X10),X177),c_Wellfounded_Oacc(X10,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__acc__down) ).

fof(fact_flat__lub__def,axiom,
    ! [X14,X12,X10] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X10,X14,X12) = X14 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X10,X14,X12) = c_HOL_OThe(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_flat__lub__def) ).

fof(fact_not__Nil__listrel1,axiom,
    ! [X110,X200,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X200)),c_List_Olistrel1(X10,X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Nil__listrel1) ).

fof(fact_Nil__notin__lex,axiom,
    ! [X110,X199,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X199)),c_List_Olex(X10,X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__notin__lex) ).

fof(fact_not__listrel1__Nil,axiom,
    ! [X110,X200,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),c_List_Olist_ONil(X10))),c_List_Olistrel1(X10,X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__listrel1__Nil) ).

fof(fact_lexord__Nil__right,axiom,
    ! [X110,X11,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),c_List_Olist_ONil(X10))),c_List_Olexord(X10,X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__right) ).

fof(fact_Nil2__notin__lex,axiom,
    ! [X110,X200,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),c_List_Olist_ONil(X10))),c_List_Olex(X10,X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil2__notin__lex) ).

fof(fact_foldl__foldr1__lemma,axiom,
    ! [X200,X13,X10] :
      ( class_Groups_Omonoid__add(X10)
     => hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),X13),X200) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),c_List_Ofoldr(X10,X10,c_Groups_Oplus__class_Oplus(X10),X200,c_Groups_Ozero__class_Ozero(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr1__lemma) ).

fof(fact_pair__in__Id__conv,axiom,
    ! [X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Relation_OId(X10)))
    <=> X13 = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).

fof(fact_finite__induct,axiom,
    ! [X42,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => ( hBOOL(hAPP(X42,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
       => ( ! [X3,X47] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X47))
             => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X47))
               => ( hBOOL(hAPP(X42,X47))
                 => hBOOL(hAPP(X42,hAPP(hAPP(c_Set_Oinsert(X10),X3),X47))) ) ) )
         => hBOOL(hAPP(X42,X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__induct) ).

fof(fact_one__add__one__is__two,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Oone__class_Oone(X27)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__add__one__is__two) ).

fof(fact_set__removeAll,axiom,
    ! [X200,X11,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_OremoveAll(X10,X11),X200)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__removeAll) ).

fof(fact_divmod__nat__step,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
       => c_Divides_Odivmod__nat(X24,X25) = 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),X24),X25)),X25))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__step) ).

fof(fact_foldl__foldr,axiom,
    ! [X200,X13,X2,X8,X10] : hAPP(c_List_Ofoldl(X10,X8,X2,X13),X200) = c_List_Ofoldr(X8,X10,hAPP(c_COMBC(X10,X8,X10),X2),hAPP(c_List_Orev(X8),X200),X13),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr) ).

fof(fact_distinct__dropWhile,axiom,
    ! [X42,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => hBOOL(hAPP(c_List_Odistinct(X10),c_List_OdropWhile(X10,X42,X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_comm__monoid__big_OF__eq,axiom,
    ! [X1,X12,X9,X19,X2,X8,X10] :
      ( c_Big__Operators_Ocomm__monoid__big(X10,X8,X2,X19,X9)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
         => hAPP(hAPP(X9,X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X8,X2),X1),X19),X12) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
         => hAPP(hAPP(X9,X1),X12) = X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).

fof(fact_in__measure,axiom,
    ! [X2,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),hAPP(c_Wellfounded_Omeasure(X10),X2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X11)),hAPP(X2,X16))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measure) ).

fof(fact_measure__def,axiom,
    ! [X10] : c_Wellfounded_Omeasure(X10) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X10),c_Wellfounded_Oless__than),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measure__def) ).

fof(fact_SigmaE2,axiom,
    ! [X15,X12,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => ~ hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(X15,X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE2) ).

fof(fact_map__concat,axiom,
    ! [X200,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_Oconcat(X8,X200)) = c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X8),tc_List_Olist(X10)),hAPP(c_List_Omap(X8,X10),X2)),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__concat) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OBit0(X45)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_diff__bin__simps_I9_J,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OBit0(X45)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I9_J) ).

fof(fact_insort__insert__insort__key,axiom,
    ! [X200,X8,X11,X2,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X11)),hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_List_Oset(X8),X200))))
       => c_List_Olinorder__class_Oinsort__insert__key(X8,X10,X2,X11,X200) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__insort__key) ).

fof(fact_total__on__diff__Id,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Ototal__on(X10,X12,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10)))
    <=> c_Relation_Ototal__on(X10,X12,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__diff__Id) ).

fof(fact_Suc__diff__eq__diff__pred,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X25))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),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,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X33)),X45) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X45))),X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit1) ).

fof(fact_number__of1,axiom,
    ! [X25] :
      ( 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),X25)))
     => ( 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(X25))))
        & 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(X25)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of1) ).

fof(fact_add__Bit1__Bit1,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OBit1(X45)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),c_Int_Osucc(X45))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit1__Bit1) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [X121,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X122)),c_Int_OBit1(X121)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X122),X121)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_rel__simps_I15_J,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X32)),c_Int_OBit1(X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [X121,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X122)),c_Int_OBit1(X121)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X122),X121)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_rel__simps_I32_J,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X32)),c_Int_OBit1(X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_antisym__reflcl,axiom,
    ! [X110,X10] :
      ( c_Relation_Oantisym(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10)))
    <=> c_Relation_Oantisym(X10,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__reflcl) ).

fof(fact_finite__trancl,axiom,
    ! [X110,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),c_Transitive__Closure_Otrancl(X10,X110)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__trancl) ).

fof(fact_card__Diff__insert,axiom,
    ! [X15,X13,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X15))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__insert) ).

fof(fact_rev__concat,axiom,
    ! [X200,X10] : hAPP(c_List_Orev(X10),c_List_Oconcat(X10,X200)) = c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Orev(X10)),hAPP(c_List_Orev(tc_List_Olist(X10)),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__concat) ).

fof(fact_fold__image__insert,axiom,
    ! [X19,X1,X13,X12,X10,X8] :
      ( class_Groups_Oab__semigroup__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),X19),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X1,X13)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),X19),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__insert) ).

fof(fact_filter__concat,axiom,
    ! [X200,X148,X10] : hAPP(c_List_Ofilter(X10,X148),c_List_Oconcat(X10,X200)) = c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Ofilter(X10,X148)),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__concat) ).

fof(fact_in__measures_I1_J,axiom,
    ! [X16,X11,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_List_Omeasures(X10,c_List_Olist_ONil(tc_fun(X10,tc_Nat_Onat))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I1_J) ).

fof(fact_divide__less__eq,axiom,
    ! [X13,X6,X14,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),X13))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__eq) ).

fof(fact_divide__le__eq,axiom,
    ! [X13,X6,X14,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),X13))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__eq) ).

fof(fact_distinct__rotate,axiom,
    ! [X200,X30,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(c_List_Orotate(X10,X30),X200)))
    <=> hBOOL(hAPP(c_List_Odistinct(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__rotate) ).

fof(fact_Not__Domain__rtrancl,axiom,
    ! [X16,X29,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_Relation_ODomain(X10,X10),X29)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X29)))
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OBit1(X45)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_comm__monoid__big_Oinfinite,axiom,
    ! [X1,X12,X9,X19,X2,X8,X10] :
      ( c_Big__Operators_Ocomm__monoid__big(X10,X8,X2,X19,X9)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => hAPP(hAPP(X9,X1),X12) = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).

fof(fact_diff__special_I2_J,axiom,
    ! [X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),c_Groups_Oone__class_Oone(X27)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),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,
    ! [X200,X11,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X11),X200)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
          & hBOOL(hAPP(c_List_Odistinct(X10),X200)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insort) ).

fof(fact_diff__special_I1_J,axiom,
    ! [X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),c_Groups_Oone__class_Oone(X27)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),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),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__special_I1_J) ).

fof(fact_r__into__trancl_H,axiom,
    ! [X110,X148,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),X110))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Transitive__Closure_Otrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).

fof(fact_concat_Osimps_I2_J,axiom,
    ! [X202,X26,X27] : c_List_Oconcat(X27,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X27)),X26),X202)) = hAPP(hAPP(c_List_Oappend(X27),X26),c_List_Oconcat(X27,X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat_Osimps_I2_J) ).

fof(fact_add__special_I2_J,axiom,
    ! [X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X6,X20)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14))
            | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X13))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X20))
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),X13))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),X20)) ) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).

fof(fact_insert__partition,axiom,
    ! [X9,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X11),X9))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X11),X9)))
           => ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X66),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X11),X9)))
               => ( X3 != X66
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X3),X66) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X11),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X9)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__partition) ).

fof(fact_reflcl__trancl,axiom,
    ! [X110,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X10,X110)),c_Relation_OId(X10)) = c_Transitive__Closure_Ortrancl(X10,X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflcl__trancl) ).

fof(fact_list__update__append,axiom,
    ! [X26,X201,X202,X27,X25] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X25),X26) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Olist__update(X27,X202),X25),X26)),X201) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X25),X26) = hAPP(hAPP(c_List_Oappend(X27),X202),hAPP(hAPP(c_List_Olist__update(X27,X201),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__append) ).

fof(fact_less__divide__eq,axiom,
    ! [X6,X14,X13,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__divide__eq) ).

fof(fact_le__divide__eq,axiom,
    ! [X6,X14,X13,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__divide__eq) ).

fof(fact_lazy__sequence_Osimps_I5_J,axiom,
    ! [X256,X13,X49,X50,X8,X10] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X10,X8,X50,X49,c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X13,X256)) = hAPP(hAPP(X49,X13),X256),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I5_J) ).

fof(fact_seq__case,axiom,
    ! [X232,X1,X2,X8,X10] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X10,X8,X2,X1,X232) = c_Option_Ooption_Ooption__case(X10,tc_prod(X8,tc_Lazy__Sequence_Olazy__sequence(X8)),X2,hAPP(c_Product__Type_Oprod_Oprod__case(X8,tc_Lazy__Sequence_Olazy__sequence(X8),X10),X1),hAPP(c_Lazy__Sequence_Oyield(X8),X232)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_seq__case) ).

fof(fact_mult__numeral__1,axiom,
    ! [X37,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(c_Int_OPls))),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1) ).

fof(fact_list__ex__iff__not__all__inverval__int,axiom,
    ! [X60,X61,X42] :
      ( c_List_Olist__ex(tc_Int_Oint,X42,c_List_Oupto(X61,X60))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X42),X61,X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__not__all__inverval__int) ).

fof(fact_rotate__add,axiom,
    ! [X30,X31,X10] : c_List_Orotate(X10,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X10),tc_List_Olist(X10),tc_List_Olist(X10),c_List_Orotate(X10,X31)),c_List_Orotate(X10,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__add) ).

fof(fact_atLeastatMost__subset__iff,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X6,X20)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X20)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__subset__iff) ).

fof(fact_less__special_I4_J,axiom,
    ! [X11,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X11)),c_Groups_Oone__class_Oone(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),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,
    ! [X11,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X11)),c_Groups_Oone__class_Oone(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Int_OBit1(c_Int_OPls))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_IdE,axiom,
    ! [X148,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Relation_OId(X10)))
     => ~ ! [X3] : X148 != hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IdE) ).

fof(fact_diff__bin__simps_I4_J,axiom,
    ! [X45] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X45)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I4_J) ).

fof(fact_IdI,axiom,
    ! [X13,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X13)),c_Relation_OId(X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IdI) ).

fof(fact_foldl__conv__concat,axiom,
    ! [X237,X200,X10] : hAPP(c_List_Ofoldl(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Oappend(X10),X200),X237) = hAPP(hAPP(c_List_Oappend(X10),X200),c_List_Oconcat(X10,X237)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__conv__concat) ).

fof(fact_diff__bin__simps_I10_J,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X33)),c_Int_OBit1(X45)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I10_J) ).

fof(fact_insort__insert__insort,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X11,X200) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X11),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__insort) ).

fof(fact_irrefl__def,axiom,
    ! [X110,X10] :
      ( c_Relation_Oirrefl(X10,X110)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__def) ).

fof(fact_wf__not__refl,axiom,
    ! [X13,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X13)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__not__refl) ).

fof(fact_wf__irrefl,axiom,
    ! [X13,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X13)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__irrefl) ).

fof(fact_rtrancl__unfold,axiom,
    ! [X110,X10] : c_Transitive__Closure_Ortrancl(X10,X110) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Relation_OId(X10)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Ortrancl(X10,X110)),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__unfold) ).

fof(fact_INT__E,axiom,
    ! [X13,X15,X12,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(X15,X13)))
       => ~ hBOOL(hAPP(hAPP(c_member(X8),X13),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__E) ).

fof(fact_rel__simps_I9_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I9_J) ).

fof(fact_rel__simps_I26_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I26_J) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_rel__simps_I22_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I22_J) ).

fof(fact_power__number__of__even__number__of,axiom,
    ! [X90,X93,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X90))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),hAPP(hAPP(c_COMBS(X10,X10,X10),c_Groups_Otimes__class_Otimes(X10)),c_COMBI(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__number__of__even__number__of) ).

fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
    ! [X11,X16,X6] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X16))
       => 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)),X6)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11),X16)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X6)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16),X6)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X16))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X16))
           => 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)),X6)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11),X16)) = 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),X11),X16))
           => 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)),X6)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11),X16)) = 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,
    ! [X200,X10] :
      ( class_Groups_Omonoid__add(X10)
     => hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X200) = c_List_Ofoldr(X10,X10,c_Groups_Oplus__class_Oplus(X10),X200,c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__foldr1) ).

fof(fact_nth__map__upt,axiom,
    ! [X2,X10,X31,X30,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30),X31)))
     => hAPP(hAPP(c_List_Onth(X10),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),X2),c_List_Oupt(X31,X30))),X61) = hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__map__upt) ).

fof(fact_rotate__rotate,axiom,
    ! [X202,X25,X24,X27] : hAPP(c_List_Orotate(X27,X24),hAPP(c_List_Orotate(X27,X25),X202)) = hAPP(c_List_Orotate(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__rotate) ).

fof(fact_foldr__conv__foldl,axiom,
    ! [X13,X200,X10] :
      ( class_Groups_Oab__semigroup__add(X10)
     => c_List_Ofoldr(X10,X10,c_Groups_Oplus__class_Oplus(X10),X200,X13) = hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),X13),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__conv__foldl) ).

fof(fact_lazy__sequence_Osimps_I4_J,axiom,
    ! [X49,X50,X8,X10] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X10,X8,X50,X49,c_Lazy__Sequence_Olazy__sequence_OEmpty(X8)) = X50,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I4_J) ).

fof(fact_rotate__conv__mod,axiom,
    ! [X202,X25,X27] : hAPP(c_List_Orotate(X27,X25),X202) = hAPP(c_List_Orotate(X27,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__conv__mod) ).

fof(fact_pred__Bit0,axiom,
    ! [X33] : c_Int_Opred(c_Int_OBit0(X33)) = c_Int_OBit1(c_Int_Opred(X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit0) ).

fof(fact_setprod__diff1,axiom,
    ! [X13,X2,X12,X10,X8] :
      ( class_Fields_Ofield(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hAPP(X2,X13) != c_Groups_Ozero__class_Ozero(X8)
         => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12)),hAPP(X2,X13)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__diff1) ).

fof(fact_refl__reflcl,axiom,
    ! [X110,X10] : c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__reflcl) ).

fof(fact_takeWhile__dropWhile__id,axiom,
    ! [X200,X42,X10] : hAPP(hAPP(c_List_Oappend(X10),c_List_OtakeWhile(X10,X42,X200)),c_List_OdropWhile(X10,X42,X200)) = X200,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_setsum__diff1,axiom,
    ! [X2,X13,X12,X10,X8] :
      ( class_Groups_Oab__group__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(X2,X13)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1) ).

fof(fact_set__concat,axiom,
    ! [X200,X10] : hAPP(c_List_Oset(X10),c_List_Oconcat(X10,X200)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X10)),X200)),c_List_Oset(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__concat) ).

fof(fact_length__concat,axiom,
    ! [X237,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oconcat(X10,X237)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X237)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__concat) ).

fof(fact_INF1__E,axiom,
    ! [X13,X14,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15),X14))
     => ( ~ hBOOL(hAPP(hAPP(X15,X13),X14))
       => ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__E) ).

fof(fact_trans__diff__Id,axiom,
    ! [X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => ( c_Relation_Oantisym(X10,X110)
       => c_Relation_Otrans(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__diff__Id) ).

fof(fact_foldr__max__sorted,axiom,
    ! [X16,X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(c_List_Orev(X10),X200))
       => ( ( X200 = c_List_Olist_ONil(X10)
           => c_List_Ofoldr(X10,X10,c_Orderings_Oord__class_Omax(X10),X200,X16) = X16 )
          & ( X200 != c_List_Olist_ONil(X10)
           => c_List_Ofoldr(X10,X10,c_Orderings_Oord__class_Omax(X10),X200,X16) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_List_Onth(X10),X200),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr__max__sorted) ).

fof(fact_trans__reflclI,axiom,
    ! [X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => c_Relation_Otrans(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__reflclI) ).

fof(fact_length__filter__less,axiom,
    ! [X42,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ( ~ hBOOL(hAPP(X42,X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X42),X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__less) ).

fof(fact_rtrancl__reflcl,axiom,
    ! [X29,X10] : c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),c_Relation_OId(X10))) = c_Transitive__Closure_Ortrancl(X10,X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).

fof(fact_rtrancl__r__diff__Id,axiom,
    ! [X110,X10] : c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10))) = c_Transitive__Closure_Ortrancl(X10,X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__r__diff__Id) ).

fof(fact_irrefl__diff__Id,axiom,
    ! [X110,X10] : c_Relation_Oirrefl(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Relation_OId(X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_irrefl__diff__Id) ).

fof(fact_divmod__int__relI,axiom,
    ! [X80,X114,X36,X37] :
      ( X37 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X114)),X80)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X80))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X80),X36)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X80))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X80),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__relI) ).

fof(fact_diff__bin__simps_I5_J,axiom,
    ! [X45] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X45)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I5_J) ).

fof(fact_setsum__diff1__nat,axiom,
    ! [X2,X12,X13,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12)),hAPP(X2,X13)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1__nat) ).

fof(fact_wf__converse__trancl,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,hAPP(c_Relation_Oconverse(X10,X10),X110))
     => c_Wellfounded_Owf(X10,hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Otrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).

fof(fact_concat__eq__Nil__conv,axiom,
    ! [X237,X10] :
      ( c_List_Oconcat(X10,X237) = c_List_Olist_ONil(X10)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X3),hAPP(c_List_Oset(tc_List_Olist(X10)),X237)))
         => X3 = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__eq__Nil__conv) ).

fof(fact_Nil__eq__concat__conv,axiom,
    ! [X237,X10] :
      ( c_List_Olist_ONil(X10) = c_List_Oconcat(X10,X237)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X3),hAPP(c_List_Oset(tc_List_Olist(X10)),X237)))
         => X3 = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__eq__concat__conv) ).

fof(fact_upt__add__eq__append,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => c_List_Oupt(X44,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X33)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X44,X43)),c_List_Oupt(X43,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X33))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__add__eq__append) ).

fof(fact_setsum__cl__ivl__Suc,axiom,
    ! [X2,X31,X30,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,hAPP(c_Nat_OSuc,X30))) = c_Groups_Ozero__class_Ozero(X10) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,hAPP(c_Nat_OSuc,X30))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30))),hAPP(X2,hAPP(c_Nat_OSuc,X30))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cl__ivl__Suc) ).

fof(fact_UnE,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnE) ).

fof(fact_dropWhile__eq__Nil__conv,axiom,
    ! [X200,X42,X10] :
      ( c_List_OdropWhile(X10,X42,X200) = c_List_Olist_ONil(X10)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).

fof(fact_folding_Oinsert,axiom,
    ! [X11,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X2,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oinsert) ).

fof(fact_sorted__dropWhile,axiom,
    ! [X42,X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,X200)
       => c_List_Olinorder__class_Osorted(X10,c_List_OdropWhile(X10,X42,X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_in__set__conv__decomp__last,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
    <=> ? [X207,X240] :
          ( X200 = hAPP(hAPP(c_List_Oappend(X10),X207),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X240))
          & ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X240))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp__last) ).

fof(fact_in__set__conv__decomp__first,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
    <=> ? [X207] :
          ( ? [X240] : X200 = hAPP(hAPP(c_List_Oappend(X10),X207),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X240))
          & ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X207))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp__first) ).

fof(fact_succ__Bit1,axiom,
    ! [X33] : c_Int_Osucc(c_Int_OBit1(X33)) = c_Int_OBit0(c_Int_Osucc(X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit1) ).

fof(fact_power__number__of__even,axiom,
    ! [X90,X19,X10] :
      ( class_Int_Onumber__ring(X10)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X90))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),hAPP(hAPP(c_COMBS(X10,X10,X10),c_Groups_Otimes__class_Otimes(X10)),c_COMBI(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__number__of__even) ).

fof(fact_Diff__iff,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
        & ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__iff) ).

fof(fact_DiffD2,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD2) ).

fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
    ! [X24,X45] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X45),X24) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X45)),c_List_Oembed__list(X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).

fof(fact_return__list__def,axiom,
    ! [X83] : c_List_Oreturn__list(X83) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X83),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_return__list__def) ).

fof(fact_embed__list__def,axiom,
    ! [X83] : c_List_Oembed__list(X83) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X83),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_embed__list__def) ).

fof(fact_card__Suc__eq,axiom,
    ! [X32,X12,X10] :
      ( hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(c_Nat_OSuc,X32)
    <=> ? [X81,X82] :
          ( X12 = hAPP(hAPP(c_Set_Oinsert(X10),X81),X82)
          & ~ hBOOL(hAPP(hAPP(c_member(X10),X81),X82))
          & hAPP(c_Finite__Set_Ocard(X10),X82) = X32
          & ( X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => X82 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Suc__eq) ).

fof(fact_distinct__remove1__removeAll,axiom,
    ! [X26,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => c_List_Oremove1(X27,X26,X202) = hAPP(c_List_OremoveAll(X27,X26),X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1__removeAll) ).

fof(fact_take__upt,axiom,
    ! [X25,X24,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X24)),X25))
     => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X24),c_List_Oupt(X44,X25)) = c_List_Oupt(X44,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__upt) ).

fof(fact_rotate__map,axiom,
    ! [X200,X2,X8,X30,X10] : hAPP(c_List_Orotate(X10,X30),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(c_List_Orotate(X8,X30),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__map) ).

fof(fact_trancl__converse,axiom,
    ! [X110,X10] : c_Transitive__Closure_Otrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X110)) = hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Otrancl(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__converse) ).

fof(fact_insort__key_Osimps_I2_J,axiom,
    ! [X199,X8,X16,X11,X2,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X11)),hAPP(X2,X16)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),hAPP(hAPP(c_List_Olist_OCons(X8),X16),X199)) = hAPP(hAPP(c_List_Olist_OCons(X8),X11),hAPP(hAPP(c_List_Olist_OCons(X8),X16),X199)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X11)),hAPP(X2,X16)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),hAPP(hAPP(c_List_Olist_OCons(X8),X16),X199)) = hAPP(hAPP(c_List_Olist_OCons(X8),X16),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),X199)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key_Osimps_I2_J) ).

fof(fact_upto__rec__number__of,axiom,
    ! [X25,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto__rec__number__of) ).

fof(fact_subset__insert,axiom,
    ! [X15,X12,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),X15)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insert) ).

fof(fact_IntE,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
         => ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntE) ).

fof(fact_upto_Opsimps,axiom,
    ! [X60,X61] :
      ( 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),X61),X60)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),X60))
         => c_List_Oupto(X61,X60) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X61),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)),X60)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),X60))
         => c_List_Oupto(X61,X60) = 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,
    ! [X19,X11,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(X2,X11),hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).

fof(fact_small__lazy_H_Opsimps,axiom,
    ! [X61,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),X61)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X61))
         => c_Lazy__Sequence_Osmall__lazy_H(X20,X61) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X61))
         => c_Lazy__Sequence_Osmall__lazy_H(X20,X61) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X61),c_Lazy__Sequence_Osmall__lazy_H(X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy_H_Opsimps) ).

fof(fact_notin__set__remove1,axiom,
    ! [X16,X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X16,X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__set__remove1) ).

fof(fact_notin__set__sublistI,axiom,
    ! [X161,X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X200,X161)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_notin__set__sublistI) ).

fof(fact_nth__upt,axiom,
    ! [X43,X33,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X33)),X43))
     => hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X44,X43)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X33) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__upt) ).

fof(fact_zpower__number__of__even,axiom,
    ! [X90,X19] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X90))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),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,X10,X8] :
      ( class_Orderings_Oord(X8)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X8)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X2),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X1),X2)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__fun__def) ).

fof(fact_pick_Osimps,axiom,
    ! [X202,X26,X27,X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X44),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X27),X26)))
       => hAPP(c_Random_Opick(X27,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X27)),X26),X202)),X44) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X27),X26) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X44),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X27),X26)))
       => hAPP(c_Random_Opick(X27,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X27)),X26),X202)),X44) = hAPP(c_Random_Opick(X27,X202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X44),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X27),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick_Osimps) ).

fof(fact_UnionE,axiom,
    ! [X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X12),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X17)))
     => ~ ! [X184] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X12),X184))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X184),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnionE) ).

fof(fact_rel__simps_I14_J,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X32)),c_Int_OBit0(X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [X121,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X122)),c_Int_OBit0(X121)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X122),X121)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_rel__simps_I31_J,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X32)),c_Int_OBit0(X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [X121,X122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X122)),c_Int_OBit0(X121)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X122),X121)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_removeAll_Osimps_I1_J,axiom,
    ! [X26,X27] : hAPP(c_List_OremoveAll(X27,X26),c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_removeAll_Osimps_I1_J) ).

fof(fact_card__Diff__singleton__if,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X10),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__singleton__if) ).

fof(fact_add__special_I3_J,axiom,
    ! [X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),c_Groups_Oone__class_Oone(X27)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),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,
    ! [X90,X93,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Orderings_Olinorder(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of__eq__not__less) ).

fof(fact_bot2E,axiom,
    ! [X16,X11,X8,X10] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X11),X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot2E) ).

fof(fact_divmod__int__rel__mod__eq,axiom,
    ! [X34,X142,X131,X132] :
      ( X132 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X131),X142)),X34)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34),X131)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X34))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X131 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X132,X131) = X34 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__mod__eq) ).

fof(fact_foldr_Osimps_I1_J,axiom,
    ! [X13,X2,X10,X8] : c_List_Ofoldr(X8,X10,X2,c_List_Olist_ONil(X8),X13) = X13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldr_Osimps_I1_J) ).

fof(fact_concat__map__maps,axiom,
    ! [X200,X2,X8,X10] : c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(X8,tc_List_Olist(X10)),X2),X200)) = c_List_Omaps(X8,X10,X2,X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__map__maps) ).

fof(fact_maps__def,axiom,
    ! [X200,X2,X10,X8] : c_List_Omaps(X8,X10,X2,X200) = c_List_Oconcat(X10,hAPP(hAPP(c_List_Omap(X8,tc_List_Olist(X10)),X2),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__def) ).

fof(fact_divmod__int__rel__div__eq,axiom,
    ! [X130,X34,X131,X132] :
      ( X132 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X131),X34)),X130)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X130))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X130),X131)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X130))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X130),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X131 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X132),X131) = X34 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__eq) ).

fof(fact_rotate__Suc,axiom,
    ! [X202,X25,X27] : hAPP(c_List_Orotate(X27,hAPP(c_Nat_OSuc,X25)),X202) = hAPP(c_List_Orotate1(X27),hAPP(c_List_Orotate(X27,X25),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__Suc) ).

fof(fact_fun__left__comm_Ofold__insert2,axiom,
    ! [X19,X11,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),hAPP(hAPP(X2,X11),X19)),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).

fof(fact_upt__eq__Cons__conv,axiom,
    ! [X200,X11,X60,X61] :
      ( c_List_Oupt(X61,X60) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X11),X200)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),X60))
        & X61 = X11
        & c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X60) = X200 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Cons__conv) ).

fof(fact_setsum__op__ivl__Suc,axiom,
    ! [X2,X31,X30,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),hAPP(c_Nat_OSuc,X30))) = c_Groups_Ozero__class_Ozero(X10) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),hAPP(c_Nat_OSuc,X30))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30))),hAPP(X2,X30)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__op__ivl__Suc) ).

fof(fact_sup1E,axiom,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11))
     => ( ~ hBOOL(hAPP(X12,X11))
       => hBOOL(hAPP(X15,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1E) ).

fof(fact_pred__Bit1,axiom,
    ! [X33] : c_Int_Opred(c_Int_OBit1(X33)) = c_Int_OBit0(X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__Bit1) ).

fof(fact_nat__number__of__add__left,axiom,
    ! [X33,X120,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X33) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = 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),X68),X120))),X33) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__add__left) ).

fof(fact_trancl__empty,axiom,
    ! [X10] : c_Transitive__Closure_Otrancl(X10,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__empty) ).

fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
    ! [X30,X31,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31,X30))) = hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),X2),c_List_Oupt(X31,X30))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).

fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
    ! [X30,X31,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),X2),c_List_Oupt(X31,X30))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31,X30))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).

fof(fact_inf1E,axiom,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11))
     => ~ ( hBOOL(hAPP(X12,X11))
         => ~ hBOOL(hAPP(X15,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1E) ).

fof(fact_rotate1__rotate__swap,axiom,
    ! [X202,X25,X27] : hAPP(c_List_Orotate1(X27),hAPP(c_List_Orotate(X27,X25),X202)) = hAPP(c_List_Orotate(X27,X25),hAPP(c_List_Orotate1(X27),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).

fof(fact_number__of__Bit1,axiom,
    ! [X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92))),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_DiffI,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffI) ).

fof(fact_code__numeral_Orecs_I2_J,axiom,
    ! [X135,X49,X50,X10] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X10,X50,X49,c_Code__Numeral_OSuc__code__numeral(X135)) = hAPP(hAPP(X49,X135),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X10,X50,X49,X135)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).

fof(fact_Suc__code__numeral__def,axiom,
    ! [X33] : c_Code__Numeral_OSuc__code__numeral(X33) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X33))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).

fof(fact_card__def,axiom,
    ! [X12,X10] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(c_Finite__Set_Ocard(X10),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__def) ).

fof(fact_Id__O__R,axiom,
    ! [X29,X8,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X8),c_Relation_OId(X10)),X29) = X29,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__O__R) ).

fof(fact_divide__Numeral1,axiom,
    ! [X26,X27] :
      ( ( class_Fields_Ofield(X27)
        & class_Int_Onumber__ring(X27) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(c_Int_OPls))) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral1) ).

fof(fact_divide__numeral__1,axiom,
    ! [X37,X27] :
      ( ( class_Fields_Ofield(X27)
        & class_Int_Onumber__ring(X27) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(c_Int_OPls))) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__numeral__1) ).

fof(fact_le__supE,axiom,
    ! [X26,X36,X37,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36)),X26))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X26))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supE) ).

fof(fact_min__max_Ole__supE,axiom,
    ! [X26,X36,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36)),X26))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X26))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supE) ).

fof(fact_mult__numeral__1__right,axiom,
    ! [X37,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(c_Int_OPls))) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__numeral__1__right) ).

fof(fact_member__rec_I1_J,axiom,
    ! [X16,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),X16))
    <=> ( X11 = X16
        | hBOOL(hAPP(hAPP(c_List_Omember(X10),X200),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I1_J) ).

fof(fact_member__set,axiom,
    ! [X10] : c_List_Omember(X10) = c_List_Oset(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__set) ).

fof(fact_hd__rotate__conv__nth,axiom,
    ! [X25,X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => hAPP(c_List_Ohd(X27),hAPP(c_List_Orotate(X27,X25),X202)) = hAPP(hAPP(c_List_Onth(X27),X202),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__rotate__conv__nth) ).

fof(fact_nat__number__of__mult__left,axiom,
    ! [X33,X120,X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = 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),X68),X120))),X33) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__mult__left) ).

fof(fact_rotate__length01,axiom,
    ! [X25,X202,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate(X27,X25),X202) = X202 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__length01) ).

fof(fact_Int__insert__left,axiom,
    ! [X15,X17,X13,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X17))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)),X17) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X17))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left) ).

fof(fact_UnCI,axiom,
    ! [X12,X15,X6,X10] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) )
     => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnCI) ).

fof(fact_not__square__less__zero,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__ring(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X37)),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__square__less__zero) ).

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X90)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

fof(fact_zdiv__number__of__Bit0,axiom,
    ! [X92,X68] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X68))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__number__of__Bit0) ).

fof(fact_add__leE,axiom,
    ! [X25,X33,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X33)),X25))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X32)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_rel__simps_I11_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X32)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I11_J) ).

fof(fact_rel__simps_I28_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X32)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I28_J) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X32)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_neg__number__of__Bit0,axiom,
    ! [X90] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X90))))
    <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Bit0) ).

fof(fact_Image__Id,axiom,
    ! [X12,X10] : hAPP(c_Relation_OImage(X10,X10,c_Relation_OId(X10)),X12) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id) ).

fof(fact_insert__Diff__if,axiom,
    ! [X12,X15,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),X15) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),X15) = hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__if) ).

fof(fact_le__iff__pred__less,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),X83))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X32)),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__pred__less) ).

fof(fact_diff__bin__simps_I6_J,axiom,
    ! [X45] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X45)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I6_J) ).

fof(fact_div__if,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X25)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__if) ).

fof(fact_div__geq,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__geq) ).

fof(fact_not__zle__0__negative,axiom,
    ! [X25] : ~ 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,X25))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__zle__0__negative) ).

fof(fact_rtrancl__reflcl__absorb,axiom,
    ! [X29,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X29)),c_Relation_OId(X10)) = c_Transitive__Closure_Ortrancl(X10,X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).

fof(fact_upt__Suc__append,axiom,
    ! [X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => c_List_Oupt(X44,hAPP(c_Nat_OSuc,X43)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X44,X43)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X43),c_List_Olist_ONil(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__Suc__append) ).

fof(fact_Int__insert__right,axiom,
    ! [X15,X12,X13,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right) ).

fof(fact_setsum_OF__eq,axiom,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Oplus__class_Oplus(X8)),X1),c_Groups_Ozero__class_Ozero(X8)),X12) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12) = c_Groups_Ozero__class_Ozero(X8) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_OF__eq) ).

fof(fact_setprod_OF__eq,axiom,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),X12) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12) = c_Groups_Oone__class_Oone(X8) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_OF__eq) ).

fof(fact_nth__append,axiom,
    ! [X201,X202,X27,X25] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X25) = hAPP(hAPP(c_List_Onth(X27),X202),X25) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X25) = hAPP(hAPP(c_List_Onth(X27),X201),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append) ).

fof(fact_Compl__iff,axiom,
    ! [X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__iff) ).

fof(fact_ComplD,axiom,
    ! [X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplD) ).

fof(fact_ComplE,axiom,
    ! [X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplE) ).

fof(fact_nat__number__of__Bit0,axiom,
    ! [X90] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X90)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),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,
    ! [X68,X69,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Orderings_Oord(X10) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X68) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X69) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__number__of) ).

fof(fact_min__number__of,axiom,
    ! [X68,X69,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Orderings_Oord(X10) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X69) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X68) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__number__of) ).

fof(fact_not__add__less1,axiom,
    ! [X43,X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).

fof(fact_not__add__less2,axiom,
    ! [X44,X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X44)),X44)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).

fof(fact_remove1__append,axiom,
    ! [X199,X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oremove1(X10,X11,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),c_List_Oremove1(X10,X11,X200)),X199) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oremove1(X10,X11,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),X200),c_List_Oremove1(X10,X11,X199)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__append) ).

fof(fact_neg__number__of__pred__iff__0,axiom,
    ! [X93] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X93))))
    <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93) = 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,
    ! [X11,X2,X10] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).

fof(fact_rel__simps_I51_J,axiom,
    ! [X83,X32] :
      ( c_Int_OBit1(X32) = c_Int_OBit1(X83)
    <=> X32 = X83 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_concat__replicate__trivial,axiom,
    ! [X44,X27] : c_List_Oconcat(X27,c_List_Oreplicate(tc_List_Olist(X27),X44,c_List_Olist_ONil(X27))) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat__replicate__trivial) ).

fof(fact_nat__diff__split__asm,axiom,
    ! [X14,X13,X42] :
      ( hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13),X14)))
    <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X14))
            & ~ hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X75] :
              ( X13 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X75)
              & ~ hBOOL(hAPP(X42,X75)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).

fof(fact_distinct_Osimps_I2_J,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
        & hBOOL(hAPP(c_List_Odistinct(X10),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I2_J) ).

fof(fact_length__rotate,axiom,
    ! [X202,X25,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(c_List_Orotate(X27,X25),X202)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [X42,X10] : c_List_OdropWhile(X10,X42,c_List_Olist_ONil(X10)) = c_List_Olist_ONil(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).

fof(fact_Diff__insert__absorb,axiom,
    ! [X12,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert__absorb) ).

fof(fact_setsum_Oinsert,axiom,
    ! [X1,X11,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(X1,X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinsert) ).

fof(fact_setsum__insert,axiom,
    ! [X2,X13,X9,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X9))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Set_Oinsert(X10),X13),X9)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(X2,X13)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X9)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__insert) ).

fof(fact_setprod_Oinsert,axiom,
    ! [X1,X11,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X1,X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinsert) ).

fof(fact_setprod__insert,axiom,
    ! [X2,X13,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X2,X13)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__insert) ).

fof(fact_drop__upt,axiom,
    ! [X43,X44,X24] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X24),c_List_Oupt(X44,X43)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X24),X43),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__upt) ).

fof(fact_filter__empty__conv,axiom,
    ! [X200,X42,X10] :
      ( hAPP(c_List_Ofilter(X10,X42),X200) = c_List_Olist_ONil(X10)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => ~ hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_not__int__zless__negative,axiom,
    ! [X24,X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__int__zless__negative) ).

fof(fact_set__rotate,axiom,
    ! [X200,X30,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_Orotate(X10,X30),X200)) = hAPP(c_List_Oset(X10),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rotate) ).

fof(fact_sup1CI,axiom,
    ! [X10,X12,X11,X15] :
      ( ( ~ hBOOL(hAPP(X15,X11))
       => hBOOL(hAPP(X12,X11)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1CI) ).

fof(fact_partition__P,axiom,
    ! [X233,X234,X200,X42,X10] :
      ( c_List_Opartition(X10,X42,X200) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X234),X233)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X234)))
           => hBOOL(hAPP(X42,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X233)))
           => ~ hBOOL(hAPP(X42,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__P) ).

fof(fact_trancl__domain,axiom,
    ! [X110,X10] : hAPP(c_Relation_ODomain(X10,X10),c_Transitive__Closure_Otrancl(X10,X110)) = hAPP(c_Relation_ODomain(X10,X10),X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__domain) ).

fof(fact_trancl__range,axiom,
    ! [X110,X10] : hAPP(c_Relation_ORange(X10,X10),c_Transitive__Closure_Otrancl(X10,X110)) = hAPP(c_Relation_ORange(X10,X10),X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__range) ).

fof(fact_le__nat__number__of,axiom,
    ! [X119,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X93),X119))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X93),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__nat__number__of) ).

fof(fact_dvd_Oless__trans,axiom,
    ! [X38,X34,X26] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X26)) )
     => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X34)) )
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__trans) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OBit0(X45)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_diff__bin__simps_I7_J,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X33)),c_Int_OBit0(X45)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I7_J) ).

fof(fact_folding__one_Oeq__fold_H,axiom,
    ! [X11,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,X2),X11),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold_H) ).

fof(fact_Abs__Integ__cases,axiom,
    ! [X11] :
      ~ ! [X51] :
          ( X11 = hAPP(c_Int_OAbs__Integ,X51)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X51),c_Int_OInteg)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).

fof(fact_upt__conv__Cons,axiom,
    ! [X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => c_List_Oupt(X44,X43) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X44),c_List_Oupt(hAPP(c_Nat_OSuc,X44),X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__conv__Cons) ).

fof(fact_filter__insort__triv,axiom,
    ! [X200,X2,X10,X11,X42,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( ~ hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X11),X200)) = hAPP(c_List_Ofilter(X10,X42),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X11),X12) ) ) ),
    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,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X11),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold_H) ).

fof(fact_not__psubset__empty,axiom,
    ! [X12,X10] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__psubset__empty) ).

fof(fact_fold1__eq__fold,axiom,
    ! [X13,X12,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Groups_Otimes__class_Otimes(X10)),X13),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__eq__fold) ).

fof(fact_number__of__Bit0,axiom,
    ! [X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit0(X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92))),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_map__nth,axiom,
    ! [X200,X10] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),hAPP(c_List_Onth(X10),X200)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))) = X200,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__nth) ).

fof(fact_le__infE,axiom,
    ! [X36,X37,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infE) ).

fof(fact_min__max_Ole__infE,axiom,
    ! [X36,X37,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infE) ).

fof(fact_length__remove1,axiom,
    ! [X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremove1(X10,X11,X200)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremove1(X10,X11,X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remove1) ).

fof(fact_Int__insert__left__if0,axiom,
    ! [X15,X17,X13,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X17))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).

fof(fact_nat__of__aux__code,axiom,
    ! [X25,X44] :
      ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(X44,X25) = X25 )
      & ( X44 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => c_Code__Numeral_Onat__of__aux(X44,X25) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X44),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__aux__code) ).

fof(fact_nat__of__aux__def,axiom,
    ! [X25,X44] : c_Code__Numeral_Onat__of__aux(X44,X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X44)),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__aux__def) ).

fof(fact_sym__trancl,axiom,
    ! [X110,X10] :
      ( c_Relation_Osym(X10,X110)
     => c_Relation_Osym(X10,c_Transitive__Closure_Otrancl(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__trancl) ).

fof(fact_wf__trancl,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(X10,c_Transitive__Closure_Otrancl(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__trancl) ).

fof(fact_R__O__Id,axiom,
    ! [X29,X8,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X8,X8),X29),c_Relation_OId(X8)) = X29,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_R__O__Id) ).

fof(fact_trancl__unfold__right,axiom,
    ! [X110,X10] : c_Transitive__Closure_Otrancl(X10,X110) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Ortrancl(X10,X110)),X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).

fof(fact_trancl__rtrancl__absorb,axiom,
    ! [X29,X10] : c_Transitive__Closure_Ortrancl(X10,c_Transitive__Closure_Otrancl(X10,X29)) = c_Transitive__Closure_Ortrancl(X10,X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).

fof(fact_concat_Osimps_I1_J,axiom,
    ! [X27] : c_List_Oconcat(X27,c_List_Olist_ONil(tc_List_Olist(X27))) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_concat_Osimps_I1_J) ).

fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
    ! [X14,X13] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff) ).

fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
    ! [X14,X13] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14)
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty__iff2) ).

fof(fact_Inf__fin_Oeq__fold_H,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X11),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold_H) ).

fof(fact_Sup__fin_Oeq__fold_H,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X11),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold_H) ).

fof(fact_Max_Oeq__fold_H,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X11),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oeq__fold_H) ).

fof(fact_Min_Oeq__fold_H,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X11),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oeq__fold_H) ).

fof(fact_trans__trancl,axiom,
    ! [X110,X10] : c_Relation_Otrans(X10,c_Transitive__Closure_Otrancl(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__trancl) ).

fof(fact_eq__nat__number__of,axiom,
    ! [X119,X93] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)
    <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X119)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93)))
         => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X119)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X119)))
             => X93 = X119 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).

fof(fact_abs__number__of,axiom,
    ! [X26,X27] :
      ( ( class_Int_Onumber__ring(X27)
        & class_Rings_Olinordered__idom(X27) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)),c_Groups_Ozero__class_Ozero(X27)))
         => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)),c_Groups_Ozero__class_Ozero(X27)))
         => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),X26) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__number__of) ).

fof(fact_converse__Id,axiom,
    ! [X10] : hAPP(c_Relation_Oconverse(X10,X10),c_Relation_OId(X10)) = c_Relation_OId(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id) ).

fof(fact_mod__nat__number__of,axiom,
    ! [X120,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).

fof(fact_min__max_OSup__fin_Oinsert,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).

fof(fact_min__max_OInf__fin_Oinsert,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).

fof(fact_mult__Bit0,axiom,
    ! [X45,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X33)),X45) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Bit0) ).

fof(fact_dvd_Ole__less__trans,axiom,
    ! [X38,X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
     => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X34)) )
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less__trans) ).

fof(fact_dvd_Oless__le__trans,axiom,
    ! [X38,X34,X26] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X26)) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X38))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le__trans) ).

fof(fact_takeWhile__append1,axiom,
    ! [X199,X42,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ( ~ hBOOL(hAPP(X42,X11))
       => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = c_List_OtakeWhile(X10,X42,X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_div__nat__number__of,axiom,
    ! [X120,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nat__number__of) ).

fof(fact_power__nat__number__of__number__of,axiom,
    ! [X92,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)) = 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),X92)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__nat__number__of__number__of) ).

fof(fact_fold1__insert,axiom,
    ! [X11,X12,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
           => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__insert) ).

fof(fact_dvd_OatLeastatMost__empty,axiom,
    ! [X13,X14] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X13))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14)) )
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastatMost__empty) ).

fof(fact_Suc__diff__number__of,axiom,
    ! [X24,X68] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X68))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X68))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__number__of) ).

fof(fact_ex__least__nat__less,axiom,
    ! [X30,X42] :
      ( ~ hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X42,X30))
       => ? [X59] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),X30))
            & ! [X91] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X91),X59))
               => ~ hBOOL(hAPP(X42,X91)) )
            & hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),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,
    ! [X31,X30] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X30,X31) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X30),hAPP(c_Nat_OSuc,X31))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__upt) ).

fof(fact_rel__simps_I8_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I8_J) ).

fof(fact_rel__simps_I25_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I25_J) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_Int__insert__right__if0,axiom,
    ! [X15,X12,X13,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).

fof(fact_rotate__id,axiom,
    ! [X202,X27,X25] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X25,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Orotate(X27,X25),X202) = X202 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__id) ).

fof(fact_rotate__is__Nil__conv,axiom,
    ! [X200,X30,X10] :
      ( hAPP(c_List_Orotate(X10,X30),X200) = c_List_Olist_ONil(X10)
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__is__Nil__conv) ).

fof(fact_simp__from__to,axiom,
    ! [X61,X60] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X61,X60) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X61,X60) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X61),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)),X60)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_simp__from__to) ).

fof(fact_double__number__of__Bit0,axiom,
    ! [X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Oone__class_Oone(X27))),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit0(X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__number__of__Bit0) ).

fof(fact_insertCI,axiom,
    ! [X14,X15,X13,X10] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X15))
       => X13 = X14 )
     => hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).

fof(fact_Bit1__def,axiom,
    ! [X33] : c_Int_OBit1(X33) = 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)),X33)),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__def) ).

fof(fact_internal__split__conv,axiom,
    ! [X14,X13,X6,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Ointernal__split(X8,X18,X10),X6),hAPP(hAPP(c_Product__Type_OPair(X8,X18),X13),X14)) = hAPP(hAPP(X6,X13),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__conv) ).

fof(fact_internal__split__def,axiom,
    ! [X18,X8,X10] : c_Product__Type_Ointernal__split(X10,X8,X18) = c_Product__Type_Oprod_Oprod__case(X10,X8,X18),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__def) ).

fof(fact_map__replicate__trivial,axiom,
    ! [X61,X11,X10] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X10),hAPP(c_COMBK(X10,tc_Nat_Onat),X11)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X61)) = c_List_Oreplicate(X10,X61,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate__trivial) ).

fof(fact_ComplI,axiom,
    ! [X12,X6,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
     => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ComplI) ).

fof(fact_vimage__const,axiom,
    ! [X8,X12,X6,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => hAPP(c_Set_Ovimage(X8,X10,hAPP(c_COMBK(X10,X8),X6)),X12) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => hAPP(c_Set_Ovimage(X8,X10,hAPP(c_COMBK(X10,X8),X6)),X12) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__const) ).

fof(fact_folding__one_Oinsert,axiom,
    ! [X11,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(X2,X11),hAPP(X9,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oinsert) ).

fof(fact_nat__dvd__not__less,axiom,
    ! [X25,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),X24),X25))
       => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__not__less) ).

fof(fact_map__Suc__upt,axiom,
    ! [X30,X31] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X31,X30)) = c_List_Oupt(hAPP(c_Nat_OSuc,X31),hAPP(c_Nat_OSuc,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__Suc__upt) ).

fof(fact_divmod__int__def,axiom,
    ! [X36,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)),X36))
           => c_Divides_Odivmod__int(X37,X36) = c_Divides_OposDivAlg(X37,X36) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => ( ( X37 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X37,X36) = 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)) )
              & ( X37 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X37,X36) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36))) ) ) ) ) )
      & ( ~ 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(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => c_Divides_Odivmod__int(X37,X36) = c_Divides_OnegDivAlg(X37,X36) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => c_Divides_Odivmod__int(X37,X36) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__def) ).

fof(fact_takeWhile__tail,axiom,
    ! [X83,X200,X10,X11,X42] :
      ( ~ hBOOL(hAPP(X42,X11))
     => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X83))) = c_List_OtakeWhile(X10,X42,X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__tail) ).

fof(fact_refl__Id,axiom,
    ! [X10] : c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Relation_OId(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__Id) ).

fof(fact_numeral__1__eq__1,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__1__eq__1) ).

fof(fact_semiring__norm_I110_J,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => c_Groups_Oone__class_Oone(X27) = hAPP(c_Int_Onumber__class_Onumber__of(X27),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,
    ! [X30,X31] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq__eq) ).

fof(fact_abs__not__less__zero,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_of__nat__less__0__iff,axiom,
    ! [X24,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).

fof(fact_iszero__number__of__Bit0,axiom,
    ! [X90,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Int_Oring__char__0(X10) )
     => ( c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),c_Int_OBit0(X90)))
      <=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__number__of__Bit0) ).

fof(fact_add__nat__number__of,axiom,
    ! [X120,X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),X120)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nat__number__of) ).

fof(fact_power__nat__number__of,axiom,
    ! [X25,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X25) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X25) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__nat__number__of) ).

fof(fact_diff__bin__simps_I3_J,axiom,
    ! [X45] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X45)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X45)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).

fof(fact_minus__shift__def,axiom,
    ! [X80,X45,X33] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33),X45))
       => c_Random_Ominus__shift(X80,X33,X45) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X80),X33)),X45) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33),X45))
       => c_Random_Ominus__shift(X80,X33,X45) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33),X45) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__shift__def) ).

fof(fact_split__zmod,axiom,
    ! [X32,X30,X42] :
      ( hBOOL(hAPP(X42,c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X32)))
    <=> ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X42,X30)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32))
         => ! [X91,X73] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X32))
                & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
             => hBOOL(hAPP(X42,X73)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X91,X73] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X73))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
             => hBOOL(hAPP(X42,X73)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zmod) ).

fof(fact_upto_Osimps,axiom,
    ! [X43,X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X44),X43))
       => c_List_Oupto(X44,X43) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X44),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X44),c_Groups_Oone__class_Oone(tc_Int_Oint)),X43)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X44),X43))
       => c_List_Oupto(X44,X43) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto_Osimps) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [X45,X33] : c_Int_OBit0(X33) != c_Int_OBit1(X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [X45,X33] : c_Int_OBit1(X33) != c_Int_OBit0(X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_divmod__nat__div__mod,axiom,
    ! [X25,X24] : c_Divides_Odivmod__nat(X24,X25) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).

fof(fact_code__numeral_Osimps_I5_J,axiom,
    ! [X135,X49,X50,X10] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X10,X50,X49,c_Code__Numeral_OSuc__code__numeral(X135)) = hAPP(X49,X135),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I5_J) ).

fof(fact_greaterThanLessThan__upt,axiom,
    ! [X31,X30] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X30,X31) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X30),X31)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanLessThan__upt) ).

fof(fact_remdups_Osimps_I2_J,axiom,
    ! [X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oremdups(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = c_List_Oremdups(X10,X200) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oremdups(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Oremdups(X10,X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I2_J) ).

fof(fact_of__int__of__nat,axiom,
    ! [X33,X27] :
      ( class_Rings_Oring__1(X27)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X27),X33) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X27),X33) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onat,X33)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat) ).

fof(fact_small__lazy_H_Osimps,axiom,
    ! [X44,X58] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X58),X44))
       => c_Lazy__Sequence_Osmall__lazy_H(X58,X44) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X58),X44))
       => c_Lazy__Sequence_Osmall__lazy_H(X58,X44) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X44),c_Lazy__Sequence_Osmall__lazy_H(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X44),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,
    ! [X10] : hAPP(c_Relation_ODomain(X10,X10),c_Relation_OId(X10)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id) ).

fof(fact_Range__Id,axiom,
    ! [X10] : hAPP(c_Relation_ORange(X10,X10),c_Relation_OId(X10)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id) ).

fof(fact_Inf__fin_Oinsert,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert) ).

fof(fact_Sup__fin_Oinsert,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert) ).

fof(fact_Max_Oinsert,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olinorder__class_OMax(X10,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oinsert) ).

fof(fact_Min_Oinsert,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olinorder__class_OMin(X10,X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oinsert) ).

fof(fact_list__all__iff__all__interval__nat,axiom,
    ! [X60,X61,X42] :
      ( c_List_Olist__all(tc_Nat_Onat,X42,c_List_Oupt(X61,X60))
    <=> c_List_Oall__interval__nat(X42,X61,X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__nat) ).

fof(fact_rtrancl__trancl__absorb,axiom,
    ! [X29,X10] : c_Transitive__Closure_Otrancl(X10,c_Transitive__Closure_Ortrancl(X10,X29)) = c_Transitive__Closure_Ortrancl(X10,X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).

fof(fact_sublist__singleton,axiom,
    ! [X11,X10,X12] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12))
       => c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)),X12) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12))
       => c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)),X12) = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__singleton) ).

fof(fact_List_Omember__def,axiom,
    ! [X11,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_List_Omember(X10),X200),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omember__def) ).

fof(fact_in__set__member,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
    <=> hBOOL(hAPP(hAPP(c_List_Omember(X10),X200),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__member) ).

fof(fact_one__mod__nat__number__of,axiom,
    ! [X120] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
       => 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),X120)) = 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),X120)))
       => 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),X120)) = 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),X120))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__mod__nat__number__of) ).

fof(fact_single__valued__Id,axiom,
    ! [X10] : c_Relation_Osingle__valued(X10,X10,c_Relation_OId(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id) ).

fof(fact_less__le__not__le,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__le__not__le) ).

fof(fact_card_Oinsert,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert) ).

fof(fact_split__zdiv,axiom,
    ! [X32,X30,X42] :
      ( hBOOL(hAPP(X42,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X32)))
    <=> ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X42,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)),X32))
         => ! [X91] :
              ( ? [X73] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X32))
                  & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
             => hBOOL(hAPP(X42,X91)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X91] :
              ( ? [X73] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X73))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
             => hBOOL(hAPP(X42,X91)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zdiv) ).

fof(fact_insert__ident,axiom,
    ! [X15,X12,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
       => ( hAPP(hAPP(c_Set_Oinsert(X10),X11),X12) = hAPP(hAPP(c_Set_Oinsert(X10),X11),X15)
        <=> X12 = X15 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).

fof(fact_card__insert__if,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Finite__Set_Ocard(X10),X12) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__if) ).

fof(fact_last__upt,axiom,
    ! [X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => c_List_Olast(tc_Nat_Onat,c_List_Oupt(X44,X43)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),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,
    ! [X25] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X25)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__code__numeral__minus__one) ).

fof(fact_not__less__eq,axiom,
    ! [X30,X31] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_OSuc,X31))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__eq) ).

fof(fact_distinct__upt,axiom,
    ! [X43,X44] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X44,X43))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upt) ).

fof(fact_relpow_Osimps_I1_J,axiom,
    ! [X29,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29) = c_Relation_OId(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_relpow_Osimps_I1_J) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [X200,X10,X11,X42] :
      ( ( hBOOL(hAPP(X42,X11))
       => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_OtakeWhile(X10,X42,X200)) )
      & ( ~ hBOOL(hAPP(X42,X11))
       => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_int__less__0__conv,axiom,
    ! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)),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,
    ! [X83] :
      ( c_Int_OMin = c_Int_OBit1(X83)
    <=> c_Int_OMin = X83 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).

fof(fact_rel__simps_I47_J,axiom,
    ! [X32] :
      ( c_Int_OBit1(X32) = c_Int_OMin
    <=> X32 = c_Int_OMin ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).

fof(fact_rel__simps_I46_J,axiom,
    ! [X33] : c_Int_OBit1(X33) != c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).

fof(fact_rel__simps_I39_J,axiom,
    ! [X45] : c_Int_OPls != c_Int_OBit1(X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).

fof(fact_sym__Id,axiom,
    ! [X10] : c_Relation_Osym(X10,c_Relation_OId(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Id) ).

fof(fact_antisym__Id,axiom,
    ! [X10] : c_Relation_Oantisym(X10,c_Relation_OId(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id) ).

fof(fact_trans__Id,axiom,
    ! [X10] : c_Relation_Otrans(X10,c_Relation_OId(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id) ).

fof(fact_of__nat__number__of__lemma,axiom,
    ! [X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => ( ( 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),X68)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),X68) )
        & ( ~ 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),X68)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = c_Groups_Ozero__class_Ozero(X27) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).

fof(fact_card__insert__disjoint,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__disjoint) ).

fof(fact_linorder__antisym__conv2,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
        <=> X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv2) ).

fof(fact_infinite__UNIV__listI,axiom,
    ! [X10] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__listI) ).

fof(fact_List_Oinsert__def,axiom,
    ! [X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oinsert(X10,X11,X200) = X200 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oinsert(X10,X11,X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oinsert__def) ).

fof(fact_xt1_I9_J,axiom,
    ! [X37,X36,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I9_J) ).

fof(fact_not__less__iff__gr__or__eq,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X11))
          | X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__iff__gr__or__eq) ).

fof(fact_leD,axiom,
    ! [X26,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leD) ).

fof(fact_linorder__not__less,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__less) ).

fof(fact_linorder__not__le,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__not__le) ).

fof(fact_order__less__asym,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym) ).

fof(fact_order__less__asym_H,axiom,
    ! [X36,X37,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__asym_H) ).

fof(fact_order__less__imp__not__less,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__less) ).

fof(fact_order__less__not__sym,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__not__sym) ).

fof(fact_mult__nat__number__of,axiom,
    ! [X120,X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X120)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nat__number__of) ).

fof(fact_hd__upt,axiom,
    ! [X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X44,X43)) = X44 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__upt) ).

fof(fact_empty__iff,axiom,
    ! [X6,X10] : ~ hBOOL(hAPP(hAPP(c_member(X10),X6),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__iff) ).

fof(fact_emptyE,axiom,
    ! [X13,X10] : ~ hBOOL(hAPP(hAPP(c_member(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_emptyE) ).

fof(fact_le__SucE,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
       => X24 = hAPP(c_Nat_OSuc,X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucE) ).

fof(fact_atLeastAtMost__upt,axiom,
    ! [X31,X30] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X30,X31) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X30,hAPP(c_Nat_OSuc,X31))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__upt) ).

fof(fact_atLeastLessThanSuc,axiom,
    ! [X30,X31] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X30),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),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_atLeastLessThanSuc) ).

fof(fact_filter_Osimps_I2_J,axiom,
    ! [X200,X10,X11,X42] :
      ( ( hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),hAPP(c_List_Ofilter(X10,X42),X200)) )
      & ( ~ hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(c_List_Ofilter(X10,X42),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_less__SucE,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => X24 = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucE) ).

fof(fact_less__antisym,axiom,
    ! [X24,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_OSuc,X24)))
       => X24 = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__antisym) ).

fof(fact_not__less__less__Suc__eq,axiom,
    ! [X31,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_OSuc,X31)))
      <=> X30 = X31 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__less__Suc__eq) ).

fof(fact_divmod__nat__rel__divmod__nat,axiom,
    ! [X25,X24] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X24,X25),c_Divides_Odivmod__nat(X24,X25))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).

fof(fact_code__numeral_Osize_I4_J,axiom,
    ! [X133] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X133)),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,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__upto) ).

fof(fact_number__of__pred,axiom,
    ! [X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_Opred(X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27))),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__pred) ).

fof(fact_trancl__id,axiom,
    ! [X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => c_Transitive__Closure_Otrancl(X10,X110) = X110 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__id) ).

fof(fact_atLeastatMost__empty__iff2,axiom,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff2) ).

fof(fact_greaterThanAtMost__empty__iff2,axiom,
    ! [X83,X32,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X32,X83)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X83)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).

fof(fact_atLeastatMost__empty__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__empty__iff) ).

fof(fact_greaterThanAtMost__empty__iff,axiom,
    ! [X83,X32,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X32,X83) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X83)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).

fof(fact_dvd_Ole__neq__trans,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X37),X36))
     => ( X37 != X36
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X37),X36))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X36),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__neq__trans) ).

fof(fact_dvd_Ole__imp__less__or__eq,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
     => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X26)) )
        | X26 = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).

fof(fact_dvd_Oneq__le__trans,axiom,
    ! [X36,X37] :
      ( X37 != X36
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X37),X36))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X36),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oneq__le__trans) ).

fof(fact_dvd_Oless__le,axiom,
    ! [X16,X11] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X11)) )
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
        & X11 != X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oless__le) ).

fof(fact_dvd_Ole__less,axiom,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
    <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X11)) )
        | X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Ole__less) ).

fof(fact_divmod__nat__base,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => c_Divides_Odivmod__nat(X24,X25) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__base) ).

fof(fact_equalityE,axiom,
    ! [X10,X15,X12] :
      ( X12 = X15
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityE) ).

fof(fact_Suc__n__not__le__n,axiom,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25)),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).

fof(fact_z3div__def,axiom,
    ! [X33,X45] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_SMT_Oz3div(X33,X45) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),X45) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_SMT_Oz3div(X33,X45) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X45))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z3div__def) ).

fof(fact_mod__geq,axiom,
    ! [X25,X24] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__geq) ).

fof(fact_mod__if,axiom,
    ! [X25,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = X24 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).

fof(fact_not__in__set__insert,axiom,
    ! [X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => c_List_Oinsert(X10,X11,X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__in__set__insert) ).

fof(fact_linorder__antisym__conv1,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
        <=> X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv1) ).

fof(fact_atLeastLessThan__empty__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff) ).

fof(fact_atLeastLessThan__empty__iff2,axiom,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).

fof(fact_part__equivpE,axiom,
    ! [X29,X10] :
      ( c_Equiv__Relations_Opart__equivp(X10,X29)
     => ~ ( ? [X3] : hBOOL(hAPP(hAPP(X29,X3),X3))
         => ( c_Predicate_Osymp(X10,X29)
           => ~ c_Predicate_Otransp(X10,X29) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivpE) ).

fof(fact_code__numeral_Oinject,axiom,
    ! [X134,X135] :
      ( c_Code__Numeral_OSuc__code__numeral(X135) = c_Code__Numeral_OSuc__code__numeral(X134)
    <=> X135 = X134 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Oinject) ).

fof(fact_code__numeral_Osize_I2_J,axiom,
    ! [X133] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X133)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X133)),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,
    ! [X33] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X33)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit0) ).

fof(fact_filter__replicate,axiom,
    ! [X30,X10,X11,X42] :
      ( ( hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),c_List_Oreplicate(X10,X30,X11)) = c_List_Oreplicate(X10,X30,X11) )
      & ( ~ hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),c_List_Oreplicate(X10,X30,X11)) = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__replicate) ).

fof(fact_transfer__nat__int__list__return__embed,axiom,
    ! [X45] :
      ( c_List_Onat__list(X45)
     => c_List_Oembed__list(c_List_Oreturn__list(X45)) = X45 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).

fof(fact_all__not__in__conv,axiom,
    ! [X12,X10] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
    <=> X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__not__in__conv) ).

fof(fact_remove1__idem,axiom,
    ! [X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => c_List_Oremove1(X10,X11,X200) = X200 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__idem) ).

fof(fact_length__upt,axiom,
    ! [X43,X44] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X44,X43)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X44),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__upt) ).

fof(fact_sgn__if,axiom,
    ! [X26,X27] :
      ( class_Groups_Osgn__if(X27)
     => ( ( X26 = c_Groups_Ozero__class_Ozero(X27)
         => c_Groups_Osgn__class_Osgn(X27,X26) = c_Groups_Ozero__class_Ozero(X27) )
        & ( X26 != c_Groups_Ozero__class_Ozero(X27)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
             => c_Groups_Osgn__class_Osgn(X27,X26) = c_Groups_Oone__class_Oone(X27) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
             => c_Groups_Osgn__class_Osgn(X27,X26) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__if) ).

fof(fact_upt__eq__Nil__conv,axiom,
    ! [X60,X61] :
      ( c_List_Oupt(X61,X60) = c_List_Olist_ONil(tc_Nat_Onat)
    <=> ( X60 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X60),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).

fof(fact_upt__conv__Nil,axiom,
    ! [X44,X43] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X43),X44))
     => c_List_Oupt(X44,X43) = c_List_Olist_ONil(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__conv__Nil) ).

fof(fact_z3mod__def,axiom,
    ! [X33,X45] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_SMT_Oz3mod(X33,X45) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,X45) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_SMT_Oz3mod(X33,X45) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X45)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_z3mod__def) ).

fof(fact_abs__if,axiom,
    ! [X37,X27] :
      ( class_Groups_Oabs__if(X27)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
         => hAPP(c_Groups_Oabs__class_Oabs(X27),X37) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
         => hAPP(c_Groups_Oabs__class_Oabs(X27),X37) = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__if) ).

fof(fact_not__one__less__zero,axiom,
    ! [X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).

fof(fact_not__one__le__zero,axiom,
    ! [X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).

fof(fact_add__diff__inverse,axiom,
    ! [X25,X24] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__inverse) ).

fof(fact_atLeast__upt,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__upt) ).

fof(fact_linorder__neqE__linordered__idom,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( X26 != X34
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__linordered__idom) ).

fof(fact_linorder__cases,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ( X26 != X34
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__cases) ).

fof(fact_linorder__neqE,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( X26 != X34
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE) ).

fof(fact_linorder__antisym__conv3,axiom,
    ! [X11,X16,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
        <=> X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__antisym__conv3) ).

fof(fact_not__leE,axiom,
    ! [X26,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__leE) ).

fof(fact_leI,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_leI) ).

fof(fact_linorder__le__cases,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__cases) ).

fof(fact_set__upt,axiom,
    ! [X60,X61] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X61,X60)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X61),X60),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__upt) ).

fof(fact_atLeastLessThan__upt,axiom,
    ! [X60,X61] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X61),X60) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X61,X60)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__upt) ).

fof(fact_succ__pred,axiom,
    ! [X26] : c_Int_Osucc(c_Int_Opred(X26)) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__pred) ).

fof(fact_number__of__succ,axiom,
    ! [X33,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_Osucc(X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__succ) ).

fof(fact_equals0D,axiom,
    ! [X13,X10,X12] :
      ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equals0D) ).

fof(fact_not__neg__eq__ge__0,axiom,
    ! [X11] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X11))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).

fof(fact_of__nat__cases,axiom,
    ! [X11] :
      ~ ! [X51] :
          ( X11 = hAPP(c_Code__Numeral_Oof__nat,X51)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X51),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__cases) ).

fof(fact_nat__eq__iff,axiom,
    ! [X31,X90] :
      ( hAPP(c_Int_Onat,X90) = X31
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => X90 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => X31 = 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,
    ! [X90,X31] :
      ( X31 = hAPP(c_Int_Onat,X90)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => X90 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => X31 = 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,
    ! [X38] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X38)) = X38 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X38)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__eq) ).

fof(fact_tsub__def,axiom,
    ! [X26,X34] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34),X26))
       => c_Nat__Transfer_Otsub(X26,X34) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X34) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34),X26))
       => c_Nat__Transfer_Otsub(X26,X34) = 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,
    ! [X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = c_Groups_Ozero__class_Ozero(X27) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),X68) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).

fof(fact_mod__nat__def,axiom,
    ! [X25,X24] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X24,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__nat__def) ).

fof(fact_remove1__filter__not,axiom,
    ! [X200,X10,X11,X42] :
      ( ~ hBOOL(hAPP(X42,X11))
     => c_List_Oremove1(X10,X11,hAPP(c_List_Ofilter(X10,X42),X200)) = hAPP(c_List_Ofilter(X10,X42),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_div__nat__def,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X24,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nat__def) ).

fof(fact_int__nat__number__of,axiom,
    ! [X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__number__of) ).

fof(fact_zabs__def,axiom,
    ! [X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X44) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X44) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X44) = X44 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).

fof(fact_linorder__neqE__nat,axiom,
    ! [X34,X26] :
      ( X26 != X34
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).

fof(fact_divmod__nat__eq,axiom,
    ! [X151,X25,X24] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X24,X25),X151))
     => c_Divides_Odivmod__nat(X24,X25) = X151 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).

fof(fact_zsgn__def,axiom,
    ! [X44] :
      ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X44) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X44 != 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)),X44))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X44) = 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)),X44))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X44) = 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,
    ! [X43,X44] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X44,X43)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__upt) ).

fof(fact_wf__measure,axiom,
    ! [X2,X10] : c_Wellfounded_Owf(X10,hAPP(c_Wellfounded_Omeasure(X10),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measure) ).

fof(fact_order__less__irrefl,axiom,
    ! [X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).

fof(fact_beyond__def,axiom,
    ! [X45,X33] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33),X45))
       => c_Quickcheck_Obeyond(X33,X45) = X45 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33),X45))
       => c_Quickcheck_Obeyond(X33,X45) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_beyond__def) ).

fof(fact_rotate0,axiom,
    ! [X10] : c_List_Orotate(X10,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate0) ).

fof(fact_less__nat__zero__code,axiom,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),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,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).

fof(fact_less__zeroE,axiom,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).

fof(fact_divmod__nat__zero,axiom,
    ! [X24] : c_Divides_Odivmod__nat(X24,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)),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).

fof(fact_less__irrefl__nat,axiom,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).

fof(fact_less__not__refl,axiom,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).

fof(fact_rel__simps_I48_J,axiom,
    ! [X83,X32] :
      ( c_Int_OBit0(X32) = c_Int_OBit0(X83)
    <=> X32 = X83 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_setsum__infinite,axiom,
    ! [X2,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12) = c_Groups_Ozero__class_Ozero(X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__infinite) ).

fof(fact_setsum_Oinfinite,axiom,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12) = c_Groups_Ozero__class_Ozero(X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinfinite) ).

fof(fact_setprod_Oinfinite,axiom,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12) = c_Groups_Oone__class_Oone(X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinfinite) ).

fof(fact_setprod__infinite,axiom,
    ! [X2,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12) = c_Groups_Oone__class_Oone(X8) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__infinite) ).

fof(fact_not__neg__int,axiom,
    ! [X25] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__int) ).

fof(fact_equivE,axiom,
    ! [X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ~ ( c_Relation_Orefl__on(X10,X12,X110)
         => ( c_Relation_Osym(X10,X110)
           => ~ c_Relation_Otrans(X10,X110) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivE) ).

fof(fact_code__numeral_Osimps_I3_J,axiom,
    ! [X140] : c_Code__Numeral_OSuc__code__numeral(X140) != 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,
    ! [X139] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X139),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).

fof(help_c__fimplies__3,axiom,
    ! [X41,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X42),X41))
      | ~ hBOOL(X42)
      | hBOOL(X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).

fof(fact_card__eq__0__iff,axiom,
    ! [X12,X10] :
      ( hAPP(c_Finite__Set_Ocard(X10),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).

fof(help_c__fdisj__3,axiom,
    ! [X41,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X42),X41))
      | hBOOL(X42)
      | hBOOL(X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fconj__2,axiom,
    ! [X41,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X42),X41))
      | hBOOL(X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [X41,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X42),X41))
      | hBOOL(X41) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).

fof(fact_empty__Collect__eq,axiom,
    ! [X42,X10] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),X42)
    <=> ! [X3] : ~ hBOOL(hAPP(X42,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__empty__eq,axiom,
    ! [X42,X10] :
      ( hAPP(c_Set_OCollect(X10),X42) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X42,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).

fof(help_c__fequal__1,axiom,
    ! [X16,X11] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X11),X16))
      | X11 = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).

fof(fact_nat__of__code,axiom,
    ! [X44] : hAPP(c_Code__Numeral_Onat__of,X44) = c_Code__Numeral_Onat__of__aux(X44,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,
    ! [X42,X10] : ~ c_List_Olist__ex1(X10,X42,c_List_Olist_ONil(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__simps_I1_J) ).

fof(fact_list__ex__simps_I2_J,axiom,
    ! [X42,X10] : ~ c_List_Olist__ex(X10,X42,c_List_Olist_ONil(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I2_J) ).

fof(fact_pred__def,axiom,
    ! [X33] : c_Int_Opred(X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__def) ).

fof(fact_succ__def,axiom,
    ! [X33] : c_Int_Osucc(X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).

fof(fact_upt__0,axiom,
    ! [X44] : c_List_Oupt(X44,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,
    ! [X41,X42] :
      ( ~ hBOOL(X42)
      | ~ hBOOL(X41)
      | hBOOL(hAPP(hAPP(c_fconj,X42),X41)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).

fof(fact_add__Min,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X33) = c_Int_Opred(X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min) ).

fof(fact_nonzero__number__of__Min,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => ~ c_Int_Oiszero(X27,hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).

fof(help_c__fdisj__1,axiom,
    ! [X41,X42] :
      ( ~ hBOOL(X42)
      | hBOOL(hAPP(hAPP(c_fdisj,X42),X41)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [X42,X41] :
      ( ~ hBOOL(X41)
      | hBOOL(hAPP(hAPP(c_fdisj,X42),X41)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).

fof(help_c__fimplies__2,axiom,
    ! [X42,X41] :
      ( ~ hBOOL(X41)
      | hBOOL(hAPP(hAPP(c_fimplies,X42),X41)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).

fof(fact_rel__simps_I38_J,axiom,
    ! [X83] :
      ( c_Int_OPls = c_Int_OBit0(X83)
    <=> c_Int_OPls = X83 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [X32] :
      ( c_Int_OBit0(X32) = c_Int_OPls
    <=> X32 = c_Int_OPls ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_rel__simps_I45_J,axiom,
    ! [X33] : c_Int_OBit0(X33) != c_Int_OMin,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).

fof(fact_rel__simps_I42_J,axiom,
    ! [X45] : c_Int_OMin != c_Int_OBit0(X45),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).

fof(fact_not__neg__nat,axiom,
    ! [X38] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X38))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X38)) = X38 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__nat) ).

fof(fact_card__infinite,axiom,
    ! [X12,X10] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(c_Finite__Set_Ocard(X10),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__infinite) ).

fof(help_c__fNot__1,axiom,
    ! [X42] :
      ( ~ hBOOL(hAPP(c_fNot,X42))
      | ~ hBOOL(X42) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).

fof(fact_not__iszero__1,axiom,
    ! [X27] :
      ( class_Rings_Osemiring__1(X27)
     => ~ c_Int_Oiszero(X27,c_Groups_Oone__class_Oone(X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__1) ).

fof(fact_equivpE,axiom,
    ! [X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => ~ ( c_Predicate_Oreflp(X10,X29)
         => ( c_Predicate_Osymp(X10,X29)
           => ~ c_Predicate_Otransp(X10,X29) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivpE) ).

fof(help_c__fNot__2,axiom,
    ! [X42] :
      ( ~ ~ hBOOL(X42)
      | hBOOL(hAPP(c_fNot,X42)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).

fof(fact_UN__equiv__class__type2,axiom,
    ! [X15,X173,X174,X2,X18,X164,X165,X8,X166,X167,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X167,X166)
     => ( c_Equiv__Relations_Oequiv(X8,X165,X164)
       => ( c_Equiv__Relations_Ocongruent2(X10,X8,tc_fun(X18,tc_HOL_Obool),X166,X164,X2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X174),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X167),X166)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X8,tc_HOL_Obool)),X173),hAPP(hAPP(c_Equiv__Relations_Oquotient(X8),X165),X164)))
             => ( ! [X136] :
                    ( hBOOL(hAPP(hAPP(c_member(X10),X136),X167))
                   => ! [X175] :
                        ( hBOOL(hAPP(hAPP(c_member(X8),X175),X165))
                       => hBOOL(hAPP(hAPP(c_member(tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(X2,X136),X175)),X15)) ) )
               => hBOOL(hAPP(hAPP(c_member(tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X18,tc_HOL_Obool)),X174),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(X18,tc_HOL_Obool)),tc_fun(X18,tc_HOL_Obool),X10),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X18,tc_HOL_Obool)),X173)),X2))),X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__type2) ).

fof(fact_rtrancl__induct2,axiom,
    ! [X42,X110,X266,X267,X268,X269,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X269),X268)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X267),X266))),c_Transitive__Closure_Ortrancl(tc_prod(X10,X8),X110)))
     => ( hBOOL(hAPP(hAPP(X42,X269),X268))
       => ( ! [X46,X81] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X269),X268)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81))),c_Transitive__Closure_Ortrancl(tc_prod(X10,X8),X110)))
             => ! [X270,X271] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X270),X271))),X110))
                 => ( hBOOL(hAPP(hAPP(X42,X46),X81))
                   => hBOOL(hAPP(hAPP(X42,X270),X271)) ) ) )
         => hBOOL(hAPP(hAPP(X42,X267),X266)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).

fof(fact_converse__rtrancl__induct2,axiom,
    ! [X42,X110,X266,X267,X268,X269,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X269),X268)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X267),X266))),c_Transitive__Closure_Ortrancl(tc_prod(X10,X8),X110)))
     => ( hBOOL(hAPP(hAPP(X42,X267),X266))
       => ( ! [X46,X81,X270,X271] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X270),X271))),X110))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X270),X271)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X267),X266))),c_Transitive__Closure_Ortrancl(tc_prod(X10,X8),X110)))
               => ( hBOOL(hAPP(hAPP(X42,X270),X271))
                 => hBOOL(hAPP(hAPP(X42,X46),X81)) ) ) )
         => hBOOL(hAPP(hAPP(X42,X269),X268)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).

fof(fact_setsum__mult__setsum__if__inj,axiom,
    ! [X15,X12,X1,X2,X8,X10,X18] :
      ( class_Rings_Osemiring__0(X18)
     => ( c_Fun_Oinj__on(tc_prod(X10,X8),X18,hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,X18),tc_fun(X8,X18)),hAPP(hAPP(c_COMBB(tc_fun(X18,X18),tc_fun(tc_fun(X8,X18),tc_fun(X8,X18)),X10),c_COMBB(X18,X18,X8)),hAPP(hAPP(c_COMBB(X18,tc_fun(X18,X18),X10),c_Groups_Otimes__class_Otimes(X18)),X2))),X1)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15)))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X18),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X18),X1),X15)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18,X18),c_Fun_Oid(X18)),hAPP(c_Set_OCollect(X18),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X18),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X18),hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X8))),hAPP(hAPP(c_COMBC(X18,tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X18),c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X8,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool))),X18),hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(X10,tc_fun(X8,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X18),hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fconj))),hAPP(hAPP(c_COMBC(X18,tc_fun(X10,tc_fun(X8,X18)),tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X18),tc_fun(X8,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X8,X18)),tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X18),c_COMBB(tc_fun(X8,X18),tc_fun(X8,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_HOL_Obool),tc_fun(tc_fun(X8,X18),tc_fun(X8,tc_HOL_Obool)),X18),c_COMBB(X18,tc_HOL_Obool,X8)),c_fequal))),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,X18),tc_fun(X8,X18)),hAPP(hAPP(c_COMBB(tc_fun(X18,X18),tc_fun(tc_fun(X8,X18),tc_fun(X8,X18)),X10),c_COMBB(X18,X18,X8)),hAPP(hAPP(c_COMBB(X18,tc_fun(X18,X18),X10),c_Groups_Otimes__class_Otimes(X18)),X2))),X1)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mult__setsum__if__inj) ).

fof(fact_rel__comp__def,axiom,
    ! [X116,X110,X8,X18,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X110),X116) = hAPP(c_Set_OCollect(tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(X18,tc_HOL_Obool)),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X18,tc_HOL_Obool),tc_HOL_Obool,X8),c_HOL_OEx(X18))),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool)),tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X18,tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),tc_fun(tc_fun(X8,tc_fun(X18,tc_HOL_Obool)),tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X18,tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool),X8)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X18,tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X10),c_COMBS(X18,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_HOL_Obool),tc_fun(X18,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X18),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X10,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X10),c_COMBC(X18,tc_fun(tc_prod(X10,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_prod(X10,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X10,X18),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X18),tc_fun(tc_fun(tc_prod(X10,X18),tc_HOL_Obool),tc_HOL_Obool),X18),c_member(tc_prod(X10,X18)))),c_Product__Type_OPair(X10,X18)))),X110))))),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X8),c_COMBC(X18,tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_prod(X18,X8)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_HOL_Obool)),X8),hAPP(c_COMBB(tc_prod(X18,X8),tc_fun(tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_HOL_Obool),X18),c_member(tc_prod(X18,X8)))),hAPP(c_COMBC(X18,X8,tc_prod(X18,X8)),c_Product__Type_OPair(X18,X8))))),X116))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__def) ).

fof(fact_min__max_Osup__Inf2__distrib,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X15)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBS(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal))),c_Orderings_Oord__class_Omax(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf2__distrib) ).

fof(fact_min__max_Oinf__Sup2__distrib,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X15)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBS(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal))),c_Orderings_Oord__class_Omin(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup2__distrib) ).

fof(fact_inf__Sup2__distrib,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Odistrib__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)),c_Big__Operators_Olattice__class_OSup__fin(X10,X15)) = c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBS(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup2__distrib) ).

fof(fact_sup__Inf2__distrib,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Odistrib__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)),c_Big__Operators_Olattice__class_OInf__fin(X10,X15)) = c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBS(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(X10,X10)),tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X10),c_COMBB(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Inf2__distrib) ).

fof(fact_set__Cons__def,axiom,
    ! [X158,X12,X10] : c_List_Oset__Cons(X10,X12,X158) = hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X10)),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),tc_List_Olist(X10)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_List_Olist(X10)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),tc_fun(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),tc_List_Olist(X10)),c_COMBS(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X10,tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),tc_List_Olist(X10)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),X10),c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X10)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),tc_List_Olist(X10)),c_COMBB(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),X10)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_List_Olist(X10),tc_HOL_Obool,tc_List_Olist(X10))),c_fequal))),c_List_Olist_OCons(X10)))))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X10))),X158)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__Cons__def) ).

fof(fact_image__INT,axiom,
    ! [X60,X15,X12,X18,X17,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X17)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X18),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(X15,X3)),X17)) )
       => ( hBOOL(hAPP(hAPP(c_member(X18),X60),X12))
         => hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X18),c_Set_Oimage(X10,X8,X2)),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__INT) ).

fof(fact_inf__Int__eq2,axiom,
    ! [X16,X11,X28,X29,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X29)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X28)),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X29),X28))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).

fof(fact_sup__Un__eq2,axiom,
    ! [X16,X11,X28,X29,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X29)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X28)),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X29),X28))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).

fof(fact_lenlex__conv,axiom,
    ! [X110,X10] : c_List_Olenlex(X10,X110) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X10)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10))))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X10)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_Nat_Onat),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10))))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBC(tc_List_Olist(X10),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_List_Olist(X10),tc_fun(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X10)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))))),c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10))))),c_List_Olex(X10,X110)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lenlex__conv) ).

fof(fact_foldl__apply,axiom,
    ! [X116,X1,X7,X2,X8,X18,X200,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hAPP(c_Fun_Ocomp(X18,X18,X8,hAPP(X2,X3)),X7) = hAPP(c_Fun_Ocomp(X8,X18,X8,X7),hAPP(X1,X3)) )
     => hAPP(c_List_Ofoldl(X18,X10,hAPP(c_COMBC(X10,X18,X18),X2),hAPP(X7,X116)),X200) = hAPP(X7,hAPP(c_List_Ofoldl(X8,X10,hAPP(c_COMBC(X10,X8,X8),X1),X116),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__apply) ).

fof(fact_INF__INT__eq2,axiom,
    ! [X16,X11,X110,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_fun(X8,tc_fun(X18,tc_HOL_Obool)),X10),hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X8),c_COMBC(X18,tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_prod(X8,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),X8),hAPP(c_COMBB(tc_prod(X8,X18),tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool),X18),c_member(tc_prod(X8,X18)))),c_Product__Type_OPair(X8,X18))))),X110)),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X18)),hAPP(hAPP(c_Product__Type_OPair(X8,X18),X11),X16)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(tc_prod(X8,X18),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__INT__eq2) ).

fof(fact_SUP__UN__eq2,axiom,
    ! [X16,X11,X110,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_fun(X8,tc_fun(X18,tc_HOL_Obool)),X10),hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X8),c_COMBC(X18,tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_prod(X8,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),X8),hAPP(c_COMBB(tc_prod(X8,X18),tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool),X18),c_member(tc_prod(X8,X18)))),c_Product__Type_OPair(X8,X18))))),X110)),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X18)),hAPP(hAPP(c_Product__Type_OPair(X8,X18),X11),X16)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_prod(X8,X18),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__UN__eq2) ).

fof(fact_pred__comp__rel__comp__eq,axiom,
    ! [X16,X11,X116,X110,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X10,X8,X18,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X110),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X8),c_COMBC(X18,tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_prod(X8,X18)),tc_fun(X18,tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool)),X8),hAPP(c_COMBB(tc_prod(X8,X18),tc_fun(tc_fun(tc_prod(X8,X18),tc_HOL_Obool),tc_HOL_Obool),X18),c_member(tc_prod(X8,X18)))),c_Product__Type_OPair(X8,X18)))),X116)),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X18)),hAPP(hAPP(c_Product__Type_OPair(X10,X18),X11),X16)),hAPP(hAPP(c_Relation_Orel__comp(X10,X8,X18),X110),X116))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp__rel__comp__eq) ).

fof(fact_UN__equiv__class__inject,axiom,
    ! [X65,X48,X2,X8,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( c_Equiv__Relations_Ocongruent(X10,tc_fun(X8,tc_HOL_Obool),X110,X2)
       => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X48),X2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X65),X2)
         => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
           => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X65),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
             => ( ! [X3] :
                    ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
                   => ! [X51] :
                        ( hBOOL(hAPP(hAPP(c_member(X10),X51),X12))
                       => ( hAPP(X2,X3) = hAPP(X2,X51)
                         => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X51)),X110)) ) ) )
               => X48 = X65 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__inject) ).

fof(fact_finite__image__set,axiom,
    ! [X2,X8,X42,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X42)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X8),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X8),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,X8),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X10,X8),tc_fun(X10,tc_HOL_Obool)),X8),c_COMBB(X8,tc_HOL_Obool,X10)),c_fequal)),X2)))),X42))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__image__set) ).

fof(fact_setsum__reindex__cong,axiom,
    ! [X7,X1,X15,X12,X2,X8,X10,X18] :
      ( class_Groups_Ocomm__monoid__add(X18)
     => ( c_Fun_Oinj__on(X10,X8,X2,X12)
       => ( X15 = hAPP(c_Set_Oimage(X10,X8,X2),X12)
         => ( ! [X46] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X46),X12))
               => hAPP(X1,X46) = hAPP(X7,hAPP(X2,X46)) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X18),X7),X15) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X18),X1),X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__cong) ).

fof(fact_conversep__converse__eq,axiom,
    ! [X16,X11,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X8,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X110)),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X11),X16)),hAPP(c_Relation_Oconverse(X10,X8),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__converse__eq) ).

fof(fact_strong__setprod__reindex__cong,axiom,
    ! [X7,X1,X15,X12,X2,X8,X10,X18] :
      ( class_Groups_Ocomm__monoid__mult(X18)
     => ( c_Fun_Oinj__on(X10,X8,X2,X12)
       => ( X15 = hAPP(c_Set_Oimage(X10,X8,X2),X12)
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
               => hAPP(X1,X3) = hAPP(hAPP(c_Fun_Ocomp(X8,X18,X10,X7),X2),X3) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X18),X7),X15) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X18),X1),X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strong__setprod__reindex__cong) ).

fof(fact_setsum__ivl__cong,axiom,
    ! [X1,X2,X20,X14,X6,X13,X10,X8] :
      ( ( class_Groups_Ocomm__monoid__add(X8)
        & class_Orderings_Oord(X10) )
     => ( X13 = X6
       => ( X14 = X20
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X3))
               => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X3),X20))
                 => hAPP(X2,X3) = hAPP(X1,X3) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X6),X20)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__ivl__cong) ).

fof(fact_minus__int__def,axiom,
    ! [X19] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19) = 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,X19)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_Nat_Onat),c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)))),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat))))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__int__def) ).

fof(fact_exE__realizer,axiom,
    ! [X18,X2,X41,X148,X10,X8,X42] :
      ( hBOOL(hAPP(hAPP(X42,hAPP(c_Product__Type_Osnd(X8,X10),X148)),hAPP(c_Product__Type_Ofst(X8,X10),X148)))
     => ( ! [X3,X51] :
            ( hBOOL(hAPP(hAPP(X42,X51),X3))
           => hBOOL(hAPP(X41,hAPP(hAPP(X2,X3),X51))) )
       => hBOOL(hAPP(X41,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X10,X18),X2),X148))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__realizer) ).

fof(fact_rp__inv__image__def,axiom,
    ! [X8,X10] : c_FunDef_Orp__inv__image(X10,X8) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X8,X10),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)),tc_fun(tc_fun(X8,X10),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool))))),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X8,X10),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)),tc_fun(tc_fun(X8,X10),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),tc_fun(tc_prod(X10,X10),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X8,X10),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)),tc_fun(tc_fun(X8,X10),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)))),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_COMBS(tc_fun(X8,X10),tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)),tc_fun(tc_fun(X8,X10),tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)))),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),tc_fun(X8,X10)),c_Product__Type_OPair(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(tc_prod(X8,X8),tc_HOL_Obool)))),c_Relation_Oinv__image(X10,X8))))),c_Relation_Oinv__image(X10,X8))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__def) ).

fof(fact_inv__image__def,axiom,
    ! [X2,X110,X10,X8] : hAPP(hAPP(c_Relation_Oinv__image(X8,X10),X110),X2) = hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X8,X8)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X8,X8),tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X8,X8)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X8),tc_fun(X10,tc_prod(X8,X8))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X8,X8)),tc_fun(tc_fun(X10,X8),tc_fun(X10,tc_prod(X8,X8))),X10),c_COMBB(X8,tc_prod(X8,X8),X10)),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_prod(X8,X8)),X10),c_Product__Type_OPair(X8,X8)),X2))),X2)))),X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__def) ).

fof(fact_set__zip,axiom,
    ! [X199,X200,X8,X10] : hAPP(c_List_Oset(tc_prod(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199)) = hAPP(c_Set_OCollect(tc_prod(X10,X8)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X10,X8)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X10,X8),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(X10,X8)),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(X10,X8)),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(X10,X8),tc_fun(tc_Nat_Onat,tc_prod(X10,X8)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X10,X8)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X10,X8)),c_COMBB(tc_prod(X10,X8),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X8,tc_prod(X10,X8)),hAPP(hAPP(c_COMBB(X10,tc_fun(X8,tc_prod(X10,X8)),tc_Nat_Onat),c_Product__Type_OPair(X10,X8)),hAPP(c_List_Onth(X10),X200))),hAPP(c_List_Onth(X8),X199)))))),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(X10)),X200)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip) ).

fof(fact_pred__subset__eq2,axiom,
    ! [X28,X29,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X29)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X28)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X29),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).

fof(fact_Pow__Compl,axiom,
    ! [X12,X10] : hAPP(c_Set_OPow(X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)) = hAPP(c_Set_OCollect(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBS(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X12)),c_Set_OPow(X10))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__Compl) ).

fof(fact_UN__equiv__class__type,axiom,
    ! [X15,X48,X2,X8,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( c_Equiv__Relations_Ocongruent(X10,tc_fun(X8,tc_HOL_Obool),X110,X2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
               => hBOOL(hAPP(hAPP(c_member(tc_fun(X8,tc_HOL_Obool)),hAPP(X2,X3)),X15)) )
           => hBOOL(hAPP(hAPP(c_member(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X48),X2)),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class__type) ).

fof(fact_INF2__I,axiom,
    ! [X18,X8,X6,X14,X15,X12,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => hBOOL(hAPP(hAPP(hAPP(X15,X3),X14),X6)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__I) ).

fof(fact_INF2__iff,axiom,
    ! [X6,X14,X15,X12,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => hBOOL(hAPP(hAPP(hAPP(X15,X3),X14),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__iff) ).

fof(fact_min__max_Osup__Inf1__distrib,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X10),X11))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf1__distrib) ).

fof(fact_min__max_Oinf__Sup1__distrib,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X10),X11))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).

fof(fact_inf__Sup1__distrib,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Odistrib__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)) = c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup1__distrib) ).

fof(fact_sup__Inf1__distrib,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Odistrib__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)) = c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Inf1__distrib) ).

fof(fact_add__Max__commute,axiom,
    ! [X32,X53,X10] :
      ( class_Groups_Olinordered__ab__semigroup__add(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
       => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),c_Big__Operators_Olinorder__class_OMax(X10,X53)) = c_Big__Operators_Olinorder__class_OMax(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X10),X32))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X53))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Max__commute) ).

fof(fact_add__Min__commute,axiom,
    ! [X32,X53,X10] :
      ( class_Groups_Olinordered__ab__semigroup__add(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
       => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X32),c_Big__Operators_Olinorder__class_OMin(X10,X53)) = c_Big__Operators_Olinorder__class_OMin(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X10),X32))))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X53))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min__commute) ).

fof(fact_listrel__iff__zip,axiom,
    ! [X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel(X10,X110)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X3),hAPP(c_List_Oset(tc_prod(X10,X10)),hAPP(hAPP(c_List_Ozip(X10,X10),X200),X199))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X110)),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__iff__zip) ).

fof(fact_DomainP__Domain__eq,axiom,
    ! [X11,X110,X8,X10] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(X10,X8,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X110)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_Relation_ODomain(X10,X8),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).

fof(fact_RangeP__Range__eq,axiom,
    ! [X11,X110,X8,X10] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(X10,X8,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X110)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X8),X11),hAPP(c_Relation_ORange(X10,X8),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).

fof(fact_accp__acc__eq,axiom,
    ! [X11,X110,X10] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X110)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X10),X11),c_Wellfounded_Oacc(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__acc__eq) ).

fof(fact_lazy__sequence__size__code,axiom,
    ! [X232,X116,X10] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X10,X116),X232) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X10,tc_Lazy__Sequence_Olazy__sequence(X10)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X10,tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X10,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat)),X10),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X10),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X10)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat)),X10),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X10),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X116))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X10,X116))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X10),X232)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence__size__code) ).

fof(fact_fold__graph_H_Oequations_I2_J,axiom,
    ! [X62,X57,X56,X63,X64,X8,X10] :
      ( c_Nitpick_Ofold__graph_H(X10,X8,X64,X63,X56,hAPP(hAPP(X64,X57),X62))
    <=> ( ( X56 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
          & hAPP(hAPP(X64,X57),X62) = X63 )
        | ? [X3,X51] :
            ( hAPP(hAPP(X64,X57),X62) = hAPP(hAPP(X64,X3),X51)
            & hBOOL(hAPP(hAPP(c_member(X10),X3),X56))
            & c_Nitpick_Ofold__graph_H(X10,X8,X64,X63,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X56),hAPP(hAPP(c_Set_Oinsert(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X51) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I2_J) ).

fof(fact_SUP2__iff,axiom,
    ! [X6,X14,X15,X12,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
          & hBOOL(hAPP(hAPP(hAPP(X15,X3),X14),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__iff) ).

fof(fact_partition_Osimps_I2_J,axiom,
    ! [X200,X11,X42,X10] : c_List_Opartition(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),tc_fun(tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),tc_List_Olist(X10)),c_COMBS(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_List_Olist(X10),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),tc_List_Olist(X10)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_List_Olist(X10)),hAPP(c_If(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(X42,X11)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_List_Olist(X10)),c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(c_List_Olist_OCons(X10),X11))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),tc_fun(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)))),tc_List_Olist(X10)),c_COMBB(tc_List_Olist(X10),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_List_Olist(X10))),c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)))),hAPP(c_List_Olist_OCons(X10),X11)))),c_List_Opartition(X10,X42,X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I2_J) ).

fof(fact_lexn_Osimps_I2_J,axiom,
    ! [X30,X110,X10] : hAPP(c_List_Olexn(X10,X110),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X10,tc_List_Olist(X10)),tc_prod(X10,tc_List_Olist(X10))),tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),c_Product__Type_Omap__pair(tc_prod(X10,tc_List_Olist(X10)),tc_List_Olist(X10),tc_prod(X10,tc_List_Olist(X10)),tc_List_Olist(X10),hAPP(c_Product__Type_Oprod_Oprod__case(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)))),c_Wellfounded_Olex__prod(X10,tc_List_Olist(X10),X110,hAPP(c_List_Olexn(X10,X110),X30)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),tc_List_Olist(X10)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),hAPP(c_Nat_OSuc,X30))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),hAPP(c_Nat_OSuc,X30)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn_Osimps_I2_J) ).

fof(fact_set__sublist,axiom,
    ! [X161,X200,X10] : hAPP(c_List_Oset(X10),c_List_Osublist(X10,X200,X161)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X10,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)),X10),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)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_Nat_Onat,X10),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X10),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X10),X200))))),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(X10)),X200)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X161))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sublist) ).

fof(fact_setsum__multicount__gen,axiom,
    ! [X32,X29,X154,X8,X116,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X116))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X154))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X8),X3),X154))
             => hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X116))),hAPP(hAPP(c_COMBC(X10,X8,tc_HOL_Obool),X29),X3)))) = hAPP(X32,X3) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_Nat_Onat,X10),c_Finite__Set_Ocard(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),c_Set_OCollect(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fconj),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X154)))),X29)))),X116) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,tc_Nat_Onat),X32),X154) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__multicount__gen) ).

fof(fact_set__conv__nth,axiom,
    ! [X200,X10] : hAPP(c_List_Oset(X10),X200) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X10,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)),X10),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)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_Nat_Onat,X10),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X10),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X10),X200))))),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(X10)),X200))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__conv__nth) ).

fof(fact_Sigma__def,axiom,
    ! [X15,X12,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X10),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool))),X15)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool))),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool))),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X8),c_Set_Oinsert(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__def) ).

fof(fact_setsum__multicount,axiom,
    ! [X32,X29,X160,X8,X28,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X160))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X8),X3),X160))
             => hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X28))),hAPP(hAPP(c_COMBC(X10,X8,tc_HOL_Obool),X29),X3)))) = X32 )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_Nat_Onat,X10),c_Finite__Set_Ocard(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),c_Set_OCollect(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fconj),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X160)))),X29)))),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),hAPP(c_Finite__Set_Ocard(X8),X160)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__multicount) ).

fof(fact_setsum__setsum__restrict,axiom,
    ! [X29,X2,X160,X8,X28,X10,X18] :
      ( class_Groups_Ocomm__monoid__add(X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X160))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X18),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),X18),hAPP(hAPP(c_COMBB(tc_fun(X8,X18),tc_fun(tc_fun(X8,tc_HOL_Obool),X18),X10),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X18)),X2)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),c_Set_OCollect(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fconj),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X160)))),X29)))),X28) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X18),hAPP(hAPP(c_COMBS(X8,tc_fun(X10,tc_HOL_Obool),X18),hAPP(hAPP(c_COMBB(tc_fun(X10,X18),tc_fun(tc_fun(X10,tc_HOL_Obool),X18),X8),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X18)),hAPP(c_COMBC(X10,X8,X18),X2))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),c_Set_OCollect(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X28)))),hAPP(c_COMBC(X10,X8,tc_HOL_Obool),X29))))),X160) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__setsum__restrict) ).

fof(fact_anamorph_Osimps,axiom,
    ! [X11,X2,X10,X8,X32] :
      ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X8,X10,X2),X32),X11) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),X8),c_List_Olist_ONil(X10)),X11) )
      & ( X32 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X8,X10,X2),X32),X11) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X10),X8),tc_prod(X10,X8),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),X8),c_List_Olist_ONil(X10)),X11),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_prod(tc_List_Olist(X10),X8)),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_prod(tc_List_Olist(X10),X8)),tc_fun(X8,tc_prod(tc_List_Olist(X10),X8))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X10),X8),tc_prod(tc_List_Olist(X10),X8)),tc_fun(tc_fun(X8,tc_prod(tc_List_Olist(X10),X8)),tc_fun(X8,tc_prod(tc_List_Olist(X10),X8))),X10),c_COMBB(tc_prod(tc_List_Olist(X10),X8),tc_prod(tc_List_Olist(X10),X8),X8)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_fun(X8,tc_prod(tc_List_Olist(X10),X8))),tc_fun(tc_prod(tc_List_Olist(X10),X8),tc_prod(tc_List_Olist(X10),X8)),X10),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X10),X8,tc_prod(tc_List_Olist(X10),X8))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_fun(X8,tc_prod(tc_List_Olist(X10),X8))),X10),hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(X8,tc_prod(tc_List_Olist(X10),X8)),tc_List_Olist(X10)),c_Product__Type_OPair(tc_List_Olist(X10),X8))),c_List_Olist_OCons(X10))))),hAPP(c_Lazy__Sequence_Oanamorph(X8,X10,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X2,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_anamorph_Osimps) ).

fof(fact_sequence__trans,axiom,
    ! [X32,X61,X110,X2,X10] :
      ( ! [X91] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X2,hAPP(c_Nat_OSuc,X91))),hAPP(X2,X91))),c_Transitive__Closure_Ortrancl(X10,X110)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),X32))),hAPP(X2,X61))),c_Transitive__Closure_Ortrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sequence__trans) ).

fof(fact_fun__lub__def,axiom,
    ! [X11,X12,X260,X18,X10,X8] : c_Partial__Function_Ofun__lub(X8,X10,X18,X260,X12,X11) = hAPP(X260,hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X18,X8),tc_HOL_Obool),tc_HOL_Obool,X8),c_HOL_OEx(tc_fun(X18,X8))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X18,X8),tc_HOL_Obool),tc_fun(tc_fun(X18,X8),tc_HOL_Obool),X8),hAPP(c_COMBS(tc_fun(X18,X8),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X18,X8)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X18,X8),tc_fun(tc_fun(X18,X8),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X18,X8))),X12)))),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_fun(X18,X8),X8),tc_fun(tc_fun(X18,X8),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X18,X8),X8),tc_fun(tc_fun(X18,X8),tc_HOL_Obool)),X8),c_COMBB(X8,tc_HOL_Obool,tc_fun(X18,X8))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X18,X8),X18,X8),c_COMBI(tc_fun(X18,X8))),X11)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__lub__def) ).

fof(fact_Sup__apply,axiom,
    ! [X11,X12,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,X10),X12),X11) = c_Complete__Lattice_OSup__class_OSup(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_fun(X8,X10))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_HOL_Obool),X10),hAPP(c_COMBS(tc_fun(X8,X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X8,X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X8,X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X8,X10))),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_fun(X8,X10),X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X8,X10),X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,tc_fun(X8,X10))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X8,X10),X8,X10),c_COMBI(tc_fun(X8,X10))),X11)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__apply) ).

fof(fact_Sup__fun__def,axiom,
    ! [X11,X12,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,X10),X12),X11) = c_Complete__Lattice_OSup__class_OSup(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_fun(X8,X10))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_HOL_Obool),X10),hAPP(c_COMBS(tc_fun(X8,X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X8,X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X8,X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X8,X10))),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_fun(X8,X10),X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X8,X10),X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,tc_fun(X8,X10))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X8,X10),X8,X10),c_COMBI(tc_fun(X8,X10))),X11)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fun__def) ).

fof(fact_Inf__apply,axiom,
    ! [X11,X12,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X8,X10),X12),X11) = c_Complete__Lattice_OInf__class_OInf(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_fun(X8,X10))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_HOL_Obool),X10),hAPP(c_COMBS(tc_fun(X8,X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X8,X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X8,X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X8,X10))),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_fun(X8,X10),X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X8,X10),X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,tc_fun(X8,X10))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X8,X10),X8,X10),c_COMBI(tc_fun(X8,X10))),X11)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__apply) ).

fof(fact_Inf__fun__def,axiom,
    ! [X11,X12,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X8,X10),X12),X11) = c_Complete__Lattice_OInf__class_OInf(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_fun(X8,X10))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_fun(tc_fun(X8,X10),tc_HOL_Obool),X10),hAPP(c_COMBS(tc_fun(X8,X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X8,X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X8,X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X8,X10))),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_fun(X8,X10),X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X8,X10),X10),tc_fun(tc_fun(X8,X10),tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,tc_fun(X8,X10))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X8,X10),X8,X10),c_COMBI(tc_fun(X8,X10))),X11)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fun__def) ).

fof(fact_congruent2I_H,axiom,
    ! [X18,X2,X164,X8,X166,X10] :
      ( ! [X272,X273] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X272),X273)),X166))
         => ! [X274,X275] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X274),X275)),X164))
             => hAPP(hAPP(X2,X272),X274) = hAPP(hAPP(X2,X273),X275) ) )
     => c_Equiv__Relations_Ocongruent2(X10,X8,X18,X166,X164,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2I_H) ).

fof(fact_divmod__int__rel__def,axiom,
    ! [X14,X13] : c_Divides_Odivmod__int__rel(X13,X14) = 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,X13))),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),X14)))))),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)),X14))),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)),X14))))),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)),X14)))),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),X14))),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,
    ! [X15,X1,X18,X12,X2,X8,X10] :
      ( class_Rings_Osemiring__0(X10)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18,X10),X1),X15)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X18,X10),tc_fun(tc_fun(X18,tc_HOL_Obool),X10),X8),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18,X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,X10),tc_fun(X18,X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,X10),tc_fun(tc_fun(X18,X10),tc_fun(X18,X10)),X8),c_COMBB(X10,X10,X18)),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Groups_Otimes__class_Otimes(X10)),X2))),X1))),X15)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__product) ).

fof(fact_fold__image__Sigma,axiom,
    ! [X1,X15,X8,X12,X10,X18] :
      ( class_Groups_Ocomm__monoid__mult(X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X15,X3))) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X18,X10,c_Groups_Otimes__class_Otimes(X18)),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),X18),hAPP(hAPP(c_COMBC(X10,X18,tc_fun(tc_fun(X8,tc_HOL_Obool),X18)),hAPP(hAPP(c_COMBB(tc_fun(X8,X18),tc_fun(X18,tc_fun(tc_fun(X8,tc_HOL_Obool),X18)),X10),c_Finite__Set_Ofold__image(X18,X8,c_Groups_Otimes__class_Otimes(X18))),X1)),c_Groups_Oone__class_Oone(X18))),X15)),c_Groups_Oone__class_Oone(X18)),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X18,tc_prod(X10,X8),c_Groups_Otimes__class_Otimes(X18)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),X1)),c_Groups_Oone__class_Oone(X18)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Sigma) ).

fof(fact_finite__lists__length__le,axiom,
    ! [X30,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),c_List_Oset(X10))),X12))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X30))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lists__length__le) ).

fof(fact_finite__lists__length__eq,axiom,
    ! [X30,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),c_List_Oset(X10))),X12))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X30))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lists__length__eq) ).

fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
    ! [X15,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X8),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),X15)))
               => hAPP(X1,X3) = X19 )
           => hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(X2,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter__neutral) ).

fof(fact_nat__def,axiom,
    ! [X19] : hAPP(c_Int_Onat,X19) = 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,X19)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool))),tc_Nat_Onat),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_Set_Oinsert(tc_Nat_Onat))),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__def) ).

fof(fact_folding__image_Ocong,axiom,
    ! [X7,X1,X12,X9,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image(X10,X8,X2,X19,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
             => hAPP(X1,X3) = hAPP(X7,X3) )
         => hAPP(hAPP(X9,X1),X12) = hAPP(hAPP(X9,X7),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Ocong) ).

fof(fact_nat__intermed__int__val,axiom,
    ! [X32,X2,X30,X31] :
      ( ! [X91] :
          ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X91))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),X30)) )
         => 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),X91),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X91)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X2,X31)),X32))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),hAPP(X2,X30)))
           => ? [X91] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X91))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X91),X30))
                & hAPP(X2,X91) = X32 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__intermed__int__val) ).

fof(fact_finite__Collect__bex,axiom,
    ! [X41,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X8),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),X41)))))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBC(X8,X10,tc_HOL_Obool),X41),X3)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__bex) ).

fof(fact_INT__anti__mono,axiom,
    ! [X1,X2,X8,X12,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(X2,X3)),hAPP(X1,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__anti__mono) ).

fof(fact_Sigma__mono,axiom,
    ! [X21,X15,X8,X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X17))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(X15,X3)),hAPP(X21,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X17),X21))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__mono) ).

fof(fact_mem__splitI2,axiom,
    ! [X6,X19,X18,X8,X10,X148] :
      ( ! [X46,X81] :
          ( X148 = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81)
         => hBOOL(hAPP(hAPP(c_member(X18),X19),hAPP(hAPP(X6,X46),X81))) )
     => hBOOL(hAPP(hAPP(c_member(X18),X19),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_fun(X18,tc_HOL_Obool)),X6),X148))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI2) ).

fof(fact_converse__def,axiom,
    ! [X110,X10,X8] : hAPP(c_Relation_Oconverse(X8,X10),X110) = hAPP(c_Set_OCollect(tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X8,X10)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X8,X10),tc_fun(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X8,X10)))),hAPP(c_COMBC(X8,X10,tc_prod(X8,X10)),c_Product__Type_OPair(X8,X10))))),X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__def) ).

fof(fact_fold__image__UN__disjoint,axiom,
    ! [X1,X12,X8,X161,X10,X18] :
      ( class_Groups_Ocomm__monoid__mult(X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X161))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X161))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X12,X3))) )
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X161))
               => ! [X66] :
                    ( hBOOL(hAPP(hAPP(c_member(X10),X66),X161))
                   => ( X3 != X66
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(X12,X3)),hAPP(X12,X66)) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X18,X8,c_Groups_Otimes__class_Otimes(X18)),X1),c_Groups_Oone__class_Oone(X18)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X161),X12)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X18,X10,c_Groups_Otimes__class_Otimes(X18)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),X18,X10),hAPP(hAPP(c_Finite__Set_Ofold__image(X18,X8,c_Groups_Otimes__class_Otimes(X18)),X1),c_Groups_Oone__class_Oone(X18))),X12)),c_Groups_Oone__class_Oone(X18)),X161) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__UN__disjoint) ).

fof(fact_INT__eq,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),c_HOL_OEx(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fconj),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X12)))),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X8,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X8)),c_fequal)),X15))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__eq) ).

fof(fact_UN__eq,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),c_HOL_OEx(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fconj),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X12)))),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X8,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X8)),c_fequal)),X15))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__eq) ).

fof(fact_part__equivp__typedef,axiom,
    ! [X29,X10] :
      ( c_Equiv__Relations_Opart__equivp(X10,X29)
     => ? [X75] : hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X75),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBS(X10,X10,tc_HOL_Obool),X29),c_COMBI(X10))))),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10)),c_fequal)),X29))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__typedef) ).

fof(fact_card__less__Suc,axiom,
    ! [X61,X143] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X143))
     => 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)),X143))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X61))))) = 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)),X143))),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,X61))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less__Suc) ).

fof(fact_setsum__image__gen,axiom,
    ! [X2,X18,X1,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X28) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18,X8),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),X8,X18),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18),c_Set_OCollect(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X28)))),hAPP(c_COMBC(X10,X18,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X18,tc_fun(X18,tc_HOL_Obool),X10),c_fequal),X2)))))),hAPP(c_Set_Oimage(X10,X18,X2),X28)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__image__gen) ).

fof(fact_refl__on__def_H,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
    <=> ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X3),X110))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__def_H) ).

fof(fact_zip__Cons,axiom,
    ! [X199,X16,X200,X8,X10] : hAPP(hAPP(c_List_Ozip(X10,X8),X200),hAPP(hAPP(c_List_Olist_OCons(X8),X16),X199)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X10,X8)),X10,c_List_Olist_ONil(tc_prod(X10,X8)),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_prod(X10,X8))),tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_prod(X10,X8)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X10,X8)),tc_List_Olist(tc_prod(X10,X8))),tc_fun(tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_prod(X10,X8))),tc_fun(tc_List_Olist(X10),tc_List_Olist(tc_prod(X10,X8)))),X10),c_COMBB(tc_List_Olist(tc_prod(X10,X8)),tc_List_Olist(tc_prod(X10,X8)),tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_List_Olist(tc_prod(X10,X8)),tc_List_Olist(tc_prod(X10,X8))),X10),c_List_Olist_OCons(tc_prod(X10,X8))),hAPP(hAPP(c_COMBC(X10,X8,tc_prod(X10,X8)),c_Product__Type_OPair(X10,X8)),X16)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X8),tc_List_Olist(tc_prod(X10,X8))),c_List_Ozip(X10,X8)),X199))),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons) ).

fof(fact_max__extp__max__ext__eq,axiom,
    ! [X159,X11,X29,X10] :
      ( c_Wellfounded_Omax__extp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X29),X11,X159)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X11),X159)),c_Wellfounded_Omax__ext(X10,X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp__max__ext__eq) ).

fof(fact_listrelp__listrel__eq,axiom,
    ! [X159,X11,X110,X10] :
      ( c_List_Olistrelp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X110),X11,X159)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X159)),c_List_Olistrel(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp__listrel__eq) ).

fof(fact_UN__Times__distrib,axiom,
    ! [X9,X185,X15,X12,X8,X10,X102,X18] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X18,X102),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X18,X102),X12),hAPP(c_COMBK(tc_fun(X102,tc_HOL_Obool),X18),X15))),hAPP(c_Product__Type_Oprod_Oprod__case(X18,X102,tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X18,tc_fun(X102,tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),tc_fun(X102,tc_fun(tc_prod(X10,X8),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),tc_fun(tc_fun(X102,tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),tc_fun(X102,tc_fun(tc_prod(X10,X8),tc_HOL_Obool))),X18),c_COMBB(tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(tc_prod(X10,X8),tc_HOL_Obool),X102)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X18),c_Product__Type_OSigma(X10,X8)),X185))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),X102),c_COMBK(tc_fun(X8,tc_HOL_Obool),X10)),X9)))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X12),X185)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X102,tc_fun(X8,tc_HOL_Obool)),X15),X9))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Times__distrib) ).

fof(fact_equivp__equiv,axiom,
    ! [X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X12)
    <=> c_Equiv__Relations_Oequivp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__equiv) ).

fof(fact_wfP__wf__eq,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_OwfP(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_prod(X10,X10)),tc_fun(X10,tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X10,X10)))),c_Product__Type_OPair(X10,X10)))),X110))
    <=> c_Wellfounded_Owf(X10,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__wf__eq) ).

fof(fact_pred__equals__eq2,axiom,
    ! [X28,X29,X8,X10] :
      ( hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X29) = hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBC(X8,tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_HOL_Obool),X8),c_member(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),X28)
    <=> X29 = X28 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq2) ).

fof(fact_map__zip__map2,axiom,
    ! [X199,X1,X102,X200,X2,X10,X18,X8] : hAPP(hAPP(c_List_Omap(tc_prod(X8,X18),X10),X2),hAPP(hAPP(c_List_Ozip(X8,X18),X200),hAPP(hAPP(c_List_Omap(X102,X18),X1),X199))) = hAPP(hAPP(c_List_Omap(tc_prod(X8,X102),X10),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X102,X10),hAPP(hAPP(c_COMBB(tc_fun(X102,tc_prod(X8,X18)),tc_fun(X102,X10),X8),hAPP(c_COMBB(tc_prod(X8,X18),X10,X102),X2)),hAPP(hAPP(c_COMBC(X8,tc_fun(X102,X18),tc_fun(X102,tc_prod(X8,X18))),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_prod(X8,X18)),tc_fun(tc_fun(X102,X18),tc_fun(X102,tc_prod(X8,X18))),X8),c_COMBB(X18,tc_prod(X8,X18),X102)),c_Product__Type_OPair(X8,X18))),X1)))),hAPP(hAPP(c_List_Ozip(X8,X102),X200),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__zip__map2) ).

fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
    ! [X13,X16,X12,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X16))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => ? [X117] :
              ( X16 = hAPP(hAPP(X2,X13),X117)
              & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X117)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).

fof(fact_zip__Cons1,axiom,
    ! [X199,X200,X11,X8,X10] : hAPP(hAPP(c_List_Ozip(X10,X8),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),X199) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X10,X8)),X8,c_List_Olist_ONil(tc_prod(X10,X8)),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_List_Olist(X8),tc_List_Olist(tc_prod(X10,X8))),tc_fun(tc_List_Olist(X8),tc_List_Olist(tc_prod(X10,X8)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X10,X8)),tc_List_Olist(tc_prod(X10,X8))),tc_fun(tc_fun(tc_List_Olist(X8),tc_List_Olist(tc_prod(X10,X8))),tc_fun(tc_List_Olist(X8),tc_List_Olist(tc_prod(X10,X8)))),X8),c_COMBB(tc_List_Olist(tc_prod(X10,X8)),tc_List_Olist(tc_prod(X10,X8)),tc_List_Olist(X8))),hAPP(hAPP(c_COMBB(tc_prod(X10,X8),tc_fun(tc_List_Olist(tc_prod(X10,X8)),tc_List_Olist(tc_prod(X10,X8))),X8),c_List_Olist_OCons(tc_prod(X10,X8))),hAPP(c_Product__Type_OPair(X10,X8),X11)))),hAPP(c_List_Ozip(X10,X8),X200))),X199),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons1) ).

fof(fact_wf__if__measure,axiom,
    ! [X10,X1,X2,X42] :
      ( ! [X3] :
          ( hBOOL(hAPP(X42,X3))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,hAPP(X1,X3))),hAPP(X2,X3))) )
     => c_Wellfounded_Owf(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X42))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X10,tc_HOL_Obool,X10)),c_fequal)),X1))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__if__measure) ).

fof(fact_max__ext__compat,axiom,
    ! [X28,X29,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X29),X28)),X29))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X10,X29)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X10,X28)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X10,X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__compat) ).

fof(fact_min__ext__compat,axiom,
    ! [X28,X29,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X29),X28)),X29))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X10,X29)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X10,X28)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X10,X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__compat) ).

fof(fact_setsum__restrict__set_H,axiom,
    ! [X15,X2,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))),X2)),c_Groups_Ozero__class_Ozero(X8))),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__restrict__set_H) ).

fof(fact_zip__map__map,axiom,
    ! [X199,X1,X102,X200,X2,X18,X8,X10] : hAPP(hAPP(c_List_Ozip(X10,X8),hAPP(hAPP(c_List_Omap(X18,X10),X2),X200)),hAPP(hAPP(c_List_Omap(X102,X8),X1),X199)) = hAPP(hAPP(c_List_Omap(tc_prod(X18,X102),tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X18,X102,tc_prod(X10,X8)),hAPP(hAPP(c_COMBC(X18,tc_fun(X102,X8),tc_fun(X102,tc_prod(X10,X8))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(tc_fun(X102,X8),tc_fun(X102,tc_prod(X10,X8))),X18),c_COMBB(X8,tc_prod(X10,X8),X102)),hAPP(hAPP(c_COMBB(X10,tc_fun(X8,tc_prod(X10,X8)),X18),c_Product__Type_OPair(X10,X8)),X2))),X1))),hAPP(hAPP(c_List_Ozip(X18,X102),X200),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map__map) ).

fof(fact_finite__psubset__def,axiom,
    ! [X10] : c_Wellfounded_Ofinite__psubset(X10) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_COMBS(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X10)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__psubset__def) ).

fof(fact_map__pair__imageI,axiom,
    ! [X1,X2,X102,X18,X29,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X29))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X102)),hAPP(hAPP(c_Product__Type_OPair(X18,X102),hAPP(X2,X13)),hAPP(X1,X14))),hAPP(c_Set_Oimage(tc_prod(X10,X8),tc_prod(X18,X102),c_Product__Type_Omap__pair(X10,X18,X8,X102,X2,X1)),X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__imageI) ).

fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
    ! [X242,X243,X244,X2,X29,X10,X8] : c_New__Random__Sequence_Oneg__decr__bind(X8,X10,X29,X2,X244,X243,X242) = c_New__DSequence_Oneg__decr__bind(X8,X10,hAPP(hAPP(hAPP(X29,X244),X243),X242),hAPP(hAPP(c_COMBC(X8,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(X10)))),hAPP(hAPP(c_COMBC(X8,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(X10))))),hAPP(hAPP(c_COMBC(X8,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(X10)))))),X2),X244)),X243)),X242)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).

fof(fact_INTER__def,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fimplies),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X12)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X8)),c_member(X10))),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__def) ).

fof(fact_congruent__def,axiom,
    ! [X2,X110,X8,X10] :
      ( c_Equiv__Relations_Ocongruent(X10,X8,X110,X2)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X3),X110))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,X8),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X10,X8),tc_fun(X10,tc_HOL_Obool)),X10),c_COMBB(X8,tc_HOL_Obool,X10)),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_fequal),X2))),X2)),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent__def) ).

fof(fact_finite__Collect__bounded__ex,axiom,
    ! [X41,X8,X42,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X42)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X8),c_HOL_OEx(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X42))),X41)))))
      <=> ! [X51] :
            ( hBOOL(hAPP(X42,X51))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBC(X8,X10,tc_HOL_Obool),X41),X51)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_setsum__Sigma,axiom,
    ! [X2,X15,X8,X12,X10,X18] :
      ( class_Groups_Ocomm__monoid__add(X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X15,X3))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X18),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),X18),hAPP(hAPP(c_COMBB(tc_fun(X8,X18),tc_fun(tc_fun(X8,tc_HOL_Obool),X18),X10),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X18)),X2)),X15)),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X10,X8),X18),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),X2)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Sigma) ).

fof(fact_setprod__Sigma,axiom,
    ! [X2,X15,X8,X12,X10,X18] :
      ( class_Groups_Ocomm__monoid__mult(X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X15,X3))) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X18),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),X18),hAPP(hAPP(c_COMBB(tc_fun(X8,X18),tc_fun(tc_fun(X8,tc_HOL_Obool),X18),X10),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X18)),X2)),X15)),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X10,X8),X18),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),X2)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Sigma) ).

fof(fact_setsum__restrict__set,axiom,
    ! [X15,X2,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))),X2)),c_Groups_Ozero__class_Ozero(X8))),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__restrict__set) ).

fof(fact_UN__finite2__subset,axiom,
    ! [X15,X32,X12,X10] :
      ( ! [X123] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X123)),X12)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,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),X123),X32))),X15)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X12)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite2__subset) ).

fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
    ! [X242,X243,X244,X2,X29,X10,X8] : c_New__Random__Sequence_Opos__decr__bind(X8,X10,X29,X2,X244,X243,X242) = c_New__DSequence_Opos__decr__bind(X8,X10,hAPP(hAPP(hAPP(X29,X244),X243),X242),hAPP(hAPP(c_COMBC(X8,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X10))),hAPP(hAPP(c_COMBC(X8,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(X10)))),hAPP(hAPP(c_COMBC(X8,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(X10))))),X2),X244)),X243)),X242)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).

fof(fact_image__split__eq__Sigma,axiom,
    ! [X12,X1,X2,X8,X10,X18] : hAPP(c_Set_Oimage(X18,tc_prod(X10,X8),hAPP(hAPP(c_COMBS(X18,X8,tc_prod(X10,X8)),hAPP(hAPP(c_COMBB(X10,tc_fun(X8,tc_prod(X10,X8)),X18),c_Product__Type_OPair(X10,X8)),X2)),X1)),X12) = hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(c_Set_Oimage(X18,X10,X2),X12)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),c_Set_Oimage(X18,X8,X1)),hAPP(hAPP(c_COMBC(X10,tc_fun(X18,tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_HOL_Obool),tc_fun(tc_fun(X18,tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X18,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X18,tc_HOL_Obool),X10),c_Set_Ovimage(X18,X10,X2)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__split__eq__Sigma) ).

fof(fact_small__lazy__list_Osimps,axiom,
    ! [X20,X10] :
      ( class_Lazy__Sequence_Osmall__lazy(X10)
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X10),X20) = c_Lazy__Sequence_Oappend(tc_List_Olist(X10),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X10))),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(X10,tc_List_Olist(X10)),tc_List_Olist(X10),c_Lazy__Sequence_Oproduct(X10,tc_List_Olist(X10),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X10,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(X10),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(X10,tc_List_Olist(X10),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),tc_fun(tc_List_Olist(X10),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X10))),X10),hAPP(c_COMBB(tc_List_Olist(X10),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X10)),tc_List_Olist(X10)),c_Lazy__Sequence_Osingle(tc_List_Olist(X10)))),c_List_Olist_OCons(X10))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X10)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__list_Osimps) ).

fof(fact_Sup__Inf,axiom,
    ! [X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OSup__class_OSup(X10,X12) = c_Complete__Lattice_OInf__class_OInf(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fimplies),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X10)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__Inf) ).

fof(fact_setsum__nonneg__leq__bound,axiom,
    ! [X61,X15,X2,X116,X10,X8] :
      ( class_Groups_Oordered__ab__group__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X116))
       => ( ! [X91] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X91),X116))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(X2,X91))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X116) = X15
           => ( hBOOL(hAPP(hAPP(c_member(X10),X61),X116))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(X2,X61)),X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__nonneg__leq__bound) ).

fof(fact_Inf__Sup,axiom,
    ! [X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OInf__class_OInf(X10,X12) = c_Complete__Lattice_OSup__class_OSup(X10,hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fimplies),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),c_Orderings_Oord__class_Oless__eq(X10))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__Sup) ).

fof(fact_Int__UN__distrib2,axiom,
    ! [X15,X176,X18,X12,X161,X8,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X176),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X176)),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X18,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X18,tc_fun(X10,tc_HOL_Obool))),X8),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X12))),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UN__distrib2) ).

fof(fact_Un__INT__distrib2,axiom,
    ! [X15,X176,X18,X12,X161,X8,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X176),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X161),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X176)),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X18,tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),tc_fun(tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X18,tc_fun(X10,tc_HOL_Obool))),X8),c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X12))),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__INT__distrib2) ).

fof(fact_neg__bind__def,axiom,
    ! [X242,X243,X244,X2,X29,X10,X8] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X8,X10,X29,X2),X244),X243),X242) = c_New__DSequence_Oneg__bind(X8,X10,hAPP(hAPP(hAPP(X29,X244),X243),X242),hAPP(hAPP(c_COMBC(X8,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(X10)))),hAPP(hAPP(c_COMBC(X8,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(X10))))),hAPP(hAPP(c_COMBC(X8,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(X10)))))),X2),X244)),X243)),X242)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__bind__def) ).

fof(fact_Union__eq,axiom,
    ! [X12,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X12) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),X10),hAPP(c_COMBS(tc_fun(X10,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(X10,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X10,tc_HOL_Obool))),X12)))),c_member(X10)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__eq) ).

fof(fact_Inter__eq,axiom,
    ! [X12,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X12) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),X10),hAPP(c_COMBS(tc_fun(X10,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(X10,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X10,tc_HOL_Obool))),X12)))),c_member(X10)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__eq) ).

fof(fact_rtrancl__Un__separatorE,axiom,
    ! [X41,X42,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X42),X41))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X3)),c_Transitive__Closure_Ortrancl(X10,X42)))
           => ! [X51] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X51)),X41))
               => X3 = X51 ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,X42))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).

fof(fact_rtrancl__Un__separator__converseE,axiom,
    ! [X41,X42,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X42),X41))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X14)),c_Transitive__Closure_Ortrancl(X10,X42)))
           => ! [X51] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X3)),X41))
               => X51 = X3 ) )
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,X42))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_zip__map2,axiom,
    ! [X199,X2,X18,X200,X8,X10] : hAPP(hAPP(c_List_Ozip(X10,X8),X200),hAPP(hAPP(c_List_Omap(X18,X8),X2),X199)) = hAPP(hAPP(c_List_Omap(tc_prod(X10,X18),tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X18,tc_prod(X10,X8)),hAPP(hAPP(c_COMBC(X10,tc_fun(X18,X8),tc_fun(X18,tc_prod(X10,X8))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(tc_fun(X18,X8),tc_fun(X18,tc_prod(X10,X8))),X10),c_COMBB(X8,tc_prod(X10,X8),X18)),c_Product__Type_OPair(X10,X8))),X2))),hAPP(hAPP(c_List_Ozip(X10,X18),X200),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map2) ).

fof(fact_int__val__lemma,axiom,
    ! [X32,X2,X30] :
      ( ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),X30))
         => 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),X91),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X91)))),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))),X32))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),hAPP(X2,X30)))
         => ? [X91] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X91),X30))
              & hAPP(X2,X91) = X32 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__val__lemma) ).

fof(fact_nat0__intermed__int__val,axiom,
    ! [X32,X2,X30] :
      ( ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),X30))
         => 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),X91),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,X91)))),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))),X32))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),hAPP(X2,X30)))
         => ? [X91] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X91),X30))
              & hAPP(X2,X91) = X32 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat0__intermed__int__val) ).

fof(fact_inj__vimage__singleton,axiom,
    ! [X13,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Set_Oinsert(X8),X13),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X10),c_HOL_OThe(X10,hAPP(hAPP(c_COMBC(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_fequal),X2)),X13))),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__vimage__singleton) ).

fof(fact_pos__bind__def,axiom,
    ! [X242,X243,X244,X2,X29,X10,X8] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X8,X10,X29,X2),X244),X243),X242) = c_New__DSequence_Opos__bind(X8,X10,hAPP(hAPP(hAPP(X29,X244),X243),X242),hAPP(hAPP(c_COMBC(X8,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X10))),hAPP(hAPP(c_COMBC(X8,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(X10)))),hAPP(hAPP(c_COMBC(X8,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(X10))))),X2),X244)),X243)),X242)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__bind__def) ).

fof(fact_Nitpick_Oprod__def,axiom,
    ! [X15,X12,X8,X10] : c_Nitpick_Oprod(X10,X8,X12,X15) = hAPP(c_Set_OCollect(tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)))),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oprod__def) ).

fof(fact_map__pair_Ocompositionality,axiom,
    ! [X188,X61,X7,X115,X104,X1,X2,X8,X102,X10,X18] : hAPP(c_Product__Type_Omap__pair(X18,X10,X102,X8,X2,X1),hAPP(c_Product__Type_Omap__pair(X104,X18,X115,X102,X7,X61),X188)) = hAPP(c_Product__Type_Omap__pair(X104,X10,X115,X8,hAPP(c_Fun_Ocomp(X18,X10,X104,X2),X7),hAPP(c_Fun_Ocomp(X102,X8,X115,X1),X61)),X188),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Ocompositionality) ).

fof(fact_less,axiom,
    ! [X93,X77,X16,X11] :
      ( 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),X11),X16)),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),X77),X93)),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),X11),X93)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X16))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less) ).

fof(fact_le,axiom,
    ! [X93,X77,X16,X11] :
      ( 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),X11),X16)),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),X77),X93)),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),X11),X93)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X16))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le) ).

fof(fact_setsum__reindex__nonzero,axiom,
    ! [X8,X7,X2,X28,X10,X18] :
      ( class_Groups_Ocomm__monoid__add(X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X28))
             => ! [X51] :
                  ( hBOOL(hAPP(hAPP(c_member(X10),X51),X28))
                 => ( X3 != X51
                   => ( hAPP(X2,X3) = hAPP(X2,X51)
                     => hAPP(X7,hAPP(X2,X3)) = c_Groups_Ozero__class_Ozero(X18) ) ) ) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X18),X7),hAPP(c_Set_Oimage(X10,X8,X2),X28)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X18),hAPP(c_Fun_Ocomp(X8,X18,X10,X7),X2)),X28) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__nonzero) ).

fof(fact_if__image__distrib,axiom,
    ! [X28,X1,X2,X42,X10,X8] : hAPP(c_Set_Oimage(X8,X10,hAPP(hAPP(c_COMBS(X8,X10,X10),hAPP(hAPP(c_COMBS(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),X42)),X2)),X1)),X28) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X28),hAPP(c_Set_OCollect(X8),X42)))),hAPP(c_Set_Oimage(X8,X10,X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X28),hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8),c_fNot),X42))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_if__image__distrib) ).

fof(fact_mult,axiom,
    ! [X93,X77,X16,X11] : 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),X11),X16)),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),X77),X93)),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),X11),X77)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X93))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X11),X93)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X16),X77)))),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,
    ! [X19,X7,X1,X12,X10,X8] :
      ( class_Groups_Oab__semigroup__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
             => hAPP(X1,X3) = hAPP(X7,X3) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),X19),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X7),X19),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__cong) ).

fof(fact_wf__map__pair__image,axiom,
    ! [X2,X8,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
       => c_Wellfounded_Owf(X8,hAPP(c_Set_Oimage(tc_prod(X10,X10),tc_prod(X8,X8),c_Product__Type_Omap__pair(X10,X8,X10,X8,X2,X2)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__map__pair__image) ).

fof(fact_inj__on__INTER,axiom,
    ! [X12,X2,X18,X8,X10,X161] :
      ( X161 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
     => ( ! [X91] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X91),X161))
           => c_Fun_Oinj__on(X8,X18,X2,hAPP(X12,X91)) )
       => c_Fun_Oinj__on(X8,X18,X2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X161),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__INTER) ).

fof(fact_listsum__mono,axiom,
    ! [X1,X2,X200,X10,X8] :
      ( ( class_Groups_Omonoid__add(X8)
        & class_Groups_Oordered__ab__semigroup__add(X8) )
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(X2,X3)),hAPP(X1,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200))),hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X1),X200)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__mono) ).

fof(fact_list__all2__all__nthI,axiom,
    ! [X42,X14,X8,X13,X10] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X13) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X14)
     => ( ! [X123] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X13)))
           => hBOOL(hAPP(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X13),X123)),hAPP(hAPP(c_List_Onth(X8),X14),X123))) )
       => c_List_Olist__all2(X10,X8,X42,X13,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__all__nthI) ).

fof(fact_list__all2__conv__all__nth,axiom,
    ! [X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X200,X199)
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)
        & ! [X91] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
           => hBOOL(hAPP(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X91)),hAPP(hAPP(c_List_Onth(X8),X199),X91))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__conv__all__nth) ).

fof(fact_setsum__strict__mono,axiom,
    ! [X1,X2,X12,X10,X8] :
      ( ( class_Groups_Ocomm__monoid__add(X8)
        & class_Groups_Oordered__cancel__ab__semigroup__add(X8) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(X2,X3)),hAPP(X1,X3))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__strict__mono) ).

fof(fact_setsum__cases,axiom,
    ! [X1,X2,X42,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBS(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),X42)),X2)),X1)),X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_OCollect(X10),X42)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X42))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cases) ).

fof(fact_folding__one__idem_Ohom__commute,axiom,
    ! [X53,X7,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one__idem(X10,X2,X9)
     => ( ! [X3,X51] : hAPP(X7,hAPP(hAPP(X2,X3),X51)) = hAPP(hAPP(X2,hAPP(X7,X3)),hAPP(X7,X51))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
         => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X7,hAPP(X9,X53)) = hAPP(X9,hAPP(c_Set_Oimage(X10,X10,X7),X53)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Ohom__commute) ).

fof(fact_set__n__lists,axiom,
    ! [X200,X30,X10] : hAPP(c_List_Oset(tc_List_Olist(X10)),c_Enum_On__lists(X10,X30,X200)) = hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X30))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),c_List_Oset(X10))),hAPP(c_List_Oset(X10),X200)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__n__lists) ).

fof(fact_map__pair_Ocomp,axiom,
    ! [X61,X7,X1,X2,X8,X10,X102,X18,X115,X104] : hAPP(c_Fun_Ocomp(tc_prod(X104,X115),tc_prod(X18,X102),tc_prod(X10,X8),c_Product__Type_Omap__pair(X104,X18,X115,X102,X2,X1)),c_Product__Type_Omap__pair(X10,X104,X8,X115,X7,X61)) = c_Product__Type_Omap__pair(X10,X18,X8,X102,hAPP(c_Fun_Ocomp(X104,X18,X10,X2),X7),hAPP(c_Fun_Ocomp(X115,X102,X8,X1),X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Ocomp) ).

fof(fact_map__pair__compose,axiom,
    ! [X186,X187,X115,X49,X50,X104,X102,X8,X18,X10] : c_Product__Type_Omap__pair(X10,X18,X8,X102,hAPP(c_Fun_Ocomp(X104,X18,X10,X50),X49),hAPP(c_Fun_Ocomp(X115,X102,X8,X187),X186)) = hAPP(c_Fun_Ocomp(tc_prod(X104,X115),tc_prod(X18,X102),tc_prod(X10,X8),c_Product__Type_Omap__pair(X104,X18,X115,X102,X50,X187)),c_Product__Type_Omap__pair(X10,X104,X8,X115,X49,X186)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__compose) ).

fof(fact_listrel__iff__nth,axiom,
    ! [X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel(X10,X110)))
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199)
        & ! [X123] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(hAPP(c_List_Onth(X10),X200),X123)),hAPP(hAPP(c_List_Onth(X10),X199),X123))),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__iff__nth) ).

fof(fact_rel__pow__Suc__D2,axiom,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30)),X29)))
     => ? [X51] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),X29))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__D2) ).

fof(fact_quotient__def,axiom,
    ! [X110,X12,X10] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X10),c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),c_Relation_OImage(X10,X10,X110)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,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,
    ! [X12,X110,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(c_Relation_OImage(X8,X10,X110),X12)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X3),X14)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__iff) ).

fof(fact_folding__one_Oclosed,axiom,
    ! [X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3,X51] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(X2,X3),X51)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X10),hAPP(X9,X12)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oclosed) ).

fof(fact_Image__Collect__split,axiom,
    ! [X12,X42,X10,X8] : hAPP(c_Relation_OImage(X8,X10,hAPP(c_Set_OCollect(tc_prod(X8,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X10,tc_HOL_Obool),X42))),X12) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fconj),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X12)))),hAPP(c_COMBC(X8,X10,tc_HOL_Obool),X42)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Collect__split) ).

fof(fact_quotient__diff1,axiom,
    ! [X13,X12,X110,X10] :
      ( c_Fun_Oinj__on(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X10),c_Equiv__Relations_Oquotient(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X110),X12)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X110) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__diff1) ).

fof(fact_Collect__ball__eq,axiom,
    ! [X42,X12,X8,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OAll(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBS(X8,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fimplies),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X12)))),X42))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),c_Set_OCollect(X10)),hAPP(c_COMBC(X10,X8,tc_HOL_Obool),X42))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__ball__eq) ).

fof(fact_sublist__append,axiom,
    ! [X12,X224,X83,X10] : c_List_Osublist(X10,hAPP(hAPP(c_List_Oappend(X10),X83),X224),X12) = hAPP(hAPP(c_List_Oappend(X10),c_List_Osublist(X10,X83,X12)),c_List_Osublist(X10,X224,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(X10)),X83)))),X12)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__append) ).

fof(fact_zip__obtain__same__length,axiom,
    ! [X42,X199,X8,X200,X10] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Otake(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199))),X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199))),X199))
       => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Ozip(X10,X8),hAPP(hAPP(c_List_Otake(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199))),X200)),hAPP(hAPP(c_List_Otake(X8),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199))),X199)))) )
     => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__obtain__same__length) ).

fof(fact_card__quotient__disjoint,axiom,
    ! [X110,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( c_Fun_Oinj__on(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X10),c_Equiv__Relations_Oquotient(X10)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X110),X12)
       => hAPP(c_Finite__Set_Ocard(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)) = hAPP(c_Finite__Set_Ocard(X10),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__quotient__disjoint) ).

fof(fact_arith__series__general,axiom,
    ! [X30,X20,X13,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),c_Groups_Oone__class_Oone(X10))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(X10,X10,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X10),X13)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X10)),c_Nat_Osemiring__1__class_Oof__nat(X10))),X20))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X20)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__series__general) ).

fof(fact_dvd_OatLeastLessThan__empty,axiom,
    ! [X13,X14] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X13))
     => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).

fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
    ! [X32,X83] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X83),X32))
     => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32,X83) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).

fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
    ! [X32,X83] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X83),X32))
     => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32,X83) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OgreaterThanLessThan__empty) ).

fof(fact_reduction__pair__def,axiom,
    ! [X42,X10] :
      ( c_FunDef_Oreduction__pair(X10,X42)
    <=> ( c_Wellfounded_Owf(X10,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X42))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X42)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X42))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X42))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pair__def) ).

fof(fact_UN__subset__iff,axiom,
    ! [X15,X12,X161,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12)),X15))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X161))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(X12,X3)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__subset__iff) ).

fof(fact_setsum__bounded,axiom,
    ! [X168,X2,X12,X10,X8] :
      ( ( class_Groups_Oordered__ab__semigroup__add(X8)
        & class_Rings_Osemiring__1(X8) )
     => ( ! [X91] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X91),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(X2,X91)),X168)) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),hAPP(c_Finite__Set_Ocard(X10),X12))),X168))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__bounded) ).

fof(fact_map__pair__def,axiom,
    ! [X1,X2,X102,X8,X18,X10] : c_Product__Type_Omap__pair(X10,X18,X8,X102,X2,X1) = hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_prod(X18,X102)),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,X102),tc_fun(X8,tc_prod(X18,X102))),hAPP(hAPP(c_COMBB(tc_fun(X102,tc_prod(X18,X102)),tc_fun(tc_fun(X8,X102),tc_fun(X8,tc_prod(X18,X102))),X10),c_COMBB(X102,tc_prod(X18,X102),X8)),hAPP(hAPP(c_COMBB(X18,tc_fun(X102,tc_prod(X18,X102)),X10),c_Product__Type_OPair(X18,X102)),X2))),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__def) ).

fof(fact_decr__lemma,axiom,
    ! [X38,X26,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),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),X26),X38))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X58))),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__lemma) ).

fof(fact_SUP__le__iff,axiom,
    ! [X77,X143,X12,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X10),X12),X143)),X77))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X143,X3)),X77)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__le__iff) ).

fof(fact_transfer__int__nat__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).

fof(fact_transfer__nat__int__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).

fof(fact_lexord__take__index__conv,axiom,
    ! [X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),c_List_Olexord(X10,X110)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X11)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16)))
          & hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X11)),X16) = X11 )
        | ? [X91] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X11)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16))))
            & hAPP(hAPP(c_List_Otake(X10),X91),X11) = hAPP(hAPP(c_List_Otake(X10),X91),X16)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(hAPP(c_List_Onth(X10),X11),X91)),hAPP(hAPP(c_List_Onth(X10),X16),X91))),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__take__index__conv) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [X41,X42,X8,X10] : hAPP(c_Set_OCollect(tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X42))),X41))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(c_Set_OCollect(X10),X42)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),c_Set_OCollect(X8)),X41)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetCompr__Sigma__eq) ).

fof(fact_card__less,axiom,
    ! [X61,X143] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X143))
     => 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)),X143))),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,X61))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__less) ).

fof(fact_Eps__split__eq,axiom,
    ! [X16,X11,X8,X10] : c_Hilbert__Choice_OEps(tc_prod(X10,X8),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X11)))),hAPP(c_fequal,X16)))) = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split__eq) ).

fof(fact_The__split__eq,axiom,
    ! [X16,X11,X8,X10] : c_HOL_OThe(tc_prod(X10,X8),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X11)))),hAPP(c_fequal,X16)))) = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_The__split__eq) ).

fof(fact_setsum__commute,axiom,
    ! [X12,X15,X2,X18,X8,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X18,X10),tc_fun(tc_fun(X18,tc_HOL_Obool),X10),X8),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18,X10)),X2)),X15)),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18,X10),hAPP(hAPP(c_COMBC(X18,tc_fun(X8,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X8,X10),tc_fun(tc_fun(X8,tc_HOL_Obool),X10),X18),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10)),hAPP(c_COMBC(X8,X18,X10),X2))),X12)),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__commute) ).

fof(fact_Collect__split,axiom,
    ! [X41,X42,X8,X10] : hAPP(c_Set_OCollect(tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X42))),X41))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(c_Set_OCollect(X10),X42)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Set_OCollect(X8),X41))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__split) ).

fof(fact_image__eq__fold__image,axiom,
    ! [X2,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(c_Set_Oimage(X10,X8,X2),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X8,tc_HOL_Obool),X10,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Set_Oinsert(X8)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eq__fold__image) ).

fof(fact_card__Diff2__less,axiom,
    ! [X16,X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X16),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X10),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff2__less) ).

fof(fact_Id__on__def_H,axiom,
    ! [X12,X10] : c_Relation_OId__on(X10,X12) = hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool)),X10),c_COMBC(X10,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj)),c_fequal))),X12)),
    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,
    ! [X7,X1,X2,X115,X104,X8,X102,X18,X10] : hAPP(hAPP(c_Product__Type_Oscomp(X10,X18,X102,X8),hAPP(hAPP(c_Product__Type_Oscomp(X10,X104,X115,tc_prod(X18,X102)),X2),X1)),X7) = hAPP(hAPP(c_Product__Type_Oscomp(X10,X104,X115,X8),X2),hAPP(hAPP(c_COMBC(X104,tc_fun(X18,tc_fun(X102,X8)),tc_fun(X115,X8)),hAPP(hAPP(c_COMBB(tc_fun(X115,tc_prod(X18,X102)),tc_fun(tc_fun(X18,tc_fun(X102,X8)),tc_fun(X115,X8)),X104),c_Product__Type_Oscomp(X115,X18,X102,X8)),X1)),X7)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__scomp) ).

fof(fact_wmax__insertI,axiom,
    ! [X158,X11,X157,X16] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16),X157))
     => ( 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)),X11),X16)),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)),X158),X157)),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)),X11),X158)),X157)),c_FunDef_Omax__weak)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmax__insertI) ).

fof(fact_smax__insertI,axiom,
    ! [X48,X11,X65,X16] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16),X65))
     => ( 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)),X11),X16)),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)),X48),X65)),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)),X11),X48)),X65)),c_FunDef_Omax__strict)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smax__insertI) ).

fof(fact_sorted__map__same,axiom,
    ! [X200,X1,X2,X8,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(c_List_Ofilter(X8,hAPP(hAPP(c_COMBC(X8,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,tc_HOL_Obool),X8),c_fequal),X2)),hAPP(X1,X200))),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__map__same) ).

fof(fact_max__ext_Osimps,axiom,
    ! [X29,X56,X57,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X57),X56)),c_Wellfounded_Omax__ext(X10,X29)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X57))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X56))
        & X56 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X57))
           => ? [X66] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X66),X56))
                & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X66)),X29)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext_Osimps) ).

fof(fact_wf__union__merge,axiom,
    ! [X28,X29,X10] :
      ( c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),X28))
    <=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X29),X29)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X28),X29))),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__union__merge) ).

fof(fact_map__pair__surj__on,axiom,
    ! [X189,X15,X1,X18,X102,X78,X12,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),X12) = X78
     => ( hAPP(c_Set_Oimage(X102,X18,X1),X15) = X189
       => hAPP(c_Set_Oimage(tc_prod(X8,X102),tc_prod(X10,X18),c_Product__Type_Omap__pair(X8,X10,X102,X18,X2,X1)),hAPP(hAPP(c_Product__Type_OSigma(X8,X102),X12),hAPP(c_COMBK(tc_fun(X102,tc_HOL_Obool),X8),X15))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X18),X78),hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X10),X189)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__surj__on) ).

fof(fact_wmin__insertI,axiom,
    ! [X157,X16,X158,X11] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X11),X158))
     => ( 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)),X11),X16)),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)),X158),X157)),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)),X158),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16),X157))),c_FunDef_Omin__weak)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmin__insertI) ).

fof(fact_smin__insertI,axiom,
    ! [X157,X16,X158,X11] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X11),X158))
     => ( 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)),X11),X16)),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)),X158),X157)),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)),X158),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X16),X157))),c_FunDef_Omin__strict)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smin__insertI) ).

fof(fact_insert__fold1SetE,axiom,
    ! [X11,X48,X13,X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X13),X48)),X11))
     => ~ ! [X46,X52] :
            ( hAPP(hAPP(c_Set_Oinsert(X10),X13),X48) = hAPP(hAPP(c_Set_Oinsert(X10),X46),X52)
           => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X46,X52),X11))
             => hBOOL(hAPP(hAPP(c_member(X10),X46),X52)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__fold1SetE) ).

fof(fact_listrel1__iff__update,axiom,
    ! [X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110)))
    <=> ? [X51,X123] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(hAPP(c_List_Onth(X10),X200),X123)),X51)),X110))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
          & X199 = hAPP(hAPP(c_List_Olist__update(X10,X200),X123),X51) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__iff__update) ).

fof(fact_map__pair__surj,axiom,
    ! [X1,X18,X102,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(X102,X18,X1),c_Orderings_Otop__class_Otop(tc_fun(X102,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X8,X102),tc_prod(X10,X18),c_Product__Type_Omap__pair(X8,X10,X102,X18,X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X8,X102),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10,X18),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__surj) ).

fof(fact_minus__fold__remove,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X12) = hAPP(hAPP(c_Finite__Set_Ofold(X10,tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X15),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__fold__remove) ).

fof(fact_fst__map__pair,axiom,
    ! [X11,X1,X2,X102,X18,X8,X10] : hAPP(c_Product__Type_Ofst(X10,X8),hAPP(c_Product__Type_Omap__pair(X18,X10,X102,X8,X2,X1),X11)) = hAPP(X2,hAPP(c_Product__Type_Ofst(X18,X102),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__map__pair) ).

fof(fact_snd__prod__fun,axiom,
    ! [X11,X1,X2,X102,X18,X10,X8] : hAPP(c_Product__Type_Osnd(X8,X10),hAPP(c_Product__Type_Omap__pair(X18,X8,X102,X10,X2,X1),X11)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X18,X102),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__prod__fun) ).

fof(fact_lexord__linear,axiom,
    ! [X16,X11,X110,X10] :
      ( ! [X46,X81] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X46),X81)),X110))
          | X46 = X81
          | hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X81),X46)),X110)) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),c_List_Olexord(X10,X110)))
        | X11 = X16
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X11)),c_List_Olexord(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__linear) ).

fof(fact_add,axiom,
    ! [X93,X77,X16,X11] : 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),X11),X16)),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),X77),X93)),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),X11),X77)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X16),X93))),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,
    ! [X12,X10] : c_Relation_OId__on(X10,X12) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X10,X10),tc_fun(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X10),c_Set_Oinsert(tc_prod(X10,X10))),hAPP(hAPP(c_COMBS(X10,X10,tc_prod(X10,X10)),c_Product__Type_OPair(X10,X10)),c_COMBI(X10)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__def) ).

fof(fact_conversep__noteq,axiom,
    ! [X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X10,hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot)),c_fequal)),X11),X16))
    <=> X11 != X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__noteq) ).

fof(fact_map__zip__map,axiom,
    ! [X199,X200,X1,X102,X2,X10,X18,X8] : hAPP(hAPP(c_List_Omap(tc_prod(X8,X18),X10),X2),hAPP(hAPP(c_List_Ozip(X8,X18),hAPP(hAPP(c_List_Omap(X102,X8),X1),X200)),X199)) = hAPP(hAPP(c_List_Omap(tc_prod(X102,X18),X10),hAPP(c_Product__Type_Oprod_Oprod__case(X102,X18,X10),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_prod(X8,X18)),tc_fun(X18,X10),X102),hAPP(c_COMBB(tc_prod(X8,X18),X10,X18),X2)),hAPP(hAPP(c_COMBB(X8,tc_fun(X18,tc_prod(X8,X18)),X102),c_Product__Type_OPair(X8,X18)),X1)))),hAPP(hAPP(c_List_Ozip(X102,X18),X200),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__zip__map) ).

fof(fact_order__fun_I2_J,axiom,
    ! [X1,X2,X10,X8] :
      ( ( class_Orderings_Oorder(X8)
        & class_Enum_Oenum(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X8)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X2),X1))
          & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBS(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_fequal),X2)),X1)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__fun_I2_J) ).

fof(fact_sublist__Cons,axiom,
    ! [X12,X83,X11,X10] : c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X83),X12) = hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X10)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10))),c_List_Olist_ONil(X10))),c_List_Osublist(X10,X83,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)),X12)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__Cons) ).

fof(fact_nth__nth__transpose__sorted,axiom,
    ! [X60,X61,X200,X10] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X200)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X200))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X200))))
         => hAPP(hAPP(c_List_Onth(X10),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),c_List_Otranspose(X10,X200)),X61)),X60) = hAPP(hAPP(c_List_Onth(X10),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X200),X60)),X61) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__nth__transpose__sorted) ).

fof(fact_INF__less__iff,axiom,
    ! [X13,X2,X12,X8,X10] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X10)
        & class_Orderings_Olinorder(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,X10),X12),X2)),X13))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X3)),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__less__iff) ).

fof(fact_ball__UN,axiom,
    ! [X42,X15,X12,X8,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)))
         => hBOOL(hAPP(X42,X3)) )
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
         => ! [X66] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X66),hAPP(X15,X3)))
             => hBOOL(hAPP(X42,X66)) ) ) ),
    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,
    ! [X21,X17,X29,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X12),X15)),c_Wellfounded_Omax__ext(X10,X29)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X17),X21)),c_Wellfounded_Omax__ext(X10,X29)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X17)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X21))),c_Wellfounded_Omax__ext(X10,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__additive) ).

fof(fact_SigmaE,axiom,
    ! [X15,X12,X6,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X6),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => ! [X51] :
                ( hBOOL(hAPP(hAPP(c_member(X8),X51),hAPP(X15,X3)))
               => X6 != hAPP(hAPP(c_Product__Type_OPair(X10,X8),X3),X51) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaE) ).

fof(fact_foldl__map,axiom,
    ! [X200,X2,X18,X13,X1,X8,X10] : hAPP(c_List_Ofoldl(X10,X8,X1,X13),hAPP(hAPP(c_List_Omap(X18,X8),X2),X200)) = hAPP(c_List_Ofoldl(X10,X18,hAPP(hAPP(c_COMBC(X10,tc_fun(X18,X8),tc_fun(X18,X10)),hAPP(hAPP(c_COMBB(tc_fun(X8,X10),tc_fun(tc_fun(X18,X8),tc_fun(X18,X10)),X10),c_COMBB(X8,X10,X18)),X1)),X2),X13),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__map) ).

fof(fact_rel__comp__UNION__distrib2,axiom,
    ! [X116,X110,X161,X102,X8,X18,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X102,tc_fun(tc_prod(X10,X18),tc_HOL_Obool)),X161),X110)),X116) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X102,tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X161),hAPP(hAPP(c_COMBC(X102,tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10,X18),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X102),c_Relation_Orel__comp(X10,X18,X8)),X110)),X116)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib2) ).

fof(fact_finite__Collect__disjI,axiom,
    ! [X41,X42,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),X42)),X41))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X42)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X41))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__disjI) ).

fof(fact_inj__transfer,axiom,
    ! [X11,X42,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( ! [X51] :
            ( hBOOL(hAPP(hAPP(c_member(X8),X51),hAPP(c_Set_Oimage(X10,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))))
           => hBOOL(hAPP(X42,hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),X51))) )
       => hBOOL(hAPP(X42,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__transfer) ).

fof(fact_enum__all__prod__def,axiom,
    ! [X42,X10,X8] :
      ( ( class_Enum_Oenum(X8)
        & class_Enum_Oenum(X10) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X10,X8)),X42))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X10),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,X10),c_Enum_Oenum__class_Oenum__all(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_HOL_Obool,X8),X42)),c_Product__Type_OPair(X10,X8))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all__prod__def) ).

fof(fact_enum__ex__prod__def,axiom,
    ! [X42,X10,X8] :
      ( ( class_Enum_Oenum(X8)
        & class_Enum_Oenum(X10) )
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X10,X8)),X42))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X10),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,X10),c_Enum_Oenum__class_Oenum__ex(X8)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_HOL_Obool,X8),X42)),c_Product__Type_OPair(X10,X8))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex__prod__def) ).

fof(fact_listsp__conj__eq,axiom,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(c_List_Olistsp(X10,hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X12)),X15)),X11))
    <=> ( hBOOL(hAPP(c_List_Olistsp(X10,X12),X11))
        & hBOOL(hAPP(c_List_Olistsp(X10,X15),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__conj__eq) ).

fof(fact_lists__IntI,axiom,
    ! [X15,X12,X83,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X83),c_List_Olists(X10,X12)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X83),c_List_Olists(X10,X15)))
       => hBOOL(hAPP(c_List_Olistsp(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))),X83)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__IntI) ).

fof(fact_UN__equiv__class2,axiom,
    ! [X56,X57,X2,X18,X164,X165,X8,X166,X167,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X167,X166)
     => ( c_Equiv__Relations_Oequiv(X8,X165,X164)
       => ( c_Equiv__Relations_Ocongruent2(X10,X8,tc_fun(X18,tc_HOL_Obool),X166,X164,X2)
         => ( hBOOL(hAPP(hAPP(c_member(X10),X57),X167))
           => ( hBOOL(hAPP(hAPP(c_member(X8),X56),X165))
             => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X18,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X166),hAPP(hAPP(c_Set_Oinsert(X10),X57),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(X18,tc_HOL_Obool)),tc_fun(X18,tc_HOL_Obool),X10),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X18,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X8,X164),hAPP(hAPP(c_Set_Oinsert(X8),X56),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))))),X2)) = hAPP(hAPP(X2,X57),X56) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class2) ).

fof(fact_length__sublist,axiom,
    ! [X161,X200,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Osublist(X10,X200,X161)) = 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(X10)),X200)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X161)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sublist) ).

fof(fact_length__filter__conv__card,axiom,
    ! [X200,X148,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X148),X200)) = 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(X10)),X200)))),hAPP(hAPP(c_COMBB(X10,tc_HOL_Obool,tc_Nat_Onat),X148),hAPP(c_List_Onth(X10),X200))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__conv__card) ).

fof(fact_fold__image__distrib,axiom,
    ! [X7,X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),hAPP(hAPP(c_COMBS(X10,X8,X8),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,X8),X10),c_Groups_Otimes__class_Otimes(X8)),X1)),X7)),c_Groups_Oone__class_Oone(X8)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),X12)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X7),c_Groups_Oone__class_Oone(X8)),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__distrib) ).

fof(fact_Cantor__Bernstein,axiom,
    ! [X1,X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),X15))
       => ( c_Fun_Oinj__on(X8,X10,X1,X15)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X1),X15)),X12))
           => ? [X262] : c_Fun_Obij__betw(X10,X8,X262,X12,X15) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cantor__Bernstein) ).

fof(fact_snoc__listrel1__snoc__iff,axiom,
    ! [X110,X16,X199,X11,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X200),hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)))),hAPP(hAPP(c_List_Oappend(X10),X199),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10))))),c_List_Olistrel1(X10,X110)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110)))
          & X11 = X16 )
        | ( X200 = X199
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).

fof(fact_list__all2__map2,axiom,
    ! [X235,X2,X18,X230,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X230,hAPP(hAPP(c_List_Omap(X18,X8),X2),X235))
    <=> c_List_Olist__all2(X10,X18,hAPP(hAPP(c_COMBC(X10,tc_fun(X18,X8),tc_fun(X18,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X18,X8),tc_fun(X18,tc_HOL_Obool)),X10),c_COMBB(X8,tc_HOL_Obool,X18)),X42)),X2),X230,X235) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__map2) ).

fof(fact_UN__finite2__eq,axiom,
    ! [X15,X32,X12,X10] :
      ( ! [X123] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X123)),X12) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,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),X123),X32))),X15)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X12) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite2__eq) ).

fof(fact_max__ext_Ointros,axiom,
    ! [X29,X65,X48,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X48))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X65))
       => ( X65 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X48))
               => ? [X66] :
                    ( hBOOL(hAPP(hAPP(c_member(X10),X66),X65))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X66)),X29)) ) )
           => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X48),X65)),c_Wellfounded_Omax__ext(X10,X29))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext_Ointros) ).

fof(fact_pred__comp_Oequations,axiom,
    ! [X64,X57,X116,X110,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X10,X8,X18,X110,X116),X57),X64))
    <=> ? [X81] :
          ( hBOOL(hAPP(hAPP(X110,X57),X81))
          & hBOOL(hAPP(hAPP(X116,X81),X64)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).

fof(fact_wf__no__infinite__down__chainE,axiom,
    ! [X2,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ~ ! [X59] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X2,hAPP(c_Nat_OSuc,X59))),hAPP(X2,X59))),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__no__infinite__down__chainE) ).

fof(fact_wf__iff__no__infinite__down__chain,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
    <=> ~ ? [X76] :
          ! [X91] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),hAPP(X76,hAPP(c_Nat_OSuc,X91))),hAPP(X76,X91))),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__iff__no__infinite__down__chain) ).

fof(fact_congruent2__implies__congruent__UN,axiom,
    ! [X13,X2,X18,X164,X165,X8,X166,X167,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X167,X166)
     => ( c_Equiv__Relations_Oequiv(X8,X165,X164)
       => ( c_Equiv__Relations_Ocongruent2(X10,X8,tc_fun(X18,tc_HOL_Obool),X166,X164,X2)
         => ( hBOOL(hAPP(hAPP(c_member(X8),X13),X165))
           => c_Equiv__Relations_Ocongruent(X10,tc_fun(X18,tc_HOL_Obool),X166,hAPP(hAPP(c_COMBB(tc_fun(X8,tc_fun(X18,tc_HOL_Obool)),tc_fun(X18,tc_HOL_Obool),X10),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X18,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X8,X164),hAPP(hAPP(c_Set_Oinsert(X8),X13),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))))),X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent__UN) ).

fof(fact_Diff1__fold__graph,axiom,
    ! [X16,X11,X12,X19,X2,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X16))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),hAPP(hAPP(X2,X11),X16))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff1__fold__graph) ).

fof(fact_setsum__mono3,axiom,
    ! [X2,X12,X15,X10,X8] :
      ( ( class_Groups_Ocomm__monoid__add(X8)
        & class_Groups_Oordered__ab__semigroup__add(X8) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X12)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(X2,X3))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X15))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono3) ).

fof(fact_setsum__mono2,axiom,
    ! [X2,X12,X15,X10,X8] :
      ( class_Groups_Oordered__comm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
         => ( ! [X81] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X81),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X12)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(X2,X81))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X15))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono2) ).

fof(fact_INF__INT__eq,axiom,
    ! [X11,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8))),X110)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X8),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__INT__eq) ).

fof(fact_SUP__UN__eq,axiom,
    ! [X11,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8))),X110)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X8),X11),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__UN__eq) ).

fof(fact_less__add__iff1,axiom,
    ! [X20,X14,X6,X72,X13,X10] :
      ( class_Rings_Oordered__ring(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X72)),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X72)),X20)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14)),X72)),X6)),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff1) ).

fof(fact_le__add__iff1,axiom,
    ! [X20,X14,X6,X72,X13,X10] :
      ( class_Rings_Oordered__ring(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X72)),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X72)),X20)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14)),X72)),X6)),X20)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff1) ).

fof(fact_fold__graph_H_Ointros_I2_J,axiom,
    ! [X16,X19,X2,X8,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( c_Nitpick_Ofold__graph_H(X10,X8,X2,X19,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X16)
       => c_Nitpick_Ofold__graph_H(X10,X8,X2,X19,X12,hAPP(hAPP(X2,X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I2_J) ).

fof(fact_INT__greatest,axiom,
    ! [X15,X17,X8,X12,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X17),hAPP(X15,X3))) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__greatest) ).

fof(fact_INT__subset__iff,axiom,
    ! [X12,X161,X8,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X161))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(X12,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__subset__iff) ).

fof(fact_refl__on__INTER,axiom,
    ! [X110,X12,X8,X28,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X28))
         => c_Relation_Orefl__on(X8,hAPP(X12,X3),hAPP(X110,X3)) )
     => c_Relation_Orefl__on(X8,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X28),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(tc_prod(X8,X8),tc_HOL_Obool)),X28),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__INTER) ).

fof(fact_refl__on__UNION,axiom,
    ! [X110,X12,X8,X28,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X28))
         => c_Relation_Orefl__on(X8,hAPP(X12,X3),hAPP(X110,X3)) )
     => c_Relation_Orefl__on(X8,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X28),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(tc_prod(X8,X8),tc_HOL_Obool)),X28),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__UNION) ).

fof(fact_zminus1__lemma,axiom,
    ! [X110,X141,X14,X13] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X13,X14),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X141),X110)))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13),X14),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X110),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X141)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X141)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X110),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),X14),X110))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus1__lemma) ).

fof(fact_INT__iff,axiom,
    ! [X15,X12,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
         => hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(X15,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__iff) ).

fof(fact_vimage__Times,axiom,
    ! [X15,X12,X2,X18,X8,X10] : hAPP(c_Set_Ovimage(X10,tc_prod(X8,X18),X2),hAPP(hAPP(c_Product__Type_OSigma(X8,X18),X12),hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X8),X15))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,hAPP(c_Fun_Ocomp(tc_prod(X8,X18),X8,X10,c_Product__Type_Ofst(X8,X18)),X2)),X12)),hAPP(c_Set_Ovimage(X10,X18,hAPP(c_Fun_Ocomp(tc_prod(X8,X18),X18,X10,c_Product__Type_Osnd(X8,X18)),X2)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Times) ).

fof(fact_size__code,axiom,
    ! [X232,X10] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X10)),X232) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X10,tc_Lazy__Sequence_Olazy__sequence(X10)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X10,tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X10),tc_Nat_Onat),X10),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X10),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(X10)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X10)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X10),X232)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_size__code) ).

fof(fact_in__lex__prod,axiom,
    ! [X116,X110,X108,X109,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X109),X108))),c_Wellfounded_Olex__prod(X10,X8,X110,X116)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X109)),X110))
        | ( X13 = X109
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X14),X108)),X116)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lex__prod) ).

fof(fact_INF1__iff,axiom,
    ! [X14,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15),X14))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => hBOOL(hAPP(hAPP(X15,X3),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__iff) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [X61,X42] : 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),X42)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X61))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__M__bounded__by__nat) ).

fof(fact_incr__lemma,axiom,
    ! [X26,X38,X58] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X58))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X38),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),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),X26),X38))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X58)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__lemma) ).

fof(fact_le__INF__iff,axiom,
    ! [X143,X12,X8,X77,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X77),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,X10),X12),X143)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X77),hAPP(X143,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__INF__iff) ).

fof(fact_insort__is__Cons,axiom,
    ! [X13,X2,X200,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(X2,X13)),hAPP(X2,X3))) )
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X13),X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X13),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__is__Cons) ).

fof(fact_setsum__nonneg__0,axiom,
    ! [X61,X2,X116,X10,X8] :
      ( class_Groups_Oordered__ab__group__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X116))
       => ( ! [X91] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X91),X116))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(X2,X91))) )
         => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X116) = c_Groups_Ozero__class_Ozero(X8)
           => ( hBOOL(hAPP(hAPP(c_member(X10),X61),X116))
             => hAPP(X2,X61) = c_Groups_Ozero__class_Ozero(X8) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__nonneg__0) ).

fof(fact_inv__into__def,axiom,
    ! [X11,X2,X12,X8,X10] : hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,X12,X2),X11) = c_Hilbert__Choice_OEps(X10,hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),hAPP(hAPP(c_COMBC(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_fequal),X2)),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__def) ).

fof(fact_the__inv__into__def,axiom,
    ! [X11,X2,X12,X8,X10] : hAPP(c_Fun_Othe__inv__into(X10,X8,X12,X2),X11) = c_HOL_OThe(X10,hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),hAPP(hAPP(c_COMBC(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_fequal),X2)),X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__def) ).

fof(fact_listrel1E,axiom,
    ! [X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110)))
     => ~ ! [X3,X51] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X51)),X110))
           => ! [X220,X225] :
                ( X200 = hAPP(hAPP(c_List_Oappend(X10),X220),hAPP(hAPP(c_List_Olist_OCons(X10),X3),X225))
               => X199 != hAPP(hAPP(c_List_Oappend(X10),X220),hAPP(hAPP(c_List_Olist_OCons(X10),X51),X225)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1E) ).

fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
    ! [X16,X11,X12,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X11))
       => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X16))
         => X16 = X11 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).

fof(fact_listsum__addf,axiom,
    ! [X200,X1,X2,X8,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),hAPP(hAPP(c_COMBS(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Groups_Oplus__class_Oplus(X10)),X2)),X1)),X200)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),X1),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__addf) ).

fof(fact_listsum__subtractf,axiom,
    ! [X200,X1,X2,X8,X10] :
      ( class_Groups_Oab__group__add(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),hAPP(hAPP(c_COMBS(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Groups_Ominus__class_Ominus(X10)),X2)),X1)),X200)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),X1),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__subtractf) ).

fof(fact_UN__Pow__subset,axiom,
    ! [X15,X12,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),X8),c_Set_OPow(X10)),X15))),hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Pow__subset) ).

fof(fact_nat__less__add__iff1,axiom,
    ! [X30,X31,X77,X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X60),X61))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X77)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X77)),X30)))
      <=> 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),X61),X60)),X77)),X31)),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff1) ).

fof(fact_nat__le__add__iff1,axiom,
    ! [X30,X31,X77,X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X60),X61))
     => ( 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),X61),X77)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X77)),X30)))
      <=> 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),X61),X60)),X77)),X31)),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff1) ).

fof(fact_listsum__mult__const,axiom,
    ! [X200,X6,X2,X8,X10] :
      ( class_Rings_Osemiring__0(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Groups_Otimes__class_Otimes(X10)),X2)),X6)),X200)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))),X6) ),
    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,X160,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X28),X160)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X8) )
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X2),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X28),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X2),c_Groups_Oone__class_Oone(X8)),X28)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X2),c_Groups_Oone__class_Oone(X8)),X160)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Un__one) ).

fof(fact_inf__Int__eq,axiom,
    ! [X11,X28,X29,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X29)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X28)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X29),X28))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Int__eq) ).

fof(fact_sup__Un__eq,axiom,
    ! [X11,X28,X29,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X29)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X28)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X29),X28))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Un__eq) ).

fof(fact_insert__Collect,axiom,
    ! [X42,X13,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(c_Set_OCollect(X10),X42)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13)))),X42)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Collect) ).

fof(fact_equiv__class__nondisjoint,axiom,
    ! [X14,X13,X11,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).

fof(fact_measures__def,axiom,
    ! [X241,X10] : c_List_Omeasures(X10,X241) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X10),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(tc_fun(X10,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X10,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X10),c_List_Omap(tc_fun(X10,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X10,tc_Nat_Onat),X10,tc_Nat_Onat),c_COMBI(tc_fun(X10,tc_Nat_Onat))))),X241)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__def) ).

fof(fact_divmod__nat__rel__add1__eq,axiom,
    ! [X144,X145,X36,X146,X147,X35,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X37,X35),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X147),X146)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X35),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X145),X144)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X36),X35),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),X147),X145)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X146),X144)),X35))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X146),X144),X35)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).

fof(fact_Random__Sequence_Omap__def,axiom,
    ! [X42,X2,X10,X8] : c_Random__Sequence_Omap(X8,X10,X2,X42) = c_Random__Sequence_Obind(X8,X10,X42,hAPP(c_Fun_Ocomp(X10,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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X8,c_Random__Sequence_Osingle(X10)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random__Sequence_Omap__def) ).

fof(fact_setprod__Un,axiom,
    ! [X2,X15,X12,X10,X8] :
      ( class_Fields_Ofield(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
               => hAPP(X2,X3) != c_Groups_Ozero__class_Ozero(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X15))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un) ).

fof(fact_zadd1__lemma,axiom,
    ! [X144,X145,X36,X146,X147,X35,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X35),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X147),X146)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X36,X35),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X145),X144)))
       => ( X35 != 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),X37),X36),X35),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),X147),X145)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X146),X144)),X35))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X146),X144),X35)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd1__lemma) ).

fof(fact_setsum__cartesian__product,axiom,
    ! [X12,X15,X2,X18,X8,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X18,X10),tc_fun(tc_fun(X18,tc_HOL_Obool),X10),X8),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X18,X10)),X2)),X15)),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X8,X18),X10),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X2)),hAPP(hAPP(c_Product__Type_OSigma(X8,X18),X12),hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X8),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__cartesian__product) ).

fof(fact_setprod__cartesian__product,axiom,
    ! [X12,X15,X2,X18,X8,X10] :
      ( class_Groups_Ocomm__monoid__mult(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,tc_HOL_Obool),X10),hAPP(hAPP(c_COMBB(tc_fun(X18,X10),tc_fun(tc_fun(X18,tc_HOL_Obool),X10),X8),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X18,X10)),X2)),X15)),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X8,X18),X10),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X2)),hAPP(hAPP(c_Product__Type_OSigma(X8,X18),X12),hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X8),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__cartesian__product) ).

fof(fact_map__pair__inj__on,axiom,
    ! [X15,X1,X102,X18,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( c_Fun_Oinj__on(X18,X102,X1,X15)
       => c_Fun_Oinj__on(tc_prod(X10,X18),tc_prod(X8,X102),c_Product__Type_Omap__pair(X10,X8,X18,X102,X2,X1),hAPP(hAPP(c_Product__Type_OSigma(X10,X18),X12),hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X10),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__inj__on) ).

fof(fact_divmod__nat__rel__mult1__eq,axiom,
    ! [X37,X80,X114,X35,X36] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X36,X35),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X114),X80)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
       => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X36),X35),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),X37),X114)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X80)),X35))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X80),X35)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult1__eq) ).

fof(fact_zmult1__lemma,axiom,
    ! [X37,X80,X114,X35,X36] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X36,X35),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)))
     => ( X35 != 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),X37),X36),X35),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),X37),X114)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X80)),X35))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X80),X35)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult1__lemma) ).

fof(fact_,axiom,
    ! [X247,X248,X8,X10] : c_Lazy__Sequence_Oproduct(X10,X8,X248,X247) = hAPP(c_Lazy__Sequence_Obind(X10,tc_prod(X10,X8),X248),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X10,X8))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X10,X8)),X10),c_Lazy__Sequence_Obind(X8,tc_prod(X10,X8),X247)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X10,X8))),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X10,X8)),X8),c_Lazy__Sequence_Osingle(tc_prod(X10,X8)))),c_Product__Type_OPair(X10,X8)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_) ).

fof(fact_Ex__inj__on__UNION__Sigma,axiom,
    ! [X12,X161,X8,X10] :
    ? [X76] :
      ( c_Fun_Oinj__on(X10,tc_prod(X8,X10),X76,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12))
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,tc_prod(X8,X10),X76),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12))),hAPP(hAPP(c_Product__Type_OSigma(X8,X10),X161),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ex__inj__on__UNION__Sigma) ).

fof(fact_sublist__shift__lemma__Suc,axiom,
    ! [X239,X200,X42,X10] : hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X10,tc_Nat_Onat)),X42),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X10,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X10,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X200),X239))) = hAPP(hAPP(c_List_Omap(tc_prod(X10,tc_Nat_Onat),X10),c_Product__Type_Ofst(X10,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X10,tc_Nat_Onat)),X42),c_Product__Type_Osnd(X10,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X10,tc_Nat_Onat),X200),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X239)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__shift__lemma__Suc) ).

fof(fact_fst__comp__map__pair,axiom,
    ! [X1,X2,X8,X10,X102,X18] : hAPP(c_Fun_Ocomp(tc_prod(X18,X102),X18,tc_prod(X10,X8),c_Product__Type_Ofst(X18,X102)),c_Product__Type_Omap__pair(X10,X18,X8,X102,X2,X1)) = hAPP(c_Fun_Ocomp(X10,X18,tc_prod(X10,X8),X2),c_Product__Type_Ofst(X10,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__comp__map__pair) ).

fof(fact_snd__comp__map__pair,axiom,
    ! [X1,X2,X8,X10,X18,X102] : hAPP(c_Fun_Ocomp(tc_prod(X102,X18),X18,tc_prod(X10,X8),c_Product__Type_Osnd(X102,X18)),c_Product__Type_Omap__pair(X10,X102,X8,X18,X2,X1)) = hAPP(c_Fun_Ocomp(X8,X18,tc_prod(X10,X8),X1),c_Product__Type_Osnd(X10,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__comp__map__pair) ).

fof(fact_INT__extend__simps_I9_J,axiom,
    ! [X17,X15,X18,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_HOL_Obool),tc_fun(tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X8),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool))),X15)),X17)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X18,tc_HOL_Obool)),X12),X15)),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I9_J) ).

fof(fact_UN__extend__simps_I9_J,axiom,
    ! [X17,X15,X18,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X8,tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X18,tc_HOL_Obool),tc_fun(tc_fun(X18,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X8),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool))),X15)),X17)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X18,tc_HOL_Obool)),X12),X15)),X17),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I9_J) ).

fof(fact_INT__simps_I9_J,axiom,
    ! [X17,X15,X12,X18,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X18,tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X18),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool))),X15)),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I9_J) ).

fof(fact_UN__simps_I9_J,axiom,
    ! [X17,X15,X12,X18,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X18,tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool))),X15)),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I9_J) ).

fof(fact_UN__UN__flatten,axiom,
    ! [X17,X15,X12,X18,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X18,tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),X18),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool))),X15)),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__UN__flatten) ).

fof(fact_congruentI,axiom,
    ! [X8,X2,X110,X10] :
      ( ! [X51,X177] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X177)),X110))
         => hAPP(X2,X51) = hAPP(X2,X177) )
     => c_Equiv__Relations_Ocongruent(X10,X8,X110,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruentI) ).

fof(fact_finite__less__ub,axiom,
    ! [X77,X2] :
      ( ! [X123] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X123),hAPP(X2,X123)))
     => 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)),X77)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__less__ub) ).

fof(fact_congruent2D,axiom,
    ! [X169,X170,X171,X172,X2,X164,X166,X18,X8,X10] :
      ( c_Equiv__Relations_Ocongruent2(X10,X8,X18,X166,X164,X2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X172),X171)),X166))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X170),X169)),X164))
         => hAPP(hAPP(X2,X172),X170) = hAPP(hAPP(X2,X171),X169) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2D) ).

fof(fact_Int__Collect__mono,axiom,
    ! [X41,X42,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => ( hBOOL(hAPP(X42,X3))
             => hBOOL(hAPP(X41,X3)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_OCollect(X10),X42))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(c_Set_OCollect(X10),X41)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Collect__mono) ).

fof(fact_UN__finite__subset,axiom,
    ! [X17,X12,X10] :
      ( ! [X123] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X123)),X12)),X17))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X12)),X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__finite__subset) ).

fof(fact_set__diff__eq,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__diff__eq) ).

fof(fact_finite__Collect__conjI,axiom,
    ! [X41,X42,X10] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X42)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X41))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X42)),X41)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__conjI) ).

fof(fact_UN__UN__finite__eq,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,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(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X12)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__UN__finite__eq) ).

fof(fact_map__pair__simp,axiom,
    ! [X14,X13,X1,X2,X8,X102,X10,X18] : hAPP(c_Product__Type_Omap__pair(X18,X10,X102,X8,X2,X1),hAPP(hAPP(c_Product__Type_OPair(X18,X102),X13),X14)) = hAPP(hAPP(c_Product__Type_OPair(X10,X8),hAPP(X2,X13)),hAPP(X1,X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__simp) ).

fof(fact_list__all2I,axiom,
    ! [X42,X14,X13,X8,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X3),hAPP(c_List_Oset(tc_prod(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X13),X14))))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),X42),X3)) )
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X13) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X14)
       => c_List_Olist__all2(X10,X8,X42,X13,X14) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2I) ).

fof(fact_list__all2__def,axiom,
    ! [X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X200,X199)
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X3),hAPP(c_List_Oset(tc_prod(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),X42),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__def) ).

fof(fact_map__pair__ident,axiom,
    ! [X19,X8,X10] : hAPP(c_Product__Type_Omap__pair(X10,X10,X8,X8,c_COMBI(X10),c_COMBI(X8)),X19) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair__ident) ).

fof(fact_folding__image__simple_Ounion__inter,axiom,
    ! [X15,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
         => hAPP(hAPP(X2,hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15))),hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(X2,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__inter) ).

fof(fact_setsum_Ounion__inter__neutral,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
               => hAPP(X1,X3) = c_Groups_Ozero__class_Ozero(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).

fof(fact_setsum__Un__zero,axiom,
    ! [X2,X160,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X28),X160)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X28),X160)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X28)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X160)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__zero) ).

fof(fact_setprod__Un__one,axiom,
    ! [X2,X160,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X28),X160)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X28),X160)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X28)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X160)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__one) ).

fof(fact_setprod_Ounion__inter__neutral,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
               => hAPP(X1,X3) = c_Groups_Oone__class_Oone(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__inter__neutral) ).

fof(fact_Image__singleton,axiom,
    ! [X13,X110,X10,X8] : hAPP(c_Relation_OImage(X8,X10,X110),hAPP(hAPP(c_Set_Oinsert(X8),X13),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X8,X10),tc_fun(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_HOL_Obool),X10),c_member(tc_prod(X8,X10))),hAPP(c_Product__Type_OPair(X8,X10),X13))),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton) ).

fof(fact_folding__image__simple_Oremove,axiom,
    ! [X11,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X8),X11),X12))
         => hAPP(X9,X12) = hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X8),X11),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oremove) ).

fof(fact_subset__image__iff,axiom,
    ! [X12,X2,X8,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(c_Set_Oimage(X8,X10,X2),X12)))
    <=> ? [X22] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X22),X12))
          & X15 = hAPP(c_Set_Oimage(X8,X10,X2),X22) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__image__iff) ).

fof(fact_UN__iff,axiom,
    ! [X15,X12,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
          & hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(X15,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__iff) ).

fof(fact_folding__image__simple_Oinsert__remove,axiom,
    ! [X11,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X8),X11),X12)) = hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X8),X11),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert__remove) ).

fof(fact_inv__into__comp,axiom,
    ! [X11,X12,X1,X18,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,hAPP(c_Set_Oimage(X18,X10,X1),X12))
     => ( c_Fun_Oinj__on(X18,X10,X1,X12)
       => ( hBOOL(hAPP(hAPP(c_member(X8),X11),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(c_Set_Oimage(X18,X10,X1),X12))))
         => hAPP(c_Hilbert__Choice_Oinv__into(X18,X8,X12,hAPP(c_Fun_Ocomp(X10,X8,X18,X2),X1)),X11) = hAPP(hAPP(c_Fun_Ocomp(X10,X18,X8,c_Hilbert__Choice_Oinv__into(X18,X10,X12,X1)),c_Hilbert__Choice_Oinv__into(X10,X8,hAPP(c_Set_Oimage(X18,X10,X1),X12),X2)),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__comp) ).

fof(fact_the__inv__into__comp,axiom,
    ! [X11,X12,X1,X18,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,hAPP(c_Set_Oimage(X18,X10,X1),X12))
     => ( c_Fun_Oinj__on(X18,X10,X1,X12)
       => ( hBOOL(hAPP(hAPP(c_member(X8),X11),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(c_Set_Oimage(X18,X10,X1),X12))))
         => hAPP(c_Fun_Othe__inv__into(X18,X8,X12,hAPP(c_Fun_Ocomp(X10,X8,X18,X2),X1)),X11) = hAPP(hAPP(c_Fun_Ocomp(X10,X18,X8,c_Fun_Othe__inv__into(X18,X10,X12,X1)),c_Fun_Othe__inv__into(X10,X8,hAPP(c_Set_Oimage(X18,X10,X1),X12),X2)),X11) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__comp) ).

fof(fact_setsum__mono__zero__right,axiom,
    ! [X2,X28,X160,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X28),X160))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X28)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X160) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X28) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono__zero__right) ).

fof(fact_setsum__mono__zero__left,axiom,
    ! [X2,X28,X160,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X28),X160))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X28)))
               => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X28) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X160) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__mono__zero__left) ).

fof(fact_setprod__mono__one__left,axiom,
    ! [X2,X28,X160,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X28),X160))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X28)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X28) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X160) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__mono__one__left) ).

fof(fact_setprod__mono__one__right,axiom,
    ! [X2,X28,X160,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X160))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X28),X160))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X160),X28)))
               => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X8) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X160) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X28) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__mono__one__right) ).

fof(fact_SUP1__iff,axiom,
    ! [X14,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15),X14))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
          & hBOOL(hAPP(hAPP(X15,X3),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__iff) ).

fof(fact_order__fun_I1_J,axiom,
    ! [X1,X2,X10,X8] :
      ( ( class_Orderings_Oorder(X8)
        & class_Enum_Oenum(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X2),X1))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X10),hAPP(hAPP(c_COMBS(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_Orderings_Oord__class_Oless__eq(X8)),X2)),X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__fun_I1_J) ).

fof(fact_rtrancl__imp__UN__rel__pow,axiom,
    ! [X29,X148,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Transitive__Closure_Ortrancl(X10,X29)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X10,X10),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(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool)),X29)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__imp__UN__rel__pow) ).

fof(fact_Int__Inter__image,axiom,
    ! [X15,X12,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBS(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X8,tc_fun(X10,tc_HOL_Obool),X12),X17))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X8,tc_fun(X10,tc_HOL_Obool),X15),X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Inter__image) ).

fof(fact_Un__Union__image,axiom,
    ! [X15,X12,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBS(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X8,tc_fun(X10,tc_HOL_Obool),X12),X17))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X8,tc_fun(X10,tc_HOL_Obool),X15),X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Union__image) ).

fof(fact_lexord__append__left__rightI,axiom,
    ! [X16,X11,X77,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X77),hAPP(hAPP(c_List_Olist_OCons(X10),X13),X11))),hAPP(hAPP(c_List_Oappend(X10),X77),hAPP(hAPP(c_List_Olist_OCons(X10),X14),X16)))),c_List_Olexord(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__left__rightI) ).

fof(fact_intrel__iff,axiom,
    ! [X93,X77,X16,X11] :
      ( 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),X11),X16)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X77),X93))),c_Int_Ointrel))
    <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X11),X93) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X77),X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_intrel__iff) ).

fof(fact_same__fstI,axiom,
    ! [X10,X29,X16,X156,X8,X11,X42] :
      ( hBOOL(hAPP(X42,X11))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X156),X16)),hAPP(X29,X11)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X156)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16))),c_Recdef_Osame__fst(X10,X8,X42,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__fstI) ).

fof(fact_less__SUP__iff,axiom,
    ! [X2,X12,X8,X13,X10] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X10)
        & class_Orderings_Olinorder(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X10),X12),X2)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(X2,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SUP__iff) ).

fof(fact_split__twice,axiom,
    ! [X148,X1,X104,X102,X2,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X102,X104,tc_prod(X8,X18)),X1),X148)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X102,X104,X10),hAPP(hAPP(c_COMBB(tc_fun(X104,tc_prod(X8,X18)),tc_fun(X104,X10),X102),hAPP(c_COMBB(tc_prod(X8,X18),X10,X104),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X2))),X1)),X148),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__twice) ).

fof(fact_list__size__pointwise,axiom,
    ! [X1,X2,X200,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => 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(X10,X2,X200)),c_List_Olist_Olist__size(X10,X1,X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__pointwise) ).

fof(fact_inj__graph,axiom,
    ! [X8,X10] : c_Fun_Oinj__on(tc_fun(X10,X8),tc_fun(tc_prod(X10,X8),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X10,X8)),c_Set_OCollect(tc_prod(X10,X8))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X10,X8)),c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool)),hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBC(X8,X8,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X8),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__graph) ).

fof(fact_numeral__3__eq__3,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(fact_max__extp_Osimps,axiom,
    ! [X56,X57,X29,X10] :
      ( c_Wellfounded_Omax__extp(X10,X29,X57,X56)
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X57))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X56))
        & X56 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X57))
           => ? [X66] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X66),X56))
                & hBOOL(hAPP(hAPP(X29,X3),X66)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Osimps) ).

fof(fact_max__extp_Oequations,axiom,
    ! [X56,X57,X29,X10] :
      ( c_Wellfounded_Omax__extp(X10,X29,X57,X56)
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X57))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X56))
        & X56 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X57))
           => ? [X66] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X66),X56))
                & hBOOL(hAPP(hAPP(X29,X3),X66)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).

fof(fact_Int__def,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__def) ).

fof(fact_Un__def,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__def) ).

fof(fact_folding__image__simple_Ounion__disjoint,axiom,
    ! [X15,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))
           => hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(X2,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Ounion__disjoint) ).

fof(fact_less__add__iff2,axiom,
    ! [X20,X14,X6,X72,X13,X10] :
      ( class_Rings_Oordered__ring(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X72)),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X72)),X20)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X14),X13)),X72)),X20))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__iff2) ).

fof(fact_le__add__iff2,axiom,
    ! [X20,X14,X6,X72,X13,X10] :
      ( class_Rings_Oordered__ring(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X72)),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X72)),X20)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X14),X13)),X72)),X20))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__iff2) ).

fof(fact_Image__INT__subset,axiom,
    ! [X15,X12,X18,X110,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X10,X110),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18),c_Relation_OImage(X8,X10,X110)),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__INT__subset) ).

fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
    ! [X15,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X15),X12))
         => hAPP(hAPP(X2,hAPP(X9,X15)),hAPP(X9,X12)) = hAPP(X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Osubset__idem) ).

fof(fact_le__fun__def,axiom,
    ! [X1,X2,X10,X8] :
      ( class_Orderings_Oord(X8)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X2),X1))
      <=> ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(X2,X3)),hAPP(X1,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__fun__def) ).

fof(fact_folding__image__simple_Oeq__fold__g,axiom,
    ! [X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => hAPP(X9,X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X8,X2),X1),X19),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).

fof(fact_map__eq__conv,axiom,
    ! [X1,X200,X2,X10,X8] :
      ( hAPP(hAPP(c_List_Omap(X8,X10),X2),X200) = hAPP(hAPP(c_List_Omap(X8,X10),X1),X200)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),hAPP(c_List_Oset(X8),X200)))
         => hAPP(X2,X3) = hAPP(X1,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__eq__conv) ).

fof(fact_pred__comp_Ointros,axiom,
    ! [X18,X8,X10,X6,X116,X14,X13,X110] :
      ( hBOOL(hAPP(hAPP(X110,X13),X14))
     => ( hBOOL(hAPP(hAPP(X116,X14),X6))
       => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X10,X8,X18,X110,X116),X13),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).

fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
    ! [X15,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
         => hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(X2,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Ounion__idem) ).

fof(fact_congruent2__implies__congruent,axiom,
    ! [X13,X2,X164,X18,X8,X166,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X166)
     => ( c_Equiv__Relations_Ocongruent2(X10,X8,X18,X166,X164,X2)
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => c_Equiv__Relations_Ocongruent(X8,X18,X164,hAPP(X2,X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).

fof(fact_append__eq__append__conv2,axiom,
    ! [X5,X206,X199,X200,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X200),X199) = hAPP(hAPP(c_List_Oappend(X10),X206),X5)
    <=> ? [X220] :
          ( ( X200 = hAPP(hAPP(c_List_Oappend(X10),X206),X220)
            & hAPP(hAPP(c_List_Oappend(X10),X220),X199) = X5 )
          | ( hAPP(hAPP(c_List_Oappend(X10),X200),X220) = X206
            & X199 = hAPP(hAPP(c_List_Oappend(X10),X220),X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__append__conv2) ).

fof(fact_inj__on__iff__card__le,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
       => ( ? [X76] :
              ( c_Fun_Oinj__on(X10,X8,X76,X12)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X76),X12)),X15)) )
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X8),X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__card__le) ).

fof(fact_folding__image__simple__idem_Oin__idem,axiom,
    ! [X11,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X8),X11),X12))
         => hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X9,X12)) = hAPP(X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oin__idem) ).

fof(fact_sublists_Osimps_I2_J,axiom,
    ! [X200,X11,X10] : c_Enum_Osublists(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),c_Enum_Osublists(X10,X200)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X10)),tc_fun(tc_List_Olist(tc_List_Olist(X10)),tc_List_Olist(tc_List_Olist(X10))),tc_List_Olist(tc_List_Olist(X10))),c_List_Oappend(tc_List_Olist(X10))),hAPP(c_List_Omap(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(c_List_Olist_OCons(X10),X11)))),c_COMBI(tc_List_Olist(tc_List_Olist(X10))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublists_Osimps_I2_J) ).

fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
    ! [X11,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X8),X11),X12)) = hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X9,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oinsert__idem) ).

fof(fact_INT__Int__distrib,axiom,
    ! [X15,X12,X161,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X161),hAPP(hAPP(c_COMBS(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X161),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__Int__distrib) ).

fof(fact_UN__Un__distrib,axiom,
    ! [X15,X12,X161,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),hAPP(hAPP(c_COMBS(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Un__distrib) ).

fof(fact_folding__image__simple_Oempty,axiom,
    ! [X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => hAPP(X9,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oempty) ).

fof(fact_folding__image__simple__idem_Oidem,axiom,
    ! [X11,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple__idem(X10,X8,X2,X19,X1,X9)
     => hAPP(hAPP(X2,X11),X11) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).

fof(fact_smax__emptyI,axiom,
    ! [X65] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X65))
     => ( X65 != 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))),X65)),c_FunDef_Omax__strict)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_smax__emptyI) ).

fof(fact_set__filter,axiom,
    ! [X200,X42,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_Ofilter(X10,X42),X200)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(c_List_Oset(X10),X200)))),X42)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__filter) ).

fof(fact_sum__diff__distrib,axiom,
    ! [X30,X42,X41] :
      ( ! [X3] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X41,X3)),hAPP(X42,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),X42),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X41),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30))) = 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)),X42)),X41)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__diff__distrib) ).

fof(fact_inj__on__iff__surj,axiom,
    ! [X78,X8,X10,X12] :
      ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
     => ( ? [X76] :
            ( c_Fun_Oinj__on(X10,X8,X76,X12)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X76),X12)),X78)) )
      <=> ? [X79] : hAPP(c_Set_Oimage(X8,X10,X79),X78) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__surj) ).

fof(fact_Range__iff,axiom,
    ! [X110,X8,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Relation_ORange(X8,X10),X110)))
    <=> ? [X51] : hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X51),X13)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__iff) ).

fof(fact_wmax__emptyI,axiom,
    ! [X48] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X48))
     => 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))),X48)),c_FunDef_Omax__weak)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wmax__emptyI) ).

fof(fact_INT__simps_I1_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I1_J) ).

fof(fact_INT__simps_I3_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I3_J) ).

fof(fact_UN__simps_I2_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I2_J) ).

fof(fact_INT__extend__simps_I1_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) = X15 )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I1_J) ).

fof(fact_UN__extend__simps_I2_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) = X15 )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I2_J) ).

fof(fact_INT__extend__simps_I3_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))),X15) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I3_J) ).

fof(fact_INT__simps_I6_J,axiom,
    ! [X15,X12,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),X12)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I6_J) ).

fof(fact_UN__simps_I4_J,axiom,
    ! [X15,X12,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),X12)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I4_J) ).

fof(fact_UN__simps_I6_J,axiom,
    ! [X15,X12,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),X12)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I6_J) ).

fof(fact_UN__extend__simps_I4_J,axiom,
    ! [X15,X12,X17,X8,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X12)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I4_J) ).

fof(fact_INT__extend__simps_I6_J,axiom,
    ! [X15,X12,X17,X8,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool))),X12)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I6_J) ).

fof(fact_UN__extend__simps_I6_J,axiom,
    ! [X15,X12,X17,X8,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool))),X12)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I6_J) ).

fof(fact_rel__comp__subset__Sigma,axiom,
    ! [X17,X116,X18,X15,X12,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15))))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X18),tc_HOL_Obool)),X116),hAPP(hAPP(c_Product__Type_OSigma(X8,X18),X15),hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X8),X17))))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X18),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X8,X18),X110),X116)),hAPP(hAPP(c_Product__Type_OSigma(X10,X18),X12),hAPP(c_COMBK(tc_fun(X18,tc_HOL_Obool),X10),X17)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__subset__Sigma) ).

fof(fact_Cons__listrel1__Cons,axiom,
    ! [X110,X199,X16,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199))),c_List_Olistrel1(X10,X110)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
          & X200 = X199 )
        | ( X11 = X16
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__listrel1__Cons) ).

fof(fact_lexord__cons__cons,axiom,
    ! [X110,X16,X14,X11,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X13),X11)),hAPP(hAPP(c_List_Olist_OCons(X10),X14),X16))),c_List_Olexord(X10,X110)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
        | ( X13 = X14
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),c_List_Olexord(X10,X110))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__cons__cons) ).

fof(fact_Cons__in__lex,axiom,
    ! [X110,X199,X16,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199))),c_List_Olex(X10,X110)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199) )
        | ( X11 = X16
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olex(X10,X110))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lex) ).

fof(fact_Sigma__Int__distrib2,axiom,
    ! [X15,X12,X161,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X12)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).

fof(fact_Sigma__Un__distrib2,axiom,
    ! [X15,X12,X161,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X12)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).

fof(fact_Sigma__Diff__distrib2,axiom,
    ! [X15,X12,X161,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),hAPP(hAPP(c_COMBS(X10,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X10),c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool))),X12)),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X12)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib2) ).

fof(fact_abs__diff__triangle__ineq,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X58)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X35))),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X36),X58))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__diff__triangle__ineq) ).

fof(fact_nat__less__add__iff2,axiom,
    ! [X30,X31,X77,X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X61),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X77)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X77)),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),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),X60),X61)),X77)),X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__add__iff2) ).

fof(fact_nat__le__add__iff2,axiom,
    ! [X30,X31,X77,X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X61),X60))
     => ( 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),X61),X77)),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X77)),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),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),X60),X61)),X77)),X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__add__iff2) ).

fof(fact_folding__image_Odistrib,axiom,
    ! [X7,X1,X12,X9,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image(X10,X8,X2,X19,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => hAPP(hAPP(X9,hAPP(hAPP(c_COMBS(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),X2),X1)),X7)),X12) = hAPP(hAPP(X2,hAPP(hAPP(X9,X1),X12)),hAPP(hAPP(X9,X7),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Odistrib) ).

fof(fact_fold__image__Un__Int,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),X12)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__Un__Int) ).

fof(fact_arith__series__nat,axiom,
    ! [X30,X20,X13] : 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),X13)),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),X30))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X13),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30),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,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X17),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X17),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).

fof(fact_rtrancl__listrel1__ConsI2,axiom,
    ! [X199,X200,X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).

fof(fact_image__diff__subset,axiom,
    ! [X15,X12,X2,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X2),X12)),hAPP(c_Set_Oimage(X8,X10,X2),X15))),hAPP(c_Set_Oimage(X8,X10,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__diff__subset) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
    ! [X42] : hAPP(c_Set_OCollect(tc_Nat_Onat),X42) = 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),X42),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,
    ! [X110,X10] : c_List_Olenlex(X10,X110) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X10)),tc_List_Olist(X10)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X10),c_Wellfounded_Oless__than,c_List_Olex(X10,X110))),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_List_Olist(X10),tc_prod(tc_Nat_Onat,tc_List_Olist(X10))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X10),tc_prod(tc_Nat_Onat,tc_List_Olist(X10))),tc_List_Olist(X10)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X10))),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),c_COMBI(tc_List_Olist(X10)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lenlex__def) ).

fof(fact_bij__betw__comp__iff2,axiom,
    ! [X12,X2,X18,X261,X78,X107,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X107,X78,X261)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18,X10,X2),X12)),X78))
       => ( c_Fun_Obij__betw(X18,X10,X2,X12,X78)
        <=> c_Fun_Obij__betw(X18,X8,hAPP(c_Fun_Ocomp(X10,X8,X18,X107),X2),X12,X261) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__comp__iff2) ).

fof(fact_refl__onI,axiom,
    ! [X12,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12))))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X110)) )
       => c_Relation_Orefl__on(X10,X12,X110) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onI) ).

fof(fact_refl__on__def,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12))))
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__def) ).

fof(fact_insert__compr__raw,axiom,
    ! [X15,X13,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X13),X15) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__compr__raw) ).

fof(fact_insert__compr,axiom,
    ! [X15,X13,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X13),X15) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__compr) ).

fof(fact_listrel_OCons,axiom,
    ! [X199,X200,X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199))),c_List_Olistrel(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_OCons) ).

fof(fact_smin__emptyI,axiom,
    ! [X48] :
      ( X48 != 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)),X48),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,
    ! [X16,X11] : 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),X11),X16)),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),X16),X11)),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,
    ! [X48] : 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)),X48),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,
    ! [X16,X12,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X16))
       => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),X12) = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).

fof(fact_empty__fold__graphE,axiom,
    ! [X11,X19,X2,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X11))
     => X11 = X19 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__fold__graphE) ).

fof(fact_subset__equiv__class,axiom,
    ! [X13,X14,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X14),X12))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__equiv__class) ).

fof(fact_ord_OatLeastLessThan__iff,axiom,
    ! [X77,X83,X84,X85,X61,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X61),c_SetInterval_Oord_OatLeastLessThan(X10,X85,X84,X83,X77)))
    <=> ( hBOOL(hAPP(hAPP(X85,X83),X61))
        & hBOOL(hAPP(hAPP(X84,X61),X77)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).

fof(fact_ord_OgreaterThanAtMost__iff,axiom,
    ! [X77,X83,X84,X85,X61,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X61),c_SetInterval_Oord_OgreaterThanAtMost(X10,X85,X84,X83,X77)))
    <=> ( hBOOL(hAPP(hAPP(X84,X83),X61))
        & hBOOL(hAPP(hAPP(X85,X61),X77)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).

fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
    ! [X1,X2,X15,X12,X10] :
      ( ( class_Groups_Ocomm__monoid__add(X10)
        & class_Groups_Ocomm__monoid__mult(X10) )
     => ( X12 = X15
       => ( c_Nat__Transfer_Onat__set(X15)
         => ( ! [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,X10),X2),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),X1),X15) ) ) ) ),
    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,X15,X12,X10] :
      ( ( class_Groups_Ocomm__monoid__add(X10)
        & class_Groups_Ocomm__monoid__mult(X10) )
     => ( X12 = X15
       => ( c_Nat__Transfer_Onat__set(X15)
         => ( ! [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,X10),X2),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X10),X1),X15) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod__cong_I2_J) ).

fof(fact_select__weigth__drop__zero,axiom,
    ! [X200,X10] : c_Random_Oselect__weight(X10,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X200)) = c_Random_Oselect__weight(X10,X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weigth__drop__zero) ).

fof(fact_pick__drop__zero,axiom,
    ! [X200,X10] : c_Random_Opick(X10,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X200)) = c_Random_Opick(X10,X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick__drop__zero) ).

fof(fact_transfer__int__nat__numerals_I3_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).

fof(fact_transfer__nat__int__numerals_I3_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I3_J) ).

fof(fact_o__inv__distrib,axiom,
    ! [X1,X18,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => ( c_Fun_Obij__betw(X18,X10,X1,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
       => c_Hilbert__Choice_Oinv__into(X18,X8,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X10,X8,X18,X2),X1)) = hAPP(c_Fun_Ocomp(X10,X18,X8,c_Hilbert__Choice_Oinv__into(X18,X10,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)),X1)),c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__inv__distrib) ).

fof(fact_Domain__Int__subset,axiom,
    ! [X15,X12,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X8),X12)),hAPP(c_Relation_ODomain(X10,X8),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).

fof(fact_Range__Int__subset,axiom,
    ! [X15,X12,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ORange(X8,X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ORange(X8,X10),X12)),hAPP(c_Relation_ORange(X8,X10),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Int__subset) ).

fof(fact_setsum_Odistrib,axiom,
    ! [X7,X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBS(X10,X8,X8),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,X8),X10),c_Groups_Oplus__class_Oplus(X8)),X1)),X7)),X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X7),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Odistrib) ).

fof(fact_setprod__dividef,axiom,
    ! [X1,X2,X12,X10,X8] :
      ( class_Fields_Ofield__inverse__zero(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBS(X10,X8,X8),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,X8),X10),c_Rings_Oinverse__class_Odivide(X8)),X2)),X1)),X12) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__dividef) ).

fof(fact_setprod_Odistrib,axiom,
    ! [X7,X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBS(X10,X8,X8),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,X8),X10),c_Groups_Otimes__class_Otimes(X8)),X1)),X7)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X7),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Odistrib) ).

fof(fact_fold__graph__imp__finite,axiom,
    ! [X11,X12,X19,X2,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X11))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).

fof(fact_rotate1__def,axiom,
    ! [X200,X10] : hAPP(c_List_Orotate1(X10),X200) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X10),X10,c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Oappend(X10))),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10)))),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__def) ).

fof(fact_setsum__addf,axiom,
    ! [X12,X1,X2,X8,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBS(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Groups_Oplus__class_Oplus(X10)),X2)),X1)),X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X1),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__addf) ).

fof(fact_setsum__subtractf,axiom,
    ! [X12,X1,X2,X8,X10] :
      ( class_Groups_Oab__group__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBS(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Groups_Ominus__class_Ominus(X10)),X2)),X1)),X12) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X1),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__subtractf) ).

fof(fact_setprod__timesf,axiom,
    ! [X12,X1,X2,X8,X10] :
      ( class_Groups_Ocomm__monoid__mult(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),hAPP(hAPP(c_COMBS(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Groups_Otimes__class_Otimes(X10)),X2)),X1)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),X1),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__timesf) ).

fof(fact_divmod__nat__rel__mult2__eq,axiom,
    ! [X35,X80,X114,X36,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X114),X80)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
         => hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X114),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X114,X35))),X80)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__mult2__eq) ).

fof(fact_lists__Int__eq,axiom,
    ! [X15,X12,X10] : c_List_Olistsp(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X15))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X10))),c_List_Olists(X10,X12))),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X10))),c_List_Olists(X10,X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__Int__eq) ).

fof(fact_select__weight__def,axiom,
    ! [X200,X10] : c_Random_Oselect__weight(X10,X200) = 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(X10,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,X10),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X10)),X200)))),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X10,X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__def) ).

fof(fact_insert__times__insert,axiom,
    ! [X15,X14,X12,X13,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),hAPP(hAPP(c_Set_Oinsert(X8),X14),X15))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),hAPP(hAPP(c_Set_Oinsert(X8),X14),X15)))),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__times__insert) ).

fof(fact_setsum__divide__distrib,axiom,
    ! [X110,X12,X2,X8,X10] :
      ( class_Fields_Ofield(X10)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),X12)),X110) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Rings_Oinverse__class_Odivide(X10)),X2)),X110)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__divide__distrib) ).

fof(fact_setsum__left__distrib,axiom,
    ! [X110,X12,X2,X8,X10] :
      ( class_Rings_Osemiring__0(X10)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),X12)),X110) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Groups_Otimes__class_Otimes(X10)),X2)),X110)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__left__distrib) ).

fof(fact_zmult2__lemma,axiom,
    ! [X35,X80,X114,X36,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)))
     => ( X36 != 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)),X35))
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X35)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X114),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X114,X35))),X80)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma) ).

fof(fact_listrel__rtrancl__trans,axiom,
    ! [X206,X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X110))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X199),X206)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X110))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X206)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X110)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__trans) ).

fof(fact_pred__subset__eq,axiom,
    ! [X28,X29,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X29)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X28)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X29),X28)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__subset__eq) ).

fof(fact_reduction__pair__lemma,axiom,
    ! [X28,X29,X42,X10] :
      ( c_FunDef_Oreduction__pair(X10,X42)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X42)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X28),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X42)))
         => ( c_Wellfounded_Owf(X10,X28)
           => c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),X28)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pair__lemma) ).

fof(fact_Union__Int__subset,axiom,
    ! [X15,X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X12)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Int__subset) ).

fof(fact_fun__upd__twist,axiom,
    ! [X20,X14,X31,X8,X10,X6,X13] :
      ( X13 != X6
     => c_Fun_Ofun__upd(X10,X8,c_Fun_Ofun__upd(X10,X8,X31,X13,X14),X6,X20) = c_Fun_Ofun__upd(X10,X8,c_Fun_Ofun__upd(X10,X8,X31,X6,X20),X13,X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__twist) ).

fof(fact_Image__subset__eq,axiom,
    ! [X15,X12,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X10,X110),X12)),X15))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X8,hAPP(c_Relation_Oconverse(X8,X10),X110)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__subset__eq) ).

fof(fact_image__eq__UN,axiom,
    ! [X12,X2,X10,X8] : hAPP(c_Set_Oimage(X8,X10,X2),X12) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X8,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X8),c_Set_Oinsert(X10)),X2)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eq__UN) ).

fof(fact_rtrancl__listrel1__ConsI1,axiom,
    ! [X11,X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X199))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).

fof(fact_pair__leqI2,axiom,
    ! [X154,X116,X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X116),X154))
       => 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),X13),X116)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X14),X154))),c_FunDef_Opair__leq)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI2) ).

fof(fact_pair__lessI2,axiom,
    ! [X154,X116,X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X13),X14))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X116),X154))
       => 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),X13),X116)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X14),X154))),c_FunDef_Opair__less)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI2) ).

fof(fact_rtrancl__Un__subset,axiom,
    ! [X28,X29,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X29)),c_Transitive__Closure_Ortrancl(X10,X28))),c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),X28)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).

fof(fact_lexord__trans,axiom,
    ! [X19,X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),c_List_Olexord(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X19)),c_List_Olexord(X10,X110)))
       => ( c_Relation_Otrans(X10,X110)
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X19)),c_List_Olexord(X10,X110))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__trans) ).

fof(fact_Image__Int__subset,axiom,
    ! [X15,X12,X29,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X10,X29),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X10,X29),X12)),hAPP(c_Relation_OImage(X8,X10,X29),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__subset) ).

fof(fact_image__Int__subset,axiom,
    ! [X15,X12,X2,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X2),X12)),hAPP(c_Set_Oimage(X8,X10,X2),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int__subset) ).

fof(fact_transfer__nat__int__set__cong,axiom,
    ! [X196,X42] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => ( hBOOL(hAPP(X42,X3))
          <=> hBOOL(hAPP(X196,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)))),X42)) = 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)))),X196)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__cong) ).

fof(fact_pair__leqI1,axiom,
    ! [X154,X116,X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X14))
     => 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),X13),X116)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X14),X154))),c_FunDef_Opair__leq)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__leqI1) ).

fof(fact_pair__lessI1,axiom,
    ! [X154,X116,X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X14))
     => 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),X13),X116)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X14),X154))),c_FunDef_Opair__less)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__lessI1) ).

fof(fact_lists__eq__set,axiom,
    ! [X12,X10] : c_List_Olists(X10,X12) = hAPP(c_Set_OCollect(tc_List_Olist(X10)),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),c_List_Oset(X10))),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__eq__set) ).

fof(fact_append__listrel1I,axiom,
    ! [X222,X223,X110,X199,X200,X10] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110)))
          & X223 = X222 )
        | ( X200 = X199
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X223),X222)),c_List_Olistrel1(X10,X110))) ) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X200),X223)),hAPP(hAPP(c_List_Oappend(X10),X199),X222))),c_List_Olistrel1(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__listrel1I) ).

fof(fact_lexord__append__leftI,axiom,
    ! [X11,X110,X93,X77,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X77),X93)),c_List_Olexord(X10,X110)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X11),X77)),hAPP(hAPP(c_List_Oappend(X10),X11),X93))),c_List_Olexord(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__leftI) ).

fof(fact_listrel1I2,axiom,
    ! [X11,X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X199))),c_List_Olistrel1(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I2) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
    ! [X42] : 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)))),X42))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).

fof(fact_bij__betw__comp__iff,axiom,
    ! [X261,X107,X18,X78,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X78)
     => ( c_Fun_Obij__betw(X8,X18,X107,X78,X261)
      <=> c_Fun_Obij__betw(X10,X18,hAPP(c_Fun_Ocomp(X8,X18,X10,X107),X2),X12,X261) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__comp__iff) ).

fof(fact_zip__map1,axiom,
    ! [X199,X200,X2,X18,X8,X10] : hAPP(hAPP(c_List_Ozip(X10,X8),hAPP(hAPP(c_List_Omap(X18,X10),X2),X200)),X199) = hAPP(hAPP(c_List_Omap(tc_prod(X18,X8),tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X18,X8,tc_prod(X10,X8)),hAPP(hAPP(c_COMBB(X10,tc_fun(X8,tc_prod(X10,X8)),X18),c_Product__Type_OPair(X10,X8)),X2))),hAPP(hAPP(c_List_Ozip(X18,X8),X200),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map1) ).

fof(fact_mlex__prod__def,axiom,
    ! [X29,X2,X10] : c_Wellfounded_Omlex__prod(X10,X2,X29) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X10),X10),c_Wellfounded_Olex__prod(tc_Nat_Onat,X10,c_Wellfounded_Oless__than,X29)),hAPP(hAPP(c_COMBS(X10,X10,tc_prod(tc_Nat_Onat,X10)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10,tc_prod(tc_Nat_Onat,X10)),X10),c_Product__Type_OPair(tc_Nat_Onat,X10)),X2)),c_COMBI(X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__prod__def) ).

fof(fact_finite__empty__induct,axiom,
    ! [X42,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(X42,X12))
       => ( ! [X46,X52] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X52))
             => ( hBOOL(hAPP(hAPP(c_member(X10),X46),X52))
               => ( hBOOL(hAPP(X42,X52))
                 => hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X52),hAPP(hAPP(c_Set_Oinsert(X10),X46),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) )
         => hBOOL(hAPP(X42,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__empty__induct) ).

fof(fact_Times__subset__cancel2,axiom,
    ! [X15,X12,X8,X17,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X17))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X8,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X8),X17))),hAPP(hAPP(c_Product__Type_OSigma(X8,X10),X15),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X8),X17))))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X12),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).

fof(fact_rel__pow__Suc__I2,axiom,
    ! [X30,X19,X29,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X29))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30)),X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__I2) ).

fof(fact_rel__pow__Suc__I,axiom,
    ! [X19,X29,X30,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X19)),X29))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30)),X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__Suc__I) ).

fof(fact_bij__comp,axiom,
    ! [X1,X18,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => ( c_Fun_Obij__betw(X8,X18,X1,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))
       => c_Fun_Obij__betw(X10,X18,hAPP(c_Fun_Ocomp(X8,X18,X10,X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__comp) ).

fof(fact_image__Pow__mono,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X2),X12)),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),c_Set_Oimage(X8,X10,X2)),hAPP(c_Set_OPow(X8),X12))),hAPP(c_Set_OPow(X10),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Pow__mono) ).

fof(fact_select__weight__member,axiom,
    ! [X116,X200,X10] :
      ( 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,X10),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X10)),X200))))
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Product__Type_Ofst(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X10,X200),X116))),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),X10),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X10)),X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__member) ).

fof(fact_setsum__abs,axiom,
    ! [X12,X2,X8,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),X12))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBB(X10,X10,X8),c_Groups_Oabs__class_Oabs(X10)),X2)),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__abs) ).

fof(fact_set__minus__filter__out,axiom,
    ! [X16,X200,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_List_Oset(X10),hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X16))),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__minus__filter__out) ).

fof(fact_filter__filter,axiom,
    ! [X200,X41,X42,X10] : hAPP(c_List_Ofilter(X10,X42),hAPP(c_List_Ofilter(X10,X41),X200)) = hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X41)),X42)),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__filter) ).

fof(fact_Domain__Diff__subset,axiom,
    ! [X15,X12,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X8),X12)),hAPP(c_Relation_ODomain(X10,X8),X15))),hAPP(c_Relation_ODomain(X10,X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X12),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).

fof(fact_Range__Diff__subset,axiom,
    ! [X15,X12,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ORange(X8,X10),X12)),hAPP(c_Relation_ORange(X8,X10),X15))),hAPP(c_Relation_ORange(X8,X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),X12),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).

fof(fact_fun__left__comm__idem__remove,axiom,
    ! [X10] : c_Finite__Set_Ofun__left__comm__idem(X10,tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X10),hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__remove) ).

fof(fact_card__Diff1__less,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X10),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff1__less) ).

fof(fact_split__comp__eq,axiom,
    ! [X1,X2,X102,X18,X8,X10] : hAPP(hAPP(c_COMBS(tc_prod(X10,X8),X8,X18),hAPP(hAPP(c_COMBB(X102,tc_fun(X8,X18),tc_prod(X10,X8)),X2),hAPP(hAPP(c_COMBB(X10,X102,tc_prod(X10,X8)),X1),c_Product__Type_Ofst(X10,X8)))),c_Product__Type_Osnd(X10,X8)) = hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),hAPP(hAPP(c_COMBB(X102,tc_fun(X8,X18),X10),X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__comp__eq) ).

fof(fact_insort__key__remove1,axiom,
    ! [X2,X200,X13,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_List_Oset(X10),X200)))
       => ( c_List_Olinorder__class_Osorted(X8,hAPP(hAPP(c_List_Omap(X10,X8),X2),X200))
         => ( hAPP(c_List_Ohd(X10),hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBB(X8,tc_HOL_Obool,X10),hAPP(c_fequal,hAPP(X2,X13))),X2)),X200)) = X13
           => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X13),c_List_Oremove1(X10,X13,X200)) = X200 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key__remove1) ).

fof(fact_bij__betw__Disj__Un,axiom,
    ! [X2,X189,X78,X8,X15,X12,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X78),X189) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))
       => ( c_Fun_Obij__betw(X10,X8,X2,X12,X78)
         => ( c_Fun_Obij__betw(X10,X8,X2,X15,X189)
           => c_Fun_Obij__betw(X10,X8,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X78),X189)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__Disj__Un) ).

fof(fact_equiv__intrel__iff,axiom,
    ! [X16,X11] :
      ( 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)),X11),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)),X16),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)),X11),X16)),c_Int_Ointrel)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__intrel__iff) ).

fof(fact_setsum__UNION__zero,axiom,
    ! [X2,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),X28))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),X28))
             => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X3)) )
         => ( ! [X257] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X257),X28))
               => ! [X258] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X258),X28))
                   => ( X257 != X258
                     => ! [X3] :
                          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X257))
                         => ( hBOOL(hAPP(hAPP(c_member(X10),X3),X258))
                           => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X8) ) ) ) ) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X28)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2)),X28) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__UNION__zero) ).

fof(fact_fold__graph_H_Oequations_I1_J,axiom,
    ! [X56,X57,X8,X10] : c_Nitpick_Ofold__graph_H(X10,X8,X57,X56,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X56),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).

fof(fact_fold__graph_H_Ointros_I1_J,axiom,
    ! [X19,X2,X8,X10] : c_Nitpick_Ofold__graph_H(X10,X8,X2,X19,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Ointros_I1_J) ).

fof(fact_map__pair_Oid,axiom,
    ! [X8,X10] : c_Product__Type_Omap__pair(X10,X10,X8,X8,c_Fun_Oid(X10),c_Fun_Oid(X8)) = c_Fun_Oid(tc_prod(X10,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Oid) ).

fof(fact_map__pair_Oidentity,axiom,
    ! [X8,X10] : c_Product__Type_Omap__pair(X10,X10,X8,X8,c_COMBI(X10),c_COMBI(X8)) = c_Fun_Oid(tc_prod(X10,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__pair_Oidentity) ).

fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
    ! [X19,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).

fof(fact_bij__betw__trans,axiom,
    ! [X17,X1,X18,X15,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X15)
     => ( c_Fun_Obij__betw(X8,X18,X1,X15,X17)
       => c_Fun_Obij__betw(X10,X18,hAPP(c_Fun_Ocomp(X8,X18,X10,X1),X2),X12,X17) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__trans) ).

fof(fact_negateSnd__def,axiom,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negateSnd__def) ).

fof(fact_card__Diff1__le,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X10),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff1__le) ).

fof(fact_rel__comp__mono,axiom,
    ! [X116,X191,X18,X110,X162,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X162),X110))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X18),tc_HOL_Obool)),X191),X116))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X18),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X8,X18),X162),X191)),hAPP(hAPP(c_Relation_Orel__comp(X10,X8,X18),X110),X116))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__mono) ).

fof(fact_equiv__class__subset,axiom,
    ! [X14,X13,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__subset) ).

fof(fact_the__inv__into__into,axiom,
    ! [X15,X11,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X8),X11),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
         => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Fun_Othe__inv__into(X10,X8,X12,X2),X11)),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__into) ).

fof(fact_finite__range__imageI,axiom,
    ! [X2,X18,X1,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_Oimage(X8,X10,X1),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X18),hAPP(c_Set_Oimage(X8,X18,hAPP(hAPP(c_COMBB(X10,X18,X8),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_Inter__Un__subset,axiom,
    ! [X15,X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X12)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X15))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__Un__subset) ).

fof(fact_listrel__subset,axiom,
    ! [X12,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel(X10,X110)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olists(X10,X12)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_HOL_Obool),tc_List_Olist(X10)),c_List_Olists(X10,X12))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset) ).

fof(fact_fold__image__reindex,axiom,
    ! [X19,X1,X7,X8,X12,X10,X18] :
      ( class_Groups_Oab__semigroup__mult(X18)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( c_Fun_Oinj__on(X10,X8,X7,X12)
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X18,X8,c_Groups_Otimes__class_Otimes(X18)),X1),X19),hAPP(c_Set_Oimage(X10,X8,X7),X12)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X18,X10,c_Groups_Otimes__class_Otimes(X18)),hAPP(c_Fun_Ocomp(X8,X18,X10,X1),X7)),X19),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__reindex) ).

fof(fact_zmult2__lemma__aux4,axiom,
    ! [X114,X36,X80,X35] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X80))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X80),X36))
         => 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),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X114,X35))),X80)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux4) ).

fof(fact_fold__sup__le__sup,axiom,
    ! [X6,X14,X12,X10] :
      ( class_Lattices_Osemilattice__sup(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X14)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X6),X12)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X14),X6))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__sup__le__sup) ).

fof(fact_min__max_Ofold__sup__le__sup,axiom,
    ! [X6,X14,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X14)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X6),X12)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X14),X6))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__le__sup) ).

fof(fact_bij__betw__combine,axiom,
    ! [X21,X17,X15,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X15)
     => ( c_Fun_Obij__betw(X10,X8,X2,X17,X21)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X15),X21) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))
         => c_Fun_Obij__betw(X10,X8,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X17),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X15),X21)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__combine) ).

fof(fact_listrel1I1,axiom,
    ! [X200,X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X200))),c_List_Olistrel1(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I1) ).

fof(fact_transpose__column,axiom,
    ! [X61,X200,X10] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X200)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X200)))
       => hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,X10),c_List_Onth(X10)),X61)),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),c_List_Otranspose(X10,X200))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X200),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__column) ).

fof(fact_split__paired__Eps,axiom,
    ! [X42,X8,X10] : c_Hilbert__Choice_OEps(tc_prod(X10,X8),X42) = c_Hilbert__Choice_OEps(tc_prod(X10,X8),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_HOL_Obool,X8),X42)),c_Product__Type_OPair(X10,X8)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__Eps) ).

fof(fact_split__paired__The,axiom,
    ! [X42,X8,X10] : c_HOL_OThe(tc_prod(X10,X8),X42) = c_HOL_OThe(tc_prod(X10,X8),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_COMBB(tc_prod(X10,X8),tc_HOL_Obool,X8),X42)),c_Product__Type_OPair(X10,X8)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__The) ).

fof(fact_total__on__def,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Ototal__on(X10,X12,X110)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => ! [X66] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X66),X12))
             => ( X3 != X66
               => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X66)),X110))
                  | hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X66),X3)),X110)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).

fof(fact_mod__lemma,axiom,
    ! [X114,X36,X80,X35] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X35))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X80),X36))
       => 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),X36),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X114,X35))),X80)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__lemma) ).

fof(fact_single__valued__confluent,axiom,
    ! [X19,X16,X11,X110,X10] :
      ( c_Relation_Osingle__valued(X10,X10,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X110)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),c_Transitive__Closure_Ortrancl(X10,X110)))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X19)),c_Transitive__Closure_Ortrancl(X10,X110)))
            | hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X19),X16)),c_Transitive__Closure_Ortrancl(X10,X110))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__confluent) ).

fof(fact_reduction__pairI,axiom,
    ! [X28,X29,X10] :
      ( c_Wellfounded_Owf(X10,X29)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X29),X28)),X29))
       => c_FunDef_Oreduction__pair(X10,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),X28)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reduction__pairI) ).

fof(fact_zmult2__lemma__aux2,axiom,
    ! [X114,X80,X36,X35] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X80))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X80),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),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X114,X35))),X80)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux2) ).

fof(fact_select__def,axiom,
    ! [X200,X10] : c_Random_Oselect(X10,X200) = 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(X10,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(X10)),X200)))),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X10),X200)),c_Code__Numeral_Onat__of))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__def) ).

fof(fact_of__int,axiom,
    ! [X60,X61,X10] :
      ( class_Rings_Oring__1(X10)
     => hAPP(c_Int_Oring__1__class_Oof__int(X10),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),X61),X60)),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(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X61)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X60)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int) ).

fof(fact_diff__single__insert,axiom,
    ! [X15,X11,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X15))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__single__insert) ).

fof(fact_nat,axiom,
    ! [X16,X11] : 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),X11),X16)),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),X11),X16),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat) ).

fof(fact_inj__on__Un,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))
    <=> ( c_Fun_Oinj__on(X10,X8,X2,X12)
        & c_Fun_Oinj__on(X10,X8,X2,X15)
        & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X12))) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Un) ).

fof(fact_in__finite__psubset,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X12),X15)),c_Wellfounded_Ofinite__psubset(X10)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__finite__psubset) ).

fof(fact_Domain__iff,axiom,
    ! [X110,X8,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Relation_ODomain(X10,X8),X110)))
    <=> ? [X51] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X51)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__iff) ).

fof(fact_Un__Pow__subset,axiom,
    ! [X15,X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X12)),hAPP(c_Set_OPow(X10),X15))),hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Pow__subset) ).

fof(fact_o__inv__o__cancel,axiom,
    ! [X1,X18,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(X8,X18,X10,hAPP(c_Fun_Ocomp(X10,X18,X8,X1),c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,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,
    ! [X25,X24,X69,X44,X43] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X43),X44))
     => 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),X44),X69)),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X69)),X25)) = 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),X44),X43)),X69)),X24)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq1) ).

fof(fact_pick__member,axiom,
    ! [X200,X10,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X61),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X10)),X200))))
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Random_Opick(X10,X200),X61)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X10),X10),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X10)),X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick__member) ).

fof(fact_rel__compI,axiom,
    ! [X116,X6,X18,X110,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X110))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X18)),hAPP(hAPP(c_Product__Type_OPair(X8,X18),X14),X6)),X116))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X18)),hAPP(hAPP(c_Product__Type_OPair(X10,X18),X13),X6)),hAPP(hAPP(c_Relation_Orel__comp(X10,X8,X18),X110),X116))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__compI) ).

fof(fact_sorted__insort__insert__key,axiom,
    ! [X11,X200,X2,X8,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))
       => c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_Olinorder__class_Oinsort__insert__key(X8,X10,X2,X11,X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__insert__key) ).

fof(fact_list__all2__append,axiom,
    ! [X222,X223,X42,X199,X8,X200,X10] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)
     => ( c_List_Olist__all2(X10,X8,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X223),hAPP(hAPP(c_List_Oappend(X8),X199),X222))
      <=> ( c_List_Olist__all2(X10,X8,X42,X200,X199)
          & c_List_Olist__all2(X10,X8,X42,X223,X222) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__append) ).

fof(fact_bex__Un,axiom,
    ! [X42,X15,X12,X10] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
          & hBOOL(hAPP(X42,X3)) )
    <=> ( ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
            & hBOOL(hAPP(X42,X3)) )
        | ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X15))
            & hBOOL(hAPP(X42,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__Un) ).

fof(fact_ball__Un,axiom,
    ! [X42,X15,X12,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
         => hBOOL(hAPP(X42,X3)) )
    <=> ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(X42,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X15))
           => hBOOL(hAPP(X42,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__Un) ).

fof(fact_INF2__D,axiom,
    ! [X13,X6,X14,X15,X12,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hBOOL(hAPP(hAPP(hAPP(X15,X13),X14),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF2__D) ).

fof(fact_list__all2__appendI,axiom,
    ! [X20,X6,X14,X13,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X13,X14)
     => ( c_List_Olist__all2(X10,X8,X42,X6,X20)
       => c_List_Olist__all2(X10,X8,X42,hAPP(hAPP(c_List_Oappend(X10),X13),X6),hAPP(hAPP(c_List_Oappend(X8),X14),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,
    ! [X16,X11,X1,X2,X10,X8,X18] : hAPP(c_Fun_Ocomp(X18,X8,X10,X2),c_Fun_Ofun__upd(X10,X18,X1,X11,X16)) = c_Fun_Ofun__upd(X10,X8,hAPP(c_Fun_Ocomp(X18,X8,X10,X2),X1),X11,hAPP(X2,X16)),
    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,
    ! [X15,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),X15) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),X10),c_member(X8)),X2)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__def) ).

fof(fact_zip__append2,axiom,
    ! [X215,X201,X202,X10,X27] : hAPP(hAPP(c_List_Ozip(X27,X10),X202),hAPP(hAPP(c_List_Oappend(X10),X201),X215)) = hAPP(hAPP(c_List_Oappend(tc_prod(X27,X10)),hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Otake(X27),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X201)),X202)),X201)),hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Odrop(X27),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X201)),X202)),X215)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append2) ).

fof(fact_in__listrel1__converse,axiom,
    ! [X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),c_List_Olistrel1(X10,hAPP(c_Relation_Oconverse(X10,X10),X110))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),hAPP(c_Relation_Oconverse(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olistrel1(X10,X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listrel1__converse) ).

fof(fact_Cons__eq__append__conv,axiom,
    ! [X206,X199,X200,X11,X10] :
      ( hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) = hAPP(hAPP(c_List_Oappend(X10),X199),X206)
    <=> ( ( X199 = c_List_Olist_ONil(X10)
          & hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) = X206 )
        | ? [X217] :
            ( hAPP(hAPP(c_List_Olist_OCons(X10),X11),X217) = X199
            & X200 = hAPP(hAPP(c_List_Oappend(X10),X217),X206) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__append__conv) ).

fof(fact_append__eq__Cons__conv,axiom,
    ! [X200,X11,X206,X199,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X199),X206) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)
    <=> ( ( X199 = c_List_Olist_ONil(X10)
          & X206 = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) )
        | ? [X217] :
            ( X199 = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X217)
            & hAPP(hAPP(c_List_Oappend(X10),X217),X206) = X200 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__Cons__conv) ).

fof(fact_inv__into__into,axiom,
    ! [X12,X2,X8,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_Set_Oimage(X8,X10,X2),X12)))
     => hBOOL(hAPP(hAPP(c_member(X8),hAPP(c_Hilbert__Choice_Oinv__into(X8,X10,X12,X2),X11)),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__into) ).

fof(fact_min__max_OSup__fin_Oclosed,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3,X51] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X3),X51)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oclosed) ).

fof(fact_min__max_OInf__fin_Oclosed,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3,X51] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X3),X51)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oclosed) ).

fof(fact_card__SigmaI,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X15,X3))) )
       => hAPP(c_Finite__Set_Ocard(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_Nat_Onat,X10),c_Finite__Set_Ocard(X8)),X15)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__SigmaI) ).

fof(fact_fold__graph_Oequations_I1_J,axiom,
    ! [X19,X2,X8,X10] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).

fof(fact_fold__graph_OemptyI,axiom,
    ! [X19,X2,X8,X10] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OemptyI) ).

fof(fact_wf__union__compatible,axiom,
    ! [X28,X29,X10] :
      ( c_Wellfounded_Owf(X10,X29)
     => ( c_Wellfounded_Owf(X10,X28)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X29),X28)),X29))
         => c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),X28)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__union__compatible) ).

fof(fact_fold1__in,axiom,
    ! [X12,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3,X51] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X3),X51)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X12)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__in) ).

fof(fact_unique__quotient__lemma,axiom,
    ! [X80,X114,X111,X112,X36] :
      ( 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),X36),X112)),X111)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X114)),X80)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X111))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X36))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X80),X36))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X114)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma) ).

fof(fact_unique__quotient__lemma__neg,axiom,
    ! [X80,X114,X111,X112,X36] :
      ( 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),X36),X112)),X111)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X114)),X80)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X80),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X80))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X111))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X112)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient__lemma__neg) ).

fof(fact_distinct__insort__insert,axiom,
    ! [X11,X2,X200,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
       => hBOOL(hAPP(c_List_Odistinct(X10),c_List_Olinorder__class_Oinsort__insert__key(X10,X8,X2,X11,X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insort__insert) ).

fof(fact_nth__transpose,axiom,
    ! [X200,X10,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X200))))
     => hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),c_List_Otranspose(X10,X200)),X61) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_Nat_Onat,X10),c_List_Onth(X10)),X61)),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__transpose) ).

fof(fact_Powp__Pow__eq,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Predicate_OPowp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X11),hAPP(c_Set_OPow(X10),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__Pow__eq) ).

fof(fact_card__bij__eq,axiom,
    ! [X1,X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),X15))
       => ( c_Fun_Oinj__on(X8,X10,X1,X15)
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X1),X15)),X12))
           => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
             => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
               => hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(c_Finite__Set_Ocard(X8),X15) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__bij__eq) ).

fof(fact_Eps__split,axiom,
    ! [X42,X8,X10] : c_Hilbert__Choice_OEps(tc_prod(X10,X8),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),X42)) = c_Hilbert__Choice_OEps(tc_prod(X10,X8),hAPP(hAPP(c_COMBS(tc_prod(X10,X8),X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10,tc_fun(X8,tc_HOL_Obool),tc_prod(X10,X8)),X42),c_Product__Type_Ofst(X10,X8))),c_Product__Type_Osnd(X10,X8))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Eps__split) ).

fof(fact_The__split,axiom,
    ! [X42,X8,X10] : c_HOL_OThe(tc_prod(X10,X8),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),X42)) = c_HOL_OThe(tc_prod(X10,X8),hAPP(hAPP(c_COMBS(tc_prod(X10,X8),X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X10,tc_fun(X8,tc_HOL_Obool),tc_prod(X10,X8)),X42),c_Product__Type_Ofst(X10,X8))),c_Product__Type_Osnd(X10,X8))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_The__split) ).

fof(fact_in__measures_I2_J,axiom,
    ! [X241,X2,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_List_Omeasures(X10,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X10,tc_Nat_Onat)),X2),X241))))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X11)),hAPP(X2,X16)))
        | ( hAPP(X2,X11) = hAPP(X2,X16)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_List_Omeasures(X10,X241))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__measures_I2_J) ).

fof(fact_inf__period_I3_J,axiom,
    ! [X154,X21,X20,X10] :
      ( ( class_Rings_Ocomm__ring(X10)
        & class_Rings_Odvd(X10) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X20),X21))
       => ! [X3,X59] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X3),X154)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X59),X21))),X154))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I3_J) ).

fof(fact_inf__period_I4_J,axiom,
    ! [X154,X21,X20,X10] :
      ( ( class_Rings_Ocomm__ring(X10)
        & class_Rings_Odvd(X10) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X20),X21))
       => ! [X3,X59] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X3),X154)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X20),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X59),X21))),X154))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__period_I4_J) ).

fof(fact_div__mod__equality,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36)),X36)),c_Divides_Odiv__class_Omod(X27,X37,X36))),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality) ).

fof(fact_fun__upd__upd,axiom,
    ! [X19,X16,X11,X2,X8,X10] : c_Fun_Ofun__upd(X10,X8,c_Fun_Ofun__upd(X10,X8,X2,X11,X16),X11,X19) = c_Fun_Ofun__upd(X10,X8,X2,X11,X19),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__upd) ).

fof(fact_fold__Un__disjoint,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),X12)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__Un__disjoint) ).

fof(fact_vimage__subset__eq,axiom,
    ! [X12,X15,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,X2),X15)),X12))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X15),hAPP(c_Set_Oimage(X10,X8,X2),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__subset__eq) ).

fof(fact_uminus__listsum__map,axiom,
    ! [X200,X2,X8,X10] :
      ( class_Groups_Oab__group__add(X10)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))) = hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),hAPP(c_Fun_Ocomp(X10,X10,X8,c_Groups_Ouminus__class_Ouminus(X10)),X2)),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__listsum__map) ).

fof(fact_neg__map__def,axiom,
    ! [X42,X2,X10,X8] : c_New__Random__Sequence_Oneg__map(X8,X10,X2,X42) = c_New__Random__Sequence_Oneg__bind(X8,X10,X42,hAPP(c_Fun_Ocomp(X10,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(X10)))))),X8,c_New__Random__Sequence_Oneg__single(X10)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__map__def) ).

fof(fact_listsp__lists__eq,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_List_Olistsp(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X11),c_List_Olists(X10,X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__lists__eq) ).

fof(fact_setsum__abs__ge__zero,axiom,
    ! [X12,X2,X8,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBB(X10,X10,X8),c_Groups_Oabs__class_Oabs(X10)),X2)),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__abs__ge__zero) ).

fof(fact_finite__Collect__subsets,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__subsets) ).

fof(fact_sum__squares__le__zero__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X16))),c_Groups_Ozero__class_Ozero(X10)))
      <=> ( X11 = c_Groups_Ozero__class_Ozero(X10)
          & X16 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__le__zero__iff) ).

fof(fact_Inf__fin_Oclosed,axiom,
    ! [X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3,X51] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X3),X51)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oclosed) ).

fof(fact_Sup__fin_Oclosed,axiom,
    ! [X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3,X51] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X3),X51)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oclosed) ).

fof(fact_Max_Oclosed,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3,X51] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X3),X51)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olinorder__class_OMax(X10,X12)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oclosed) ).

fof(fact_Min_Oclosed,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3,X51] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X3),X51)),hAPP(hAPP(c_Set_Oinsert(X10),X3),hAPP(hAPP(c_Set_Oinsert(X10),X51),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
           => hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olinorder__class_OMin(X10,X12)),X12)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oclosed) ).

fof(fact_folding__image_Oreindex,axiom,
    ! [X1,X7,X12,X9,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image(X10,X8,X2,X19,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( c_Fun_Oinj__on(X8,X8,X7,X12)
         => hAPP(hAPP(X9,X1),hAPP(c_Set_Oimage(X8,X8,X7),X12)) = hAPP(hAPP(X9,hAPP(c_Fun_Ocomp(X8,X10,X8,X1),X7)),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Oreindex) ).

fof(fact_transpose__column__length,axiom,
    ! [X61,X200,X10] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X200)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),X200)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),hAPP(c_List_Ofilter(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X10)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61)),c_Nat_Osize__class_Osize(tc_List_Olist(X10)))),c_List_Otranspose(X10,X200))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X200),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__column__length) ).

fof(fact_pair__imageI,axiom,
    ! [X2,X18,X12,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X12))
     => hBOOL(hAPP(hAPP(c_member(X18),hAPP(hAPP(X2,X13),X14)),hAPP(c_Set_Oimage(tc_prod(X10,X8),X18,hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),X2)),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__imageI) ).

fof(fact_length__filter__map,axiom,
    ! [X200,X2,X8,X42,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(c_List_Ofilter(X8,hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,X8,X42),X2)),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__map) ).

fof(fact_trancl__subset__Sigma__aux,axiom,
    ! [X12,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12))))
       => ( X13 = X14
          | hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__subset__Sigma__aux) ).

fof(fact_sum__length__filter__compl,axiom,
    ! [X200,X42,X10] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X42),X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X42)),X200))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__length__filter__compl) ).

fof(fact_rtrancl__trans,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),c_Transitive__Closure_Ortrancl(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Ortrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__trans) ).

fof(fact_zdiv__zadd1__eq,axiom,
    ! [X35,X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),X36)),X35) = 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),X37),X35)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X36),X35))),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,X37,X35)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X35))),X35)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zadd1__eq) ).

fof(fact_div__add1__eq,axiom,
    ! [X35,X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X37),X36)),X35) = 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),X37),X35)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X35))),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,X37,X35)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X35))),X35)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add1__eq) ).

fof(fact_inf2D1,axiom,
    ! [X16,X11,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16))
     => hBOOL(hAPP(hAPP(X12,X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D1) ).

fof(fact_inf2D2,axiom,
    ! [X16,X11,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16))
     => hBOOL(hAPP(hAPP(X15,X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2D2) ).

fof(fact_length__takeWhile__less__P__nth,axiom,
    ! [X200,X10,X42,X60] :
      ( ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),X60))
         => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X91))) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X60),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X60),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__less__P__nth) ).

fof(fact_converse__rtrancl__into__rtrancl,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),c_Transitive__Closure_Ortrancl(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Ortrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).

fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [X6,X110,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Transitive__Closure_Ortrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),X110))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),c_Transitive__Closure_Ortrancl(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).

fof(fact_rtrancl__listrel1__if__listrel,axiom,
    ! [X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel(X10,X110)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).

fof(fact_folding_Ocommute__comps_I1_J,axiom,
    ! [X7,X1,X115,X2,X18,X102,X104,X9,X95,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X95,X9)
     => hAPP(c_Fun_Ocomp(X104,X102,X18,X2),hAPP(c_Fun_Ocomp(X115,X104,X18,X1),X7)) = hAPP(c_Fun_Ocomp(X115,X102,X18,hAPP(c_Fun_Ocomp(X104,X102,X115,X2),X1)),X7) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comps_I1_J) ).

fof(fact_zdiv__mono2__neg__lemma,axiom,
    ! [X111,X112,X113,X80,X114,X36] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X114)),X80) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X113),X112)),X111)
     => ( 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),X113),X112)),X111)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X80),X36))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X111))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X113))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X36))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),X114)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [X42] : 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)))),X42)) = 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),X42),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,
    ! [X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).

fof(fact_lexord__lex,axiom,
    ! [X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),c_List_Olex(X10,X110)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),c_List_Olexord(X10,X110)))
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X11) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__lex) ).

fof(fact_filter__map,axiom,
    ! [X200,X2,X8,X42,X10] : hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(c_List_Ofilter(X8,hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,X8,X42),X2)),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__map) ).

fof(fact_wfP__SUP,axiom,
    ! [X10,X110,X8] :
      ( ! [X91] : c_Wellfounded_OwfP(X8,hAPP(X110,X91))
     => ( ! [X91,X73] :
            ( hAPP(X110,X91) != hAPP(X110,X73)
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),c_Predicate_ODomainP(X8,X8,hAPP(X110,X91))),c_Predicate_ORangeP(X8,X8,hAPP(X110,X73))) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) )
       => c_Wellfounded_OwfP(X8,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_fun(X8,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__SUP) ).

fof(fact_partition__filter__conv,axiom,
    ! [X200,X2,X10] : c_List_Opartition(X10,X2,X200) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X2),X200)),hAPP(c_List_Ofilter(X10,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X10,c_fNot),X2)),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter__conv) ).

fof(fact_upto_Opinduct,axiom,
    ! [X42,X57,X152] :
      ( 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),X152),X57)))
     => ( ! [X91,X73] :
            ( 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),X91),X73)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X91),X73))
               => hBOOL(hAPP(hAPP(X42,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X91),c_Groups_Oone__class_Oone(tc_Int_Oint))),X73)) )
             => hBOOL(hAPP(hAPP(X42,X91),X73)) ) )
       => hBOOL(hAPP(hAPP(X42,X152),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto_Opinduct) ).

fof(fact_list__all2__map1,axiom,
    ! [X235,X230,X2,X18,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,hAPP(hAPP(c_List_Omap(X18,X10),X2),X230),X235)
    <=> c_List_Olist__all2(X18,X8,hAPP(hAPP(c_COMBB(X10,tc_fun(X8,tc_HOL_Obool),X18),X42),X2),X230,X235) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__map1) ).

fof(fact_measures__lesseq,axiom,
    ! [X241,X10,X16,X11,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X11)),hAPP(X2,X16)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_List_Omeasures(X10,X241)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_List_Omeasures(X10,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X10,tc_Nat_Onat)),X2),X241)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measures__lesseq) ).

fof(fact_transD,axiom,
    ! [X6,X14,X13,X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X6)),X110))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X6)),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transD) ).

fof(fact_trans__def,axiom,
    ! [X110,X10] :
      ( c_Relation_Otrans(X10,X110)
    <=> ! [X3,X51] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X51)),X110))
         => ! [X177] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X177)),X110))
             => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X177)),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__def) ).

fof(fact_Ints__odd__less__0,axiom,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Int_Oring__1__class_OInts(X10)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),X13)),X13)),c_Groups_Ozero__class_Ozero(X10)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__less__0) ).

fof(fact_zdiv__zmod__equality2,axiom,
    ! [X33,X36,X37] : 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),X37),X36)),X36)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36))),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality2) ).

fof(fact_INFI__set__fold,axiom,
    ! [X2,X200,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,X10),hAPP(c_List_Oset(X8),X200)),X2) = hAPP(c_List_Ofoldl(X10,X8,hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Lattices_Osemilattice__inf__class_Oinf(X10)),X2)),c_Orderings_Otop__class_Otop(X10)),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__set__fold) ).

fof(fact_SUPR__set__fold,axiom,
    ! [X2,X200,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X10),hAPP(c_List_Oset(X8),X200)),X2) = hAPP(c_List_Ofoldl(X10,X8,hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),c_Lattices_Osemilattice__sup__class_Osup(X10)),X2)),c_Orderings_Obot__class_Obot(X10)),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__set__fold) ).

fof(fact_finite__UN__I,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ! [X46] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X46),X12))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X15,X46))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UN__I) ).

fof(fact_finite__UN,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X15,X3))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UN) ).

fof(fact_rel__comp__UNION__distrib,axiom,
    ! [X110,X161,X102,X116,X8,X18,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X116),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X102,tc_fun(tc_prod(X18,X8),tc_HOL_Obool)),X161),X110)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X102,tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X161),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X18,X8),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool),X102),hAPP(c_Relation_Orel__comp(X10,X18,X8),X116)),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__UNION__distrib) ).

fof(fact_o__assoc,axiom,
    ! [X7,X1,X102,X2,X10,X8,X18] : hAPP(c_Fun_Ocomp(X18,X8,X10,X2),hAPP(c_Fun_Ocomp(X102,X18,X10,X1),X7)) = hAPP(c_Fun_Ocomp(X102,X8,X10,hAPP(c_Fun_Ocomp(X18,X8,X102,X2),X1)),X7),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__assoc) ).

fof(fact_surj__Compl__image__subset,axiom,
    ! [X12,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X2),X12))),hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__Compl__image__subset) ).

fof(fact_bij__image__INT,axiom,
    ! [X15,X12,X18,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X18),c_Set_Oimage(X10,X8,X2)),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__image__INT) ).

fof(fact_in__inv__image,axiom,
    ! [X2,X110,X8,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),hAPP(hAPP(c_Relation_Oinv__image(X8,X10),X110),X2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),hAPP(X2,X11)),hAPP(X2,X16))),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__inv__image) ).

fof(fact_sym__trans__comp__subset,axiom,
    ! [X110,X10] :
      ( c_Relation_Osym(X10,X110)
     => ( c_Relation_Otrans(X10,X110)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Relation_Oconverse(X10,X10),X110)),X110)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__trans__comp__subset) ).

fof(fact_folding_Oremove,axiom,
    ! [X11,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(X9,X12) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(X2,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oremove) ).

fof(fact_Image__subset,axiom,
    ! [X17,X15,X12,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15))))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X8,X110),X17)),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__subset) ).

fof(fact_tl__append,axiom,
    ! [X199,X200,X10] : hAPP(c_List_Otl(X10),hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X10),X10,hAPP(c_List_Otl(X10),X199),hAPP(c_COMBK(tc_fun(tc_List_Olist(X10),tc_List_Olist(X10)),X10),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Oappend(X10)),X199))),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__append) ).

fof(fact_pos__map__def,axiom,
    ! [X42,X2,X10,X8] : c_New__Random__Sequence_Opos__map(X8,X10,X2,X42) = c_New__Random__Sequence_Opos__bind(X8,X10,X42,hAPP(c_Fun_Ocomp(X10,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(X10))))),X8,c_New__Random__Sequence_Opos__single(X10)),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__map__def) ).

fof(fact_inj__image__Compl__subset,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__Compl__subset) ).

fof(fact_bij__imp__bij__inv,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => c_Fun_Obij__betw(X8,X10,c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__imp__bij__inv) ).

fof(fact_folding_Oinsert__remove,axiom,
    ! [X11,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),hAPP(X2,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oinsert__remove) ).

fof(fact_list__all2__update__cong2,axiom,
    ! [X61,X16,X11,X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X200,X199)
     => ( hBOOL(hAPP(hAPP(X42,X11),X16))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)))
         => c_List_Olist__all2(X10,X8,X42,hAPP(hAPP(c_List_Olist__update(X10,X200),X61),X11),hAPP(hAPP(c_List_Olist__update(X8,X199),X61),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__update__cong2) ).

fof(fact_list__all2__update__cong,axiom,
    ! [X16,X11,X199,X42,X8,X200,X10,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => ( c_List_Olist__all2(X10,X8,X42,X200,X199)
       => ( hBOOL(hAPP(hAPP(X42,X11),X16))
         => c_List_Olist__all2(X10,X8,X42,hAPP(hAPP(c_List_Olist__update(X10,X200),X61),X11),hAPP(hAPP(c_List_Olist__update(X8,X199),X61),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__update__cong) ).

fof(fact_bij__image__Collect__eq,axiom,
    ! [X42,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X10,X8,X2),hAPP(c_Set_OCollect(X10),X42)) = hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBB(X10,tc_HOL_Obool,X8),X42),c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__image__Collect__eq) ).

fof(fact_setprod__pos,axiom,
    ! [X2,X12,X10,X8] :
      ( class_Rings_Olinordered__semidom(X8)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__pos) ).

fof(fact_setprod__nonneg,axiom,
    ! [X2,X12,X10,X8] :
      ( class_Rings_Olinordered__semidom(X8)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(X2,X3))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__nonneg) ).

fof(fact_converse__pred__comp,axiom,
    ! [X116,X110,X18,X10,X8] : c_Predicate_Oconversep(X8,X10,c_Predicate_Opred__comp(X8,X18,X10,X110,X116)) = c_Predicate_Opred__comp(X10,X18,X8,c_Predicate_Oconversep(X18,X10,X116),c_Predicate_Oconversep(X8,X18,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__pred__comp) ).

fof(fact_folding_Ocommute__left__comp_H_H,axiom,
    ! [X1,X18,X15,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X9,X15)),hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X9,X12)),X1)) = hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X9,X12)),hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X9,X15)),X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).

fof(fact_inv__def,axiom,
    ! [X16,X2,X8,X10] : hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),X16) = c_Hilbert__Choice_OEps(X10,hAPP(hAPP(c_COMBC(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_fequal),X2)),X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__def) ).

fof(fact_finite__SigmaI,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ! [X46] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X46),X12))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X15,X46))) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__SigmaI) ).

fof(fact_convex__bound__lt,axiom,
    ! [X68,X69,X34,X37,X26,X27] :
      ( class_Rings_Olinordered__semiring__1__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X37))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X69))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X68))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X69),X68) = c_Groups_Oone__class_Oone(X27)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X69),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X68),X34))),X37)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__lt) ).

fof(fact_convex__bound__le,axiom,
    ! [X68,X69,X34,X37,X26,X27] :
      ( class_Rings_Olinordered__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X37))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X69))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X68))
             => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X69),X68) = c_Groups_Oone__class_Oone(X27)
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X69),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X68),X34))),X37)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_convex__bound__le) ).

fof(fact_aset_I6_J,axiom,
    ! [X12,X154,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X154),c_Groups_Oone__class_Oone(tc_Int_Oint))),X12))
       => ! [X3] :
            ( ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
               => ! [X163] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X12))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X163),X66) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X154))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X21)),X154)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I6_J) ).

fof(fact_lazy__sequence_Orecs_I2_J,axiom,
    ! [X256,X13,X49,X50,X8,X10] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X10,X8,X50,X49,c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X13,X256)) = hAPP(hAPP(hAPP(X49,X13),X256),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X10,X8,X50,X49,X256)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Orecs_I2_J) ).

fof(fact_max__extp_Ointros,axiom,
    ! [X29,X65,X48,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X48))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X65))
       => ( X65 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X48))
               => ? [X66] :
                    ( hBOOL(hAPP(hAPP(c_member(X10),X66),X65))
                    & hBOOL(hAPP(hAPP(X29,X3),X66)) ) )
           => c_Wellfounded_Omax__extp(X10,X29,X48,X65) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Ointros) ).

fof(fact_folding_Ocommute__left__comp_H,axiom,
    ! [X1,X11,X18,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X11)),hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X9,X12)),X1)) = hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X9,X12)),hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X11)),X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).

fof(fact_listrel1I,axiom,
    ! [X199,X222,X223,X200,X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
     => ( X200 = hAPP(hAPP(c_List_Oappend(X10),X223),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X222))
       => ( X199 = hAPP(hAPP(c_List_Oappend(X10),X223),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X222))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1I) ).

fof(fact_bex__reg__right,axiom,
    ! [X42,X41,X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => ( ! [X3] :
            ( hBOOL(hAPP(X41,X3))
           => hBOOL(hAPP(X42,X3)) )
       => ( ? [X136] : hBOOL(hAPP(X41,X136))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),c_Quotient_ORespects(X10,X29)))
              & hBOOL(hAPP(X42,X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__reg__right) ).

fof(fact_all__nth__imp__all__set,axiom,
    ! [X11,X42,X200,X10] :
      ( ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
         => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X91))) )
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => hBOOL(hAPP(X42,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nth__imp__all__set) ).

fof(fact_inf__le__fold__inf,axiom,
    ! [X6,X14,X12,X10] :
      ( class_Lattices_Osemilattice__inf(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X3)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X14),X6)),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X6),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le__fold__inf) ).

fof(fact_min__max_Oinf__le__fold__inf,axiom,
    ! [X6,X14,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X3)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X14),X6)),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X6),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le__fold__inf) ).

fof(fact_setsum__shift__bounds__nat__ivl,axiom,
    ! [X30,X32,X31,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X32))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X32))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__nat__ivl) ).

fof(fact_bij__betw__subset,axiom,
    ! [X189,X15,X78,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X78)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
       => ( hAPP(c_Set_Oimage(X10,X8,X2),X15) = X189
         => c_Fun_Obij__betw(X10,X8,X2,X15,X189) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__subset) ).

fof(fact_in__rtrancl__UnI,axiom,
    ! [X28,X29,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X11),c_Transitive__Closure_Ortrancl(X10,X29)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X11),c_Transitive__Closure_Ortrancl(X10,X28))) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X11),c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),X28)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).

fof(fact_folding_Ocommute__left__comp,axiom,
    ! [X1,X11,X16,X18,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X16)),hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X11)),X1)) = hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X11)),hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X16)),X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__left__comp) ).

fof(fact_range__ex1__eq,axiom,
    ! [X14,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(c_Set_Oimage(X10,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))))
      <=> ? [X3] :
            ( X14 = hAPP(X2,X3)
            & ! [X51] :
                ( X14 = hAPP(X2,X51)
               => X51 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__ex1__eq) ).

fof(fact_setsum__Un,axiom,
    ! [X2,X15,X12,X10,X8] :
      ( class_Groups_Oab__group__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X15))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un) ).

fof(fact_rev__update,axiom,
    ! [X34,X202,X27,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(c_List_Orev(X27),hAPP(hAPP(c_List_Olist__update(X27,X202),X33),X34)) = hAPP(hAPP(c_List_Olist__update(X27,hAPP(c_List_Orev(X27),X202)),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(X27)),X202)),X33)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__update) ).

fof(fact_equiv__imp__dvd__card,axiom,
    ! [X32,X110,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( c_Equiv__Relations_Oequiv(X10,X12,X110)
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
             => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),hAPP(c_Finite__Set_Ocard(X10),X3))) )
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),hAPP(c_Finite__Set_Ocard(X10),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__imp__dvd__card) ).

fof(fact_Collect__imp__eq,axiom,
    ! [X41,X42,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fimplies),X42)),X41)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X42))),hAPP(c_Set_OCollect(X10),X41)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__imp__eq) ).

fof(fact_single__valued__def,axiom,
    ! [X110,X8,X10] :
      ( c_Relation_Osingle__valued(X10,X8,X110)
    <=> ! [X3,X51] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X3),X51)),X110))
         => ! [X177] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X3),X177)),X110))
             => X51 = X177 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).

fof(fact_prod__size__simp,axiom,
    ! [X148,X1,X2,X8,X10] : c_Product__Type_Oprod_Oprod__size(X10,X8,X2,X1,X148) = 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(X10,X8),X148))),hAPP(X1,hAPP(c_Product__Type_Osnd(X10,X8),X148)))),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,
    ! [X30,X32,X31,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X32))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X32))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__nat__ivl) ).

fof(fact_bset_I8_J,axiom,
    ! [X15,X154,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X154),c_Groups_Oone__class_Oone(tc_Int_Oint))),X15))
       => ! [X3] :
            ( ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
               => ! [X163] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X15))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X163),X66) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X154),X3))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X154),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X21))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I8_J) ).

fof(fact_finite__equiv__class,axiom,
    ! [X48,X110,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12))))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
         => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X48)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__equiv__class) ).

fof(fact_quotient__eqI,axiom,
    ! [X16,X11,X65,X48,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X65),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
         => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X48))
           => ( hBOOL(hAPP(hAPP(c_member(X10),X16),X65))
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
               => X48 = X65 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__eqI) ).

fof(fact_quotient__eq__iff,axiom,
    ! [X16,X11,X65,X48,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X65),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
         => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X48))
           => ( hBOOL(hAPP(hAPP(c_member(X10),X16),X65))
             => ( X48 = X65
              <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).

fof(fact_field__le__mult__one__interval,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field__inverse__zero(X27)
     => ( ! [X177] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X177))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X177),c_Groups_Oone__class_Oone(X27)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X177),X26)),X34)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__mult__one__interval) ).

fof(fact_eq__comp__r,axiom,
    ! [X29,X10] : c_Predicate_Opred__comp(X10,X10,X10,c_fequal,c_Predicate_Opred__comp(X10,X10,X10,X29,c_fequal)) = X29,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__comp__r) ).

fof(fact_curryE,axiom,
    ! [X14,X13,X2,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X10,X8,tc_HOL_Obool,X2),X13),X14))
     => hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryE) ).

fof(fact_curryD,axiom,
    ! [X14,X13,X2,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X10,X8,tc_HOL_Obool,X2),X13),X14))
     => hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryD) ).

fof(fact_vimage__eq__UN,axiom,
    ! [X15,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),c_Set_Ovimage(X10,X8,X2)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),c_Set_Oinsert(X8)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq__UN) ).

fof(fact_Image__eq__UN,axiom,
    ! [X15,X110,X10,X8] : hAPP(c_Relation_OImage(X8,X10,X110),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),c_Relation_OImage(X8,X10,X110)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),c_Set_Oinsert(X8)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__eq__UN) ).

fof(fact_distrib__inf__le,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X38))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X38)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distrib__inf__le) ).

fof(fact_min__max_Odistrib__inf__le,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X38))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),X38)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Odistrib__inf__le) ).

fof(fact_bij__betw__inv__into,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X15)
     => c_Fun_Obij__betw(X8,X10,c_Hilbert__Choice_Oinv__into(X10,X8,X12,X2),X15,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__inv__into) ).

fof(fact_bij__betw__the__inv__into,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X15)
     => c_Fun_Obij__betw(X8,X10,c_Fun_Othe__inv__into(X10,X8,X12,X2),X15,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__the__inv__into) ).

fof(fact_inv__into__inv__into__eq,axiom,
    ! [X13,X78,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X78)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(c_Hilbert__Choice_Oinv__into(X8,X10,X78,c_Hilbert__Choice_Oinv__into(X10,X8,X12,X2)),X13) = hAPP(X2,X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__inv__into__eq) ).

fof(fact_SUP2__I,axiom,
    ! [X18,X8,X6,X14,X15,X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => ( hBOOL(hAPP(hAPP(hAPP(X15,X13),X14),X6))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP2__I) ).

fof(fact_splitD_H,axiom,
    ! [X6,X14,X13,X29,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_fun(X18,tc_HOL_Obool)),X29),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X6))
     => hBOOL(hAPP(hAPP(hAPP(X29,X13),X14),X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD_H) ).

fof(fact_rel__comp__distrib2,axiom,
    ! [X29,X160,X28,X8,X18,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X18),tc_HOL_Obool)),X28),X160)),X29) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X28),X29)),hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X160),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__distrib2) ).

fof(fact_inf__INFI__fold__inf,axiom,
    ! [X2,X15,X12,X10,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X15),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X8),X12),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,X8),X10),c_Lattices_Osemilattice__inf__class_Oinf(X8)),X2)),X15),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__INFI__fold__inf) ).

fof(fact_sup__SUPR__fold__sup,axiom,
    ! [X2,X15,X12,X10,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X15),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X8),X12),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,X8),X10),c_Lattices_Osemilattice__sup__class_Osup(X8)),X2)),X15),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__SUPR__fold__sup) ).

fof(fact_setsum__Un__nat,axiom,
    ! [X2,X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = 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(X10,tc_Nat_Onat),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X15))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__nat) ).

fof(fact_finite__Collect__not,axiom,
    ! [X42,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),X42)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X42))))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__not) ).

fof(fact_bij__vimage__eq__inv__image,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(X10,X8,X2),X12) = hAPP(c_Set_Oimage(X8,X10,c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__vimage__eq__inv__image) ).

fof(fact_zmult2__lemma__aux1,axiom,
    ! [X114,X80,X36,X35] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X80))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X80),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),X36),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X114,X35))),X80))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux1) ).

fof(fact_nat__diff__add__eq2,axiom,
    ! [X25,X24,X69,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => 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),X44),X69)),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X69)),X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),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),X43),X44)),X69)),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__add__eq2) ).

fof(fact_abs__setsum__abs,axiom,
    ! [X12,X2,X8,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => hAPP(c_Groups_Oabs__class_Oabs(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBB(X10,X10,X8),c_Groups_Oabs__class_Oabs(X10)),X2)),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBB(X10,X10,X8),c_Groups_Oabs__class_Oabs(X10)),X2)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__setsum__abs) ).

fof(fact_inj__image__subset__iff,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),hAPP(c_Set_Oimage(X10,X8,X2),X15)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__subset__iff) ).

fof(fact_gt__half__sum,axiom,
    ! [X36,X37,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Oone__class_Oone(X27)))),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gt__half__sum) ).

fof(fact_inv__into__injective,axiom,
    ! [X16,X11,X2,X12,X8,X10] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,X12,X2),X11) = hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,X12,X2),X16)
     => ( hBOOL(hAPP(hAPP(c_member(X8),X11),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => ( hBOOL(hAPP(hAPP(c_member(X8),X16),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
         => X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__injective) ).

fof(fact_list__all2__Cons,axiom,
    ! [X199,X16,X200,X11,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200),hAPP(hAPP(c_List_Olist_OCons(X8),X16),X199))
    <=> ( hBOOL(hAPP(hAPP(X42,X11),X16))
        & c_List_Olist__all2(X10,X8,X42,X200,X199) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Cons) ).

fof(fact_q__neg__lemma,axiom,
    ! [X111,X112,X113] :
      ( 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),X113),X112)),X111)),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)),X111))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X113))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X112),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__neg__lemma) ).

fof(fact_zip__same,axiom,
    ! [X200,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),hAPP(c_List_Oset(tc_prod(X10,X10)),hAPP(hAPP(c_List_Ozip(X10,X10),X200),X200))))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_List_Oset(X10),X200)))
        & X13 = X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__same) ).

fof(fact_set__zip__leftD,axiom,
    ! [X199,X200,X16,X11,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),hAPP(c_List_Oset(tc_prod(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199))))
     => hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip__leftD) ).

fof(fact_set__zip__rightD,axiom,
    ! [X199,X200,X16,X11,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),hAPP(c_List_Oset(tc_prod(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199))))
     => hBOOL(hAPP(hAPP(c_member(X8),X16),hAPP(c_List_Oset(X8),X199))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__zip__rightD) ).

fof(fact_folding_Ounion__inter,axiom,
    ! [X15,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ounion__inter) ).

fof(fact_abs__triangle__ineq3,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)))),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq3) ).

fof(fact_odd__less__0,axiom,
    ! [X19] :
      ( 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)),X19)),X19)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19),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,X12,X10,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X8),X12),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,X8),X10),c_Lattices_Osemilattice__inf__class_Oinf(X8)),X2)),c_Orderings_Otop__class_Otop(X8)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__fold__inf) ).

fof(fact_SUPR__fold__sup,axiom,
    ! [X2,X12,X10,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X8),X12),X2) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,hAPP(hAPP(c_COMBB(X8,tc_fun(X8,X8),X10),c_Lattices_Osemilattice__sup__class_Osup(X8)),X2)),c_Orderings_Obot__class_Obot(X8)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__fold__sup) ).

fof(fact_single__valuedD,axiom,
    ! [X19,X16,X11,X110,X8,X10] :
      ( c_Relation_Osingle__valued(X10,X8,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),X110))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X19)),X110))
         => X16 = X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valuedD) ).

fof(fact_Collect__disj__eq,axiom,
    ! [X41,X42,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),X42)),X41)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X42)),hAPP(c_Set_OCollect(X10),X41)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__disj__eq) ).

fof(fact_Collect__conj__eq,axiom,
    ! [X41,X42,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),X42)),X41)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X42)),hAPP(c_Set_OCollect(X10),X41)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__conj__eq) ).

fof(fact_list__all2__dropI,axiom,
    ! [X30,X235,X230,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X230,X235)
     => c_List_Olist__all2(X10,X8,X42,hAPP(hAPP(c_List_Odrop(X10),X30),X230),hAPP(hAPP(c_List_Odrop(X8),X30),X235)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__dropI) ).

fof(fact_list__all2__takeI,axiom,
    ! [X30,X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X200,X199)
     => c_List_Olist__all2(X10,X8,X42,hAPP(hAPP(c_List_Otake(X10),X30),X200),hAPP(hAPP(c_List_Otake(X8),X30),X199)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__takeI) ).

fof(fact_rtrancl__converseD,axiom,
    ! [X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X110))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X11)),c_Transitive__Closure_Ortrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).

fof(fact_antisymD,axiom,
    ! [X14,X13,X110,X10] :
      ( c_Relation_Oantisym(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
       => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X13)),X110))
         => X13 = X14 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisymD) ).

fof(fact_antisym__def,axiom,
    ! [X110,X10] :
      ( c_Relation_Oantisym(X10,X110)
    <=> ! [X3,X51] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X51)),X110))
         => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X3)),X110))
           => X3 = X51 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__def) ).

fof(fact_listsum__const__mult,axiom,
    ! [X200,X2,X6,X8,X10] :
      ( class_Rings_Osemiring__0(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),hAPP(hAPP(c_COMBB(X10,X10,X8),hAPP(c_Groups_Otimes__class_Otimes(X10),X6)),X2)),X200)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__const__mult) ).

fof(fact_Image__mono,axiom,
    ! [X12,X78,X110,X162,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X162),X110))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X78),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X8,X162),X78)),hAPP(c_Relation_OImage(X10,X8,X110),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__mono) ).

fof(fact_mlex__leq,axiom,
    ! [X29,X10,X16,X11,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X2,X11)),hAPP(X2,X16)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X29))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Wellfounded_Omlex__prod(X10,X2,X29))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__leq) ).

fof(fact_swap__product,axiom,
    ! [X15,X12,X10,X8] : hAPP(c_Set_Oimage(tc_prod(X8,X10),tc_prod(X10,X8),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X10,tc_prod(X10,X8)),hAPP(c_COMBC(X10,X8,tc_prod(X10,X8)),c_Product__Type_OPair(X10,X8)))),hAPP(hAPP(c_Product__Type_OSigma(X8,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X8),X15))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X15),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__product) ).

fof(fact_quotientI,axiom,
    ! [X110,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotientI) ).

fof(fact_Image__singleton__iff,axiom,
    ! [X13,X110,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(c_Relation_OImage(X8,X10,X110),hAPP(hAPP(c_Set_Oinsert(X8),X13),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X13),X14)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).

fof(fact_list__all2__rev,axiom,
    ! [X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,hAPP(c_List_Orev(X10),X200),hAPP(c_List_Orev(X8),X199))
    <=> c_List_Olist__all2(X10,X8,X42,X200,X199) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__rev) ).

fof(fact_norm__frac_Opinduct,axiom,
    ! [X42,X57,X152] :
      ( 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),X152),X57)))
     => ( ! [X46,X81] :
            ( 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),X46),X81)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X81),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
               => hBOOL(hAPP(hAPP(X42,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X46)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X81))) )
             => hBOOL(hAPP(hAPP(X42,X46),X81)) ) )
       => hBOOL(hAPP(hAPP(X42,X152),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_norm__frac_Opinduct) ).

fof(fact_aset_I5_J,axiom,
    ! [X12,X154,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X154),X12))
       => ! [X3] :
            ( ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
               => ! [X163] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X12))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X163),X66) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X154))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X21)),X154)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I5_J) ).

fof(fact_div__mod__equality2,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36))),c_Divides_Odiv__class_Omod(X27,X37,X36))),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality2) ).

fof(fact_list__all2__rev1,axiom,
    ! [X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,hAPP(c_List_Orev(X10),X200),X199)
    <=> c_List_Olist__all2(X10,X8,X42,X200,hAPP(c_List_Orev(X8),X199)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__rev1) ).

fof(fact_lexord__Nil__left,axiom,
    ! [X110,X16,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X16)),c_List_Olexord(X10,X110)))
    <=> ? [X46,X3] : X16 = hAPP(hAPP(c_List_Olist_OCons(X10),X46),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__Nil__left) ).

fof(fact_image__vimage__subset,axiom,
    ! [X12,X2,X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_Set_Ovimage(X8,X10,X2),X12))),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__vimage__subset) ).

fof(fact_map__sorted__distinct__set__unique,axiom,
    ! [X199,X200,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(c_List_Oset(X10),X199)))
       => ( c_List_Olinorder__class_Osorted(X8,hAPP(hAPP(c_List_Omap(X10,X8),X2),X200))
         => ( hBOOL(hAPP(c_List_Odistinct(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)))
           => ( c_List_Olinorder__class_Osorted(X8,hAPP(hAPP(c_List_Omap(X10,X8),X2),X199))
             => ( hBOOL(hAPP(c_List_Odistinct(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X199)))
               => ( hAPP(c_List_Oset(X10),X200) = hAPP(c_List_Oset(X10),X199)
                 => X200 = X199 ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__sorted__distinct__set__unique) ).

fof(fact_zmult2__lemma__aux3,axiom,
    ! [X114,X36,X80,X35] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X80))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X80),X36))
         => 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),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X114,X35))),X80))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult2__lemma__aux3) ).

fof(fact_finite__quotient,axiom,
    ! [X110,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__quotient) ).

fof(fact_foldl__append,axiom,
    ! [X199,X200,X13,X2,X8,X10] : hAPP(c_List_Ofoldl(X10,X8,X2,X13),hAPP(hAPP(c_List_Oappend(X8),X200),X199)) = hAPP(c_List_Ofoldl(X10,X8,X2,hAPP(c_List_Ofoldl(X10,X8,X2,X13),X200)),X199),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__append) ).

fof(fact_rtrancl__converseI,axiom,
    ! [X110,X11,X16,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X11)),c_Transitive__Closure_Ortrancl(X10,X110)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).

fof(fact_zip__append1,axiom,
    ! [X215,X201,X202,X10,X27] : hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X215) = hAPP(hAPP(c_List_Oappend(tc_prod(X27,X10)),hAPP(hAPP(c_List_Ozip(X27,X10),X202),hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X215))),hAPP(hAPP(c_List_Ozip(X27,X10),X201),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X215))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append1) ).

fof(fact_Diff__subset__conv,axiom,
    ! [X17,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X17))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).

fof(fact_image__surj__f__inv__f,axiom,
    ! [X12,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_Set_Oimage(X10,X8,c_Hilbert__Choice_Oinv__into(X8,X10,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),X2)),X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__surj__f__inv__f) ).

fof(fact_bset_I5_J,axiom,
    ! [X154,X15,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ! [X3] :
          ( ! [X66] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
             => ! [X163] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X15))
                 => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X163),X66) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X3),X154))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X21)),X154)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I5_J) ).

fof(fact_bset_I6_J,axiom,
    ! [X154,X15,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ! [X3] :
          ( ! [X66] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
             => ! [X163] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X15))
                 => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X163),X66) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X3),X154))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X21)),X154)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I6_J) ).

fof(fact_setprod__Un__Int,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__Int) ).

fof(fact_setprod_Ounion__inter,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__inter) ).

fof(fact_setsum__Un__Int,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__Int) ).

fof(fact_inf2I,axiom,
    ! [X8,X10,X15,X16,X11,X12] :
      ( hBOOL(hAPP(hAPP(X12,X11),X16))
     => ( hBOOL(hAPP(hAPP(X15,X11),X16))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf2I) ).

fof(fact_vimage__subsetD,axiom,
    ! [X12,X15,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X8,X10,X2),X15)),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(c_Set_Oimage(X8,X10,X2),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__subsetD) ).

fof(fact_bset_I7_J,axiom,
    ! [X15,X154,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X154),X15))
       => ! [X3] :
            ( ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
               => ! [X163] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X15))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X163),X66) ) )
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X154),X3))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X154),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X21))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I7_J) ).

fof(fact_zdiv__mono2__lemma,axiom,
    ! [X111,X112,X113,X80,X114,X36] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X114)),X80) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X113),X112)),X111)
     => ( 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),X113),X112)),X111)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X113))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X80))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X113))
             => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X36))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),X112)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__lemma) ).

fof(fact_converse__INTER,axiom,
    ! [X110,X28,X18,X10,X8] : hAPP(c_Relation_Oconverse(X8,X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),X28),X110)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X28),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool),X18),c_Relation_Oconverse(X8,X10)),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__INTER) ).

fof(fact_converse__UNION,axiom,
    ! [X110,X28,X18,X10,X8] : hAPP(c_Relation_Oconverse(X8,X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),X28),X110)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X28),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool),X18),c_Relation_Oconverse(X8,X10)),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__UNION) ).

fof(fact_eq__Abs__Integ,axiom,
    ! [X19] :
      ~ ! [X3,X51] : X19 != 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),X51)),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,
    ! [X12,X2,X8,X19,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X19),hAPP(c_Set_Oimage(X8,X10,X2),X12)))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
          & X19 = hAPP(X2,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).

fof(fact_eq__equiv__class__iff2,axiom,
    ! [X16,X11,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X16),X12))
         => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X110) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X110)
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).

fof(fact_image__inv__into__cancel,axiom,
    ! [X189,X78,X12,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),X12) = X78
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X189),X78))
       => hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_Set_Oimage(X10,X8,c_Hilbert__Choice_Oinv__into(X8,X10,X12,X2)),X189)) = X189 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__into__cancel) ).

fof(fact_inj__iff,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
    <=> hAPP(c_Fun_Ocomp(X8,X10,X10,c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2)),X2) = c_Fun_Oid(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__iff) ).

fof(fact_split__comp,axiom,
    ! [X11,X1,X2,X102,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),hAPP(c_Fun_Ocomp(X102,tc_fun(X18,X10),X8,X2),X1)),X11) = hAPP(hAPP(X2,hAPP(X1,hAPP(c_Product__Type_Ofst(X8,X18),X11))),hAPP(c_Product__Type_Osnd(X8,X18),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__comp) ).

fof(fact_inv__inv__eq,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => c_Hilbert__Choice_Oinv__into(X8,X10,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2)) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__inv__eq) ).

fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
    ! [X15,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X12),X15))
    <=> 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)),X12)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15))) ),
    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,
    ! [X15,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X12),X15))
    <=> 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)),X12)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I5_J) ).

fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
    ! [X53,X7,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ! [X3,X51] : hAPP(X7,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X3),X51)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(X7,X3)),hAPP(X7,X51))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
         => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X7,c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X53)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(c_Set_Oimage(X10,X10,X7),X53)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ohom__commute) ).

fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
    ! [X53,X7,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ! [X3,X51] : hAPP(X7,hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X3),X51)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(X7,X3)),hAPP(X7,X51))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
         => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X7,c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X53)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(c_Set_Oimage(X10,X10,X7),X53)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ohom__commute) ).

fof(fact_list__all2__nthD,axiom,
    ! [X148,X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X200,X199)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X148),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
       => hBOOL(hAPP(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X148)),hAPP(hAPP(c_List_Onth(X8),X199),X148))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__nthD) ).

fof(fact_list__all2__nthD2,axiom,
    ! [X148,X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X200,X199)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X148),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)))
       => hBOOL(hAPP(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X148)),hAPP(hAPP(c_List_Onth(X8),X199),X148))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__nthD2) ).

fof(fact_vimage__subsetI,axiom,
    ! [X12,X15,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X15),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,X2),X15)),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__subsetI) ).

fof(fact_converseD,axiom,
    ! [X110,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(c_Relation_Oconverse(X8,X10),X110)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X14),X13)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseD) ).

fof(fact_converse__iff,axiom,
    ! [X110,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(c_Relation_Oconverse(X8,X10),X110)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X14),X13)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__iff) ).

fof(fact_finite__vimage__iff,axiom,
    ! [X9,X7,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X7,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_Ovimage(X10,X8,X7),X9)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__vimage__iff) ).

fof(fact_sup2I1,axiom,
    ! [X15,X8,X10,X16,X11,X12] :
      ( hBOOL(hAPP(hAPP(X12,X11),X16))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2I1) ).

fof(fact_sup2I2,axiom,
    ! [X12,X8,X10,X16,X11,X15] :
      ( hBOOL(hAPP(hAPP(X15,X11),X16))
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup2I2) ).

fof(fact_Int__mono,axiom,
    ! [X21,X15,X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X17))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X17),X21))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__mono) ).

fof(fact_Un__mono,axiom,
    ! [X21,X15,X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X17))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X21))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X17),X21))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__mono) ).

fof(fact_Diff__mono,axiom,
    ! [X15,X21,X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X17))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X21),X15))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X17),X21))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__mono) ).

fof(fact_hom__fold1__commute,axiom,
    ! [X53,X7,X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => ( ! [X3,X51] : hAPP(X7,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X3),X51)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(X7,X3)),hAPP(X7,X51))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
         => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X7,hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X53)) = hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Set_Oimage(X10,X10,X7),X53)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hom__fold1__commute) ).

fof(fact_setsum_Oreindex,axiom,
    ! [X1,X7,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( c_Fun_Oinj__on(X10,X10,X7,X12)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(c_Set_Oimage(X10,X10,X7),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(c_Fun_Ocomp(X10,X8,X10,X1),X7)),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oreindex) ).

fof(fact_setprod_Oreindex,axiom,
    ! [X1,X7,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( c_Fun_Oinj__on(X10,X10,X7,X12)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(c_Set_Oimage(X10,X10,X7),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(c_Fun_Ocomp(X10,X8,X10,X1),X7)),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oreindex) ).

fof(fact_acc_OaccI,axiom,
    ! [X110,X11,X10] :
      ( ! [X51] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X11)),X110))
         => hBOOL(hAPP(hAPP(c_member(X10),X51),c_Wellfounded_Oacc(X10,X110))) )
     => hBOOL(hAPP(hAPP(c_member(X10),X11),c_Wellfounded_Oacc(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_OaccI) ).

fof(fact_acc_Osimps,axiom,
    ! [X110,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Wellfounded_Oacc(X10,X110)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X13)),X110))
         => hBOOL(hAPP(hAPP(c_member(X10),X3),c_Wellfounded_Oacc(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc_Osimps) ).

fof(fact_rtrancl__listrel1__eq__len,axiom,
    ! [X110,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),X16)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X11) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).

fof(conj_1,hypothesis,
    ! [X281] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X281),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
     => ( hAPP(c_Finite__Set_Ocard(t_a),X281) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n)
       => ! [X181] :
            ( v_wt(X181)
           => v_P(X281,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X181)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

fof(fact_list__update_Osimps_I2_J,axiom,
    ! [X93,X61,X200,X11,X10] : hAPP(hAPP(c_List_Olist__update(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),X61),X93) = c_Nat_Onat_Onat__case(tc_List_Olist(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X93),X200),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_List_Olist(X10),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X10),X11)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X10,tc_List_Olist(X10)),c_List_Olist__update(X10,X200)),X93)),X61),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update_Osimps_I2_J) ).

fof(fact_split__eta,axiom,
    ! [X2,X18,X8,X10] : hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_prod(X10,X8)),tc_fun(X8,X18),X10),hAPP(c_COMBB(tc_prod(X10,X8),X18,X8),X2)),c_Product__Type_OPair(X10,X8))) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__eta) ).

fof(fact_aset_I7_J,axiom,
    ! [X154,X12,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ! [X3] :
          ( ! [X66] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
             => ! [X163] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X12))
                 => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X163),X66) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X154),X3))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I7_J) ).

fof(fact_aset_I8_J,axiom,
    ! [X154,X12,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ! [X3] :
          ( ! [X66] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
             => ! [X163] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X12))
                 => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X163),X66) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X154),X3))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X154),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X21))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I8_J) ).

fof(fact_nth__take__lemma,axiom,
    ! [X201,X202,X27,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X201)))
       => ( ! [X91] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),X33))
             => hAPP(hAPP(c_List_Onth(X27),X202),X91) = hAPP(hAPP(c_List_Onth(X27),X201),X91) )
         => hAPP(hAPP(c_List_Otake(X27),X33),X202) = hAPP(hAPP(c_List_Otake(X27),X33),X201) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__take__lemma) ).

fof(fact_rel__pow__0__E,axiom,
    ! [X29,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29)))
     => X11 = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__0__E) ).

fof(fact_exI__realizer,axiom,
    ! [X10,X8,X11,X16,X42] :
      ( hBOOL(hAPP(hAPP(X42,X16),X11))
     => hBOOL(hAPP(hAPP(X42,hAPP(c_Product__Type_Osnd(X8,X10),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X11),X16))),hAPP(c_Product__Type_Ofst(X8,X10),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X11),X16)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exI__realizer) ).

fof(fact_comp__inj__on__iff,axiom,
    ! [X107,X18,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( c_Fun_Oinj__on(X8,X18,X107,hAPP(c_Set_Oimage(X10,X8,X2),X12))
      <=> c_Fun_Oinj__on(X10,X18,hAPP(c_Fun_Ocomp(X8,X18,X10,X107),X2),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__inj__on__iff) ).

fof(fact_comp__surj,axiom,
    ! [X1,X18,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
     => ( hAPP(c_Set_Oimage(X10,X18,X1),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X8,X18,hAPP(c_Fun_Ocomp(X10,X18,X8,X1),X2)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__surj) ).

fof(fact_zdiv__zmod__equality,axiom,
    ! [X33,X37,X36] : 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),X36),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36))),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmod__equality) ).

fof(fact_setsum__reindex,axiom,
    ! [X7,X15,X2,X8,X10,X18] :
      ( class_Groups_Ocomm__monoid__add(X18)
     => ( c_Fun_Oinj__on(X10,X8,X2,X15)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X18),X7),hAPP(c_Set_Oimage(X10,X8,X2),X15)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X18),hAPP(c_Fun_Ocomp(X8,X18,X10,X7),X2)),X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex) ).

fof(fact_setprod__reindex,axiom,
    ! [X7,X15,X2,X8,X10,X18] :
      ( class_Groups_Ocomm__monoid__mult(X18)
     => ( c_Fun_Oinj__on(X10,X8,X2,X15)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X18),X7),hAPP(c_Set_Oimage(X10,X8,X2),X15)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X18),hAPP(c_Fun_Ocomp(X8,X18,X10,X7),X2)),X15) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex) ).

fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__inter) ).

fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__inter) ).

fof(fact_lexn__length,axiom,
    ! [X30,X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),hAPP(c_List_Olexn(X10,X110),X30)))
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = X30
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199) = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn__length) ).

fof(fact_converseI,axiom,
    ! [X110,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X110))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X14),X13)),hAPP(c_Relation_Oconverse(X10,X8),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converseI) ).

fof(fact_rel__comp__distrib,axiom,
    ! [X160,X28,X29,X8,X18,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X29),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X18,X8),tc_HOL_Obool)),X28),X160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X29),X28)),hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X29),X160)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__distrib) ).

fof(fact_bot__empty__eq2,axiom,
    ! [X16,X11,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq2) ).

fof(fact_transpose__transpose,axiom,
    ! [X200,X10] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X200)))
     => c_List_Otranspose(X10,c_List_Otranspose(X10,X200)) = c_List_OtakeWhile(tc_List_Olist(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X10)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_List_Olist(X10),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X10))),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__transpose) ).

fof(fact_Inf__fin_Ohom__commute,axiom,
    ! [X53,X7,X10] :
      ( class_Lattices_Olattice(X10)
     => ( ! [X3,X51] : hAPP(X7,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X3),X51)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),hAPP(X7,X3)),hAPP(X7,X51))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
         => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X7,c_Big__Operators_Olattice__class_OInf__fin(X10,X53)) = c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(c_Set_Oimage(X10,X10,X7),X53)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ohom__commute) ).

fof(fact_Sup__fin_Ohom__commute,axiom,
    ! [X53,X7,X10] :
      ( class_Lattices_Olattice(X10)
     => ( ! [X3,X51] : hAPP(X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X3),X51)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),hAPP(X7,X3)),hAPP(X7,X51))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
         => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X7,c_Big__Operators_Olattice__class_OSup__fin(X10,X53)) = c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(c_Set_Oimage(X10,X10,X7),X53)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ohom__commute) ).

fof(fact_Max_Ohom__commute,axiom,
    ! [X53,X7,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ! [X3,X51] : hAPP(X7,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X3),X51)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(X7,X3)),hAPP(X7,X51))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
         => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X7,c_Big__Operators_Olinorder__class_OMax(X10,X53)) = c_Big__Operators_Olinorder__class_OMax(X10,hAPP(c_Set_Oimage(X10,X10,X7),X53)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ohom__commute) ).

fof(fact_Min_Ohom__commute,axiom,
    ! [X53,X7,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ! [X3,X51] : hAPP(X7,hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X3),X51)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(X7,X3)),hAPP(X7,X51))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
         => ( X53 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X7,c_Big__Operators_Olinorder__class_OMin(X10,X53)) = c_Big__Operators_Olinorder__class_OMin(X10,hAPP(c_Set_Oimage(X10,X10,X7),X53)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ohom__commute) ).

fof(fact_periodic__finite__ex,axiom,
    ! [X42,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( ! [X3,X59] :
            ( hBOOL(hAPP(X42,X3))
          <=> hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X59),X20)))) )
       => ( ? [X136] : hBOOL(hAPP(X42,X136))
        <=> ? [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(X42,X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_periodic__finite__ex) ).

fof(fact_listrel__Nil1,axiom,
    ! [X110,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X200)),c_List_Olistrel(X10,X110)))
     => X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil1) ).

fof(fact_the__elem__def,axiom,
    ! [X48,X10] : c_Set_Othe__elem(X10,X48) = c_HOL_OThe(X10,hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool,X10),hAPP(c_fequal,X48)),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__def) ).

fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
    ! [X15,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( c_Nat__Transfer_Onat__set(X15)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12),X15))
        <=> 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),X12)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X15))) ) ) ),
    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,
    ! [X15,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( c_Nat__Transfer_Onat__set(X15)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12),X15))
        <=> 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),X12)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).

fof(fact_union__comp__emptyL,axiom,
    ! [X15,X17,X12,X10] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X12),X17) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X15),X17) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X12),X15)),X17) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_union__comp__emptyL) ).

fof(fact_int__def,axiom,
    ! [X31] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) = 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),X31),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__def) ).

fof(fact_distrib__sup__le,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X38))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X38)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distrib__sup__le) ).

fof(fact_min__max_Odistrib__sup__le,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),X38))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X38)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Odistrib__sup__le) ).

fof(fact_fold__inf__le__inf,axiom,
    ! [X14,X13,X12,X10] :
      ( class_Lattices_Osemilattice__inf(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X14),X12)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X13),X14))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__inf__le__inf) ).

fof(fact_min__max_Ofold__inf__le__inf,axiom,
    ! [X14,X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X14),X12)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X13),X14))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__le__inf) ).

fof(fact_set__update__subsetI,axiom,
    ! [X61,X11,X12,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist__update(X10,X200),X61),X11))),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__subsetI) ).

fof(fact_setsum__ub__add__nat,axiom,
    ! [X148,X2,X30,X31,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X148))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X148)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__ub__add__nat) ).

fof(fact_trans__O__subset,axiom,
    ! [X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X110),X110)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__O__subset) ).

fof(fact_Times__Int__distrib1,axiom,
    ! [X17,X15,X12,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17))),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X15),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Int__distrib1) ).

fof(fact_Times__Un__distrib1,axiom,
    ! [X17,X15,X12,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17))),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X15),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Un__distrib1) ).

fof(fact_Times__Diff__distrib1,axiom,
    ! [X17,X15,X12,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17))),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X15),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X17))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__Diff__distrib1) ).

fof(fact_card__inj__on__le,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),X15))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X8),X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__inj__on__le) ).

fof(fact_fold__image__1,axiom,
    ! [X2,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X28))
             => hAPP(X2,X3) = c_Groups_Oone__class_Oone(X8) )
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X2),c_Groups_Oone__class_Oone(X8)),X28) = c_Groups_Oone__class_Oone(X8) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__1) ).

fof(fact_list__ball__nth,axiom,
    ! [X42,X200,X10,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
           => hBOOL(hAPP(X42,X3)) )
       => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ball__nth) ).

fof(fact_listrel__Nil2,axiom,
    ! [X110,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),c_List_Olist_ONil(X10))),c_List_Olistrel(X10,X110)))
     => X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil2) ).

fof(fact_INF__commute,axiom,
    ! [X2,X15,X18,X12,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,X10),X12),hAPP(hAPP(c_COMBB(tc_fun(X18,X10),X10,X8),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,X10),X15)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,X10),X15),hAPP(hAPP(c_COMBB(tc_fun(X8,X10),X10,X18),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,X10),X12)),hAPP(c_COMBC(X8,X18,X10),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__commute) ).

fof(fact_SUP__commute,axiom,
    ! [X2,X15,X18,X12,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X10),X12),hAPP(hAPP(c_COMBB(tc_fun(X18,X10),X10,X8),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X10),X15)),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,X10),X15),hAPP(hAPP(c_COMBB(tc_fun(X8,X10),X10,X18),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X10),X12)),hAPP(c_COMBC(X8,X18,X10),X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__commute) ).

fof(fact_eq__equiv__class__iff,axiom,
    ! [X16,X11,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X16),X12))
         => ( hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).

fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
    ! [X2,X12,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Int_Oint),X2),X12) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X10),c_Int_Onat),X2)),X12)) ),
    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,X12,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => c_Nat__Transfer_Ois__nat(hAPP(X2,X3)) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Int_Oint),X2),X12) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X10),c_Int_Onat),X2)),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod2_I2_J) ).

fof(fact_listrel__eq__len,axiom,
    ! [X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel(X10,X110)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__eq__len) ).

fof(fact_listrel1__eq__len,axiom,
    ! [X110,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X199)),c_List_Olistrel1(X10,X110)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__eq__len) ).

fof(fact_symD,axiom,
    ! [X14,X13,X110,X10] :
      ( c_Relation_Osym(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X13)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_symD) ).

fof(fact_sym__def,axiom,
    ! [X110,X10] :
      ( c_Relation_Osym(X10,X110)
    <=> ! [X3,X51] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X51)),X110))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X3)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__def) ).

fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
    ! [X154,X200,X2,X8,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(c_List_Orev(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)))
       => hAPP(c_List_Ofilter(X8,hAPP(hAPP(c_COMBB(X10,tc_HOL_Obool,X8),hAPP(c_Orderings_Oord__class_Oless(X10),X154)),X2)),X200) = c_List_OtakeWhile(X8,hAPP(hAPP(c_COMBB(X10,tc_HOL_Obool,X8),hAPP(c_Orderings_Oord__class_Oless(X10),X154)),X2),X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).

fof(fact_Sigma__Union,axiom,
    ! [X15,X48,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X48)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X48),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_fun(X8,tc_HOL_Obool)),tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),c_Product__Type_OSigma(X10,X8)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Union) ).

fof(fact_bset_I4_J,axiom,
    ! [X15,X154,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X154),X15))
       => ! [X3] :
            ( ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
               => ! [X163] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X15))
                   => X3 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X163),X66) ) )
           => ( X3 != X154
             => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),X21) != X154 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I4_J) ).

fof(fact_aset_I4_J,axiom,
    ! [X12,X154,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X154),X12))
       => ! [X3] :
            ( ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X21)))
               => ! [X163] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X163),X12))
                   => X3 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X163),X66) ) )
           => ( X3 != X154
             => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),X21) != X154 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I4_J) ).

fof(fact_fold__def,axiom,
    ! [X12,X19,X2,X10,X8] : hAPP(hAPP(c_Finite__Set_Ofold(X8,X10,X2),X19),X12) = c_HOL_OThe(X10,c_Finite__Set_Ofold__graph(X8,X10,X2,X19,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__def) ).

fof(fact_split__paired__All,axiom,
    ! [X8,X10,X42] :
      ( ! [X136] : hBOOL(hAPP(X42,X136))
    <=> ! [X46,X81] : hBOOL(hAPP(X42,hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).

fof(fact_curryI,axiom,
    ! [X14,X13,X8,X10,X2] :
      ( hBOOL(hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)))
     => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X10,X8,tc_HOL_Obool,X2),X13),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curryI) ).

fof(fact_diff__card__le__card__Diff,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => 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(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15))),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__card__le__card__Diff) ).

fof(fact_inj__on__Inter,axiom,
    ! [X2,X8,X10,X28] :
      ( X28 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))
     => ( ! [X52] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X52),X28))
           => c_Fun_Oinj__on(X10,X8,X2,X52) )
       => c_Fun_Oinj__on(X10,X8,X2,c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X28)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Inter) ).

fof(fact_Bex__set__replicate,axiom,
    ! [X42,X13,X30,X10] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),c_List_Oreplicate(X10,X30,X13))))
          & hBOOL(hAPP(X42,X3)) )
    <=> ( hBOOL(hAPP(X42,X13))
        & X30 != 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,
    ! [X110,X10] :
      ( c_Nitpick_Orefl_H(X10,X110)
    <=> ! [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).

fof(fact_incr__mult__lemma,axiom,
    ! [X32,X42,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( ! [X3] :
            ( hBOOL(hAPP(X42,X3))
           => hBOOL(hAPP(X42,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)),X32))
         => ! [X3] :
              ( hBOOL(hAPP(X42,X3))
             => hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X20)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_incr__mult__lemma) ).

fof(fact_decr__mult__lemma,axiom,
    ! [X32,X42,X20] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20))
     => ( ! [X3] :
            ( hBOOL(hAPP(X42,X3))
           => hBOOL(hAPP(X42,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)),X32))
         => ! [X3] :
              ( hBOOL(hAPP(X42,X3))
             => hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X20)))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_decr__mult__lemma) ).

fof(fact_measures__less,axiom,
    ! [X241,X10,X16,X11,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X11)),hAPP(X2,X16)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_List_Omeasures(X10,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X10,tc_Nat_Onat)),X2),X241)))) ),
    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,X11,X18,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__idem(X10,X8,X2,X9)
     => hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X11)),hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X11)),X1)) = hAPP(c_Fun_Ocomp(X8,X8,X18,hAPP(X2,X11)),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oidem__left__comp) ).

fof(fact_mem__splitI,axiom,
    ! [X18,X8,X14,X13,X6,X19,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X19),hAPP(hAPP(X6,X13),X14)))
     => hBOOL(hAPP(hAPP(c_member(X10),X19),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,tc_fun(X10,tc_HOL_Obool)),X6),hAPP(hAPP(c_Product__Type_OPair(X8,X18),X13),X14)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__splitI) ).

fof(fact_Ball__set__replicate,axiom,
    ! [X42,X13,X30,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),c_List_Oreplicate(X10,X30,X13))))
         => hBOOL(hAPP(X42,X3)) )
    <=> ( hBOOL(hAPP(X42,X13))
        | X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ball__set__replicate) ).

fof(fact_listrel__Cons,axiom,
    ! [X200,X11,X110,X10] : hAPP(c_Relation_OImage(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Olistrel(X10,X110)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))) = c_List_Oset__Cons(X10,hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Olistrel(X10,X110)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),X200),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Cons) ).

fof(fact_UN__le__add__shift,axiom,
    ! [X32,X143,X30,X10] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool),tc_Nat_Onat),X143),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X32))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X32,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X32))),X143),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__le__add__shift) ).

fof(fact_numeral__2__eq__2,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).

fof(fact_semiring__norm_I115_J,axiom,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).

fof(fact_bij__image__Compl__eq,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X10,X8,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__image__Compl__eq) ).

fof(fact_lexord__append__rightI,axiom,
    ! [X110,X11,X10,X16] :
      ( ? [X81,X177] : X16 = hAPP(hAPP(c_List_Olist_OCons(X10),X81),X177)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),hAPP(hAPP(c_List_Oappend(X10),X11),X16))),c_List_Olexord(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__append__rightI) ).

fof(fact_list__eq__iff__zip__eq,axiom,
    ! [X10,X199,X200] :
      ( X200 = X199
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199)
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X3),hAPP(c_List_Oset(tc_prod(X10,X10)),hAPP(hAPP(c_List_Ozip(X10,X10),X200),X199))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,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,
    ! [X42,X57,X152] :
      ( 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),X152),X57)))
     => ( ! [X3,X51] :
            ( 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),X51)))
           => ( ( X51 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
               => hBOOL(hAPP(hAPP(X42,X51),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X51))) )
             => hBOOL(hAPP(hAPP(X42,X3),X51)) ) )
       => hBOOL(hAPP(hAPP(X42,X152),X57)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Opinduct) ).

fof(fact_inj__on__strict__subset,axiom,
    ! [X12,X15,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),hAPP(c_Set_Oimage(X10,X8,X2),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__strict__subset) ).

fof(fact_inj__on__image__Int,axiom,
    ! [X15,X12,X17,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X17))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X17))
         => hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),hAPP(c_Set_Oimage(X10,X8,X2),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__image__Int) ).

fof(fact_inj__on__image__set__diff,axiom,
    ! [X15,X12,X17,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X17)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X17))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X17))
         => hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),hAPP(c_Set_Oimage(X10,X8,X2),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__image__set__diff) ).

fof(fact_filter__in__sublist,axiom,
    ! [X116,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X200,X116)))),X200) = c_List_Osublist(X10,X200,X116) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__in__sublist) ).

fof(fact_surj__iff__all,axiom,
    ! [X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
    <=> ! [X3] : hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X8,X10,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),X2),X3)) = X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff__all) ).

fof(fact_list__ex1__iff__raw,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__ex1(X10,X42,X200)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
          & hBOOL(hAPP(X42,X3))
          & ! [X51] :
              ( ( hBOOL(hAPP(hAPP(c_member(X10),X51),hAPP(c_List_Oset(X10),X200)))
                & hBOOL(hAPP(X42,X51)) )
             => X51 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff__raw) ).

fof(fact_list__ex1__iff,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__ex1(X10,X42,X200)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
          & hBOOL(hAPP(X42,X3))
          & ! [X51] :
              ( ( hBOOL(hAPP(hAPP(c_member(X10),X51),hAPP(c_List_Oset(X10),X200)))
                & hBOOL(hAPP(X42,X51)) )
             => X51 = X3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff) ).

fof(fact_endo__inj__surj,axiom,
    ! [X2,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X10,X2),X12)),X12))
       => ( c_Fun_Oinj__on(X10,X10,X2,X12)
         => hAPP(c_Set_Oimage(X10,X10,X2),X12) = X12 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_endo__inj__surj) ).

fof(fact_insort__insert__key__triv,axiom,
    ! [X200,X8,X11,X2,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X11)),hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_List_Oset(X8),X200))))
       => c_List_Olinorder__class_Oinsort__insert__key(X8,X10,X2,X11,X200) = X200 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__key__triv) ).

fof(fact_set__insort__insert,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(c_List_Oset(X10),c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X11,X200)) = hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(c_List_Oset(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__insort__insert) ).

fof(fact_listrel1__subset__listrel,axiom,
    ! [X162,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X162))
     => ( c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X162)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel1(X10,X110)),c_List_Olistrel(X10,X162))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__subset__listrel) ).

fof(fact_folding__image_Oeq__fold,axiom,
    ! [X1,X12,X9,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image(X10,X8,X2,X19,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => hAPP(hAPP(X9,X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X8,X2),X1),X19),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image_Oeq__fold) ).

fof(fact_fun__left__comm_Ofold__rec,axiom,
    ! [X19,X11,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),X12) = hAPP(hAPP(X2,X11),hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).

fof(fact_vimage__compose,axiom,
    ! [X11,X2,X1,X18,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,hAPP(c_Fun_Ocomp(X18,X8,X10,X1),X2)),X11) = hAPP(c_Set_Ovimage(X10,X18,X2),hAPP(c_Set_Ovimage(X18,X8,X1),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__compose) ).

fof(fact_image__compose,axiom,
    ! [X110,X1,X2,X18,X10,X8] : hAPP(c_Set_Oimage(X8,X10,hAPP(c_Fun_Ocomp(X18,X10,X8,X2),X1)),X110) = hAPP(c_Set_Oimage(X18,X10,X2),hAPP(c_Set_Oimage(X8,X18,X1),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__compose) ).

fof(fact_rtrancl__power,axiom,
    ! [X29,X148,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Transitive__Closure_Ortrancl(X10,X29)))
    <=> ? [X123] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X123),X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__power) ).

fof(fact_scomp__unfold,axiom,
    ! [X11,X1,X2,X10,X102,X18,X8] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X8,X18,X102,X10),X2),X1),X11) = hAPP(hAPP(X1,hAPP(c_Product__Type_Ofst(X18,X102),hAPP(X2,X11))),hAPP(c_Product__Type_Osnd(X18,X102),hAPP(X2,X11))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__unfold) ).

fof(fact_equiv__class__eq__iff,axiom,
    ! [X16,X11,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
      <=> ( hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X16),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
          & hBOOL(hAPP(hAPP(c_member(X10),X16),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).

fof(fact_sum__squares__gt__zero__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X16))))
      <=> ( X11 != c_Groups_Ozero__class_Ozero(X10)
          | X16 != c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__gt__zero__iff) ).

fof(fact_rtrancl__is__UN__rel__pow,axiom,
    ! [X29,X10] : c_Transitive__Closure_Ortrancl(X10,X29) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X10,X10),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(X10,X10),tc_HOL_Obool),tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool)),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__is__UN__rel__pow) ).

fof(fact_takeWhile__append2,axiom,
    ! [X199,X42,X200,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,X3)) )
     => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),X200),c_List_OtakeWhile(X10,X42,X199)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__append2) ).

fof(fact_inj__on__imageI,axiom,
    ! [X12,X2,X1,X18,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,hAPP(c_Fun_Ocomp(X18,X8,X10,X1),X2),X12)
     => c_Fun_Oinj__on(X18,X8,X1,hAPP(c_Set_Oimage(X10,X18,X2),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imageI) ).

fof(fact_setsum__eq__Suc0__iff,axiom,
    ! [X2,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
            & hAPP(X2,X3) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X66),X12))
               => ( X3 != X66
                 => hAPP(X2,X66) = 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,
    ! [X11,X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,X200)
       => c_List_Olinorder__class_Osorted(X10,c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X11,X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__insert) ).

fof(fact_abs__mult__less,axiom,
    ! [X58,X36,X35,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),X35))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__less) ).

fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
    ! [X11,X19,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(X2,X11),hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).

fof(fact_takeWhile__map,axiom,
    ! [X200,X2,X8,X42,X10] : c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_OtakeWhile(X8,hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,X8,X42),X2),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__map) ).

fof(fact_fun__upd__def,axiom,
    ! [X14,X2,X8,X10,X13,X11] :
      ( ( X11 = X13
       => hAPP(c_Fun_Ofun__upd(X10,X8,X2,X13,X14),X11) = X14 )
      & ( X11 != X13
       => hAPP(c_Fun_Ofun__upd(X10,X8,X2,X13,X14),X11) = hAPP(X2,X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__def) ).

fof(fact_fun__upd__apply,axiom,
    ! [X16,X2,X8,X10,X11,X19] :
      ( ( X19 = X11
       => hAPP(c_Fun_Ofun__upd(X10,X8,X2,X11,X16),X19) = X16 )
      & ( X19 != X11
       => hAPP(c_Fun_Ofun__upd(X10,X8,X2,X11,X16),X19) = hAPP(X2,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__apply) ).

fof(fact_fun__upd__other,axiom,
    ! [X16,X2,X8,X10,X11,X19] :
      ( X19 != X11
     => hAPP(c_Fun_Ofun__upd(X10,X8,X2,X11,X16),X19) = hAPP(X2,X19) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__other) ).

fof(fact_setsum__eq__1__iff,axiom,
    ! [X2,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
            & hAPP(X2,X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X66),X12))
               => ( X3 != X66
                 => hAPP(X2,X66) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).

fof(fact_refl__on__comp__subset,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Relation_Oconverse(X10,X10),X110)),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__comp__subset) ).

fof(fact_fun__upd__same,axiom,
    ! [X16,X11,X2,X10,X8] : hAPP(c_Fun_Ofun__upd(X8,X10,X2,X11,X16),X11) = X16,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).

fof(fact_comp__inj__on,axiom,
    ! [X1,X18,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( c_Fun_Oinj__on(X8,X18,X1,hAPP(c_Set_Oimage(X10,X8,X2),X12))
       => c_Fun_Oinj__on(X10,X18,hAPP(c_Fun_Ocomp(X8,X18,X10,X1),X2),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__inj__on) ).

fof(fact_product_Osimps_I2_J,axiom,
    ! [X199,X200,X11,X8,X10] : c_Enum_Oproduct(X10,X8,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200),X199) = hAPP(hAPP(c_List_Oappend(tc_prod(X10,X8)),hAPP(hAPP(c_List_Omap(X8,tc_prod(X10,X8)),hAPP(c_Product__Type_OPair(X10,X8),X11)),X199)),c_Enum_Oproduct(X10,X8,X200,X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product_Osimps_I2_J) ).

fof(fact_elem__le__sum,axiom,
    ! [X209,X30] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30),hAPP(c_List_Oset(tc_Nat_Onat),X209)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),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)),X209))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__le__sum) ).

fof(fact_rev__ImageI,axiom,
    ! [X110,X14,X8,X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X110))
       => hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(c_Relation_OImage(X10,X8,X110),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__ImageI) ).

fof(fact_map__map,axiom,
    ! [X200,X1,X18,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(hAPP(c_List_Omap(X18,X8),X1),X200)) = hAPP(hAPP(c_List_Omap(X18,X10),hAPP(c_Fun_Ocomp(X8,X10,X18,X2),X1)),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__map) ).

fof(fact_List_Omap_Ocompositionality,axiom,
    ! [X204,X1,X18,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(hAPP(c_List_Omap(X18,X8),X1),X204)) = hAPP(hAPP(c_List_Omap(X18,X10),hAPP(c_Fun_Ocomp(X8,X10,X18,X2),X1)),X204),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Ocompositionality) ).

fof(fact_take__Cons,axiom,
    ! [X200,X11,X30,X10] : hAPP(hAPP(c_List_Otake(X10),X30),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = c_Nat_Onat_Onat__case(tc_List_Olist(X10),c_List_Olist_ONil(X10),hAPP(hAPP(c_COMBB(tc_List_Olist(X10),tc_List_Olist(X10),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X10),X11)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Otake(X10)),X200)),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons) ).

fof(fact_Un__Image,axiom,
    ! [X12,X28,X29,X10,X8] : hAPP(c_Relation_OImage(X8,X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),X29),X28)),X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X10,X29),X12)),hAPP(c_Relation_OImage(X8,X10,X28),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Image) ).

fof(fact_iterate_Osimps,axiom,
    ! [X11,X2,X10,X8,X32] :
      ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(X8,X10,X32,X2),X11) = hAPP(c_Product__Type_OPair(X8,X10),X11) )
      & ( X32 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Random_Oiterate(X8,X10,X32,X2),X11) = hAPP(hAPP(c_Product__Type_Oscomp(X10,X8,X10,tc_prod(X8,X10)),hAPP(X2,X11)),c_Random_Oiterate(X8,X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32),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,
    ! [X14,X13,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
       => hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__eq) ).

fof(fact_mem__Sigma__iff,axiom,
    ! [X15,X12,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
        & hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(X15,X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Sigma__iff) ).

fof(fact_SigmaD2,axiom,
    ! [X15,X12,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)))
     => hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(X15,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD2) ).

fof(fact_listrel__mono,axiom,
    ! [X116,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel(X10,X110)),c_List_Olistrel(X10,X116))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__mono) ).

fof(fact_listrel1__mono,axiom,
    ! [X116,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel1(X10,X110)),c_List_Olistrel1(X10,X116))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__mono) ).

fof(fact_bij__def,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
    <=> ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
        & hAPP(c_Set_Oimage(X10,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__def) ).

fof(fact_bij__is__inj,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__is__inj) ).

fof(fact_scomp__def,axiom,
    ! [X11,X1,X2,X10,X102,X18,X8] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X8,X18,X102,X10),X2),X1),X11) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X18,X102,X10),X1),hAPP(X2,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__def) ).

fof(fact_scomp__apply,axiom,
    ! [X11,X1,X2,X10,X102,X18,X8] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X8,X18,X102,X10),X2),X1),X11) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X18,X102,X10),X1),hAPP(X2,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__apply) ).

fof(fact_Un__least,axiom,
    ! [X15,X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X17))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X17))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__least) ).

fof(fact_folding__one_Ounion__inter,axiom,
    ! [X15,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(X2,hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(X2,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Ounion__inter) ).

fof(fact_f__the__inv__into__f,axiom,
    ! [X16,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X8),X16),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => hAPP(X2,hAPP(c_Fun_Othe__inv__into(X10,X8,X12,X2),X16)) = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__the__inv__into__f) ).

fof(fact_INT__extend__simps_I8_J,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool))),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,tc_HOL_Obool),X12)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I8_J) ).

fof(fact_UN__extend__simps_I8_J,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool))),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,tc_HOL_Obool),X12)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I8_J) ).

fof(fact_INT__simps_I8_J,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,tc_HOL_Obool),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool))),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I8_J) ).

fof(fact_UN__simps_I8_J,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,tc_HOL_Obool),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_fun(X10,tc_HOL_Obool)),tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool))),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I8_J) ).

fof(fact_inj__on__def,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => ! [X66] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X66),X12))
             => ( hAPP(X2,X3) = hAPP(X2,X66)
               => X3 = X66 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__def) ).

fof(fact_rtrancl__subset,axiom,
    ! [X28,X29,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),X28))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X28),c_Transitive__Closure_Ortrancl(X10,X29)))
       => c_Transitive__Closure_Ortrancl(X10,X28) = c_Transitive__Closure_Ortrancl(X10,X29) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset) ).

fof(fact_eq__equiv__class,axiom,
    ! [X12,X14,X13,X110,X10] :
      ( hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
     => ( c_Equiv__Relations_Oequiv(X10,X12,X110)
       => ( hBOOL(hAPP(hAPP(c_member(X10),X14),X12))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__equiv__class) ).

fof(fact_SigmaD1,axiom,
    ! [X15,X12,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)))
     => hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaD1) ).

fof(fact_setprod__zero__iff,axiom,
    ! [X2,X12,X10,X8] :
      ( ( class_Rings_Ocomm__semiring__1(X8)
        & class_Rings_Ono__zero__divisors(X8) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12) = c_Groups_Ozero__class_Ozero(X8)
        <=> ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
              & hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X8) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__zero__iff) ).

fof(fact_card__image__le,axiom,
    ! [X2,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8),hAPP(c_Set_Oimage(X10,X8,X2),X12))),hAPP(c_Finite__Set_Ocard(X10),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image__le) ).

fof(fact_INTER__UNIV__conv_I2_J,axiom,
    ! [X15,X12,X10,X8] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
         => hAPP(X15,X3) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I2_J) ).

fof(fact_UNION__empty__conv_I2_J,axiom,
    ! [X15,X12,X10,X8] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
         => hAPP(X15,X3) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__empty__conv_I2_J) ).

fof(fact_INTER__UNIV__conv_I1_J,axiom,
    ! [X15,X12,X8,X10] :
      ( c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
         => hAPP(X15,X3) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__UNIV__conv_I1_J) ).

fof(fact_UNION__empty__conv_I1_J,axiom,
    ! [X15,X12,X8,X10] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X8),X3),X12))
         => hAPP(X15,X3) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__empty__conv_I1_J) ).

fof(fact_setsum__SucD,axiom,
    ! [X30,X12,X2,X10] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12) = hAPP(c_Nat_OSuc,X30)
     => ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X2,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__SucD) ).

fof(fact_Inf__fin_Ounion__inter,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)),c_Big__Operators_Olattice__class_OInf__fin(X10,X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__inter) ).

fof(fact_Sup__fin_Ounion__inter,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)),c_Big__Operators_Olattice__class_OSup__fin(X10,X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__inter) ).

fof(fact_Max_Ounion__inter,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,X12)),c_Big__Operators_Olinorder__class_OMax(X10,X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ounion__inter) ).

fof(fact_Min_Ounion__inter,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,X12)),c_Big__Operators_Olinorder__class_OMin(X10,X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ounion__inter) ).

fof(fact_sorted_Osimps,axiom,
    ! [X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,X13)
      <=> ( X13 = c_List_Olist_ONil(X10)
          | ? [X208,X3] :
              ( X13 = hAPP(hAPP(c_List_Olist_OCons(X10),X3),X208)
              & ! [X66] :
                  ( hBOOL(hAPP(hAPP(c_member(X10),X66),hAPP(c_List_Oset(X10),X208)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X66)) )
              & c_List_Olinorder__class_Osorted(X10,X208) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Osimps) ).

fof(fact_type__definition_OAbs__inject,axiom,
    ! [X16,X11,X12,X178,X179,X8,X10] :
      ( c_Typedef_Otype__definition(X10,X8,X179,X178,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X8),X11),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X8),X16),X12))
         => ( hAPP(X178,X11) = hAPP(X178,X16)
          <=> X11 = X16 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).

fof(fact_acyclicP__converse,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Oacyclic(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),c_Predicate_Oconversep(X10,X10,X110))))
    <=> c_Wellfounded_Oacyclic(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclicP__converse) ).

fof(fact_Field__insert,axiom,
    ! [X110,X14,X13,X10] : hAPP(c_Relation_OField(X10),hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),hAPP(c_Relation_OField(X10),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__insert) ).

fof(fact_start__le__sum,axiom,
    ! [X209,X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X209))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_start__le__sum) ).

fof(fact_pair__box_Osize_I1_J,axiom,
    ! [X14,X13,X94,X95,X8,X10] : c_Nitpick_Opair__box_Opair__box__size(X10,X8,X95,X94,c_Nitpick_Opair__box_OPairBox(X10,X8,X13,X14)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X95,X13)),hAPP(X94,X14))),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,
    ! [X32,X17,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),X17))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X17)))
       => ( ! [X181] :
              ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X181),X17))
             => hAPP(c_Finite__Set_Ocard(X10),X181) = X32 )
         => ( ! [X182] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X182),X17))
               => ! [X183] :
                    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X183),X17))
                   => ( X182 != X183
                     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X182),X183) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) )
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),hAPP(c_Finite__Set_Ocard(tc_fun(X10,tc_HOL_Obool)),X17)) = hAPP(c_Finite__Set_Ocard(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X17)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__partition) ).

fof(fact_bij__is__surj,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X10,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__is__surj) ).

fof(fact_sorted__same,axiom,
    ! [X200,X1,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_List_Olinorder__class_Osorted(X10,hAPP(c_List_Ofilter(X10,hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),hAPP(X1,X200))),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__same) ).

fof(fact_inj__comp,axiom,
    ! [X1,X18,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( c_Fun_Oinj__on(X18,X10,X1,c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool)))
       => c_Fun_Oinj__on(X18,X8,hAPP(c_Fun_Ocomp(X10,X8,X18,X2),X1),c_Orderings_Otop__class_Otop(tc_fun(X18,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__comp) ).

fof(fact_set__update__subset__insert,axiom,
    ! [X11,X61,X200,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist__update(X10,X200),X61),X11))),hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(c_List_Oset(X10),X200)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__subset__insert) ).

fof(fact_min__max_OSup__fin_Oremove,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12) = X11 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oremove) ).

fof(fact_min__max_OInf__fin_Oremove,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12) = X11 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,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,
    ! [X12,X2,X10] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X12)),
    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,
    ! [X12,X2,X10] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Nat_Onat),X2),X12) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).

fof(fact_vimage__singleton__eq,axiom,
    ! [X14,X2,X8,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Set_Oinsert(X8),X14),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))))))
    <=> hAPP(X2,X13) = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__singleton__eq) ).

fof(fact_inj__on__imageI2,axiom,
    ! [X12,X2,X107,X18,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,hAPP(c_Fun_Ocomp(X18,X8,X10,X107),X2),X12)
     => c_Fun_Oinj__on(X10,X18,X2,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imageI2) ).

fof(fact_finite__Diff__insert,axiom,
    ! [X15,X13,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff__insert) ).

fof(fact_insert__def,axiom,
    ! [X15,X13,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X13),X15) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__def) ).

fof(fact_eq__add__iff1,axiom,
    ! [X20,X14,X6,X72,X13,X10] :
      ( class_Rings_Oring(X10)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X72)),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X72)),X20)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14)),X72)),X6) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff1) ).

fof(fact_eq__add__iff2,axiom,
    ! [X20,X14,X6,X72,X13,X10] :
      ( class_Rings_Oring(X10)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X72)),X6) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X72)),X20)
      <=> X6 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X14),X13)),X72)),X20) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__add__iff2) ).

fof(fact_Image__INT__eq,axiom,
    ! [X15,X18,X12,X110,X8,X10] :
      ( c_Relation_Osingle__valued(X10,X8,hAPP(c_Relation_Oconverse(X8,X10),X110))
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X18,tc_HOL_Obool))
       => hAPP(c_Relation_OImage(X8,X10,X110),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18),c_Relation_OImage(X8,X10,X110)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__INT__eq) ).

fof(fact_partition__filter2,axiom,
    ! [X200,X42,X10] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Opartition(X10,X42,X200)) = hAPP(c_List_Ofilter(X10,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X10,c_fNot),X42)),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter2) ).

fof(fact_inv__into__image__cancel,axiom,
    ! [X28,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X28),X12))
       => hAPP(c_Set_Oimage(X8,X10,c_Hilbert__Choice_Oinv__into(X10,X8,X12,X2)),hAPP(c_Set_Oimage(X10,X8,X2),X28)) = X28 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__image__cancel) ).

fof(fact_vimage__mono,axiom,
    ! [X2,X8,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X8,X10,X2),X12)),hAPP(c_Set_Ovimage(X8,X10,X2),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__mono) ).

fof(fact_image__mono,axiom,
    ! [X2,X8,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),hAPP(c_Set_Oimage(X10,X8,X2),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__mono) ).

fof(fact_UN__equiv__class,axiom,
    ! [X13,X2,X8,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( c_Equiv__Relations_Ocongruent(X10,tc_fun(X8,tc_HOL_Obool),X110,X2)
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X2) = hAPP(X2,X13) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__equiv__class) ).

fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = X11 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,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,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = X11 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).

fof(fact_comp__cong,axiom,
    ! [X104,X102,X18,X10,X8,X105,X106,X107,X11,X1,X2] :
      ( hAPP(X2,hAPP(X1,X11)) = hAPP(X107,hAPP(X106,X105))
     => hAPP(hAPP(c_Fun_Ocomp(X8,X10,X18,X2),X1),X11) = hAPP(hAPP(c_Fun_Ocomp(X102,X10,X104,X107),X106),X105) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__cong) ).

fof(fact_inv__o__cancel,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Fun_Ocomp(X8,X10,X10,c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2)),X2) = c_Fun_Oid(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__o__cancel) ).

fof(fact_bij__betw__imp__surj,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X10,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__imp__surj) ).

fof(fact_folding__one_Oremove,axiom,
    ! [X11,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => hAPP(X9,X12) = X11 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => hAPP(X9,X12) = hAPP(hAPP(X2,X11),hAPP(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oremove) ).

fof(fact_card_Ounion__inter,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Ounion__inter) ).

fof(fact_card__Un__Int,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Un__Int) ).

fof(fact_wf__same__fst,axiom,
    ! [X10,X29,X8,X42] :
      ( ! [X3] :
          ( hBOOL(hAPP(X42,X3))
         => c_Wellfounded_Owf(X8,hAPP(X29,X3)) )
     => c_Wellfounded_Owf(tc_prod(X10,X8),c_Recdef_Osame__fst(X10,X8,X42,X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__same__fst) ).

fof(fact_in__rel__def,axiom,
    ! [X16,X11,X29,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X10,X8,X29),X11),X16))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__rel__def) ).

fof(fact_bij__betw__def,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X15)
    <=> ( c_Fun_Oinj__on(X10,X8,X2,X12)
        & hAPP(c_Set_Oimage(X10,X8,X2),X12) = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__def) ).

fof(fact_bij__betw__imp__inj__on,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X15)
     => c_Fun_Oinj__on(X10,X8,X2,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__imp__inj__on) ).

fof(fact_Image__closed__trancl,axiom,
    ! [X48,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X110),X48)),X48))
     => hAPP(c_Relation_OImage(X10,X10,c_Transitive__Closure_Ortrancl(X10,X110)),X48) = X48 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).

fof(fact_acc__downwards__aux,axiom,
    ! [X110,X13,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X13)),c_Transitive__Closure_Ortrancl(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Wellfounded_Oacc(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(X10),X14),c_Wellfounded_Oacc(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).

fof(fact_acc__downwards,axiom,
    ! [X14,X110,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Wellfounded_Oacc(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X14),X13)),c_Transitive__Closure_Ortrancl(X10,X110)))
       => hBOOL(hAPP(hAPP(c_member(X10),X14),c_Wellfounded_Oacc(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downwards) ).

fof(fact_INT__simps_I2_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I2_J) ).

fof(fact_INT__simps_I4_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I4_J) ).

fof(fact_UN__simps_I3_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I3_J) ).

fof(fact_INT__extend__simps_I2_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) = X12 )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I2_J) ).

fof(fact_UN__extend__simps_I3_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) = X12 )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I3_J) ).

fof(fact_INT__extend__simps_I4_J,axiom,
    ! [X15,X12,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) = X12 )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I4_J) ).

fof(fact_folding__one_Oinsert__remove,axiom,
    ! [X11,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = X11 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(X2,X11),hAPP(X9,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oinsert__remove) ).

fof(fact_Inf__fin_Oremove,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X10,X12) = X11 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X10,X12) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oremove) ).

fof(fact_Sup__fin_Oremove,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X10,X12) = X11 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X10,X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oremove) ).

fof(fact_Max_Oremove,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X10,X12) = X11 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X10,X12) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oremove) ).

fof(fact_Min_Oremove,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X10,X12) = X11 )
            & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X10,X12) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oremove) ).

fof(fact_type__definition_ORep,axiom,
    ! [X11,X12,X178,X179,X8,X10] :
      ( c_Typedef_Otype__definition(X10,X8,X179,X178,X12)
     => hBOOL(hAPP(hAPP(c_member(X8),hAPP(X179,X11)),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep) ).

fof(fact_type__definition_OAbs__inverse,axiom,
    ! [X16,X12,X178,X179,X8,X10] :
      ( c_Typedef_Otype__definition(X10,X8,X179,X178,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X8),X16),X12))
       => hAPP(X179,hAPP(X178,X16)) = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).

fof(fact_sorted__insort__key,axiom,
    ! [X200,X11,X2,X8,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),X200)))
      <=> c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort__key) ).

fof(fact_mod__induct__0,axiom,
    ! [X61,X42,X148] :
      ( ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),X148))
         => ( hBOOL(hAPP(X42,X91))
           => hBOOL(hAPP(X42,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X91),X148))) ) )
     => ( hBOOL(hAPP(X42,X61))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),X148))
         => hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__induct__0) ).

fof(fact_bijI,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(X10,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))
       => c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bijI) ).

fof(fact_zdiv__zmult1__eq,axiom,
    ! [X35,X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X36)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X36),X35))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X35))),X35)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult1__eq) ).

fof(fact_div__mult1__eq,axiom,
    ! [X35,X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),X36)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X36),X35))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X37),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X36,X35))),X35)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult1__eq) ).

fof(fact_nat__eq__add__iff1,axiom,
    ! [X30,X31,X77,X61,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X60),X61))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X77)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X77)),X30)
      <=> 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),X61),X60)),X77)),X31) = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff1) ).

fof(fact_nat__eq__add__iff2,axiom,
    ! [X30,X31,X77,X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X61),X60))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X77)),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X60),X77)),X30)
      <=> X31 = 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),X60),X61)),X77)),X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__add__iff2) ).

fof(fact_Un__Int__assoc__eq,axiom,
    ! [X17,X15,X12,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X17),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).

fof(fact_INT__simps_I7_J,axiom,
    ! [X15,X12,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I7_J) ).

fof(fact_UN__simps_I5_J,axiom,
    ! [X15,X12,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I5_J) ).

fof(fact_UN__simps_I7_J,axiom,
    ! [X15,X12,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12)),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I7_J) ).

fof(fact_Int__UN__distrib,axiom,
    ! [X12,X161,X8,X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X161),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UN__distrib) ).

fof(fact_UN__extend__simps_I5_J,axiom,
    ! [X15,X17,X8,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I5_J) ).

fof(fact_Un__INT__distrib,axiom,
    ! [X12,X161,X8,X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X161),X12)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X161),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__INT__distrib) ).

fof(fact_INT__extend__simps_I7_J,axiom,
    ! [X15,X17,X8,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I7_J) ).

fof(fact_UN__extend__simps_I7_J,axiom,
    ! [X15,X17,X8,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I7_J) ).

fof(fact_union__comp__emptyR,axiom,
    ! [X17,X15,X12,X10] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
     => ( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X12),X17) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
       => hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X15),X17)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_union__comp__emptyR) ).

fof(fact_BIJ,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
       => ( ? [X76] : c_Fun_Obij__betw(X10,X8,X76,X12,X15)
        <=> hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(c_Finite__Set_Ocard(X8),X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_BIJ) ).

fof(fact_type__definition_ORep__range,axiom,
    ! [X12,X178,X179,X8,X10] :
      ( c_Typedef_Otype__definition(X10,X8,X179,X178,X12)
     => hAPP(c_Set_Oimage(X10,X8,X179),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__range) ).

fof(fact_singleton__quotient,axiom,
    ! [X110,X11,X10] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X110) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__quotient) ).

fof(fact_congruentD,axiom,
    ! [X19,X16,X2,X110,X8,X10] :
      ( c_Equiv__Relations_Ocongruent(X10,X8,X110,X2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X19)),X110))
       => hAPP(X2,X16) = hAPP(X2,X19) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_congruentD) ).

fof(conj_7,conjecture,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),v_G)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7) ).

fof(fact_rtrancl__subset__rtrancl,axiom,
    ! [X116,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),c_Transitive__Closure_Ortrancl(X10,X116)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X110)),c_Transitive__Closure_Ortrancl(X10,X116))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).

fof(fact_rel__pow__imp__rtrancl,axiom,
    ! [X29,X30,X148,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Transitive__Closure_Ortrancl(X10,X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__imp__rtrancl) ).

fof(fact_acc__downward,axiom,
    ! [X13,X110,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),c_Wellfounded_Oacc(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),X110))
       => hBOOL(hAPP(hAPP(c_member(X10),X13),c_Wellfounded_Oacc(X10,X110))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__downward) ).

fof(fact_Inf__fin_Oinsert__remove,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = X11 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__remove) ).

fof(fact_Sup__fin_Oinsert__remove,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = X11 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__remove) ).

fof(fact_Max_Oinsert__remove,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = X11 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oinsert__remove) ).

fof(fact_Min_Oinsert__remove,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = X11 )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oinsert__remove) ).

fof(fact_type__definition_OAbs__image,axiom,
    ! [X12,X178,X179,X8,X10] :
      ( c_Typedef_Otype__definition(X10,X8,X179,X178,X12)
     => hAPP(c_Set_Oimage(X8,X10,X178),X12) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__image) ).

fof(fact_inj__on__mapI,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),c_List_Oset(X10)),X12)))
     => c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X8),hAPP(c_List_Omap(X10,X8),X2),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__mapI) ).

fof(fact_image__inv__f__f,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X8,X10,c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2)),hAPP(c_Set_Oimage(X10,X8,X2),X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__inv__f__f) ).

fof(fact_inv__image__comp,axiom,
    ! [X48,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X8,X10,c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2)),hAPP(c_Set_Oimage(X10,X8,X2),X48)) = X48 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__image__comp) ).

fof(fact_update__zip,axiom,
    ! [X211,X44,X201,X202,X10,X27] : hAPP(hAPP(c_List_Olist__update(tc_prod(X27,X10),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201)),X44),X211) = hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),hAPP(c_Product__Type_Ofst(X27,X10),X211))),hAPP(hAPP(c_List_Olist__update(X10,X201),X44),hAPP(c_Product__Type_Osnd(X27,X10),X211))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_update__zip) ).

fof(fact_finite__Collect__less__nat,axiom,
    ! [X32] : 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)),X32)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__less__nat) ).

fof(fact_finite__Collect__le__nat,axiom,
    ! [X32] : 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)),X32)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Collect__le__nat) ).

fof(fact_O__assoc,axiom,
    ! [X160,X28,X29,X102,X8,X18,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),hAPP(hAPP(c_Relation_Orel__comp(X10,X102,X18),X29),X28)),X160) = hAPP(hAPP(c_Relation_Orel__comp(X10,X102,X8),X29),hAPP(hAPP(c_Relation_Orel__comp(X102,X18,X8),X28),X160)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_O__assoc) ).

fof(fact_setsum__diff1_H,axiom,
    ! [X2,X13,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(X2,X13)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1_H) ).

fof(fact_setsum_Oremove,axiom,
    ! [X1,X11,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(X1,X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oremove) ).

fof(fact_setprod_Oremove,axiom,
    ! [X1,X11,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X1,X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oremove) ).

fof(fact_Pow__INT__eq,axiom,
    ! [X15,X12,X8,X10] : hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),X8),c_Set_OPow(X10)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__INT__eq) ).

fof(fact_q__pos__lemma,axiom,
    ! [X111,X112,X113] :
      ( 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),X113),X112)),X111)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X111),X113))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X113))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X112)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_q__pos__lemma) ).

fof(fact_bij__betw__finite,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X15)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__finite) ).

fof(fact_bij__betw__empty1,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X12)
     => X12 = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__empty1) ).

fof(fact_bij__betw__empty2,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))
     => X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__empty2) ).

fof(fact_UN__le__eq__Un0,axiom,
    ! [X143,X30,X10] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30)),X143) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X30)),X143)),hAPP(X143,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,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ),
    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,
    ! [X143,X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15)),X143) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X143)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X15),X143)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__Un) ).

fof(fact_UN__Un,axiom,
    ! [X143,X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15)),X143) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X143)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X15),X143)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__Un) ).

fof(fact_Compl__subset__Compl__iff,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__subset__Compl__iff) ).

fof(fact_INT__lower,axiom,
    ! [X15,X8,X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15)),hAPP(X15,X13))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__lower) ).

fof(fact_rtrancl__mono,axiom,
    ! [X116,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X110)),c_Transitive__Closure_Ortrancl(X10,X116))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__mono) ).

fof(fact_vimage__INT,axiom,
    ! [X15,X12,X18,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18),c_Set_Ovimage(X10,X8,X2)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__INT) ).

fof(fact_vimage__UN,axiom,
    ! [X15,X12,X18,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18),c_Set_Ovimage(X10,X8,X2)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__UN) ).

fof(fact_Image__UN,axiom,
    ! [X15,X12,X18,X110,X10,X8] : hAPP(c_Relation_OImage(X8,X10,X110),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18),c_Relation_OImage(X8,X10,X110)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__UN) ).

fof(fact_image__UN,axiom,
    ! [X15,X12,X18,X2,X10,X8] : hAPP(c_Set_Oimage(X8,X10,X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X18),c_Set_Oimage(X8,X10,X2)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__UN) ).

fof(fact_add__frac__eq,axiom,
    ! [X92,X26,X38,X34,X27] :
      ( class_Fields_Ofield(X27)
     => ( X34 != c_Groups_Ozero__class_Ozero(X27)
       => ( X38 != c_Groups_Ozero__class_Ozero(X27)
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X92),X38)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X92),X34))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__eq) ).

fof(fact_diff__frac__eq,axiom,
    ! [X92,X26,X38,X34,X27] :
      ( class_Fields_Ofield(X27)
     => ( X34 != c_Groups_Ozero__class_Ozero(X27)
       => ( X38 != c_Groups_Ozero__class_Ozero(X27)
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X92),X38)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X92),X34))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__frac__eq) ).

fof(fact_Compl__eq,axiom,
    ! [X12,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq) ).

fof(fact_list__all2__lengthD,axiom,
    ! [X199,X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X200,X199)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__lengthD) ).

fof(fact_Suc__mult__less__cancel1,axiom,
    ! [X30,X31,X32] :
      ( 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,X32)),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__less__cancel1) ).

fof(fact_Suc__mult__le__cancel1,axiom,
    ! [X30,X31,X32] :
      ( 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,X32)),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__le__cancel1) ).

fof(fact_split__pos__lemma,axiom,
    ! [X30,X42,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32))
     => ( hBOOL(hAPP(hAPP(X42,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X32)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X32)))
      <=> ! [X91,X73] :
            ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X32))
              & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
           => hBOOL(hAPP(hAPP(X42,X91),X73)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__pos__lemma) ).

fof(fact_inj__on__inv__into,axiom,
    ! [X12,X2,X8,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(c_Set_Oimage(X8,X10,X2),X12)))
     => c_Fun_Oinj__on(X10,X8,c_Hilbert__Choice_Oinv__into(X8,X10,X12,X2),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__inv__into) ).

fof(fact_UN__o,axiom,
    ! [X2,X1,X18,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Fun_Ocomp(X18,tc_fun(X10,tc_HOL_Obool),X8,X1),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X18,X2),X12)),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__o) ).

fof(fact_setsum_Oinsert__remove,axiom,
    ! [X11,X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(X1,X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oinsert__remove) ).

fof(fact_setprod_Oinsert__remove,axiom,
    ! [X11,X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X1,X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oinsert__remove) ).

fof(fact_f__inv__into__f,axiom,
    ! [X12,X2,X8,X16,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_Set_Oimage(X8,X10,X2),X12)))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X8,X10,X12,X2),X16)) = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_f__inv__into__f) ).

fof(fact_split__neg__lemma,axiom,
    ! [X30,X42,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(X42,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X32)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X32)))
      <=> ! [X91,X73] :
            ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X73))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
           => hBOOL(hAPP(hAPP(X42,X91),X73)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_zip__same__conv__map,axiom,
    ! [X200,X10] : hAPP(hAPP(c_List_Ozip(X10,X10),X200),X200) = hAPP(hAPP(c_List_Omap(X10,tc_prod(X10,X10)),hAPP(hAPP(c_COMBS(X10,X10,tc_prod(X10,X10)),c_Product__Type_OPair(X10,X10)),c_COMBI(X10))),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__same__conv__map) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
    ! [X15,X12] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X12),X15) = 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)),X12)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15))),
    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,
    ! [X15,X12] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X12),X15) = 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)),X12)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J) ).

fof(fact_surj__iff,axiom,
    ! [X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
    <=> hAPP(c_Fun_Ocomp(X8,X10,X10,X2),c_Hilbert__Choice_Oinv__into(X8,X10,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),X2)) = c_Fun_Oid(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__iff) ).

fof(fact_power__Suc__less,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Oone__class_Oone(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less) ).

fof(fact_type__definition_ORep__inject,axiom,
    ! [X16,X11,X12,X178,X179,X8,X10] :
      ( c_Typedef_Otype__definition(X10,X8,X179,X178,X12)
     => ( hAPP(X179,X11) = hAPP(X179,X16)
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).

fof(fact_finite__cartesian__productD2,axiom,
    ! [X15,X12,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15))))
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__productD2) ).

fof(fact_finite__cartesian__productD1,axiom,
    ! [X15,X12,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15))))
     => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__productD1) ).

fof(fact_type__definition_ORep__inverse,axiom,
    ! [X11,X12,X178,X179,X8,X10] :
      ( c_Typedef_Otype__definition(X10,X8,X179,X178,X12)
     => hAPP(X178,hAPP(X179,X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).

fof(fact_bij__betw__same__card,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Obij__betw(X10,X8,X2,X12,X15)
     => hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(c_Finite__Set_Ocard(X8),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__same__card) ).

fof(fact_abs__triangle__ineq2,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36))),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2) ).

fof(fact_abs__triangle__ineq2__sym,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36))),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X36),X37)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq2__sym) ).

fof(fact_vimage__insert,axiom,
    ! [X15,X13,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Set_Oinsert(X8),X13),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Set_Oinsert(X8),X13),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X10,X8,X2),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__insert) ).

fof(fact_fun__upd__idem__iff,axiom,
    ! [X16,X11,X2,X8,X10] :
      ( c_Fun_Ofun__upd(X10,X8,X2,X11,X16) = X2
    <=> hAPP(X2,X11) = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).

fof(fact_list__all2__Nil,axiom,
    ! [X199,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,c_List_Olist_ONil(X10),X199)
    <=> X199 = c_List_Olist_ONil(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Nil) ).

fof(fact_list__all2__Nil2,axiom,
    ! [X200,X42,X8,X10] :
      ( c_List_Olist__all2(X10,X8,X42,X200,c_List_Olist_ONil(X8))
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Nil2) ).

fof(fact_bij__betw__id__iff,axiom,
    ! [X15,X12,X10] :
      ( c_Fun_Obij__betw(X10,X10,c_Fun_Oid(X10),X12,X15)
    <=> X12 = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__id__iff) ).

fof(fact_DomainI,axiom,
    ! [X110,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X110))
     => hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Relation_ODomain(X10,X8),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainI) ).

fof(fact_RangeI,axiom,
    ! [X110,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X110))
     => hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(c_Relation_ORange(X10,X8),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeI) ).

fof(fact_set__drop__subset__set__drop,axiom,
    ! [X200,X10,X31,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X31))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Odrop(X10),X31),X200))),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Odrop(X10),X30),X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__drop__subset__set__drop) ).

fof(fact_set__take__subset__set__take,axiom,
    ! [X200,X10,X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),X31),X200))),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),X30),X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__take__subset__set__take) ).

fof(fact_list__all2__eq,axiom,
    ! [X10,X199,X200] :
      ( X200 = X199
    <=> c_List_Olist__all2(X10,X10,c_fequal,X200,X199) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__eq) ).

fof(fact_sorted__list__of__set__insert,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_List_Olinorder__class_Osorted__list__of__set(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X11),c_List_Olinorder__class_Osorted__list__of__set(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__insert) ).

fof(fact_power__le__imp__le__base,axiom,
    ! [X36,X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(c_Nat_OSuc,X25))),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),hAPP(c_Nat_OSuc,X25))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__base) ).

fof(fact_sup__le__fold__sup,axiom,
    ! [X14,X13,X12,X10] :
      ( class_Lattices_Osemilattice__sup(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X13),X14)),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X14),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__le__fold__sup) ).

fof(fact_min__max_Osup__le__fold__sup,axiom,
    ! [X14,X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),X14)),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X14),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__le__fold__sup) ).

fof(fact_Domain__mono,axiom,
    ! [X116,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X110),X116))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X8),X110)),hAPP(c_Relation_ODomain(X10,X8),X116))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__mono) ).

fof(fact_inj__imp__surj__inv,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X8,X10,c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__imp__surj__inv) ).

fof(fact_less__half__sum,axiom,
    ! [X36,X37,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Oone__class_Oone(X27))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__half__sum) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
    ! [X15,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( c_Nat__Transfer_Onat__set(X15)
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12),X15) = 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),X12)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X15))) ) ),
    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,
    ! [X15,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( c_Nat__Transfer_Onat__set(X15)
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12),X15) = 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),X12)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J) ).

fof(fact_combine__common__factor,axiom,
    ! [X35,X36,X67,X37,X27] :
      ( class_Rings_Osemiring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X67)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X67)),X35)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X67)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_combine__common__factor) ).

fof(fact_Id__on__subset__Times,axiom,
    ! [X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Relation_OId__on(X10,X12)),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__subset__Times) ).

fof(fact_sort__foldl__insort,axiom,
    ! [X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_List_Olinorder__class_Osort__key(X10,X10,c_COMBI(X10),X200) = hAPP(c_List_Ofoldl(tc_List_Olist(X10),X10,hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10))),c_List_Olist_ONil(X10)),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__foldl__insort) ).

fof(fact_Range__Collect__split,axiom,
    ! [X42,X10,X8] : hAPP(c_Relation_ORange(X8,X10),hAPP(c_Set_OCollect(tc_prod(X8,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X10,tc_HOL_Obool),X42))) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X8)),hAPP(c_COMBC(X8,X10,tc_HOL_Obool),X42))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Collect__split) ).

fof(fact_inj__on__imp__bij__betw,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => c_Fun_Obij__betw(X10,X8,X2,X12,hAPP(c_Set_Oimage(X10,X8,X2),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__imp__bij__betw) ).

fof(fact_equiv__type,axiom,
    ! [X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(hAPP(c_Product__Type_OSigma(X10,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__type) ).

fof(fact_map__comp__map,axiom,
    ! [X1,X2,X10,X8,X18] : hAPP(c_Fun_Ocomp(tc_List_Olist(X18),tc_List_Olist(X8),tc_List_Olist(X10),hAPP(c_List_Omap(X18,X8),X2)),hAPP(c_List_Omap(X10,X18),X1)) = hAPP(c_List_Omap(X10,X8),hAPP(c_Fun_Ocomp(X18,X8,X10,X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__comp__map) ).

fof(fact_List_Omap_Ocomp,axiom,
    ! [X1,X2,X10,X8,X18] : hAPP(c_Fun_Ocomp(tc_List_Olist(X18),tc_List_Olist(X8),tc_List_Olist(X10),hAPP(c_List_Omap(X18,X8),X2)),hAPP(c_List_Omap(X10,X18),X1)) = hAPP(c_List_Omap(X10,X8),hAPP(c_Fun_Ocomp(X18,X8,X10,X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Ocomp) ).

fof(fact_refl__onD1,axiom,
    ! [X16,X11,X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
       => hBOOL(hAPP(hAPP(c_member(X10),X11),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD1) ).

fof(fact_refl__onD2,axiom,
    ! [X16,X11,X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),X110))
       => hBOOL(hAPP(hAPP(c_member(X10),X16),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD2) ).

fof(fact_listrel_ONil,axiom,
    ! [X110,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_List_Olist_ONil(X10))),c_List_Olistrel(X10,X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel_ONil) ).

fof(fact_Int__Union2,axiom,
    ! [X12,X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X15)),X12) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool))),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Union2) ).

fof(fact_Id__on__iff,axiom,
    ! [X12,X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Relation_OId__on(X10,X12)))
    <=> ( X11 = X16
        & hBOOL(hAPP(hAPP(c_member(X10),X11),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__iff) ).

fof(fact_finite__Plus__iff,axiom,
    ! [X15,X12,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X8)),c_Sum__Type_OPlus(X10,X8,X12,X15)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [X15,X12,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X8)),c_Sum__Type_OPlus(X10,X8,X12,X15)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [X15,X12,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X8)),c_Sum__Type_OPlus(X10,X8,X12,X15)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_SigmaI,axiom,
    ! [X15,X14,X8,X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(X15,X13)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SigmaI) ).

fof(fact_foldl__assoc,axiom,
    ! [X206,X16,X11,X10] :
      ( class_Groups_Osemigroup__add(X10)
     => hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X11),X16)),X206) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X11),hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),X16),X206)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__assoc) ).

fof(fact_rel__pow__0__I,axiom,
    ! [X29,X11,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X11)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__0__I) ).

fof(fact_quotient__disj,axiom,
    ! [X65,X48,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X65),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
         => ( X48 = X65
            | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X48),X65) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__disj) ).

fof(fact_pick__same,axiom,
    ! [X200,X10,X83] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X83),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => hAPP(c_Random_Opick(X10,hAPP(hAPP(c_List_Omap(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,X10)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X10),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X200)),hAPP(c_Code__Numeral_Oof__nat,X83)) = hAPP(hAPP(c_List_Onth(X10),X200),X83) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pick__same) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [X32,X12] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X12),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X12)))))
     => X12 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_ord_OgreaterThanLessThan__iff,axiom,
    ! [X77,X83,X84,X61,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X61),c_SetInterval_Oord_OgreaterThanLessThan(X10,X84,X83,X77)))
    <=> ( hBOOL(hAPP(hAPP(X84,X83),X61))
        & hBOOL(hAPP(hAPP(X84,X61),X77)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).

fof(fact_ord_OatLeastAtMost__iff,axiom,
    ! [X77,X83,X85,X61,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X61),c_SetInterval_Oord_OatLeastAtMost(X10,X85,X83,X77)))
    <=> ( hBOOL(hAPP(hAPP(X85,X83),X61))
        & hBOOL(hAPP(hAPP(X85,X61),X77)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).

fof(fact_set__Cons__sing__Nil,axiom,
    ! [X12,X10] : c_List_Oset__Cons(X10,X12,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X10,tc_List_Olist(X10),hAPP(hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10))),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__Cons__sing__Nil) ).

fof(fact_INT__insert__distrib,axiom,
    ! [X15,X13,X8,X12,X77,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X77),X12))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X8),X13)),X15)) = hAPP(hAPP(c_Set_Oinsert(X8),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__insert__distrib) ).

fof(fact_UN__insert__distrib,axiom,
    ! [X15,X13,X8,X12,X77,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X77),X12))
     => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X8),X13)),X15)) = hAPP(hAPP(c_Set_Oinsert(X8),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__insert__distrib) ).

fof(fact_finite__conv__nat__seg__image,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
    <=> ? [X123,X76] : X12 = hAPP(c_Set_Oimage(tc_Nat_Onat,X10,X76),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)),X123))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__conv__nat__seg__image) ).

fof(fact_nat__seg__image__imp__finite,axiom,
    ! [X30,X2,X10,X12] :
      ( X12 = hAPP(c_Set_Oimage(tc_Nat_Onat,X10,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)),X30)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__seg__image__imp__finite) ).

fof(fact_take__hd__drop,axiom,
    ! [X202,X27,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Otake(X27),X25),X202)),hAPP(hAPP(c_List_Olist_OCons(X27),hAPP(c_List_Ohd(X27),hAPP(hAPP(c_List_Odrop(X27),X25),X202))),c_List_Olist_ONil(X27))) = hAPP(hAPP(c_List_Otake(X27),hAPP(c_Nat_OSuc,X25)),X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__hd__drop) ).

fof(fact_Diff__insert2,axiom,
    ! [X15,X13,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert2) ).

fof(fact_listrel__rtrancl__refl,axiom,
    ! [X110,X200,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),X200)),c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X110)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__refl) ).

fof(fact_Inter__subset,axiom,
    ! [X15,X12,X10] :
      ( ! [X184] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X184),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X184),X15)) )
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X12)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__subset) ).

fof(fact_zmod__zmult2__eq,axiom,
    ! [X36,X37,X35] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X35)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36),X35))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult2__eq) ).

fof(fact_Int__greatest,axiom,
    ! [X15,X12,X17,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X17),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X17),X15))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greatest) ).

fof(fact_max__Suc2,axiom,
    ! [X30,X31] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X30),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)),X30)),X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc2) ).

fof(fact_rel__pow__add,axiom,
    ! [X29,X30,X31,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30)),X29) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X31),X29)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__add) ).

fof(fact_Union__mono,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X12)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__mono) ).

fof(fact_Inter__anti__mono,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X15),X12))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X12)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__anti__mono) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_abs__triangle__ineq4,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__triangle__ineq4) ).

fof(fact_min__Suc2,axiom,
    ! [X30,X31] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30)) = 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)),X30)),X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc2) ).

fof(fact_card_Oremove,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oremove) ).

fof(fact_zip__update,axiom,
    ! [X34,X201,X26,X44,X202,X10,X27] : hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)),hAPP(hAPP(c_List_Olist__update(X10,X201),X44),X34)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X27,X10),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201)),X44),hAPP(hAPP(c_Product__Type_OPair(X27,X10),X26),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__update) ).

fof(fact_image__Int,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),hAPP(c_Set_Oimage(X10,X8,X2),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Int) ).

fof(fact_image__set__diff,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X10,X8,X2),X12)),hAPP(c_Set_Oimage(X10,X8,X2),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__set__diff) ).

fof(fact_the__inv__into__onto,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => hAPP(c_Set_Oimage(X8,X10,c_Fun_Othe__inv__into(X10,X8,X12,X2)),hAPP(c_Set_Oimage(X10,X8,X2),X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__onto) ).

fof(fact_pair__box_Osimps_I2_J,axiom,
    ! [X14,X13,X50,X10,X18,X8] : c_Nitpick_Opair__box_Opair__box__case(X8,X18,X10,X50,c_Nitpick_Opair__box_OPairBox(X8,X18,X13,X14)) = hAPP(hAPP(X50,X13),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).

fof(fact_pair__box_Orecs,axiom,
    ! [X14,X13,X50,X10,X18,X8] : c_Nitpick_Opair__box_Opair__box__rec(X8,X18,X10,X50,c_Nitpick_Opair__box_OPairBox(X8,X18,X13,X14)) = hAPP(hAPP(X50,X13),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).

fof(fact_setprod__dvd__setprod__subset,axiom,
    ! [X2,X12,X15,X10,X8] :
      ( ( class_Groups_Ocomm__monoid__mult(X8)
        & class_Rings_Odvd(X8) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X15))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__dvd__setprod__subset) ).

fof(fact_zip__takeWhile__fst,axiom,
    ! [X199,X200,X42,X8,X10] : hAPP(hAPP(c_List_Ozip(X10,X8),c_List_OtakeWhile(X10,X42,X200)),X199) = c_List_OtakeWhile(tc_prod(X10,X8),hAPP(c_Fun_Ocomp(X10,tc_HOL_Obool,tc_prod(X10,X8),X42),c_Product__Type_Ofst(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__takeWhile__fst) ).

fof(fact_zmult__zless__mono2__lemma,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
       => 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),X33)),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)),X43))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2__lemma) ).

fof(fact_Diff__Int2,axiom,
    ! [X15,X17,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X17)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X17)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int2) ).

fof(fact_Int__Un__distrib2,axiom,
    ! [X12,X17,X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17)),X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X12)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X17),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).

fof(fact_Diff__Int__distrib2,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X17)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib2) ).

fof(fact_Un__Int__distrib2,axiom,
    ! [X12,X17,X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)),X12) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X12)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X17),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).

fof(fact_Un__Diff,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X17)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff) ).

fof(fact_aset_I3_J,axiom,
    ! [X12,X154,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X154),c_Groups_Oone__class_Oone(tc_Int_Oint))),X12))
       => ( ! [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),X21)))
             => ! [X66] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),X12))
                 => X154 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X66),X3) ) )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X154),X21) = X154 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_aset_I3_J) ).

fof(fact_bset_I3_J,axiom,
    ! [X15,X154,X21] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X154),c_Groups_Oone__class_Oone(tc_Int_Oint))),X15))
       => ( ! [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),X21)))
             => ! [X66] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X66),X15))
                 => X154 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X66),X3) ) )
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X154),X21) = X154 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bset_I3_J) ).

fof(fact_take__add,axiom,
    ! [X202,X27,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),X202) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Otake(X27),X44),X202)),hAPP(hAPP(c_List_Otake(X27),X43),hAPP(hAPP(c_List_Odrop(X27),X44),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__add) ).

fof(fact_card_Ounion__inter__neutral,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
           => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).

fof(fact_card__Suc__Diff1,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X10),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).

fof(fact_folding_Ocommute__comp_H_H,axiom,
    ! [X15,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X15)),hAPP(X9,X12)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).

fof(fact_takeWhile__not__last,axiom,
    ! [X10,X200] :
      ( X200 != c_List_Olist_ONil(X10)
     => ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
       => c_List_OtakeWhile(X10,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),c_List_Olast(X10,X200))),X200) = c_List_Obutlast(X10,X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__not__last) ).

fof(fact_Compl__INT,axiom,
    ! [X15,X12,X8,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool))),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__INT) ).

fof(fact_Compl__UN,axiom,
    ! [X15,X12,X8,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool))),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UN) ).

fof(fact_fold1Set__sing,axiom,
    ! [X14,X13,X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X14))
    <=> X13 = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set__sing) ).

fof(fact_folding_Ounion,axiom,
    ! [X15,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ounion) ).

fof(fact_split__div_H,axiom,
    ! [X30,X31,X42] :
      ( hBOOL(hAPP(X42,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X31),X30)))
    <=> ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        | ? [X138] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X138)),X31))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(c_Nat_OSuc,X138))))
            & hBOOL(hAPP(X42,X138)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div_H) ).

fof(fact_card_Oinsert__remove,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oinsert__remove) ).

fof(fact_o__eq__dest,axiom,
    ! [X93,X20,X6,X102,X14,X13,X10,X8,X18] :
      ( hAPP(c_Fun_Ocomp(X18,X8,X10,X13),X14) = hAPP(c_Fun_Ocomp(X102,X8,X10,X6),X20)
     => hAPP(X13,hAPP(X14,X93)) = hAPP(X6,hAPP(X20,X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest) ).

fof(fact_o__eq__elim,axiom,
    ! [X20,X6,X102,X14,X13,X10,X8,X18] :
      ( hAPP(c_Fun_Ocomp(X18,X8,X10,X13),X14) = hAPP(c_Fun_Ocomp(X102,X8,X10,X6),X20)
     => ! [X103] : hAPP(X13,hAPP(X14,X103)) = hAPP(X6,hAPP(X20,X103)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__elim) ).

fof(fact_insort__left__comm,axiom,
    ! [X200,X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X11),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),X200)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X16),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X11),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__left__comm) ).

fof(fact_o__eq__id__dest,axiom,
    ! [X93,X6,X14,X13,X10,X8,X18] :
      ( hAPP(c_Fun_Ocomp(X18,X8,X10,X13),X14) = hAPP(c_Fun_Ocomp(X8,X8,X10,c_Fun_Oid(X8)),X6)
     => hAPP(X13,hAPP(X14,X93)) = hAPP(X6,X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__id__dest) ).

fof(fact_distinct__sort,axiom,
    ! [X200,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( hBOOL(hAPP(c_List_Odistinct(X10),c_List_Olinorder__class_Osort__key(X10,X8,X2,X200)))
      <=> hBOOL(hAPP(c_List_Odistinct(X10),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__sort) ).

fof(fact_equiv__class__self,axiom,
    ! [X13,X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__class__self) ).

fof(fact_inj__image__mem__iff,axiom,
    ! [X12,X13,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hBOOL(hAPP(hAPP(c_member(X8),hAPP(X2,X13)),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
      <=> hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__mem__iff) ).

fof(fact_INF__subset,axiom,
    ! [X2,X15,X12,X10,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X8),X15),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X8),X12),X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__subset) ).

fof(fact_SUP__subset,axiom,
    ! [X2,X15,X12,X10,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X8),X12),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X8),X15),X2))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__subset) ).

fof(fact_UN__simps_I1_J,axiom,
    ! [X15,X13,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X8),X13)),X15)) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X8),X13)),X15)) = hAPP(hAPP(c_Set_Oinsert(X8),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I1_J) ).

fof(fact_UN__extend__simps_I1_J,axiom,
    ! [X15,X13,X8,X10,X17] :
      ( ( X17 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(X8),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Set_Oinsert(X8),X13),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) )
      & ( X17 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Set_Oinsert(X8),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Set_Oinsert(X8),X13)),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I1_J) ).

fof(fact_setsum__right__distrib,axiom,
    ! [X12,X2,X8,X110,X10] :
      ( class_Rings_Osemiring__0(X10)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X110),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBB(X10,X10,X8),hAPP(c_Groups_Otimes__class_Otimes(X10),X110)),X2)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__right__distrib) ).

fof(fact_mlex__less,axiom,
    ! [X29,X10,X16,X11,X2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X2,X11)),hAPP(X2,X16)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Wellfounded_Omlex__prod(X10,X2,X29))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mlex__less) ).

fof(fact_range__composition,axiom,
    ! [X1,X2,X18,X10,X8] : hAPP(c_Set_Oimage(X8,X10,hAPP(hAPP(c_COMBB(X18,X10,X8),X2),X1)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X18,X10,X2),hAPP(c_Set_Oimage(X8,X18,X1),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__composition) ).

fof(fact_sorted__nth__monoI,axiom,
    ! [X202,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ! [X91,X73] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X91),X73))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X73),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_List_Onth(X27),X202),X91)),hAPP(hAPP(c_List_Onth(X27),X202),X73))) ) )
       => c_List_Olinorder__class_Osorted(X27,X202) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__nth__monoI) ).

fof(fact_sorted__equals__nth__mono,axiom,
    ! [X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,X200)
      <=> ! [X73] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X73),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
           => ! [X91] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X91),X73))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_List_Onth(X10),X200),X91)),hAPP(hAPP(c_List_Onth(X10),X200),X73))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__equals__nth__mono) ).

fof(fact_INT__D,axiom,
    ! [X13,X15,X12,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ( hBOOL(hAPP(hAPP(c_member(X8),X13),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(X15,X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__D) ).

fof(fact_foldl__absorb0,axiom,
    ! [X206,X11,X10] :
      ( class_Groups_Omonoid__add(X10)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X11),hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)),X206)) = hAPP(c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),X11),X206) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__absorb0) ).

fof(fact_list__update__swap,axiom,
    ! [X212,X26,X202,X27,X213,X44] :
      ( X44 != X213
     => hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)),X213),X212) = hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Olist__update(X27,X202),X213),X212)),X44),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__swap) ).

fof(fact_rel__pow__commute,axiom,
    ! [X30,X29,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X29),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)),X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__commute) ).

fof(fact_card__insert,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert) ).

fof(fact_divide__strict__left__mono,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X35),X37)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X35),X36))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono) ).

fof(fact_divide__left__mono,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X35),X37)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X35),X36))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono) ).

fof(fact_mono__Field,axiom,
    ! [X116,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OField(X10),X110)),hAPP(c_Relation_OField(X10),X116))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__Field) ).

fof(fact_folding_Ocommute__comp_H,axiom,
    ! [X11,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X2,X11)),hAPP(X9,X12)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X2,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp_H) ).

fof(fact_INT__simps_I5_J,axiom,
    ! [X15,X13,X17,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Set_Oinsert(X10),X13)),X15)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I5_J) ).

fof(fact_INT__extend__simps_I5_J,axiom,
    ! [X15,X17,X8,X13,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),X8),hAPP(c_Set_Oinsert(X10),X13)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I5_J) ).

fof(fact_left__add__mult__distrib,axiom,
    ! [X33,X43,X69,X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X69)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X69)),X33)) = 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),X44),X43)),X69)),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__add__mult__distrib) ).

fof(fact_zip__takeWhile__snd,axiom,
    ! [X199,X42,X200,X8,X10] : hAPP(hAPP(c_List_Ozip(X10,X8),X200),c_List_OtakeWhile(X8,X42,X199)) = c_List_OtakeWhile(tc_prod(X10,X8),hAPP(c_Fun_Ocomp(X8,tc_HOL_Obool,tc_prod(X10,X8),X42),c_Product__Type_Osnd(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__takeWhile__snd) ).

fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
    ! [X2,X11,X10,X8,X61] :
      ( ( X61 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(X8,X10,X11,X2),X61) = c_Lazy__Sequence_Ohit__bound(X10) )
      & ( X61 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(X8,X10,X11,X2),X61) = c_Lazy__Sequence_Ohb__bind(X8,X10,hAPP(X11,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X61),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X8,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X10))),X2),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).

fof(fact_inj__fun,axiom,
    ! [X18,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => c_Fun_Oinj__on(X10,tc_fun(X18,X8),hAPP(hAPP(c_COMBB(X8,tc_fun(X18,X8),X10),c_COMBK(X8,X18)),X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__fun) ).

fof(fact_Int__eq__Inter,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X15),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__eq__Inter) ).

fof(fact_Un__eq__Union,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X15),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,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,
    ! [X35,X36,X37,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),c_Groups_Ozero__class_Ozero(X27)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X35),X37)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X35),X36))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__left__mono__neg) ).

fof(fact_divide__left__mono__neg,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Fields_Olinordered__field__inverse__zero(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),c_Groups_Ozero__class_Ozero(X27)))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X35),X37)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X35),X36))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__left__mono__neg) ).

fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
    ! [X2,X11,X10,X8,X61] :
      ( ( X61 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(X8,X10,X11,X2),X61) = c_Lazy__Sequence_Oempty(X10) )
      & ( X61 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(X8,X10,X11,X2),X61) = hAPP(c_Lazy__Sequence_Obind(X8,X10,hAPP(X11,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X61),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X8,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X10)),X2),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).

fof(fact_nth__zip,axiom,
    ! [X201,X10,X202,X27,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X201)))
       => hAPP(hAPP(c_List_Onth(tc_prod(X27,X10)),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201)),X44) = hAPP(hAPP(c_Product__Type_OPair(X27,X10),hAPP(hAPP(c_List_Onth(X27),X202),X44)),hAPP(hAPP(c_List_Onth(X10),X201),X44)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__zip) ).

fof(fact_mod__mult2__eq,axiom,
    ! [X35,X36,X37] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X37,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X37),X36),X35))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X37,X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult2__eq) ).

fof(fact_list__update__length,axiom,
    ! [X34,X201,X26,X202,X27] : hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Oappend(X27),X202),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X201))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X34) = hAPP(hAPP(c_List_Oappend(X27),X202),hAPP(hAPP(c_List_Olist_OCons(X27),X34),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__length) ).

fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
    ! [X110,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel1(X10,c_Transitive__Closure_Ortrancl(X10,X110))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).

fof(fact_rtrancl__Un__rtrancl,axiom,
    ! [X28,X29,X10] : c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X29)),c_Transitive__Closure_Ortrancl(X10,X28))) = c_Transitive__Closure_Ortrancl(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X29),X28)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).

fof(fact_div__dvd__div,axiom,
    ! [X6,X14,X13,X10] :
      ( class_Divides_Osemiring__div(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X13),X14))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X13),X6))
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X14),X13)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X6),X13)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X14),X6)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__dvd__div) ).

fof(fact_unity__coeff__ex,axiom,
    ! [X83,X42,X10] :
      ( ( class_Rings_Odvd(X10)
        & class_Rings_Osemiring__0(X10) )
     => ( ? [X3] : hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X83),X3)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X83),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X3),c_Groups_Ozero__class_Ozero(X10))))
            & hBOOL(hAPP(X42,X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unity__coeff__ex) ).

fof(fact_zip__map__fst__snd,axiom,
    ! [X206,X8,X10] : hAPP(hAPP(c_List_Ozip(X10,X8),hAPP(hAPP(c_List_Omap(tc_prod(X10,X8),X10),c_Product__Type_Ofst(X10,X8)),X206)),hAPP(hAPP(c_List_Omap(tc_prod(X10,X8),X8),c_Product__Type_Osnd(X10,X8)),X206)) = X206,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__map__fst__snd) ).

fof(fact_setprod__reindex__cong,axiom,
    ! [X7,X1,X15,X12,X2,X8,X10,X18] :
      ( class_Groups_Ocomm__monoid__mult(X18)
     => ( c_Fun_Oinj__on(X10,X8,X2,X12)
       => ( X15 = hAPP(c_Set_Oimage(X10,X8,X2),X12)
         => ( X1 = hAPP(c_Fun_Ocomp(X8,X18,X10,X7),X2)
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X18),X7),X15) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X18),X1),X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex__cong) ).

fof(fact_sum__squares__ge__zero,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__ring(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X34)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__ge__zero) ).

fof(fact_pred__nat__trancl__eq__le,axiom,
    ! [X30,X31] :
      ( 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),X31),X30)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__nat__trancl__eq__le) ).

fof(fact_folding_Ocommute__comp,axiom,
    ! [X11,X16,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X2,X16)),hAPP(X2,X11)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X2,X11)),hAPP(X2,X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Ocommute__comp) ).

fof(fact_Sigma__Int__distrib1,axiom,
    ! [X17,X176,X161,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X161),X176)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X17)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X176),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Int__distrib1) ).

fof(fact_Sigma__Un__distrib1,axiom,
    ! [X17,X176,X161,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X161),X176)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X17)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X176),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Un__distrib1) ).

fof(fact_Sigma__Diff__distrib1,axiom,
    ! [X17,X176,X161,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X161),X176)),X17) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X161),X17)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X176),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__Diff__distrib1) ).

fof(fact_in__set__butlast__appendI,axiom,
    ! [X199,X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Obutlast(X10,X200))))
        | hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Obutlast(X10,X199)))) )
     => hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Obutlast(X10,hAPP(hAPP(c_List_Oappend(X10),X200),X199))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__butlast__appendI) ).

fof(fact_acc__subset,axiom,
    ! [X149,X150,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X150),X149))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Wellfounded_Oacc(X10,X149)),c_Wellfounded_Oacc(X10,X150))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__subset) ).

fof(fact_insort__key__left__comm,axiom,
    ! [X200,X8,X16,X11,X2,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hAPP(X2,X11) != hAPP(X2,X16)
       => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X16),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),X200)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X16),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key__left__comm) ).

fof(fact_surj__f__inv__f,axiom,
    ! [X16,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
     => hAPP(X2,hAPP(c_Hilbert__Choice_Oinv__into(X8,X10,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),X2),X16)) = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__f__inv__f) ).

fof(fact_divmod__int__rel__div__mod,axiom,
    ! [X37,X36] :
      ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div__mod) ).

fof(fact_INT__extend__simps_I10_J,axiom,
    ! [X2,X15,X18,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(X18,tc_fun(X10,tc_HOL_Obool),X8),X15),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X18,X2),X12)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__extend__simps_I10_J) ).

fof(fact_UN__extend__simps_I10_J,axiom,
    ! [X2,X15,X18,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(X18,tc_fun(X10,tc_HOL_Obool),X8),X15),X2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X18,X2),X12)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__extend__simps_I10_J) ).

fof(fact_INT__simps_I10_J,axiom,
    ! [X15,X12,X2,X18,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18,X8,X2),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(X8,tc_fun(X10,tc_HOL_Obool),X18),X15),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__simps_I10_J) ).

fof(fact_UN__simps_I10_J,axiom,
    ! [X15,X12,X2,X18,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18,X8,X2),X12)),X15) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X18,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBB(X8,tc_fun(X10,tc_HOL_Obool),X18),X15),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__simps_I10_J) ).

fof(fact_divmod__nat__rel,axiom,
    ! [X25,X24] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X24,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).

fof(fact_Compl__anti__mono,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__anti__mono) ).

fof(fact_finite__surj__inj,axiom,
    ! [X2,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_Oimage(X10,X10,X2),X12)))
       => c_Fun_Oinj__on(X10,X10,X2,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj__inj) ).

fof(fact_Compl__Times__UNIV1,axiom,
    ! [X12,X8,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X12))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X8),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Times__UNIV1) ).

fof(fact_Compl__Times__UNIV2,axiom,
    ! [X12,X8,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Times__UNIV2) ).

fof(fact_Cons__acc__listrel1I,axiom,
    ! [X200,X110,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),c_Wellfounded_Oacc(X10,X110)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X200),c_Wellfounded_Oacc(tc_List_Olist(X10),c_List_Olistrel1(X10,X110))))
       => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),c_Wellfounded_Oacc(tc_List_Olist(X10),c_List_Olistrel1(X10,X110)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__acc__listrel1I) ).

fof(fact_neg__divide__less__eq,axiom,
    ! [X13,X14,X6,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),X13))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__less__eq) ).

fof(fact_neg__divide__le__eq,axiom,
    ! [X13,X14,X6,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),X13))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__divide__le__eq) ).

fof(fact_accp__subset,axiom,
    ! [X149,X150,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X150),X149))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Wellfounded_Oaccp(X10,X149)),c_Wellfounded_Oaccp(X10,X150))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__subset) ).

fof(fact_folding__idem_Osubset__comp__idem,axiom,
    ! [X15,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__idem(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
         => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X9,X15)) = hAPP(X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).

fof(fact_insort__insert__triv,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X11,X200) = X200 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__insert__triv) ).

fof(fact_split__div__lemma,axiom,
    ! [X31,X141,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),X141)),X31))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),hAPP(c_Nat_OSuc,X141)))) )
      <=> X141 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X31),X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div__lemma) ).

fof(fact_setsum__diff,axiom,
    ! [X2,X15,X12,X10,X8] :
      ( class_Groups_Oab__group__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff) ).

fof(fact_id__take__nth__drop,axiom,
    ! [X202,X27,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => X202 = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Otake(X27),X44),X202)),hAPP(hAPP(c_List_Olist_OCons(X27),hAPP(hAPP(c_List_Onth(X27),X202),X44)),hAPP(hAPP(c_List_Odrop(X27),hAPP(c_Nat_OSuc,X44)),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__take__nth__drop) ).

fof(fact_less__than__iff,axiom,
    ! [X16,X11] :
      ( 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),X11),X16)),c_Wellfounded_Oless__than))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__iff) ).

fof(fact_image__image,axiom,
    ! [X12,X1,X18,X2,X10,X8] : hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_Set_Oimage(X18,X8,X1),X12)) = hAPP(c_Set_Oimage(X18,X10,hAPP(hAPP(c_COMBB(X8,X10,X18),X2),X1)),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__image) ).

fof(fact_map__inj__on,axiom,
    ! [X199,X200,X2,X10,X8] :
      ( hAPP(hAPP(c_List_Omap(X8,X10),X2),X200) = hAPP(hAPP(c_List_Omap(X8,X10),X2),X199)
     => ( c_Fun_Oinj__on(X8,X10,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),hAPP(c_List_Oset(X8),X200)),hAPP(c_List_Oset(X8),X199)))
       => X200 = X199 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__inj__on) ).

fof(fact_inj__on__map__eq__map,axiom,
    ! [X199,X200,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(c_List_Oset(X10),X199)))
     => ( hAPP(hAPP(c_List_Omap(X10,X8),X2),X200) = hAPP(hAPP(c_List_Omap(X10,X8),X2),X199)
      <=> X200 = X199 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__map__eq__map) ).

fof(fact_zdiff__int__split,axiom,
    ! [X16,X11,X42] :
      ( hBOOL(hAPP(X42,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X16))))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16),X11))
         => hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X16))
         => hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int__split) ).

fof(fact_listsp__infI,axiom,
    ! [X15,X83,X12,X10] :
      ( hBOOL(hAPP(c_List_Olistsp(X10,X12),X83))
     => ( hBOOL(hAPP(c_List_Olistsp(X10,X15),X83))
       => hBOOL(hAPP(c_List_Olistsp(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X83)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__infI) ).

fof(fact_power__le__dvd,axiom,
    ! [X24,X36,X25,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X24)),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__dvd) ).

fof(fact_ex__bij__betw__nat__finite__1,axiom,
    ! [X143,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X143))
     => ? [X262] : c_Fun_Obij__betw(tc_Nat_Onat,X10,X262,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X143)),X143) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__bij__betw__nat__finite__1) ).

fof(fact_Image__Int__eq,axiom,
    ! [X15,X12,X29,X8,X10] :
      ( c_Relation_Osingle__valued(X10,X8,hAPP(c_Relation_Oconverse(X8,X10),X29))
     => hAPP(c_Relation_OImage(X8,X10,X29),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X10,X29),X12)),hAPP(c_Relation_OImage(X8,X10,X29),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Int__eq) ).

fof(fact_frac__less2,axiom,
    ! [X38,X92,X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X92))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X92),X38))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X38)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X34),X92))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less2) ).

fof(fact_frac__less,axiom,
    ! [X38,X92,X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X92))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X92),X38))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X38)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X34),X92))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__less) ).

fof(fact_mult__strict__mono,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),X58))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X58))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono) ).

fof(fact_mult__strict__mono_H,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),X58))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X58))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__mono_H) ).

fof(fact_mult__le__less__imp__less,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),X58))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X58))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__less__imp__less) ).

fof(fact_mult__less__le__imp__less,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),X58))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X58))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__le__imp__less) ).

fof(fact_frac__le,axiom,
    ! [X38,X92,X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X92))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X92),X38))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X38)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X34),X92))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__le) ).

fof(fact_mult__mono_H,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Rings_Oordered__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),X58))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X58))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono_H) ).

fof(fact_mult__mono,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Rings_Oordered__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),X58))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X58))) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__mono) ).

fof(fact_setsum__diff1__ring,axiom,
    ! [X2,X13,X12,X10,X8] :
      ( class_Rings_Oring(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(X2,X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff1__ring) ).

fof(fact_geometric__sum,axiom,
    ! [X30,X11,X10] :
      ( class_Fields_Ofield(X10)
     => ( X11 != c_Groups_Oone__class_Oone(X10)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(c_Power_Opower__class_Opower(X10),X11)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X11),X30)),c_Groups_Oone__class_Oone(X10))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X11),c_Groups_Oone__class_Oone(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_geometric__sum) ).

fof(fact_listsum__abs,axiom,
    ! [X200,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),hAPP(c_List_Omonoid__add__class_Olistsum(X10),X200))),hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X10,X10),c_Groups_Oabs__class_Oabs(X10)),X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__abs) ).

fof(fact_ex__bij__betw__nat__finite,axiom,
    ! [X143,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X143))
     => ? [X262] : c_Fun_Obij__betw(tc_Nat_Onat,X10,X262,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X143)),X143) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__bij__betw__nat__finite) ).

fof(fact_ex__bij__betw__finite__nat,axiom,
    ! [X143,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X143))
     => ? [X262] : c_Fun_Obij__betw(X10,tc_Nat_Onat,X262,X143,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X143))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__bij__betw__finite__nat) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [X60,X61,X32] : 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)),X32)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X61),X60)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),X32)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X32)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_setsum__add__nat__ivl,axiom,
    ! [X2,X148,X30,X31,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X148))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X30),X148))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X148)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__add__nat__ivl) ).

fof(fact_setsum__diff__nat__ivl,axiom,
    ! [X2,X148,X30,X31,X10] :
      ( class_Groups_Oab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X148))
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X148))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X30),X148)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff__nat__ivl) ).

fof(fact_mult__right__less__imp__less,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Rings_Olinordered__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__less__imp__less) ).

fof(fact_mult__less__imp__less__right,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__right) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [X36,X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),X25)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_mult__left__less__imp__less,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Rings_Olinordered__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__less__imp__less) ).

fof(fact_mult__less__imp__less__left,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__imp__less__left) ).

fof(fact_mult__less__cancel__left__pos,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X14)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__pos) ).

fof(fact_mult__right__le__imp__le,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__imp__le) ).

fof(fact_mult__left__le__imp__le,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__imp__le) ).

fof(fact_mult__le__cancel__left__pos,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X14)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__pos) ).

fof(fact_setsum__diff__nat,axiom,
    ! [X2,X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__diff__nat) ).

fof(fact_fold1__strict__below__iff,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X12)),X11))
          <=> ? [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X3),X11)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__strict__below__iff) ).

fof(fact_fold1__below__iff,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X12)),X11))
          <=> ? [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X11)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__below__iff) ).

fof(fact_INF1__D,axiom,
    ! [X13,X14,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15),X14))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hBOOL(hAPP(hAPP(X15,X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF1__D) ).

fof(fact_power__less__imp__less__exp,axiom,
    ! [X25,X24,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__imp__less__exp) ).

fof(fact_power__strict__increasing__iff,axiom,
    ! [X16,X11,X14,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X14),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X14),X16)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_power__le__imp__le__exp,axiom,
    ! [X25,X24,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__le__imp__le__exp) ).

fof(fact_power__increasing__iff,axiom,
    ! [X16,X11,X14,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X14),X11)),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X14),X16)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing__iff) ).

fof(fact_select,axiom,
    ! [X116,X10,X200] :
      ( X200 != c_List_Olist_ONil(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Product__Type_Ofst(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X10,X200),X116))),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select) ).

fof(fact_card__cartesian__product__singleton,axiom,
    ! [X12,X11,X8,X10] : hAPP(c_Finite__Set_Ocard(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X12))) = hAPP(c_Finite__Set_Ocard(X8),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__cartesian__product__singleton) ).

fof(fact_splitD,axiom,
    ! [X14,X13,X2,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)))
     => hBOOL(hAPP(hAPP(X2,X13),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitD) ).

fof(fact_swap__inj__on,axiom,
    ! [X12,X8,X10] : c_Fun_Oinj__on(tc_prod(X10,X8),tc_prod(X8,X10),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_prod(X8,X10)),hAPP(c_COMBC(X8,X10,tc_prod(X8,X10)),c_Product__Type_OPair(X8,X10))),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_swap__inj__on) ).

fof(fact_setprod__pos__nat,axiom,
    ! [X2,X28,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X28))
           => 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(X10,tc_Nat_Onat),X2),X28))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__pos__nat) ).

fof(fact_setprod__pos__nat__iff,axiom,
    ! [X2,X28,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
     => ( 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(X10,tc_Nat_Onat),X2),X28)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X28))
           => 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,
    ! [X30,X31,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X31),hAPP(c_Nat_OSuc,X30))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Nat_Onat),X2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__cl__Suc__ivl) ).

fof(fact_mult__less__cancel__left__neg,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X14)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__neg) ).

fof(fact_mult__le__cancel__left__neg,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X14)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel__left__neg) ).

fof(fact_Int__lower1,axiom,
    ! [X15,X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower1) ).

fof(fact_Int__lower2,axiom,
    ! [X15,X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__lower2) ).

fof(fact_Diff__subset,axiom,
    ! [X15,X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__subset) ).

fof(fact_listsum__map__remove1,axiom,
    ! [X2,X200,X11,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(X2,X11)),hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),c_List_Oremove1(X10,X11,X200)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__map__remove1) ).

fof(fact_Int__Un__distrib,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).

fof(fact_Diff__Int__distrib,axiom,
    ! [X15,X12,X17,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X17),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X17),X12)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X17),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int__distrib) ).

fof(fact_Un__Int__distrib,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).

fof(fact_Diff__Int,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Int) ).

fof(fact_Diff__Un,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Un) ).

fof(fact_prod_Orecs,axiom,
    ! [X14,X13,X50,X10,X18,X8] : c_Product__Type_Oprod_Oprod__rec(X8,X18,X10,X50,hAPP(hAPP(c_Product__Type_OPair(X8,X18),X13),X14)) = hAPP(hAPP(X50,X13),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).

fof(fact_New__DSequence_Oneg__bind__def,axiom,
    ! [X61,X2,X11,X10,X8] : hAPP(c_New__DSequence_Oneg__bind(X8,X10,X11,X2),X61) = c_Lazy__Sequence_Ohb__bind(X8,X10,hAPP(X11,X61),hAPP(hAPP(c_COMBC(X8,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X10))),X2),X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).

fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
    ! [X30,X31,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X31)),hAPP(c_Nat_OSuc,X30))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,tc_Nat_Onat),X2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__bounds__Suc__ivl) ).

fof(fact_image__add__atLeastAtMost,axiom,
    ! [X60,X61,X32] : 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)),X32)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X61,X60)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X32)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__atLeastAtMost) ).

fof(fact_Int__Collect,axiom,
    ! [X42,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_OCollect(X10),X42))))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
        & hBOOL(hAPP(X42,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Collect) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X6),X20)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X13))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X20)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_folding__idem_Ounion__idem,axiom,
    ! [X15,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__idem(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Ounion__idem) ).

fof(fact_wf__Un,axiom,
    ! [X116,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ( c_Wellfounded_Owf(X10,X116)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X10),X110)),hAPP(c_Relation_ORange(X10,X10),X116)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Un) ).

fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
    ! [X200,X16,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X16),hAPP(c_List_Oset(X10),X200)) = hAPP(c_List_Ofoldl(X8,X10,hAPP(c_COMBC(X10,X8,X8),X2),X16),c_List_Oremdups(X10,X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).

fof(fact_converse__meet,axiom,
    ! [X116,X110,X10,X8] : c_Predicate_Oconversep(X8,X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_fun(X10,tc_HOL_Obool))),X110),X116)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),c_Predicate_Oconversep(X8,X10,X110)),c_Predicate_Oconversep(X8,X10,X116)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__meet) ).

fof(fact_converse__join,axiom,
    ! [X116,X110,X10,X8] : c_Predicate_Oconversep(X8,X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_fun(X10,tc_HOL_Obool))),X110),X116)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),c_Predicate_Oconversep(X8,X10,X110)),c_Predicate_Oconversep(X8,X10,X116)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__join) ).

fof(fact_less__diff__iff,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X31))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),X32)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30),X32)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__iff) ).

fof(fact_le__diff__iff,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X31))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X30))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),X32)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30),X32)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__iff) ).

fof(fact_mult__less__cancel__left__disj,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X14)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).

fof(fact_mult__less__cancel__right__disj,axiom,
    ! [X14,X6,X13,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),X13)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).

fof(fact_insert__subset,axiom,
    ! [X15,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),X15))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__subset) ).

fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
    ! [X2,X12,X10] :
      ( ( class_Groups_Ocomm__monoid__add(X10)
        & class_Groups_Ocomm__monoid__mult(X10) )
     => ( c_Nat__Transfer_Onat__set(X12)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),X2),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10,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),X12)) ) ),
    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,X12,X10] :
      ( ( class_Groups_Ocomm__monoid__add(X10)
        & class_Groups_Ocomm__monoid__mult(X10) )
     => ( c_Nat__Transfer_Onat__set(X12)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X10),X2),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10,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),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__sum__prod_I2_J) ).

fof(fact_setsum__Un__disjoint,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__Un__disjoint) ).

fof(fact_setprod_Ounion__disjoint,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Ounion__disjoint) ).

fof(fact_setprod__Un__disjoint,axiom,
    ! [X1,X15,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X15)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__Un__disjoint) ).

fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
    ! [X12,X2,X10] :
      ( ( class_Groups_Ocomm__monoid__add(X10)
        & class_Groups_Ocomm__monoid__mult(X10) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X12)) ),
    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,
    ! [X12,X2,X10] :
      ( ( class_Groups_Ocomm__monoid__add(X10)
        & class_Groups_Ocomm__monoid__mult(X10) )
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X10),X2),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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)),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__sum__prod_I2_J) ).

fof(fact_listrel__subset__rtrancl__listrel1,axiom,
    ! [X110,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_List_Olistrel(X10,X110)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).

fof(fact_image__add__int__atLeastLessThan,axiom,
    ! [X77,X83] : 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)),X83)),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),X77),X83))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X83),X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__add__int__atLeastLessThan) ).

fof(fact_drop__append,axiom,
    ! [X201,X202,X25,X27] : hAPP(hAPP(c_List_Odrop(X27),X25),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Odrop(X27),X25),X202)),hAPP(hAPP(c_List_Odrop(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__append) ).

fof(fact_take__append,axiom,
    ! [X201,X202,X25,X27] : hAPP(hAPP(c_List_Otake(X27),X25),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Otake(X27),X25),X202)),hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__append) ).

fof(fact_set__remove1__subset,axiom,
    ! [X200,X11,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X11,X200))),hAPP(c_List_Oset(X10),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remove1__subset) ).

fof(fact_set__sublist__subset,axiom,
    ! [X161,X200,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X200,X161))),hAPP(c_List_Oset(X10),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sublist__subset) ).

fof(fact_inj__on__the__inv__into,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => c_Fun_Oinj__on(X8,X10,c_Fun_Othe__inv__into(X10,X8,X12,X2),hAPP(c_Set_Oimage(X10,X8,X2),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__the__inv__into) ).

fof(fact_Domain__Collect__split,axiom,
    ! [X42,X8,X10] : hAPP(c_Relation_ODomain(X10,X8),hAPP(c_Set_OCollect(tc_prod(X10,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),X42))) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool,X10),c_HOL_OEx(X8)),X42)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Collect__split) ).

fof(fact_fun__left__comm__idem_Ofold__set,axiom,
    ! [X200,X16,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm__idem(X10,X8,X2)
     => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X16),hAPP(c_List_Oset(X10),X200)) = hAPP(c_List_Ofoldl(X8,X10,hAPP(c_COMBC(X10,X8,X8),X2),X16),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__set) ).

fof(fact_assms_I2_J,axiom,
    ! [X4,X23] :
      ( v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X23)),X4),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X23)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
     => v_P(X4,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X23)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I2_J) ).

fof(fact_setsum__negf,axiom,
    ! [X12,X2,X8,X10] :
      ( class_Groups_Oab__group__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBB(X10,X10,X8),c_Groups_Ouminus__class_Ouminus(X10)),X2)),X12) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__negf) ).

fof(fact_abs__setprod,axiom,
    ! [X12,X2,X8,X10] :
      ( class_Fields_Olinordered__field(X10)
     => hAPP(c_Groups_Oabs__class_Oabs(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),X2),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),hAPP(hAPP(c_COMBB(X10,X10,X8),c_Groups_Oabs__class_Oabs(X10)),X2)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__setprod) ).

fof(fact_all__set__conv__all__nth,axiom,
    ! [X42,X200,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,X3)) )
    <=> ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
         => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X91))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__set__conv__all__nth) ).

fof(fact_insert__mono,axiom,
    ! [X13,X21,X17,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X17),X21))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X17)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X21))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__mono) ).

fof(fact_sorted__append,axiom,
    ! [X199,X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Oappend(X10),X200),X199))
      <=> ( c_List_Olinorder__class_Osorted(X10,X200)
          & c_List_Olinorder__class_Osorted(X10,X199)
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
             => ! [X66] :
                  ( hBOOL(hAPP(hAPP(c_member(X10),X66),hAPP(c_List_Oset(X10),X199)))
                 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X66)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__append) ).

fof(fact_power__less__power__Suc,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__less__power__Suc) ).

fof(fact_double__diff,axiom,
    ! [X17,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X17))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X17),X12)) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__diff) ).

fof(fact_Pow__mono,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X12)),hAPP(c_Set_OPow(X10),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__mono) ).

fof(fact_K__record__comp,axiom,
    ! [X11,X2,X6,X18,X10,X8] : hAPP(hAPP(c_Fun_Ocomp(X8,X10,X18,hAPP(c_COMBK(X10,X8),X6)),X2),X11) = X6,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_K__record__comp) ).

fof(fact_set__drop__subset,axiom,
    ! [X200,X30,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Odrop(X10),X30),X200))),hAPP(c_List_Oset(X10),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__drop__subset) ).

fof(fact_set__take__subset,axiom,
    ! [X200,X30,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),X30),X200))),hAPP(c_List_Oset(X10),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__take__subset) ).

fof(fact_pos__less__divide__eq,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__less__divide__eq) ).

fof(fact_pos__divide__less__eq,axiom,
    ! [X13,X14,X6,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),X13))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__less__eq) ).

fof(fact_mult__imp__less__div__pos,axiom,
    ! [X26,X38,X34,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X34)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X38),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__less__div__pos) ).

fof(fact_pos__le__divide__eq,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__le__divide__eq) ).

fof(fact_pos__divide__le__eq,axiom,
    ! [X13,X14,X6,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),X13))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__divide__le__eq) ).

fof(fact_mult__imp__le__div__pos,axiom,
    ! [X26,X38,X34,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X34)),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X38),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__le__div__pos) ).

fof(fact_takeWhile__nth,axiom,
    ! [X200,X42,X10,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200))))
     => hAPP(hAPP(c_List_Onth(X10),c_List_OtakeWhile(X10,X42,X200)),X60) = hAPP(hAPP(c_List_Onth(X10),X200),X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__nth) ).

fof(fact_of__int__setprod,axiom,
    ! [X12,X2,X8,X10] :
      ( ( class_Groups_Ocomm__monoid__mult(X10)
        & class_Rings_Oring__1(X10) )
     => hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,tc_Int_Oint),X2),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10,X8),c_Int_Oring__1__class_Oof__int(X10)),X2)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__setprod) ).

fof(fact_of__nat__setprod,axiom,
    ! [X12,X2,X8,X10] :
      ( ( class_Groups_Ocomm__monoid__mult(X10)
        & class_Rings_Osemiring__1(X10) )
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,tc_Nat_Onat),X2),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,X8),c_Nat_Osemiring__1__class_Oof__nat(X10)),X2)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__setprod) ).

fof(fact_converse__Int,axiom,
    ! [X116,X110,X10,X8] : hAPP(c_Relation_Oconverse(X8,X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),X110),X116)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X8,X10),X110)),hAPP(c_Relation_Oconverse(X8,X10),X116)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Int) ).

fof(fact_converse__Un,axiom,
    ! [X116,X110,X10,X8] : hAPP(c_Relation_Oconverse(X8,X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),X110),X116)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X8,X10),X110)),hAPP(c_Relation_Oconverse(X8,X10),X116)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Un) ).

fof(fact_length__takeWhile__le,axiom,
    ! [X200,X42,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__takeWhile__le) ).

fof(fact_funpow__add,axiom,
    ! [X2,X30,X31,X10] : hAPP(hAPP(c_Nat_Ocompow(X10,X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30)),X2) = hAPP(c_Fun_Ocomp(X10,X10,X10,hAPP(hAPP(c_Nat_Ocompow(X10,X10),X31),X2)),hAPP(hAPP(c_Nat_Ocompow(X10,X10),X30),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__add) ).

fof(fact_of__int__setsum,axiom,
    ! [X12,X2,X8,X10] :
      ( class_Rings_Oring__1(X10)
     => hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,tc_Int_Oint),X2),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBB(tc_Int_Oint,X10,X8),c_Int_Oring__1__class_Oof__int(X10)),X2)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__setsum) ).

fof(fact_of__nat__setsum,axiom,
    ! [X12,X2,X8,X10] :
      ( class_Rings_Osemiring__1(X10)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,tc_Nat_Onat),X2),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,X8),c_Nat_Osemiring__1__class_Oof__nat(X10)),X2)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__setsum) ).

fof(fact_inj__singleton,axiom,
    ! [X10] : c_Fun_Oinj__on(X10,tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__singleton) ).

fof(fact_finite__cartesian__product,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__cartesian__product) ).

fof(fact_card__psubset,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__psubset) ).

fof(fact_finite__surj,axiom,
    ! [X2,X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X15),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__surj) ).

fof(fact_bij__id,axiom,
    ! [X10] : c_Fun_Obij__betw(X10,X10,c_Fun_Oid(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__id) ).

fof(fact_inj__on__Int,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( c_Fun_Oinj__on(X10,X8,X2,X15)
       => c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Int) ).

fof(fact_nth__drop,axiom,
    ! [X202,X27,X44,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X44)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Odrop(X27),X25),X202)),X44) = hAPP(hAPP(c_List_Onth(X27),X202),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X44)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__drop) ).

fof(fact_sorted__rev__nth__mono,axiom,
    ! [X43,X44,X202,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( c_List_Olinorder__class_Osorted(X27,hAPP(c_List_Orev(X27),X202))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_List_Onth(X27),X202),X43)),hAPP(hAPP(c_List_Onth(X27),X202),X44))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__rev__nth__mono) ).

fof(fact_zip__append,axiom,
    ! [X221,X201,X219,X10,X202,X27] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X219)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X201) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X221)
       => hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),hAPP(hAPP(c_List_Oappend(X10),X219),X221)) = hAPP(hAPP(c_List_Oappend(tc_prod(X27,X10)),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X219)),hAPP(hAPP(c_List_Ozip(X27,X10),X201),X221)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__append) ).

fof(fact_list__size__map,axiom,
    ! [X200,X1,X8,X2,X10] : c_List_Olist_Olist__size(X10,X2,hAPP(hAPP(c_List_Omap(X8,X10),X1),X200)) = c_List_Olist_Olist__size(X8,hAPP(c_Fun_Ocomp(X10,tc_Nat_Onat,X8,X2),X1),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__map) ).

fof(fact_refl__onD,axiom,
    ! [X13,X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X13)),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__onD) ).

fof(fact_UN__upper,axiom,
    ! [X15,X8,X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(X15,X13)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__upper) ).

fof(fact_take__Cons__number__of,axiom,
    ! [X202,X26,X27,X68] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = c_List_Olist_ONil(X27) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons__number__of) ).

fof(fact_predicate2D,axiom,
    ! [X16,X11,X41,X42,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X42),X41))
     => ( hBOOL(hAPP(hAPP(X42,X11),X16))
       => hBOOL(hAPP(hAPP(X41,X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [X41,X8,X10,X16,X11,X42] :
      ( hBOOL(hAPP(hAPP(X42,X11),X16))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X42),X41))
       => hBOOL(hAPP(hAPP(X41,X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate2D) ).

fof(fact_fold1__antimono,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X15)),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X12))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__antimono) ).

fof(fact_Un__iff,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
        | hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__iff) ).

fof(fact_field__le__epsilon,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( ! [X251] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X251))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X34),X251))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__le__epsilon) ).

fof(fact_foldl__Cons,axiom,
    ! [X200,X11,X13,X2,X8,X10] : hAPP(c_List_Ofoldl(X10,X8,X2,X13),hAPP(hAPP(c_List_Olist_OCons(X8),X11),X200)) = hAPP(c_List_Ofoldl(X10,X8,X2,hAPP(hAPP(X2,X13),X11)),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Cons) ).

fof(fact_length__transpose__sorted,axiom,
    ! [X200,X10] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),X200)))
     => ( ( X200 = c_List_Olist_ONil(tc_List_Olist(X10))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X200)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X200 != c_List_Olist_ONil(tc_List_Olist(X10))
         => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X10))),c_List_Otranspose(X10,X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X10)),X200),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,
    ! [X25,X36,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),X25))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__mono) ).

fof(fact_power__strict__decreasing,axiom,
    ! [X37,X126,X25,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X126))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Oone__class_Oone(X27)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X126)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__decreasing) ).

fof(fact_power__decreasing,axiom,
    ! [X37,X126,X25,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X126))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Oone__class_Oone(X27)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X126)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__decreasing) ).

fof(fact_vimage__Int,axiom,
    ! [X15,X12,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,X2),X12)),hAPP(c_Set_Ovimage(X10,X8,X2),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Int) ).

fof(fact_vimage__Un,axiom,
    ! [X15,X12,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,X2),X12)),hAPP(c_Set_Ovimage(X10,X8,X2),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Un) ).

fof(fact_vimage__Diff,axiom,
    ! [X15,X12,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,X2),X12)),hAPP(c_Set_Ovimage(X10,X8,X2),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Diff) ).

fof(fact_Image__Un,axiom,
    ! [X15,X12,X29,X10,X8] : hAPP(c_Relation_OImage(X8,X10,X29),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OImage(X8,X10,X29),X12)),hAPP(c_Relation_OImage(X8,X10,X29),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Un) ).

fof(fact_image__Un,axiom,
    ! [X15,X12,X2,X10,X8] : hAPP(c_Set_Oimage(X8,X10,X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X10,X2),X12)),hAPP(c_Set_Oimage(X8,X10,X2),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Un) ).

fof(fact_append__in__lists__conv,axiom,
    ! [X12,X199,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X200),X199)),c_List_Olists(X10,X12)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X200),c_List_Olists(X10,X12)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X199),c_List_Olists(X10,X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__lists__conv) ).

fof(fact_Powp__mono,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X10,X12)),c_Predicate_OPowp(X10,X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__mono) ).

fof(fact_distinct__product,axiom,
    ! [X201,X10,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => ( hBOOL(hAPP(c_List_Odistinct(X10),X201))
       => hBOOL(hAPP(c_List_Odistinct(tc_prod(X27,X10)),c_Enum_Oproduct(X27,X10,X202,X201))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__product) ).

fof(fact_finite__Plus,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X8)),c_Sum__Type_OPlus(X10,X8,X12,X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus) ).

fof(fact_Id__on__eqI,axiom,
    ! [X12,X10,X14,X13] :
      ( X13 = X14
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X14)),c_Relation_OId__on(X10,X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__eqI) ).

fof(fact_Rep__Integ__induct,axiom,
    ! [X42,X16] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X16),c_Int_OInteg))
     => ( ! [X3] : hBOOL(hAPP(X42,hAPP(c_Int_ORep__Integ,X3)))
       => hBOOL(hAPP(X42,X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__induct) ).

fof(fact_list__update__append1,axiom,
    ! [X26,X201,X202,X27,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X44),X26) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)),X201) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__append1) ).

fof(fact_dvd__mult__cancel,axiom,
    ! [X25,X24,X33] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X25)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel) ).

fof(fact_nat__mult__dvd__cancel1,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel1) ).

fof(fact_nat__power__less__imp__less,axiom,
    ! [X25,X24,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X44),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X44),X25)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__less__imp__less) ).

fof(fact_nat__mult__less__cancel1,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_mult__le__cancel2,axiom,
    ! [X30,X32,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X32)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel2) ).

fof(fact_nat__mult__le__cancel1,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__le__cancel1) ).

fof(fact_mult__le__cancel1,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__cancel1) ).

fof(fact_power__dvd__imp__le,axiom,
    ! [X25,X24,X44] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X44),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X44),X25)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X44))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__dvd__imp__le) ).

fof(fact_wfE__pf,axiom,
    ! [X12,X29,X10] :
      ( c_Wellfounded_Owf(X10,X29)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Relation_OImage(X10,X10,X29),X12)))
       => X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfE__pf) ).

fof(fact_int__setsum,axiom,
    ! [X12,X2,X10] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__setsum) ).

fof(fact_int__setprod,axiom,
    ! [X12,X2,X10] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Nat_Onat),X2),X12)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X10),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X2)),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__setprod) ).

fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
    ! [X16,X11,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X2,X11)),hAPP(X2,X16)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X2,X16)),hAPP(X2,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).

fof(fact_set__update__memI,axiom,
    ! [X11,X200,X10,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist__update(X10,X200),X30),X11)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__update__memI) ).

fof(fact_UN__I,axiom,
    ! [X15,X14,X8,X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(X15,X13)))
       => hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__I) ).

fof(fact_unique__quotient,axiom,
    ! [X111,X112,X80,X114,X36,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))
       => ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => X114 = X112 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__quotient) ).

fof(fact_unique__remainder,axiom,
    ! [X111,X112,X80,X114,X36,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X112),X111)))
       => ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => X80 = X111 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_unique__remainder) ).

fof(fact_finite__imageD,axiom,
    ! [X12,X2,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_Oimage(X8,X10,X2),X12)))
     => ( c_Fun_Oinj__on(X8,X10,X2,X12)
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageD) ).

fof(fact_dvd__mult__cancel__left,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Rings_Oidom(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X13)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X14)))
      <=> ( X6 = c_Groups_Ozero__class_Ozero(X10)
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X13),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__left) ).

fof(fact_dvd__mult__cancel__right,axiom,
    ! [X14,X6,X13,X10] :
      ( class_Rings_Oidom(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X6)))
      <=> ( X6 = c_Groups_Ozero__class_Ozero(X10)
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X13),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel__right) ).

fof(fact_single__valued__subset,axiom,
    ! [X116,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X110),X116))
     => ( c_Relation_Osingle__valued(X10,X8,X116)
       => c_Relation_Osingle__valued(X10,X8,X110) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__subset) ).

fof(fact_add__less__cancel__right,axiom,
    ! [X14,X6,X13,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X14),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__right) ).

fof(fact_add__less__imp__less__right,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X35)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__right) ).

fof(fact_add__less__cancel__left,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X6),X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X6),X14)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__cancel__left) ).

fof(fact_add__less__imp__less__left,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X36)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__imp__less__left) ).

fof(fact_add__le__cancel__right,axiom,
    ! [X14,X6,X13,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X6)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X14),X6)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__right) ).

fof(fact_add__le__imp__le__right,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X35)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__right) ).

fof(fact_add__le__cancel__left,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X6),X13)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X6),X14)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__cancel__left) ).

fof(fact_add__le__imp__le__left,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X36)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__imp__le__left) ).

fof(fact_sorted__nth__mono,axiom,
    ! [X43,X44,X202,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( c_List_Olinorder__class_Osorted(X27,X202)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_List_Onth(X27),X202),X44)),hAPP(hAPP(c_List_Onth(X27),X202),X43))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__nth__mono) ).

fof(fact_relpow_Osimps_I2_J,axiom,
    ! [X29,X30,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30)),X29) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)),X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_relpow_Osimps_I2_J) ).

fof(fact_add__divide__eq__iff,axiom,
    ! [X34,X26,X38,X27] :
      ( class_Fields_Ofield(X27)
     => ( X38 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X34),X38)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X26)),X34)),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__eq__iff) ).

fof(fact_diff__divide__eq__iff,axiom,
    ! [X34,X26,X38,X27] :
      ( class_Fields_Ofield(X27)
     => ( X38 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X26),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X34),X38)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X26)),X34)),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__eq__iff) ).

fof(fact_filter__insort,axiom,
    ! [X11,X42,X200,X2,X8,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))
       => ( hBOOL(hAPP(X42,X11))
         => hAPP(c_List_Ofilter(X8,X42),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),X200)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),hAPP(c_List_Ofilter(X8,X42),X200)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__insort) ).

fof(fact_subset__singletonD,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
     => ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        | X12 = hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__singletonD) ).

fof(fact_DiffE,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
         => hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffE) ).

fof(fact_fun__upd__triv,axiom,
    ! [X11,X2,X8,X10] : c_Fun_Ofun__upd(X10,X8,X2,X11,hAPP(X2,X11)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).

fof(fact_fun__upd__idem,axiom,
    ! [X10,X8,X16,X11,X2] :
      ( hAPP(X2,X11) = X16
     => c_Fun_Ofun__upd(X8,X10,X2,X11,X16) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem) ).

fof(fact_folding__idem_Oin__comp__idem,axiom,
    ! [X11,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__idem(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X2,X11)) = hAPP(X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).

fof(fact_take__Suc__conv__app__nth,axiom,
    ! [X202,X27,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Otake(X27),hAPP(c_Nat_OSuc,X44)),X202) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Otake(X27),X44),X202)),hAPP(hAPP(c_List_Olist_OCons(X27),hAPP(hAPP(c_List_Onth(X27),X202),X44)),c_List_Olist_ONil(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc__conv__app__nth) ).

fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__disjoint) ).

fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
               => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__disjoint) ).

fof(fact_comp__funpow,axiom,
    ! [X2,X30,X8,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X10,X8),tc_fun(X10,X8)),X30),c_Fun_Ocomp(X8,X8,X10,X2)) = c_Fun_Ocomp(X8,X8,X10,hAPP(hAPP(c_Nat_Ocompow(X8,X8),X30),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__funpow) ).

fof(fact_New__DSequence_Opos__bind__def,axiom,
    ! [X61,X2,X11,X10,X8] : hAPP(c_New__DSequence_Opos__bind(X8,X10,X11,X2),X61) = hAPP(c_Lazy__Sequence_Obind(X8,X10,hAPP(X11,X61)),hAPP(hAPP(c_COMBC(X8,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X10)),X2),X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).

fof(fact_curry__conv,axiom,
    ! [X14,X13,X2,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Ocurry(X8,X18,X10,X2),X13),X14) = hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(X8,X18),X13),X14)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__conv) ).

fof(fact_curry__def,axiom,
    ! [X16,X11,X6,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Ocurry(X8,X18,X10,X6),X11),X16) = hAPP(X6,hAPP(hAPP(c_Product__Type_OPair(X8,X18),X11),X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__def) ).

fof(fact_inj__on__Un__image__eq__iff,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hAPP(c_Set_Oimage(X10,X8,X2),X12) = hAPP(c_Set_Oimage(X10,X8,X2),X15)
      <=> X12 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__Un__image__eq__iff) ).

fof(fact_mult__imp__div__pos__less,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X34)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__less) ).

fof(fact_mult__imp__div__pos__le,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X34)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__imp__div__pos__le) ).

fof(fact_refl__on__Int,axiom,
    ! [X116,X15,X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
     => ( c_Relation_Orefl__on(X10,X15,X116)
       => c_Relation_Orefl__on(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Int) ).

fof(fact_refl__on__Un,axiom,
    ! [X116,X15,X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
     => ( c_Relation_Orefl__on(X10,X15,X116)
       => c_Relation_Orefl__on(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Un) ).

fof(fact_lazy__sequence_Orecs_I1_J,axiom,
    ! [X49,X50,X8,X10] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X10,X8,X50,X49,c_Lazy__Sequence_Olazy__sequence_OEmpty(X8)) = X50,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Orecs_I1_J) ).

fof(fact_surj__imp__inj__inv,axiom,
    ! [X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
     => c_Fun_Oinj__on(X10,X8,c_Hilbert__Choice_Oinv__into(X8,X10,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__imp__inj__inv) ).

fof(fact_bij__betw__id,axiom,
    ! [X12,X10] : c_Fun_Obij__betw(X10,X10,c_Fun_Oid(X10),X12,X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bij__betw__id) ).

fof(fact_Domain__insert,axiom,
    ! [X110,X14,X13,X8,X10] : hAPP(c_Relation_ODomain(X10,X8),hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),X110)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(c_Relation_ODomain(X10,X8),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__insert) ).

fof(fact_Range__insert,axiom,
    ! [X110,X14,X13,X10,X8] : hAPP(c_Relation_ORange(X8,X10),hAPP(hAPP(c_Set_Oinsert(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X13),X14)),X110)) = hAPP(hAPP(c_Set_Oinsert(X10),X14),hAPP(c_Relation_ORange(X8,X10),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__insert) ).

fof(fact_psubset__trans,axiom,
    ! [X17,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X15),X17))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__trans) ).

fof(fact_subset__psubset__trans,axiom,
    ! [X17,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X15),X17))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__psubset__trans) ).

fof(fact_psubset__subset__trans,axiom,
    ! [X17,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X17))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__subset__trans) ).

fof(fact_subset__trans,axiom,
    ! [X17,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X17))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X17)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__trans) ).

fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
    ! [X12,X11] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X11),X12))
    <=> hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(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)),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I2_J) ).

fof(fact_Pair__scomp,axiom,
    ! [X2,X11,X8,X18,X10] : hAPP(hAPP(c_Product__Type_Oscomp(X10,X18,X10,X8),hAPP(c_Product__Type_OPair(X18,X10),X11)),X2) = hAPP(X2,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__scomp) ).

fof(fact_mod__div__equality,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36)),X36)),c_Divides_Odiv__class_Omod(X27,X37,X36)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality) ).

fof(fact_mod__div__decomp,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => X37 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36)),X36)),c_Divides_Odiv__class_Omod(X27,X37,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__decomp) ).

fof(fact_sorted__sort__key,axiom,
    ! [X200,X2,X8,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_Olinorder__class_Osort__key(X8,X10,X2,X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__sort__key) ).

fof(fact_UN__singleton,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),c_Set_Oinsert(X10)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__singleton) ).

fof(fact_upd__conv__take__nth__drop,axiom,
    ! [X37,X202,X27,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X37) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Otake(X27),X44),X202)),hAPP(hAPP(c_List_Olist_OCons(X27),X37),hAPP(hAPP(c_List_Odrop(X27),hAPP(c_Nat_OSuc,X44)),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upd__conv__take__nth__drop) ).

fof(fact_distinct__set__sublists,axiom,
    ! [X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => hBOOL(hAPP(c_List_Odistinct(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool)),c_List_Oset(X10)),c_Enum_Osublists(X10,X200)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__set__sublists) ).

fof(fact_Pow__insert,axiom,
    ! [X12,X13,X10] : hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X12)),hAPP(c_Set_Oimage(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oinsert(X10),X13)),hAPP(c_Set_OPow(X10),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__insert) ).

fof(fact_finite__vimageD,axiom,
    ! [X9,X7,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_Ovimage(X10,X8,X7),X9)))
     => ( hAPP(c_Set_Oimage(X10,X8,X7),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X9)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__vimageD) ).

fof(fact_Cons__in__lists__iff,axiom,
    ! [X12,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),c_List_Olists(X10,X12)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X200),c_List_Olists(X10,X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__in__lists__iff) ).

fof(fact_range,axiom,
    ! [X55,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X33))
     => 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(X33),X55))),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range) ).

fof(fact_IntD1,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD1) ).

fof(fact_Int__iff,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
        & hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__iff) ).

fof(fact_DiffD1,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DiffD1) ).

fof(fact_IntD2,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntD2) ).

fof(fact_Diff__insert,axiom,
    ! [X15,X13,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__insert) ).

fof(fact_fold1__Un,axiom,
    ! [X15,X12,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
               => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X12)),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__Un) ).

fof(fact_folding__idem_Oinsert__idem,axiom,
    ! [X11,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__idem(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X2,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oinsert__idem) ).

fof(fact_scomp__Pair,axiom,
    ! [X11,X18,X8,X10] : hAPP(hAPP(c_Product__Type_Oscomp(X10,X8,X18,tc_prod(X8,X18)),X11),c_Product__Type_OPair(X8,X18)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_scomp__Pair) ).

fof(fact_Pow__def,axiom,
    ! [X12,X10] : hAPP(c_Set_OPow(X10),X12) = hAPP(c_Set_OCollect(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool))),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__def) ).

fof(fact_rev__foldl__cons,axiom,
    ! [X200,X10] : hAPP(c_List_Orev(X10),X200) = hAPP(c_List_Ofoldl(tc_List_Olist(X10),X10,hAPP(c_COMBC(X10,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_OCons(X10)),c_List_Olist_ONil(X10)),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__foldl__cons) ).

fof(fact_gauss__sum,axiom,
    ! [X30,X10] :
      ( class_Rings_Ocomm__semiring__1(X10)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),c_Groups_Oone__class_Oone(X10))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),c_Nat_Osemiring__1__class_Oof__nat(X10)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X30))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)),c_Groups_Oone__class_Oone(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gauss__sum) ).

fof(fact_length__n__lists__elem,axiom,
    ! [X200,X30,X199,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X199),hAPP(c_List_Oset(tc_List_Olist(X10)),c_Enum_On__lists(X10,X30,X200))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199) = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__n__lists__elem) ).

fof(fact_antisym__subset,axiom,
    ! [X116,X110,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116))
     => ( c_Relation_Oantisym(X10,X116)
       => c_Relation_Oantisym(X10,X110) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__subset) ).

fof(fact_acyclic__subset,axiom,
    ! [X110,X116,X10] :
      ( c_Wellfounded_Oacyclic(X10,X116)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116))
       => c_Wellfounded_Oacyclic(X10,X110) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__subset) ).

fof(fact_wf__subset,axiom,
    ! [X148,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X148),X110))
       => c_Wellfounded_Owf(X10,X148) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__subset) ).

fof(fact_in__set__remove1,axiom,
    ! [X200,X10,X14,X13] :
      ( X13 != X14
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X14,X200))))
      <=> hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_List_Oset(X10),X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__remove1) ).

fof(fact_Int__assoc,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__assoc) ).

fof(fact_Un__assoc,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__assoc) ).

fof(fact_Int__Diff,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Diff) ).

fof(fact_le__add__diff,axiom,
    ! [X24,X25,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)),X33))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff) ).

fof(fact_set__takeWhileD,axiom,
    ! [X200,X42,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_OtakeWhile(X10,X42,X200))))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
        & hBOOL(hAPP(X42,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__takeWhileD) ).

fof(fact_in__set__sublistD,axiom,
    ! [X161,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X200,X161))))
     => hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__sublistD) ).

fof(fact_filter__is__subset,axiom,
    ! [X200,X42,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),hAPP(c_List_Ofilter(X10,X42),X200))),hAPP(c_List_Oset(X10),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__is__subset) ).

fof(fact_crossproduct__noteq,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
     => ( ( X13 != X14
          & X6 != X20 )
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X20)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X20)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__noteq) ).

fof(fact_crossproduct__eq,axiom,
    ! [X19,X11,X16,X90,X10] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X90),X16)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X19)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X90),X19)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X16))
      <=> ( X90 = X11
          | X16 = X19 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_crossproduct__eq) ).

fof(fact_reflp__def,axiom,
    ! [X110,X10] :
      ( c_Predicate_Oreflp(X10,X110)
    <=> c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflp__def) ).

fof(fact_le__diff__conv2,axiom,
    ! [X61,X60,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X60))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X61),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X60),X32)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),X32)),X60)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv2) ).

fof(fact_THE__default__def,axiom,
    ! [X20,X10,X42] :
      ( ( ? [X3] :
            ( hBOOL(hAPP(X42,X3))
            & ! [X51] :
                ( hBOOL(hAPP(X42,X51))
               => X51 = X3 ) )
       => c_FunDef_OTHE__default(X10,X20,X42) = c_HOL_OThe(X10,X42) )
      & ( ~ ? [X3] :
              ( hBOOL(hAPP(X42,X3))
              & ! [X51] :
                  ( hBOOL(hAPP(X42,X51))
                 => X51 = X3 ) )
       => c_FunDef_OTHE__default(X10,X20,X42) = X20 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_THE__default__def) ).

fof(fact_vimageD,axiom,
    ! [X12,X2,X8,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Set_Ovimage(X10,X8,X2),X12)))
     => hBOOL(hAPP(hAPP(c_member(X8),hAPP(X2,X13)),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageD) ).

fof(fact_vimage__eq,axiom,
    ! [X15,X2,X8,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Set_Ovimage(X10,X8,X2),X15)))
    <=> hBOOL(hAPP(hAPP(c_member(X8),hAPP(X2,X13)),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq) ).

fof(fact_drop__Cons,axiom,
    ! [X200,X11,X30,X10] : hAPP(hAPP(c_List_Odrop(X10),X30),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = c_Nat_Onat_Onat__case(tc_List_Olist(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Odrop(X10)),X200),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons) ).

fof(fact_mult__right__le__one__le,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),c_Groups_Oone__class_Oone(X27)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X34)),X26)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__le__one__le) ).

fof(fact_mult__left__le__one__le,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),c_Groups_Oone__class_Oone(X27)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X26)),X26)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__le__one__le) ).

fof(fact_Union__disjoint,axiom,
    ! [X12,X17,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X17)),X12) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),X17))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X3),X12) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__disjoint) ).

fof(fact_zdiv__mono2,axiom,
    ! [X36,X113,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(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X113))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X113))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2) ).

fof(fact_Domain__Un__eq,axiom,
    ! [X15,X12,X8,X10] : hAPP(c_Relation_ODomain(X10,X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X8),X12)),hAPP(c_Relation_ODomain(X10,X8),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).

fof(fact_Range__Un__eq,axiom,
    ! [X15,X12,X10,X8] : hAPP(c_Relation_ORange(X8,X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ORange(X8,X10),X12)),hAPP(c_Relation_ORange(X8,X10),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Un__eq) ).

fof(fact_map__update,axiom,
    ! [X16,X32,X200,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(hAPP(c_List_Olist__update(X8,X200),X32),X16)) = hAPP(hAPP(c_List_Olist__update(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)),X32),hAPP(X2,X16)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__update) ).

fof(fact_set__ConsD,axiom,
    ! [X200,X11,X16,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))))
     => ( X16 = X11
        | hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__ConsD) ).

fof(fact_code__numeral__decr,axiom,
    ! [X33] :
      ( X33 != 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,X33)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X33))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__decr) ).

fof(fact_in__set__dropD,axiom,
    ! [X200,X30,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Odrop(X10),X30),X200))))
     => hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__dropD) ).

fof(fact_in__set__takeD,axiom,
    ! [X200,X30,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Otake(X10),X30),X200))))
     => hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__takeD) ).

fof(fact_power__Suc__less__one,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Oone__class_Oone(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(c_Nat_OSuc,X25))),c_Groups_Oone__class_Oone(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__less__one) ).

fof(fact_zdiv__mono2__neg,axiom,
    ! [X36,X113,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),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)),X113))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X113),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X113)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono2__neg) ).

fof(fact_Id__onE,axiom,
    ! [X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X6),c_Relation_OId__on(X10,X12)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => X6 != hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__onE) ).

fof(fact_inv__f__f,axiom,
    ! [X11,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),hAPP(X2,X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__f) ).

fof(fact_the__inv__f__f,axiom,
    ! [X11,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Fun_Othe__inv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),hAPP(X2,X11)) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__f__f) ).

fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
    ! [X19,X11,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(X2,X11),hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),hAPP(hAPP(X2,X11),X19)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).

fof(fact_inv__f__eq,axiom,
    ! [X16,X11,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hAPP(X2,X11) = X16
       => hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X2),X16) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__f__eq) ).

fof(fact_wfP__subset,axiom,
    ! [X148,X110,X10] :
      ( c_Wellfounded_OwfP(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_fun(X10,tc_HOL_Obool))),X148),X110))
       => c_Wellfounded_OwfP(X10,X148) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__subset) ).

fof(fact_pred__equals__eq,axiom,
    ! [X28,X29,X10] :
      ( hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X29) = hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X28)
    <=> X29 = X28 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__equals__eq) ).

fof(fact_mult__less__cancel1,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel1) ).

fof(fact_mult__less__cancel2,axiom,
    ! [X30,X32,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X32)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel2) ).

fof(fact_sort__key__simps_I2_J,axiom,
    ! [X200,X11,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => c_List_Olinorder__class_Osort__key(X10,X8,X2,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X11),c_List_Olinorder__class_Osort__key(X10,X8,X2,X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__key__simps_I2_J) ).

fof(fact_divide__strict__right__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X35)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono) ).

fof(fact_mult__strict__right__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono) ).

fof(fact_mult__strict__left__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono) ).

fof(fact_comm__mult__strict__left__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Olinordered__comm__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__strict__left__mono) ).

fof(fact_divide__right__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Fields_Olinordered__field__inverse__zero(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X35)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono) ).

fof(fact_power__mono,axiom,
    ! [X25,X36,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),X25))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mono) ).

fof(fact_mult__right__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Oordered__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono) ).

fof(fact_comm__mult__left__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Oordered__comm__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__mult__left__mono) ).

fof(fact_mult__left__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Oordered__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono) ).

fof(fact_zip__Cons__Cons,axiom,
    ! [X201,X34,X202,X26,X10,X27] : hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),hAPP(hAPP(c_List_Olist_OCons(X10),X34),X201)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X27,X10)),hAPP(hAPP(c_Product__Type_OPair(X27,X10),X26),X34)),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Cons__Cons) ).

fof(fact_divide__less__0__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X13),X14)),c_Groups_Ozero__class_Ozero(X10)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),c_Groups_Ozero__class_Ozero(X10))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X14)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__less__0__iff) ).

fof(fact_divide__le__0__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X13),X14)),c_Groups_Ozero__class_Ozero(X10)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),c_Groups_Ozero__class_Ozero(X10))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X14)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__le__0__iff) ).

fof(fact_mult__le__0__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X14)),c_Groups_Ozero__class_Ozero(X10)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),c_Groups_Ozero__class_Ozero(X10))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X14)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).

fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
    ! [X12,X11] :
      ( c_Nat__Transfer_Ois__nat(X11)
     => ( c_Nat__Transfer_Onat__set(X12)
       => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11),X12))
        <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X11)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).

fof(fact_Max__eqI,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X51] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X51),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X51),X11)) )
         => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
           => c_Big__Operators_Olinorder__class_OMax(X10,X12) = X11 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__eqI) ).

fof(fact_nat__mult__dvd__cancel__disj,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)))
    <=> ( X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).

fof(fact_list__all__length,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__all(X10,X42,X200)
    <=> ! [X123] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
         => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X123))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__length) ).

fof(fact_mod__pos__neg__1__number__of,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),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),X92)) = 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),X92))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg__1__number__of) ).

fof(fact_subset__inj__on,axiom,
    ! [X12,X15,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X15)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => c_Fun_Oinj__on(X10,X8,X2,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__inj__on) ).

fof(fact_length__filter__le,axiom,
    ! [X200,X42,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X42),X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__filter__le) ).

fof(fact_rtrancl_Ortrancl__refl,axiom,
    ! [X110,X13,X10] : hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X13)),c_Transitive__Closure_Ortrancl(X10,X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).

fof(fact_nat__add__left__cancel__less,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).

fof(fact_nat__add__left__cancel__le,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).

fof(fact_inv__into__f__f,axiom,
    ! [X11,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,X12,X2),hAPP(X2,X11)) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__f) ).

fof(fact_the__inv__into__f__f,axiom,
    ! [X11,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Fun_Othe__inv__into(X10,X8,X12,X2),hAPP(X2,X11)) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__f) ).

fof(fact_div__pos__neg__1__number__of,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),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),X92)) = 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),X92))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__neg__1__number__of) ).

fof(fact_inv__into__f__eq,axiom,
    ! [X16,X11,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => ( hAPP(X2,X11) = X16
         => hAPP(c_Hilbert__Choice_Oinv__into(X10,X8,X12,X2),X16) = X11 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__into__f__eq) ).

fof(fact_the__inv__into__f__eq,axiom,
    ! [X16,X11,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hAPP(X2,X11) = X16
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Fun_Othe__inv__into(X10,X8,X12,X2),X16) = X11 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__inv__into__f__eq) ).

fof(fact_finite__INT,axiom,
    ! [X12,X8,X161,X10] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X161))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(X12,X3))) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X161),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__INT) ).

fof(fact_power__strict__increasing,axiom,
    ! [X37,X126,X25,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X126))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X37))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X126))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__strict__increasing) ).

fof(fact_power__increasing,axiom,
    ! [X37,X126,X25,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X126))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Oone__class_Oone(X27)),X37))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X126))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__increasing) ).

fof(fact_divide__strict__right__mono__neg,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X35)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__strict__right__mono__neg) ).

fof(fact_mult__strict__right__mono__neg,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Rings_Olinordered__ring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__right__mono__neg) ).

fof(fact_mult__strict__left__mono__neg,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Rings_Olinordered__ring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__strict__left__mono__neg) ).

fof(fact_divide__right__mono__neg,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Fields_Olinordered__field__inverse__zero(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__right__mono__neg) ).

fof(fact_mult__right__mono__neg,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Rings_Oordered__ring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__right__mono__neg) ).

fof(fact_mult__left__mono__neg,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Rings_Oordered__ring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__mono__neg) ).

fof(fact_card__Diff__singleton,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).

fof(fact_finite__Diff2,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff2) ).

fof(fact_listsum__update__nat,axiom,
    ! [X25,X210,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X210)))
     => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X210),X33),X25)) = 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),X210)),X25)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X210),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__update__nat) ).

fof(fact_o__def,axiom,
    ! [X11,X1,X2,X18,X10,X8] : hAPP(hAPP(c_Fun_Ocomp(X8,X10,X18,X2),X1),X11) = hAPP(X2,hAPP(X1,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__def) ).

fof(fact_o__apply,axiom,
    ! [X11,X1,X2,X18,X10,X8] : hAPP(hAPP(c_Fun_Ocomp(X8,X10,X18,X2),X1),X11) = hAPP(X2,hAPP(X1,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__apply) ).

fof(fact_mult__dvd__mono,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X35),X58))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__dvd__mono) ).

fof(fact_add__strict__mono,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__mono) ).

fof(fact_add__le__less__mono,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X35),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__less__mono) ).

fof(fact_add__less__le__mono,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__le__mono) ).

fof(fact_inf__mono,axiom,
    ! [X58,X36,X35,X37,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X35))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X35),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__mono) ).

fof(fact_sup__mono,axiom,
    ! [X58,X36,X35,X37,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X35))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X35),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__mono) ).

fof(fact_min__max_Osup__mono,axiom,
    ! [X58,X36,X35,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X35))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X35),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__mono) ).

fof(fact_min__max_Oinf__mono,axiom,
    ! [X58,X36,X35,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X35))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X35),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__mono) ).

fof(fact_add__mono,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Groups_Oordered__ab__semigroup__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X35),X58))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X58))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mono) ).

fof(fact_right__distrib__number__of,axiom,
    ! [X35,X36,X68,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Rings_Osemiring(X10) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X36),X35)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__distrib__number__of) ).

fof(fact_right__diff__distrib__number__of,axiom,
    ! [X35,X36,X68,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Rings_Oring(X10) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X36),X35)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__diff__distrib__number__of) ).

fof(fact_div__mult__div__if__dvd,axiom,
    ! [X92,X38,X26,X34,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X34),X26))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X38),X92))
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X26),X34)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X92),X38)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X92)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__div__if__dvd) ).

fof(fact_fold__inf__insert,axiom,
    ! [X13,X14,X12,X10] :
      ( class_Lattices_Osemilattice__inf(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X14),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X13),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X14),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__inf__insert) ).

fof(fact_fold__sup__insert,axiom,
    ! [X13,X14,X12,X10] :
      ( class_Lattices_Osemilattice__sup(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X14),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X13),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X14),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__sup__insert) ).

fof(fact_min__max_Ofold__sup__insert,axiom,
    ! [X13,X14,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X14),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X14),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__sup__insert) ).

fof(fact_min__max_Ofold__inf__insert,axiom,
    ! [X13,X14,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X14),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X13),hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X14),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold__inf__insert) ).

fof(fact_finite__vimageI,axiom,
    ! [X7,X8,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => ( c_Fun_Oinj__on(X8,X10,X7,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_Ovimage(X8,X10,X7),X9))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__vimageI) ).

fof(fact_INF__leI,axiom,
    ! [X143,X12,X61,X10,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X61),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X8),X12),X143)),hAPP(X143,X61))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__leI) ).

fof(fact_add__number__of__diff2,axiom,
    ! [X92,X35,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X35),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)))),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff2) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X31)),X30))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_SUP1__I,axiom,
    ! [X8,X14,X15,X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => ( hBOOL(hAPP(hAPP(X15,X13),X14))
       => hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP1__I) ).

fof(fact_Sup__le__iff,axiom,
    ! [X14,X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Complete__Lattice_OSup__class_OSup(X10,X12)),X14))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X3),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__le__iff) ).

fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
    ! [X11,X19,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm__idem(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(X2,X11),hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem) ).

fof(fact_sum__eq__0__conv,axiom,
    ! [X209,X31] :
      ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X209) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X31 = 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),X209)))
           => 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,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X24))
       => 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),X24),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__mult) ).

fof(fact_one__le__mult__iff,axiom,
    ! [X30,X31] :
      ( 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),X31),X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__mult__iff) ).

fof(fact_mod__mult__self4,axiom,
    ! [X24,X25,X33] : 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),X33),X25)),X24)),X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self4) ).

fof(fact_Union__Un__distrib,axiom,
    ! [X15,X12,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X12)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Un__distrib) ).

fof(fact_Inter__Un__distrib,axiom,
    ! [X15,X12,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X12)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__Un__distrib) ).

fof(fact_split__mod,axiom,
    ! [X32,X30,X42] :
      ( hBOOL(hAPP(X42,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30,X32)))
    <=> ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(X42,X30)) )
        & ( X32 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [X91,X73] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X73),X32))
             => ( X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X91)),X73)
               => hBOOL(hAPP(X42,X73)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mod) ).

fof(fact_in__lists__conv__set,axiom,
    ! [X12,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X200),c_List_Olists(X10,X12)))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(hAPP(c_member(X10),X3),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__lists__conv__set) ).

fof(fact_list_Osize_I2_J,axiom,
    ! [X204,X13,X95,X10] : c_List_Olist_Olist__size(X10,X95,hAPP(hAPP(c_List_Olist_OCons(X10),X13),X204)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X95,X13)),c_List_Olist_Olist__size(X10,X95,X204))),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_dvd__power__le,axiom,
    ! [X24,X25,X34,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X34),X24))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__le) ).

fof(fact_select__weight__cons__zero,axiom,
    ! [X200,X11,X10] : c_Random_Oselect__weight(X10,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X10)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X10),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X11)),X200)) = c_Random_Oselect__weight(X10,X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weight__cons__zero) ).

fof(fact_transpose_Opsimps_I2_J,axiom,
    ! [X237,X10] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X10)),c_List_Otranspose__rel(X10)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X237)))
     => c_List_Otranspose(X10,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X237)) = c_List_Otranspose(X10,X237) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Opsimps_I2_J) ).

fof(fact_disjoint__eq__subset__Compl,axiom,
    ! [X15,X12,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__eq__subset__Compl) ).

fof(fact_card__seteq,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X15)),hAPP(c_Finite__Set_Ocard(X10),X12)))
         => X12 = X15 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__seteq) ).

fof(fact_Inter__lower,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X15),X12))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X12)),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__lower) ).

fof(fact_converse__rel__comp,axiom,
    ! [X116,X110,X18,X10,X8] : hAPP(c_Relation_Oconverse(X8,X10),hAPP(hAPP(c_Relation_Orel__comp(X8,X18,X10),X110),X116)) = hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),hAPP(c_Relation_Oconverse(X18,X10),X116)),hAPP(c_Relation_Oconverse(X8,X18),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__rel__comp) ).

fof(fact_min__less__iff__disj,axiom,
    ! [X19,X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),X16)),X19))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X19))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__less__iff__disj) ).

fof(fact_min__le__iff__disj,axiom,
    ! [X19,X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),X16)),X19))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X19))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__le__iff__disj) ).

fof(fact_split__div,axiom,
    ! [X32,X30,X42] :
      ( hBOOL(hAPP(X42,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X30),X32)))
    <=> ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ( X32 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => ! [X91,X73] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X73),X32))
             => ( X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X91)),X73)
               => hBOOL(hAPP(X42,X91)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div) ).

fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X15)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).

fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X15)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).

fof(fact_subset__Pow__Union,axiom,
    ! [X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),X12),hAPP(c_Set_OPow(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X12)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Pow__Union) ).

fof(fact_IntI,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X6),X15))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_IntI) ).

fof(fact_conjI__realizer,axiom,
    ! [X8,X10,X141,X41,X148,X42] :
      ( hBOOL(hAPP(X42,X148))
     => ( hBOOL(hAPP(X41,X141))
       => ( hBOOL(hAPP(X42,hAPP(c_Product__Type_Ofst(X10,X8),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X148),X141))))
          & hBOOL(hAPP(X41,hAPP(c_Product__Type_Osnd(X10,X8),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X148),X141)))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conjI__realizer) ).

fof(fact_INFI__apply,axiom,
    ! [X11,X2,X12,X18,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X18,X10)),X12),X2),X11) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,X10),X12),hAPP(hAPP(c_COMBC(X8,X18,X10),X2),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INFI__apply) ).

fof(fact_SUPR__apply,axiom,
    ! [X11,X2,X12,X18,X8,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X18,X10)),X12),X2),X11) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,X10),X12),hAPP(hAPP(c_COMBC(X8,X18,X10),X2),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUPR__apply) ).

fof(fact_finite__Un,axiom,
    ! [X4,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X9),X4)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X4)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Un) ).

fof(fact_assms_I3_J,axiom,
    ! [X4,X6] :
      ( v_wt(X6)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X3),v_U))
           => v_P(X4,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X3)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) )
       => v_P(X4,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X6)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I3_J) ).

fof(fact_Un__Diff__Int,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).

fof(fact_listsp__mono,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),c_List_Olistsp(X10,X12)),c_List_Olistsp(X10,X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__mono) ).

fof(fact_lists__mono,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),c_List_Olists(X10,X12)),c_List_Olists(X10,X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__mono) ).

fof(fact_neg__less__divide__eq,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__divide__eq) ).

fof(fact_neg__le__divide__eq,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Fields_Olinordered__field(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__divide__eq) ).

fof(fact_symp__def,axiom,
    ! [X110,X10] :
      ( c_Predicate_Osymp(X10,X110)
    <=> c_Relation_Osym(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_symp__def) ).

fof(fact_transp__def,axiom,
    ! [X110,X10] :
      ( c_Predicate_Otransp(X10,X110)
    <=> c_Relation_Otrans(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transp__def) ).

fof(fact_wfP__def,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_OwfP(X10,X110)
    <=> c_Wellfounded_Owf(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__def) ).

fof(fact_pos__imp__zdiv__neg__iff,axiom,
    ! [X13,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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13),X14)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X13),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,
    ! [X15,X12,X8,X17,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X17))
     => ( hAPP(hAPP(c_Product__Type_OSigma(X8,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X8),X17)) = hAPP(hAPP(c_Product__Type_OSigma(X8,X10),X15),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X8),X17))
      <=> X12 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).

fof(fact_mod__pos__neg__trivial,axiom,
    ! [X36,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__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),X36)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg__trivial) ).

fof(fact_wfI__pf,axiom,
    ! [X29,X10] :
      ( ! [X52] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X52),hAPP(c_Relation_OImage(X10,X10,X29),X52)))
         => X52 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) )
     => c_Wellfounded_Owf(X10,X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfI__pf) ).

fof(fact_splitI,axiom,
    ! [X8,X10,X14,X13,X2] :
      ( hBOOL(hAPP(hAPP(X2,X13),X14))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),X2),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splitI) ).

fof(fact_prod__caseI,axiom,
    ! [X8,X10,X14,X13,X50] :
      ( hBOOL(hAPP(hAPP(X50,X13),X14))
     => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_HOL_Obool),X50),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__caseI) ).

fof(fact_neg__imp__zdiv__neg__iff,axiom,
    ! [X13,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),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),X13),X14)),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)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__imp__zdiv__neg__iff) ).

fof(fact_less__diff__conv,axiom,
    ! [X32,X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X60),X32)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),X32)),X60)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__diff__conv) ).

fof(fact_le__diff__conv,axiom,
    ! [X61,X32,X60] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X60),X32)),X61))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X61),X32))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__diff__conv) ).

fof(fact_card__Diff__subset,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
       => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Diff__subset) ).

fof(fact_folding__idem_Oidem__comp,axiom,
    ! [X11,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__idem(X10,X8,X2,X9)
     => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X2,X11)),hAPP(X2,X11)) = hAPP(X2,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__idem_Oidem__comp) ).

fof(fact_Field__Un,axiom,
    ! [X116,X110,X10] : hAPP(c_Relation_OField(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_OField(X10),X110)),hAPP(c_Relation_OField(X10),X116)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__Un) ).

fof(fact_product__list__set,axiom,
    ! [X199,X200,X8,X10] : hAPP(c_List_Oset(tc_prod(X10,X8)),c_Enum_Oproduct(X10,X8,X200,X199)) = hAPP(hAPP(c_Product__Type_OSigma(X10,X8),hAPP(c_List_Oset(X10),X200)),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),hAPP(c_List_Oset(X8),X199))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product__list__set) ).

fof(fact_zip__eq__conv,axiom,
    ! [X206,X199,X8,X200,X10] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)
     => ( hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199) = X206
      <=> ( hAPP(hAPP(c_List_Omap(tc_prod(X10,X8),X10),c_Product__Type_Ofst(X10,X8)),X206) = X200
          & hAPP(hAPP(c_List_Omap(tc_prod(X10,X8),X8),c_Product__Type_Osnd(X10,X8)),X206) = X199 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__eq__conv) ).

fof(fact_inf1D1,axiom,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11))
     => hBOOL(hAPP(X12,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D1) ).

fof(fact_inf1D2,axiom,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11))
     => hBOOL(hAPP(X15,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1D2) ).

fof(fact_listrelp_Oequations_I2_J,axiom,
    ! [X63,X56,X64,X57,X110,X10] :
      ( c_List_Olistrelp(X10,X110,hAPP(hAPP(c_List_Olist_OCons(X10),X57),X64),hAPP(hAPP(c_List_Olist_OCons(X10),X56),X63))
    <=> ( hBOOL(hAPP(hAPP(X110,X57),X56))
        & c_List_Olistrelp(X10,X110,X64,X63) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I2_J) ).

fof(fact_listrelp_OCons,axiom,
    ! [X199,X200,X10,X16,X11,X110] :
      ( hBOOL(hAPP(hAPP(X110,X11),X16))
     => ( c_List_Olistrelp(X10,X110,X200,X199)
       => c_List_Olistrelp(X10,X110,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_OCons) ).

fof(fact_Rep__Integ__cases,axiom,
    ! [X16] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X16),c_Int_OInteg))
     => ~ ! [X3] : X16 != hAPP(c_Int_ORep__Integ,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__cases) ).

fof(fact_InterI,axiom,
    ! [X12,X17,X10] :
      ( ! [X184] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X184),X17))
         => hBOOL(hAPP(hAPP(c_member(X10),X12),X184)) )
     => hBOOL(hAPP(hAPP(c_member(X10),X12),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X17))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterI) ).

fof(fact_lists_Osimps,axiom,
    ! [X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X13),c_List_Olists(X10,X12)))
    <=> ( X13 = c_List_Olist_ONil(X10)
        | ? [X46,X231] :
            ( X13 = hAPP(hAPP(c_List_Olist_OCons(X10),X46),X231)
            & hBOOL(hAPP(hAPP(c_member(X10),X46),X12))
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X231),c_List_Olists(X10,X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_Osimps) ).

fof(fact_in__set__replicate,axiom,
    ! [X16,X30,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Oreplicate(X10,X30,X16))))
    <=> ( X11 = X16
        & X30 != 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,
    ! [X15,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
               => hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(X2,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Ounion__disjoint) ).

fof(fact_mod__mult__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Divides_Odiv__class_Omod(X27,X37,X35)),c_Divides_Odiv__class_Omod(X27,X36,X35)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__eq) ).

fof(fact_mod__add__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Divides_Odiv__class_Omod(X27,X37,X35)),c_Divides_Odiv__class_Omod(X27,X36,X35)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__eq) ).

fof(fact_mod__diff__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Oring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),c_Divides_Odiv__class_Omod(X27,X37,X35)),c_Divides_Odiv__class_Omod(X27,X36,X35)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__eq) ).

fof(fact_div__add,axiom,
    ! [X34,X26,X38,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X38),X26))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X38),X34))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),X34)),X38) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X26),X38)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X34),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add) ).

fof(fact_power__gt1__lemma,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1__lemma) ).

fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X13)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).

fof(fact_even__less__0__iff,axiom,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X13)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_even__less__0__iff) ).

fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X13)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__add__le__zero__iff__single__add__le__zero) ).

fof(fact_inj__on__diff__nat,axiom,
    ! [X32,X53] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X53))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),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)),X32),X53) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__diff__nat) ).

fof(fact_InterD,axiom,
    ! [X48,X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X12),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X17)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),X17))
       => hBOOL(hAPP(hAPP(c_member(X10),X12),X48)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterD) ).

fof(fact_InterE,axiom,
    ! [X48,X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X12),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X17)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),X17))
       => hBOOL(hAPP(hAPP(c_member(X10),X12),X48)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_InterE) ).

fof(fact_div__pos__neg__trivial,axiom,
    ! [X36,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__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X37),X36)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = 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,
    ! [X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,X8)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X8),tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(X8),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD1) ).

fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).

fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).

fof(fact_zmult__zless__mono2,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X33),X43))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zless__mono2) ).

fof(fact_mult__less__mono1,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X33))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono1) ).

fof(fact_mult__less__mono2,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X43))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__mono2) ).

fof(fact_zdiv__mono1,axiom,
    ! [X36,X127,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),X127))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X127),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1) ).

fof(fact_div__le__mono2,axiom,
    ! [X33,X25,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__eq(tc_Nat_Onat),X24),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X33),X25)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X33),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).

fof(fact_inj__map,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X8),hAPP(c_List_Omap(X10,X8),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))
    <=> c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__map) ).

fof(fact_inj__mapD,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X8),hAPP(c_List_Omap(X10,X8),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))
     => c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__mapD) ).

fof(fact_subset__insertI2,axiom,
    ! [X14,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X14),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI2) ).

fof(fact_replicate__app__Cons__same,axiom,
    ! [X202,X26,X25,X27] : hAPP(hAPP(c_List_Oappend(X27),c_List_Oreplicate(X27,X25,X26)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),hAPP(hAPP(c_List_Oappend(X27),c_List_Oreplicate(X27,X25,X26)),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__app__Cons__same) ).

fof(fact_INT__insert,axiom,
    ! [X15,X12,X13,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X8),X13),X12)),X15) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(X15,X13)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__insert) ).

fof(fact_UN__insert,axiom,
    ! [X15,X12,X13,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X8),X13),X12)),X15) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(X15,X13)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__insert) ).

fof(fact_below__fold1__iff,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Osemilattice__inf(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),hAPP(c_Finite__Set_Ofold1(X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X12)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_below__fold1__iff) ).

fof(fact_min__max_Obelow__fold1__iff,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X12)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).

fof(fact_strict__below__fold1__iff,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X12)))
          <=> ! [X3] :
                ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X3)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__below__fold1__iff) ).

fof(fact_maps__simps_I1_J,axiom,
    ! [X200,X11,X2,X10,X8] : c_List_Omaps(X8,X10,X2,hAPP(hAPP(c_List_Olist_OCons(X8),X11),X200)) = hAPP(hAPP(c_List_Oappend(X10),hAPP(X2,X11)),c_List_Omaps(X8,X10,X2,X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I1_J) ).

fof(fact_less__iff__diff__less__0,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14)),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__diff__less__0) ).

fof(fact_le__iff__diff__le__0,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14)),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__diff__le__0) ).

fof(fact_zdiv__mono1__neg,axiom,
    ! [X36,X127,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),X127))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),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),X127),X36)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__mono1__neg) ).

fof(fact_nth__mem,axiom,
    ! [X200,X10,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_List_Onth(X10),X200),X30)),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__mem) ).

fof(fact_n__less__n__mult__m,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X24))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__n__mult__m) ).

fof(fact_n__less__m__mult__n,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X24))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__less__m__mult__n) ).

fof(fact_card_Oeq__fold__g,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oeq__fold__g) ).

fof(fact_divide__add__eq__iff,axiom,
    ! [X34,X26,X38,X27] :
      ( class_Fields_Ofield(X27)
     => ( X38 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X38)),X34) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X34))),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__add__eq__iff) ).

fof(fact_add__frac__num,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => ( X34 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),X38) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X34))),X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__frac__num) ).

fof(fact_divide__diff__eq__iff,axiom,
    ! [X34,X26,X38,X27] :
      ( class_Fields_Ofield(X27)
     => ( X38 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X38)),X34) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X34))),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__diff__eq__iff) ).

fof(fact_in__set__conv__nth,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
    <=> ? [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
          & hAPP(hAPP(c_List_Onth(X10),X200),X91) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__nth) ).

fof(fact_zadd__zless__mono,axiom,
    ! [X38,X100,X92,X101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X101),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X100),X38))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X101),X100)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X92),X38))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zless__mono) ).

fof(fact_add__less__mono,axiom,
    ! [X45,X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X45))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X45))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).

fof(fact_diff__less__mono,axiom,
    ! [X35,X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X37),X36))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X35),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X37),X35)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X36),X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono) ).

fof(fact_diff__less__mono2,axiom,
    ! [X45,X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X45))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X25)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X24))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_mult__le__mono,axiom,
    ! [X45,X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X45))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X45))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono) ).

fof(fact_add__le__mono,axiom,
    ! [X45,X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X45))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X45))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
    ! [X86,X87,X88,X89,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X88)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X87),X86)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X88)),X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) ).

fof(fact_lessThan__strict__subset__iff,axiom,
    ! [X30,X31,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X31)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__strict__subset__iff) ).

fof(fact_atMost__subset__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X11)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__subset__iff) ).

fof(fact_lessThan__subset__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X11)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__subset__iff) ).

fof(fact_atLeast__subset__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X11)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__subset__iff) ).

fof(fact_greaterThan__subset__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X11)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__subset__iff) ).

fof(fact_divide__neg__pos,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__pos) ).

fof(fact_divide__pos__neg,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__neg) ).

fof(fact_mult__neg__pos,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__pos) ).

fof(fact_mult__pos__neg,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg) ).

fof(fact_mult__pos__neg2,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X37)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__neg2) ).

fof(fact_divide__nonneg__neg,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__neg) ).

fof(fact_divide__nonpos__pos,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__pos) ).

fof(fact_split__mult__neg__le,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oordered__cancel__semiring(X27)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),c_Groups_Ozero__class_Ozero(X27))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36)) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__neg__le) ).

fof(fact_mult__nonpos__nonneg,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oordered__cancel__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonneg) ).

fof(fact_mult__nonneg__nonpos,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oordered__cancel__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos) ).

fof(fact_mult__nonneg__nonpos2,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oordered__cancel__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X37)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonpos2) ).

fof(fact_set__subset__Cons,axiom,
    ! [X11,X200,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__subset__Cons) ).

fof(fact__06,axiom,
    ! [X232,X11,X2,X10,X8] : c_Lazy__Sequence_Omap(X8,X10,X2,c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X11,X232)) = c_Lazy__Sequence_Olazy__sequence_OInsert(X10,hAPP(X2,X11),c_Lazy__Sequence_Omap(X8,X10,X2,X232)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__06) ).

fof(fact_transpose__map__map,axiom,
    ! [X200,X2,X8,X10] : c_List_Otranspose(X10,hAPP(hAPP(c_List_Omap(tc_List_Olist(X8),tc_List_Olist(X10)),hAPP(c_List_Omap(X8,X10),X2)),X200)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X8),tc_List_Olist(X10)),hAPP(c_List_Omap(X8,X10),X2)),c_List_Otranspose(X8,X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__map__map) ).

fof(fact_dvd__mult__left,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),X35))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X35)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__left) ).

fof(fact_dvd__mult__right,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),X35))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X36),X35)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__right) ).

fof(fact_max__less__iff__conj,axiom,
    ! [X19,X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),X16)),X19))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X19))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__less__iff__conj) ).

fof(fact_le__sup__iff,axiom,
    ! [X19,X16,X11,X10] :
      ( class_Lattices_Osemilattice__sup(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),X16)),X19))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X19))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__sup__iff) ).

fof(fact_min__max_Ole__sup__iff,axiom,
    ! [X19,X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),X16)),X19))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X19))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__sup__iff) ).

fof(fact_distinct__conv__nth,axiom,
    ! [X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
    <=> ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
         => ! [X73] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X73),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
             => ( X91 != X73
               => hAPP(hAPP(c_List_Onth(X10),X200),X91) != hAPP(hAPP(c_List_Onth(X10),X200),X73) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).

fof(fact_nth__eq__iff__index__eq,axiom,
    ! [X60,X61,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X60),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
         => ( hAPP(hAPP(c_List_Onth(X10),X200),X61) = hAPP(hAPP(c_List_Onth(X10),X200),X60)
          <=> X61 = X60 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__eq__iff__index__eq) ).

fof(fact_distinct__map,axiom,
    ! [X200,X2,X8,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(X8),X200))
        & c_Fun_Oinj__on(X8,X10,X2,hAPP(c_List_Oset(X8),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__map) ).

fof(fact_min__max_OInf__le__Sup,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__le__Sup) ).

fof(fact_inj__on__diff,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__diff) ).

fof(fact_lazy__sequence_Osize_I2_J,axiom,
    ! [X256,X13,X95,X10] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X10,X95),c_Lazy__Sequence_Olazy__sequence_OInsert(X10,X13,X256)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X95,X13)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X10,X95),X256))),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,
    ! [X11,X19,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm__idem(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),hAPP(hAPP(X2,X11),X19)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofold__insert__idem2) ).

fof(fact_insert__Diff,axiom,
    ! [X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff) ).

fof(fact_finite__Prod__UNIV,axiom,
    ! [X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X8)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Prod__UNIV) ).

fof(fact_finite__Plus__UNIV__iff,axiom,
    ! [X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X10,X8)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X10,X8),tc_HOL_Obool))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X8),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Plus__UNIV__iff) ).

fof(fact_setsum__head__Suc,axiom,
    ! [X2,X30,X31,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(X2,X31)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X31),X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head__Suc) ).

fof(fact_vimageI2,axiom,
    ! [X8,X12,X13,X2,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X13)),X12))
     => hBOOL(hAPP(hAPP(c_member(X8),X13),hAPP(c_Set_Ovimage(X8,X10,X2),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI2) ).

fof(fact_sorted__insort,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X11),X200))
      <=> c_List_Olinorder__class_Osorted(X10,X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__insort) ).

fof(fact_setsum__head__upt__Suc,axiom,
    ! [X2,X30,X31,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(X2,X31)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X31)),X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head__upt__Suc) ).

fof(fact_set__eq__subset,axiom,
    ! [X10,X15,X12] :
      ( X12 = X15
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__eq__subset) ).

fof(fact_equalityI,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
       => X12 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityI) ).

fof(fact_rev__nth,axiom,
    ! [X202,X27,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Onth(X27),hAPP(c_List_Orev(X27),X202)),X25) = hAPP(hAPP(c_List_Onth(X27),X202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),hAPP(c_Nat_OSuc,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__nth) ).

fof(fact_INT__absorb,axiom,
    ! [X12,X8,X161,X32,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X32),X161))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(X12,X32)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X161),X12)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X161),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__absorb) ).

fof(fact_UN__absorb,axiom,
    ! [X12,X8,X161,X32,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X32),X161))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),hAPP(X12,X32)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X161),X12)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X161),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__absorb) ).

fof(fact_list__update__overwrite,axiom,
    ! [X34,X26,X44,X202,X27] : hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)),X44),X34) = hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X34),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__overwrite) ).

fof(fact_negative__zless,axiom,
    ! [X24,X25] : 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,X25)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zless) ).

fof(fact_add__neg__neg,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__neg) ).

fof(fact_add__nonpos__neg,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__neg) ).

fof(fact_add__neg__nonpos,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__neg__nonpos) ).

fof(fact_Nats__mult,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Osemiring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Nat_Osemiring__1__class_ONats(X10)))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X14),c_Nat_Osemiring__1__class_ONats(X10)))
         => hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X14)),c_Nat_Osemiring__1__class_ONats(X10))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__mult) ).

fof(fact_Ints__mult,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Oring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Int_Oring__1__class_OInts(X10)))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X14),c_Int_Oring__1__class_OInts(X10)))
         => hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X14)),c_Int_Oring__1__class_OInts(X10))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__mult) ).

fof(fact_Nats__add,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Osemiring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Nat_Osemiring__1__class_ONats(X10)))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X14),c_Nat_Osemiring__1__class_ONats(X10)))
         => hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X14)),c_Nat_Osemiring__1__class_ONats(X10))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__add) ).

fof(fact_Ints__add,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Oring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Int_Oring__1__class_OInts(X10)))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X14),c_Int_Oring__1__class_OInts(X10)))
         => hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X14)),c_Int_Oring__1__class_OInts(X10))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__add) ).

fof(fact_Ints__diff,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Oring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Int_Oring__1__class_OInts(X10)))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X14),c_Int_Oring__1__class_OInts(X10)))
         => hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14)),c_Int_Oring__1__class_OInts(X10))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__diff) ).

fof(fact_add__nonpos__nonpos,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),c_Groups_Ozero__class_Ozero(X27))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonpos__nonpos) ).

fof(fact_list__size__conv__listsum,axiom,
    ! [X200,X2,X10] : c_List_Olist_Olist__size(X10,X2,X200) = 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(X10,tc_Nat_Onat),X2),X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).

fof(fact_finite__UNIV__inj__surj,axiom,
    ! [X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
     => ( c_Fun_Oinj__on(X10,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
       => hAPP(c_Set_Oimage(X10,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__inj__surj) ).

fof(fact_listsum__triv,axiom,
    ! [X200,X110,X8,X10] :
      ( class_Rings_Osemiring__1(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),hAPP(c_COMBK(X10,X8),X110)),X200)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X200))),X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__triv) ).

fof(fact_power__minus,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27))),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__minus) ).

fof(fact_rangeI,axiom,
    ! [X8,X11,X2,X10] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X11)),hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rangeI) ).

fof(fact_left__distrib__number__of,axiom,
    ! [X68,X36,X37,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Rings_Osemiring(X10) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X37),X36)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X37),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X36),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__distrib__number__of) ).

fof(fact_left__diff__distrib__number__of,axiom,
    ! [X68,X36,X37,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Rings_Oring(X10) )
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X37),X36)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X37),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X36),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__diff__distrib__number__of) ).

fof(fact_Inf__fin_Ounion__disjoint,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)),c_Big__Operators_Olattice__class_OInf__fin(X10,X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__disjoint) ).

fof(fact_Sup__fin_Ounion__disjoint,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
               => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)),c_Big__Operators_Olattice__class_OSup__fin(X10,X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__disjoint) ).

fof(fact_Max_Ounion__disjoint,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,X12)),c_Big__Operators_Olinorder__class_OMax(X10,X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Ounion__disjoint) ).

fof(fact_Min_Ounion__disjoint,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
               => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,X12)),c_Big__Operators_Olinorder__class_OMin(X10,X15)) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Ounion__disjoint) ).

fof(fact_dvd__power__same,axiom,
    ! [X25,X34,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X26),X34))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X34),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power__same) ).

fof(fact_add__strict__right__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__right__mono) ).

fof(fact_add__strict__left__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oordered__cancel__ab__semigroup__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__left__mono) ).

fof(fact_add__right__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oordered__ab__semigroup__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__mono) ).

fof(fact_add__left__mono,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oordered__ab__semigroup__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__mono) ).

fof(fact_fold1__Un2,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X12)),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__Un2) ).

fof(fact_rev__drop,axiom,
    ! [X202,X44,X27] : hAPP(c_List_Orev(X27),hAPP(hAPP(c_List_Odrop(X27),X44),X202)) = hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X44)),hAPP(c_List_Orev(X27),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__drop) ).

fof(fact_rev__take,axiom,
    ! [X202,X44,X27] : hAPP(c_List_Orev(X27),hAPP(hAPP(c_List_Otake(X27),X44),X202)) = hAPP(hAPP(c_List_Odrop(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X44)),hAPP(c_List_Orev(X27),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__take) ).

fof(fact_ivl__disj__un_I5_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X83),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X77)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X77) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I5_J) ).

fof(fact_subset__Compl__self__eq,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)))
    <=> X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Compl__self__eq) ).

fof(fact_pdivmod__def,axiom,
    ! [X45,X33] : c_Divides_Opdivmod(X33,X45) = 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),X33)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X45))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X33),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X45))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__def) ).

fof(fact_Union__upper,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X15),X12))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__upper) ).

fof(fact_fold__image__def,axiom,
    ! [X1,X2,X8,X10] : hAPP(c_Finite__Set_Ofold__image(X10,X8,X2),X1) = c_Finite__Set_Ofold(X8,X10,hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X8),X2),X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__def) ).

fof(fact_max__Suc1,axiom,
    ! [X31,X30] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X30),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),X30)),X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc1) ).

fof(fact_Field__Union,axiom,
    ! [X29,X10] : hAPP(c_Relation_OField(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),X29)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X10,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),c_Relation_OField(X10)),X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__Union) ).

fof(fact_dvd__mult__cancel2,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X31)),X31))
      <=> X30 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel2) ).

fof(fact_dvd__mult__cancel1,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X30)),X31))
      <=> X30 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__cancel1) ).

fof(fact_Diff__partition,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X12)) = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__partition) ).

fof(fact_inj__mapI,axiom,
    ! [X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X8),hAPP(c_List_Omap(X10,X8),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__mapI) ).

fof(fact_Compl__Int,axiom,
    ! [X15,X12,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Int) ).

fof(fact_Compl__Un,axiom,
    ! [X15,X12,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Un) ).

fof(fact_conversep__iff,axiom,
    ! [X14,X13,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X8,X110),X13),X14))
    <=> hBOOL(hAPP(hAPP(X110,X14),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__iff) ).

fof(fact_conversep_Oequations,axiom,
    ! [X57,X56,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X8,X110),X56),X57))
    <=> hBOOL(hAPP(hAPP(X110,X57),X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Oequations) ).

fof(fact_conversepD,axiom,
    ! [X14,X13,X110,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X8,X110),X13),X14))
     => hBOOL(hAPP(hAPP(X110,X14),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversepD) ).

fof(fact_vimage__code,axiom,
    ! [X11,X12,X2,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Set_Ovimage(X10,X8,X2),X12),X11))
    <=> hBOOL(hAPP(X12,hAPP(X2,X11))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).

fof(fact_Inf__less__iff,axiom,
    ! [X13,X28,X10] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X10)
        & class_Orderings_Olinorder(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Complete__Lattice_OInf__class_OInf(X10,X28)),X13))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X28))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X3),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__less__iff) ).

fof(fact_mult__number__of__left,axiom,
    ! [X38,X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)),X38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X92))),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_add__number__of__left,axiom,
    ! [X38,X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)),X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),X92))),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__left) ).

fof(fact_add__number__of__diff1,axiom,
    ! [X35,X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)),X35)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),X92))),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__diff1) ).

fof(fact_ivl__disj__un_I3_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X83),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X77)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X77) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I3_J) ).

fof(fact_nth__map,axiom,
    ! [X2,X8,X200,X10,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => hAPP(hAPP(c_List_Onth(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)),X30) = hAPP(X2,hAPP(hAPP(c_List_Onth(X10),X200),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__map) ).

fof(fact_le__imp__power__dvd,axiom,
    ! [X37,X25,X24,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__power__dvd) ).

fof(fact_nat__gcd_Opsimps,axiom,
    ! [X16,X11] :
      ( 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),X11),X16)))
     => ( ( X16 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(X11,X16) = X11 )
        & ( X16 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(X11,X16) = c_Nitpick_Onat__gcd(X16,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X11,X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Opsimps) ).

fof(fact_UnionI,axiom,
    ! [X12,X17,X48,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),X17))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X12),X48))
       => hBOOL(hAPP(hAPP(c_member(X10),X12),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X17))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnionI) ).

fof(fact_zero__less__mult__pos2,axiom,
    ! [X37,X36,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X37)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos2) ).

fof(fact_zero__less__mult__pos,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__mult__pos) ).

fof(fact_in__set__conv__decomp,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
    <=> ? [X207,X240] : X200 = hAPP(hAPP(c_List_Oappend(X10),X207),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X240)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__conv__decomp) ).

fof(fact_sym__Int__converse,axiom,
    ! [X110,X10] : c_Relation_Osym(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(c_Relation_Oconverse(X10,X10),X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Int__converse) ).

fof(fact_sym__Un__converse,axiom,
    ! [X110,X10] : c_Relation_Osym(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),hAPP(c_Relation_Oconverse(X10,X10),X110))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Un__converse) ).

fof(fact_card__Un__disjoint,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Un__disjoint) ).

fof(fact_min__Suc1,axiom,
    ! [X31,X30] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31) = 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),X30)),X31),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc1) ).

fof(fact_sorted__list__of__set__remove,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_List_Olinorder__class_Osorted__list__of__set(X10,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = c_List_Oremove1(X10,X11,c_List_Olinorder__class_Osorted__list__of__set(X10,X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__remove) ).

fof(fact_finite__fun__UNIVD2,axiom,
    ! [X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,X8)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,X8),tc_HOL_Obool))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__fun__UNIVD2) ).

fof(fact_filter__sort,axiom,
    ! [X200,X2,X42,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => hAPP(c_List_Ofilter(X10,X42),c_List_Olinorder__class_Osort__key(X10,X8,X2,X200)) = c_List_Olinorder__class_Osort__key(X10,X8,X2,hAPP(c_List_Ofilter(X10,X42),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__sort) ).

fof(fact_PowD,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_OPow(X10),X15)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PowD) ).

fof(fact_Pow__iff,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_OPow(X10),X15)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__iff) ).

fof(fact_zero__less__zpower__abs__iff,axiom,
    ! [X30,X11] :
      ( 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),X11)),X30)))
    <=> ( X11 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X30 = 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,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X31),X77))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X31)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X31,X77)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I22_J) ).

fof(fact_ivl__disj__un_I20_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X31),X77))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X31)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X31,X77)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I20_J) ).

fof(fact_ivl__disj__un_I16_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X77))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X31)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X31,X77)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I16_J) ).

fof(fact_ivl__disj__un_I19_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X83),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X31),X77))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X31)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X31,X77)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I19_J) ).

fof(fact_Un__upper1,axiom,
    ! [X15,X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__upper1) ).

fof(fact_Un__upper2,axiom,
    ! [X12,X15,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__upper2) ).

fof(fact_r__into__rtrancl,axiom,
    ! [X110,X148,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),X110))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),X148),c_Transitive__Closure_Ortrancl(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).

fof(fact_card__Plus__conv__if,axiom,
    ! [X15,X8,X12,X10] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(X10,X8)),c_Sum__Type_OPlus(X10,X8,X12,X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X8),X15)) )
      & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
            & hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(X10,X8)),c_Sum__Type_OPlus(X10,X8,X12,X15)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_card__Plus,axiom,
    ! [X15,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X15))
       => hAPP(c_Finite__Set_Ocard(tc_sum(X10,X8)),c_Sum__Type_OPlus(X10,X8,X12,X15)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X8),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Plus) ).

fof(fact_le__supI,axiom,
    ! [X36,X26,X37,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36)),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI) ).

fof(fact_sup__least,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X38),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X38)),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__least) ).

fof(fact_min__max_Ole__supI,axiom,
    ! [X36,X26,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36)),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI) ).

fof(fact_min__max_Osup__least,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X38),X26))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),X38)),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__least) ).

fof(fact_Int__left__commute,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__commute) ).

fof(fact_Un__left__commute,axiom,
    ! [X17,X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__commute) ).

fof(fact_Un__Diff__cancel2,axiom,
    ! [X12,X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X12)),X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).

fof(fact_Diff__idemp,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)),X15) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__idemp) ).

fof(fact_imageI,axiom,
    ! [X2,X8,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => hBOOL(hAPP(hAPP(c_member(X8),hAPP(X2,X11)),hAPP(c_Set_Oimage(X10,X8,X2),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).

fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
    ! [X1,X18,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => c_Finite__Set_Ofun__left__comm(X18,X8,hAPP(hAPP(c_COMBB(X10,tc_fun(X8,X8),X18),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,X18,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm__idem(X10,X8,X2)
     => c_Finite__Set_Ofun__left__comm__idem(X18,X8,hAPP(hAPP(c_COMBB(X10,tc_fun(X8,X8),X18),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,
    ! [X15,X17,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X17))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)),X17) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).

fof(fact_inj__image__eq__iff,axiom,
    ! [X15,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(X10,X8,X2),X12) = hAPP(c_Set_Oimage(X10,X8,X2),X15)
      <=> X12 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_o__eq__dest__lhs,axiom,
    ! [X93,X6,X14,X13,X10,X8,X18] :
      ( hAPP(c_Fun_Ocomp(X18,X8,X10,X13),X14) = X6
     => hAPP(X13,hAPP(X14,X93)) = hAPP(X6,X93) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__eq__dest__lhs) ).

fof(fact_negative__zless__0,axiom,
    ! [X25] : 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,X25)))),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,
    ! [X202,X27,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Olist_OCons(X27),hAPP(hAPP(c_List_Onth(X27),X202),X44)),hAPP(hAPP(c_List_Odrop(X27),hAPP(c_Nat_OSuc,X44)),X202)) = hAPP(hAPP(c_List_Odrop(X27),X44),X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__drop_H) ).

fof(fact_image__vimage__eq,axiom,
    ! [X12,X2,X10,X8] : hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_Set_Ovimage(X8,X10,X2),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__vimage__eq) ).

fof(fact_add1__zle__eq,axiom,
    ! [X19,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X90),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add1__zle__eq) ).

fof(fact_ivl__disj__un_I18_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X31),X77))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X31)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X31,X77)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I18_J) ).

fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
    ! [X12] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X12))
    <=> 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)),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I1_J) ).

fof(fact_psubset__card__mono,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__card__mono) ).

fof(fact_card__mono,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__mono) ).

fof(fact_UnI1,axiom,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
     => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnI1) ).

fof(fact_UnI2,axiom,
    ! [X12,X15,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),X15))
     => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UnI2) ).

fof(fact_finite__UNIV__surj__inj,axiom,
    ! [X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
     => ( hAPP(c_Set_Oimage(X10,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
       => c_Fun_Oinj__on(X10,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__surj__inj) ).

fof(fact_abs__less__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),X13)),X14))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__less__iff) ).

fof(fact_abs__leI,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__leI) ).

fof(fact_abs__le__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),X13)),X14))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__iff) ).

fof(fact_lists__accI,axiom,
    ! [X110,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X200),c_Wellfounded_Oacc(tc_List_Olist(X10),c_List_Olistrel1(X10,X110))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X200),c_List_Olists(X10,c_Wellfounded_Oacc(X10,X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accI) ).

fof(fact_inj__vimage__image__eq,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(c_Set_Oimage(X10,X8,X2),X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__vimage__image__eq) ).

fof(fact_ivl__disj__un_I15_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X83),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X31),X77))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X31)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X31),X77)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I15_J) ).

fof(fact_div__mult__self2,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35))),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2) ).

fof(fact_div__mult__self1,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36))),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1) ).

fof(fact_add__num__frac,axiom,
    ! [X26,X38,X34,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => ( X34 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X38),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),X34))),X34) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__num__frac) ).

fof(fact_setsum__reindex__id,axiom,
    ! [X15,X2,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( c_Fun_Oinj__on(X10,X8,X2,X15)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X15) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X8),c_Fun_Oid(X8)),hAPP(c_Set_Oimage(X10,X8,X2),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__reindex__id) ).

fof(fact_setprod__reindex__id,axiom,
    ! [X15,X2,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( c_Fun_Oinj__on(X10,X8,X2,X15)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X15) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X8),c_Fun_Oid(X8)),hAPP(c_Set_Oimage(X10,X8,X2),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__reindex__id) ).

fof(fact_wf__comp__self,axiom,
    ! [X29,X10] :
      ( c_Wellfounded_Owf(X10,X29)
    <=> c_Wellfounded_Owf(X10,hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X29),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__comp__self) ).

fof(fact_less__by__empty,axiom,
    ! [X15,X10,X12] :
      ( X12 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__by__empty) ).

fof(fact_distinct__append,axiom,
    ! [X199,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Oappend(X10),X200),X199)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
        & hBOOL(hAPP(c_List_Odistinct(X10),X199))
        & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(c_List_Oset(X10),X199)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__append) ).

fof(fact_min__max_OSup__fin__set__fold,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))) = hAPP(c_List_Ofoldl(X10,X10,c_Orderings_Oord__class_Omax(X10),X11),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin__set__fold) ).

fof(fact_min__max_OInf__fin__set__fold,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))) = hAPP(c_List_Ofoldl(X10,X10,c_Orderings_Oord__class_Omin(X10),X11),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin__set__fold) ).

fof(fact_setsum__head,axiom,
    ! [X42,X30,X31,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X42),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(X42,X31)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X42),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X31,X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__head) ).

fof(fact_funpow_Osimps_I2_J,axiom,
    ! [X2,X30,X10] : hAPP(hAPP(c_Nat_Ocompow(X10,X10),hAPP(c_Nat_OSuc,X30)),X2) = hAPP(c_Fun_Ocomp(X10,X10,X10,X2),hAPP(hAPP(c_Nat_Ocompow(X10,X10),X30),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow_Osimps_I2_J) ).

fof(fact_list__size__estimation,axiom,
    ! [X2,X16,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),hAPP(X2,X11)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X16),c_List_Olist_Olist__size(X10,X2,X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__estimation) ).

fof(fact_list__size__estimation_H,axiom,
    ! [X2,X16,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16),hAPP(X2,X11)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X16),c_List_Olist_Olist__size(X10,X2,X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__size__estimation_H) ).

fof(fact_elem__le__listsum__nat,axiom,
    ! [X210,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X210)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X210),X33)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X210))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_elem__le__listsum__nat) ).

fof(fact_le__div__geq,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__div__geq) ).

fof(fact_lists__accD,axiom,
    ! [X110,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X200),c_List_Olists(X10,c_Wellfounded_Oacc(X10,X110))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X200),c_Wellfounded_Oacc(tc_List_Olist(X10),c_List_Olistrel1(X10,X110)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__accD) ).

fof(fact_dvd__diffD,axiom,
    ! [X25,X24,X33] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD) ).

fof(fact_dvd__diffD1,axiom,
    ! [X25,X24,X33] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X25)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diffD1) ).

fof(fact_semiring__1__class_Oof__nat__code,axiom,
    ! [X30,X10] :
      ( class_Rings_Osemiring__1(X10)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30) = c_Nat_Osemiring__1__class_Oof__nat__aux(X10,hAPP(hAPP(c_COMBC(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_Groups_Oone__class_Oone(X10)),X30,c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).

fof(fact_impossible__Cons,axiom,
    ! [X26,X201,X202,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X201)))
     => X202 != hAPP(hAPP(c_List_Olist_OCons(X27),X26),X201) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_impossible__Cons) ).

fof(fact_PowI,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_OPow(X10),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_PowI) ).

fof(fact_power_Opower_Opower__Suc,axiom,
    ! [X30,X13,X128,X129,X10] : hAPP(hAPP(c_Power_Opower_Opower(X10,X129,X128),X13),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(X128,X13),hAPP(hAPP(c_Power_Opower_Opower(X10,X129,X128),X13),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).

fof(fact_Max__mono,axiom,
    ! [X53,X143,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X143),X53))
       => ( X143 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olinorder__class_OMax(X10,X143)),c_Big__Operators_Olinorder__class_OMax(X10,X53))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__mono) ).

fof(fact_Min__antimono,axiom,
    ! [X53,X143,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X143),X53))
       => ( X143 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X53))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olinorder__class_OMin(X10,X53)),c_Big__Operators_Olinorder__class_OMin(X10,X143))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__antimono) ).

fof(fact_less__bin__lemma,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X83))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32),X83)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__bin__lemma) ).

fof(fact_singleton__iff,axiom,
    ! [X13,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
    <=> X14 = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__iff) ).

fof(fact_singletonE,axiom,
    ! [X13,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
     => X14 = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singletonE) ).

fof(fact_range__eqI,axiom,
    ! [X8,X10,X11,X2,X14] :
      ( X14 = hAPP(X2,X11)
     => hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_range__eqI) ).

fof(fact_snd__image__times,axiom,
    ! [X15,X8,X10,X12] :
      ( ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X10,X8),X8,c_Product__Type_Osnd(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15))) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) )
      & ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X10,X8),X8,c_Product__Type_Osnd(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15))) = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__image__times) ).

fof(fact_fst__image__times,axiom,
    ! [X12,X8,X10,X15] :
      ( ( X15 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X8,X10),X8,c_Product__Type_Ofst(X8,X10)),hAPP(hAPP(c_Product__Type_OSigma(X8,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X8),X15))) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) )
      & ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(tc_prod(X8,X10),X8,c_Product__Type_Ofst(X8,X10)),hAPP(hAPP(c_Product__Type_OSigma(X8,X10),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X8),X15))) = X12 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__image__times) ).

fof(fact_doubleton__eq__iff,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X10),X6),hAPP(hAPP(c_Set_Oinsert(X10),X20),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
    <=> ( ( X13 = X6
          & X14 = X20 )
        | ( X13 = X20
          & X14 = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).

fof(fact_dvd__setprod,axiom,
    ! [X2,X61,X12,X10,X8] :
      ( class_Rings_Ocomm__semiring__1(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X61),X12))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X8),hAPP(X2,X61)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__setprod) ).

fof(fact_nth__list__update,axiom,
    ! [X26,X43,X202,X27,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => ( ( X44 = X43
         => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)),X43) = X26 )
        & ( X44 != X43
         => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)),X43) = hAPP(hAPP(c_List_Onth(X27),X202),X43) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update) ).

fof(fact_add__lessD1,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),X33))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).

fof(fact_add__leD1,axiom,
    ! [X25,X33,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X33)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).

fof(fact_add__leD2,axiom,
    ! [X25,X33,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X33)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).

fof(fact_diff__Suc__less,axiom,
    ! [X44,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_OSuc,X44))),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__less) ).

fof(fact_ivl__disj__un_I21_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X31),X77))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X31)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X31,X77)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I21_J) ).

fof(fact_atLeastLessThan__add__Un,axiom,
    ! [X32,X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X61),X60))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X61),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X32)) = 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,X61),X60)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X60),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X60),X32))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__add__Un) ).

fof(fact_insert__Diff__single,axiom,
    ! [X12,X13,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X10),X13),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff__single) ).

fof(fact_card__insert__le,axiom,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__insert__le) ).

fof(fact_zadd__int__left,axiom,
    ! [X38,X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)),X38)) = 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),X24),X25))),X38),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int__left) ).

fof(fact_less__Sup__iff,axiom,
    ! [X28,X13,X10] :
      ( ( class_Complete__Lattice_Ocomplete__lattice(X10)
        & class_Orderings_Olinorder(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Complete__Lattice_OSup__class_OSup(X10,X28)))
      <=> ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X28))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Sup__iff) ).

fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
    ! [X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X12))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I1_J) ).

fof(fact_transfer__nat__int__relations_I2_J,axiom,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X11)),hAPP(c_Int_Onat,X16)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).

fof(fact_transfer__nat__int__relations_I3_J,axiom,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X11)),hAPP(c_Int_Onat,X16)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I3_J) ).

fof(fact_ivl__disj__un_I4_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X77)),hAPP(hAPP(c_Set_Oinsert(X10),X77),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X77) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I4_J) ).

fof(fact_Min__eqI,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ! [X51] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X51),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X51)) )
         => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
           => c_Big__Operators_Olinorder__class_OMin(X10,X12) = X11 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__eqI) ).

fof(fact_map__append,axiom,
    ! [X199,X200,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(hAPP(c_List_Oappend(X8),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)),hAPP(hAPP(c_List_Omap(X8,X10),X2),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__append) ).

fof(fact_finite__Union,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),X12))
     => ( ! [X180] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X180),X12))
           => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X180)) )
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Union) ).

fof(fact_div__power,axiom,
    ! [X25,X26,X34,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X34),X26))
       => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X26),X34)),X25) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X34),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__power) ).

fof(fact_int__div__less__self,axiom,
    ! [X33,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_Groups_Oone__class_Oone(tc_Int_Oint)),X33))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X33)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__div__less__self) ).

fof(fact_div__less__dividend,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25))
     => ( 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),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25)),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less__dividend) ).

fof(fact_diff__less,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => ( 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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X24)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less) ).

fof(fact_insert__inter__insert,axiom,
    ! [X15,X12,X13,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__inter__insert) ).

fof(fact_div__neg__pos__less0,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),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)),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36)),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,
    ! [X36,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(tc_Int_Oint),X36),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),X37),X36)),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,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),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)),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__nonpos__pos__le0) ).

fof(fact_dvd__mod__iff,axiom,
    ! [X31,X30,X32,X10] :
      ( class_Divides_Osemiring__div(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X32),X30))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X32),c_Divides_Odiv__class_Omod(X10,X31,X30)))
        <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X32),X31)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__iff) ).

fof(fact_dvd__mod__imp__dvd,axiom,
    ! [X25,X24,X33,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X33),c_Divides_Odiv__class_Omod(X27,X24,X25)))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X33),X25))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X33),X24)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod__imp__dvd) ).

fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Divides_Odiv__class_Omod(X27,X37,X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36)),X36)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__div__class_Omod__div__equality_H) ).

fof(fact_zero__less__divide__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X13),X14)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X14)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__divide__iff) ).

fof(fact_zero__le__divide__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X13),X14)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X14)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__divide__iff) ).

fof(fact_zero__le__mult__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X14)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X14)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).

fof(fact_all__interval__int__def,axiom,
    ! [X60,X61,X42] :
      ( c_List_Oall__interval__int(X42,X61,X60)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X61,X60)))
         => hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__interval__int__def) ).

fof(fact_zadd__strict__right__mono,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X44),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X43),X33))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__strict__right__mono) ).

fof(fact_add__less__mono1,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X33))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).

fof(fact_zadd__left__mono,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),X44)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__mono) ).

fof(fact_div__le__mono,axiom,
    ! [X33,X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X33)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X25),X33))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).

fof(fact_mult__le__mono1,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X43),X33))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono1) ).

fof(fact_mult__le__mono2,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X44)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__mono2) ).

fof(fact_add__le__mono1,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X33))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).

fof(fact_diff__le__mono,axiom,
    ! [X45,X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X45)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X45))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono) ).

fof(fact_diff__le__mono2,axiom,
    ! [X45,X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X25)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X24))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__mono2) ).

fof(fact_Inf__fin__set__fold,axiom,
    ! [X200,X11,X10] :
      ( class_Lattices_Olattice(X10)
     => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))) = hAPP(c_List_Ofoldl(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin__set__fold) ).

fof(fact_Sup__fin__set__fold,axiom,
    ! [X200,X11,X10] :
      ( class_Lattices_Olattice(X10)
     => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))) = hAPP(c_List_Ofoldl(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10),X11),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin__set__fold) ).

fof(fact_Max__fin__set__fold,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))) = hAPP(c_List_Ofoldl(X10,X10,c_Orderings_Oord__class_Omax(X10),X11),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__fin__set__fold) ).

fof(fact_Min__fin__set__fold,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))) = hAPP(c_List_Ofoldl(X10,X10,c_Orderings_Oord__class_Omin(X10),X11),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__fin__set__fold) ).

fof(fact_diff__Suc__diff__eq2,axiom,
    ! [X24,X43,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X43))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X33))),X24) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X43)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq2) ).

fof(fact_mod__div__equality2,axiom,
    ! [X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36))),c_Divides_Odiv__class_Omod(X27,X37,X36)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__equality2) ).

fof(fact_list__update__code_I3_J,axiom,
    ! [X34,X44,X202,X26,X27] : hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),hAPP(c_Nat_OSuc,X44)),X34) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I3_J) ).

fof(fact_pair__box_Oinject,axiom,
    ! [X108,X109,X14,X13,X8,X10] :
      ( c_Nitpick_Opair__box_OPairBox(X10,X8,X13,X14) = c_Nitpick_Opair__box_OPairBox(X10,X8,X109,X108)
    <=> ( X13 = X109
        & X14 = X108 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).

fof(fact_vimageI,axiom,
    ! [X8,X15,X10,X14,X13,X2] :
      ( hAPP(X2,X13) = X14
     => ( hBOOL(hAPP(hAPP(c_member(X10),X14),X15))
       => hBOOL(hAPP(hAPP(c_member(X8),X13),hAPP(c_Set_Ovimage(X8,X10,X2),X15))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI) ).

fof(fact_image__eqI,axiom,
    ! [X10,X12,X8,X11,X2,X14] :
      ( X14 = hAPP(X2,X11)
     => ( hBOOL(hAPP(hAPP(c_member(X8),X11),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(c_Set_Oimage(X8,X10,X2),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).

fof(fact_rev__image__eqI,axiom,
    ! [X8,X2,X14,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( X14 = hAPP(X2,X11)
       => hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(c_Set_Oimage(X10,X8,X2),X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).

fof(fact_inj__on__iff,axiom,
    ! [X16,X11,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X16),X12))
         => ( hAPP(X2,X11) = hAPP(X2,X16)
          <=> X11 = X16 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff) ).

fof(fact_inj__onD,axiom,
    ! [X16,X11,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( hAPP(X2,X11) = hAPP(X2,X16)
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( hBOOL(hAPP(hAPP(c_member(X10),X16),X12))
           => X11 = X16 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__onD) ).

fof(fact_inj__on__contraD,axiom,
    ! [X16,X11,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( X11 != X16
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( hBOOL(hAPP(hAPP(c_member(X10),X16),X12))
           => hAPP(X2,X11) != hAPP(X2,X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__contraD) ).

fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
    ! [X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))
     => ( 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),X13),X14)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),X13))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonneg1__imp__zdiv__pos__iff) ).

fof(fact_list__ex__length,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__ex(X10,X42,X200)
    <=> ? [X123] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X123),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
          & hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X123))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__length) ).

fof(fact_folding__one__idem_Osubset__idem,axiom,
    ! [X15,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one__idem(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
           => hAPP(hAPP(X2,hAPP(X9,X15)),hAPP(X9,X12)) = hAPP(X9,X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Osubset__idem) ).

fof(fact_part__equivp__def,axiom,
    ! [X29,X10] :
      ( c_Equiv__Relations_Opart__equivp(X10,X29)
    <=> ( ? [X3] : hBOOL(hAPP(hAPP(X29,X3),X3))
        & ! [X3,X51] :
            ( hBOOL(hAPP(hAPP(X29,X3),X51))
          <=> ( hBOOL(hAPP(hAPP(X29,X3),X3))
              & hBOOL(hAPP(hAPP(X29,X51),X51))
              & hAPP(X29,X3) = hAPP(X29,X51) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__def) ).

fof(fact_comp__equivI,axiom,
    ! [X12,X110,X10] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Relation_Oconverse(X10,X10),X110)),X110) = X110
     => ( hAPP(c_Relation_ODomain(X10,X10),X110) = X12
       => c_Equiv__Relations_Oequiv(X10,X12,X110) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comp__equivI) ).

fof(fact_zip__replicate,axiom,
    ! [X34,X43,X26,X44,X10,X27] : hAPP(hAPP(c_List_Ozip(X27,X10),c_List_Oreplicate(X27,X44,X26)),c_List_Oreplicate(X10,X43,X34)) = c_List_Oreplicate(tc_prod(X27,X10),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X44),X43),hAPP(hAPP(c_Product__Type_OPair(X27,X10),X26),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__replicate) ).

fof(fact_le__funE,axiom,
    ! [X11,X1,X2,X10,X8] :
      ( class_Orderings_Oord(X8)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X2),X1))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(X2,X11)),hAPP(X1,X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funE) ).

fof(fact_le__funD,axiom,
    ! [X11,X1,X2,X10,X8] :
      ( class_Orderings_Oord(X8)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X2),X1))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(X2,X11)),hAPP(X1,X11))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__funD) ).

fof(fact_map__injective,axiom,
    ! [X199,X200,X2,X10,X8] :
      ( hAPP(hAPP(c_List_Omap(X8,X10),X2),X200) = hAPP(hAPP(c_List_Omap(X8,X10),X2),X199)
     => ( c_Fun_Oinj__on(X8,X10,X2,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))
       => X200 = X199 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__injective) ).

fof(fact_inj__map__eq__map,axiom,
    ! [X199,X200,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hAPP(hAPP(c_List_Omap(X10,X8),X2),X200) = hAPP(hAPP(c_List_Omap(X10,X8),X2),X199)
      <=> X200 = X199 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__map__eq__map) ).

fof(fact_nth__list__update__eq,axiom,
    ! [X26,X202,X27,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)),X44) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update__eq) ).

fof(fact_setsum__atMost__Suc,axiom,
    ! [X30,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30))),hAPP(X2,hAPP(c_Nat_OSuc,X30))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__atMost__Suc) ).

fof(fact_sym__Int,axiom,
    ! [X116,X110,X10] :
      ( c_Relation_Osym(X10,X110)
     => ( c_Relation_Osym(X10,X116)
       => c_Relation_Osym(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Int) ).

fof(fact_sym__Un,axiom,
    ! [X116,X110,X10] :
      ( c_Relation_Osym(X10,X110)
     => ( c_Relation_Osym(X10,X116)
       => c_Relation_Osym(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Un) ).

fof(fact_trans__Int,axiom,
    ! [X116,X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => ( c_Relation_Otrans(X10,X116)
       => c_Relation_Otrans(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X116)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Int) ).

fof(fact_ivl__disj__un_I17_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X31))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X31),X77))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X31)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X31),X77)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X77) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I17_J) ).

fof(fact_butlast__conv__take,axiom,
    ! [X202,X27] : c_List_Obutlast(X27,X202) = hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__conv__take) ).

fof(fact_fold1__belowI,axiom,
    ! [X13,X12,X10] :
      ( class_Lattices_Osemilattice__inf(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X12)),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__belowI) ).

fof(fact_min__max_Ofold1__belowI,axiom,
    ! [X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X12)),X13)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofold1__belowI) ).

fof(fact_sorted_OCons,axiom,
    ! [X11,X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X3)) )
       => ( c_List_Olinorder__class_Osorted(X10,X200)
         => c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_OCons) ).

fof(fact_sorted_Oequations_I2_J,axiom,
    ! [X57,X56,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X56),X57))
      <=> ( ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X57)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X56),X3)) )
          & c_List_Olinorder__class_Osorted(X10,X57) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Oequations_I2_J) ).

fof(fact_sorted__Cons,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))
      <=> ( c_List_Olinorder__class_Osorted(X10,X200)
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X3)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__Cons) ).

fof(fact_int__power__div__base,axiom,
    ! [X33,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_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X33),X24)),X33) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),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,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__pos__pos) ).

fof(fact_mult__pos__pos,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Olinordered__semiring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__pos__pos) ).

fof(fact_add__pos__pos,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__pos) ).

fof(fact_add__nonneg__pos,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__pos) ).

fof(fact_add__pos__nonneg,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__pos__nonneg) ).

fof(fact_less__1__mult,axiom,
    ! [X25,X24,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X24))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X24),X25))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__1__mult) ).

fof(fact_divide__nonneg__pos,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonneg__pos) ).

fof(fact_split__mult__pos__le,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oordered__ring(X27)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36)) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),c_Groups_Ozero__class_Ozero(X27))) ) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mult__pos__le) ).

fof(fact_mult__nonneg__nonneg,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oordered__cancel__semiring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonneg__nonneg) ).

fof(fact_add__nonneg__nonneg,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__nonneg) ).

fof(fact_eq__card__imp__inj__on,axiom,
    ! [X2,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hAPP(c_Finite__Set_Ocard(X8),hAPP(c_Set_Oimage(X10,X8,X2),X12)) = hAPP(c_Finite__Set_Ocard(X10),X12)
       => c_Fun_Oinj__on(X10,X8,X2,X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [X2,X8,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( c_Fun_Oinj__on(X10,X8,X2,X12)
      <=> hAPP(c_Finite__Set_Ocard(X8),hAPP(c_Set_Oimage(X10,X8,X2),X12)) = hAPP(c_Finite__Set_Ocard(X10),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_Compl__Diff__eq,axiom,
    ! [X15,X12,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__Diff__eq) ).

fof(fact_power__eq__imp__eq__base,axiom,
    ! [X36,X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),X25)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
             => X37 = X36 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_card__cartesian__product,axiom,
    ! [X15,X12,X8,X10] : hAPP(c_Finite__Set_Ocard(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),hAPP(c_Finite__Set_Ocard(X8),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__cartesian__product) ).

fof(fact_Int__insert__right__if1,axiom,
    ! [X15,X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).

fof(fact_list__eq__iff__nth__eq,axiom,
    ! [X10,X199,X200] :
      ( X200 = X199
    <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X199)
        & ! [X91] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
           => hAPP(hAPP(c_List_Onth(X10),X200),X91) = hAPP(hAPP(c_List_Onth(X10),X199),X91) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__eq__iff__nth__eq) ).

fof(fact_folding_Oeq__fold,axiom,
    ! [X116,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(X9,X12),X116) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X116),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oeq__fold) ).

fof(fact_le__SUPI,axiom,
    ! [X143,X12,X61,X10,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X61),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(X143,X61)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X8),X12),X143))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SUPI) ).

fof(fact_zmod__simps_I4_J,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Divides_Odiv__class_Omod(X27,X37,X35)),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I4_J) ).

fof(fact_zmod__simps_I1_J,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Divides_Odiv__class_Omod(X27,X37,X35)),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I1_J) ).

fof(fact_mod__mult__left__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Divides_Odiv__class_Omod(X27,X37,X35)),X36),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__left__eq) ).

fof(fact_mod__add__left__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Divides_Odiv__class_Omod(X27,X37,X35)),X36),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__left__eq) ).

fof(fact_mod__diff__left__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Oring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),c_Divides_Odiv__class_Omod(X27,X37,X35)),X36),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__left__eq) ).

fof(fact_psubset__eq,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
        & X12 != X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).

fof(fact_subset__iff__psubset__eq,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
        | X12 = X15 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__iff__psubset__eq) ).

fof(fact_finite__UnI,axiom,
    ! [X4,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X4))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X9),X4))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UnI) ).

fof(fact_Pow__Int__eq,axiom,
    ! [X15,X12,X10] : hAPP(c_Set_OPow(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X12)),hAPP(c_Set_OPow(X10),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__Int__eq) ).

fof(fact_finite__maxlen,axiom,
    ! [X143,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),X143))
     => ? [X123] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X3),X143))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X3)),X123)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__maxlen) ).

fof(fact_setsum_Oeq__fold,axiom,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Oplus__class_Oplus(X8)),X1),c_Groups_Ozero__class_Ozero(X8)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oeq__fold) ).

fof(fact_setprod_Oeq__fold,axiom,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oeq__fold) ).

fof(fact_psubset__imp__subset,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__imp__subset) ).

fof(fact_append__replicate__commute,axiom,
    ! [X33,X26,X25,X27] : hAPP(hAPP(c_List_Oappend(X27),c_List_Oreplicate(X27,X25,X26)),c_List_Oreplicate(X27,X33,X26)) = hAPP(hAPP(c_List_Oappend(X27),c_List_Oreplicate(X27,X33,X26)),c_List_Oreplicate(X27,X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__replicate__commute) ).

fof(fact_mod__pos__neg,axiom,
    ! [X36,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),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = 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),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__neg) ).

fof(fact_ex__nat__less,axiom,
    ! [X42,X30] :
      ( ? [X74] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X74),X30))
          & hBOOL(hAPP(X42,X74)) )
    <=> ? [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),X30)))
          & hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less) ).

fof(fact_drop__Cons__number__of,axiom,
    ! [X202,X26,X27,X68] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Odrop(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X202) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons__number__of) ).

fof(fact_Abs__Integ__induct,axiom,
    ! [X11,X42] :
      ( ! [X51] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X51),c_Int_OInteg))
         => hBOOL(hAPP(X42,hAPP(c_Int_OAbs__Integ,X51))) )
     => hBOOL(hAPP(X42,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).

fof(fact_wf__Int1,axiom,
    ! [X162,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X110),X162)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Int1) ).

fof(fact_wf__Int2,axiom,
    ! [X162,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),X162),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__Int2) ).

fof(fact_div__pos__neg,axiom,
    ! [X36,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),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = 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),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__neg) ).

fof(fact_fold1__set,axiom,
    ! [X200,X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => ( X200 != c_List_Olist_ONil(X10)
       => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(c_List_Oset(X10),X200)) = hAPP(c_List_Ofoldl(X10,X10,c_Groups_Otimes__class_Otimes(X10),hAPP(c_List_Ohd(X10),X200)),hAPP(c_List_Otl(X10),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__set) ).

fof(fact_drop__zip,axiom,
    ! [X201,X202,X25,X10,X27] : hAPP(hAPP(c_List_Odrop(tc_prod(X27,X10)),X25),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201)) = hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Odrop(X27),X25),X202)),hAPP(hAPP(c_List_Odrop(X10),X25),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__zip) ).

fof(fact_take__zip,axiom,
    ! [X201,X202,X25,X10,X27] : hAPP(hAPP(c_List_Otake(tc_prod(X27,X10)),X25),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201)) = hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(hAPP(c_List_Otake(X27),X25),X202)),hAPP(hAPP(c_List_Otake(X10),X25),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__zip) ).

fof(fact_ivl__disj__un_I6_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X77)),hAPP(hAPP(c_Set_Oinsert(X10),X77),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X77) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I6_J) ).

fof(fact_mod__neg__neg,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = 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),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__neg) ).

fof(fact_single__valued__rel__comp,axiom,
    ! [X116,X18,X110,X8,X10] :
      ( c_Relation_Osingle__valued(X10,X8,X110)
     => ( c_Relation_Osingle__valued(X8,X18,X116)
       => c_Relation_Osingle__valued(X10,X18,hAPP(hAPP(c_Relation_Orel__comp(X10,X8,X18),X110),X116)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__rel__comp) ).

fof(fact_sorted__transpose,axiom,
    ! [X200,X10] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X10),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X10))),c_List_Otranspose(X10,X200)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__transpose) ).

fof(fact_Int__atLeastLessThan,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X6),X20)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),X6)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X14),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastLessThan) ).

fof(fact_Int__atLeastAtMost,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X6,X20)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),X6),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X14),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_Int__greaterThanAtMost,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X13,X14)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X6,X20)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),X6),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X14),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greaterThanAtMost) ).

fof(fact_Int__greaterThanLessThan,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X13,X14)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X6,X20)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),X6),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X14),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__greaterThanLessThan) ).

fof(fact_set__rev__mp,axiom,
    ! [X15,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => hBOOL(hAPP(hAPP(c_member(X10),X11),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev__mp) ).

fof(fact_psubsetD,axiom,
    ! [X6,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubsetD) ).

fof(fact_in__mono,axiom,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X11),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__mono) ).

fof(fact_set__mp,axiom,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X11),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__mp) ).

fof(fact_subsetD,axiom,
    ! [X6,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subsetD) ).

fof(fact_nth__append__length,axiom,
    ! [X201,X26,X202,X27] : hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Oappend(X27),X202),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X201))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length) ).

fof(fact_div__neg__neg,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = 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),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__neg) ).

fof(fact_inj__on__add__nat,axiom,
    ! [X53,X32] : 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)),X32),X53),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).

fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
    ! [X13,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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13),X14)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__nonneg__iff) ).

fof(fact_times__divide__times__eq,axiom,
    ! [X92,X38,X34,X26,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X38),X92)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X38)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__times__eq) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
    ! [X86,X87,X88,X89,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X88)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X87),X86)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X87)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X88),X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
    ! [X58,X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
    ! [X86,X87,X88,X89,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X88)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X87),X86)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X88),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X87),X86))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) ).

fof(fact_sorted__map__remove1,axiom,
    ! [X11,X200,X2,X8,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))
       => c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_Oremove1(X8,X11,X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__map__remove1) ).

fof(fact_Domain__Union,axiom,
    ! [X28,X8,X10] : hAPP(c_Relation_ODomain(X10,X8),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),X28)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X10,X8),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X28),c_Relation_ODomain(X10,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Union) ).

fof(fact_Range__Union,axiom,
    ! [X28,X10,X8] : hAPP(c_Relation_ORange(X8,X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),X28)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X8,X10),tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X28),c_Relation_ORange(X8,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Union) ).

fof(fact_all__nat__less,axiom,
    ! [X42,X30] :
      ( ! [X74] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X74),X30))
         => hBOOL(hAPP(X42,X74)) )
    <=> ! [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),X30)))
         => hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less) ).

fof(fact_Ints__power,axiom,
    ! [X30,X13,X10] :
      ( class_Rings_Oring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Int_Oring__1__class_OInts(X10)))
       => hBOOL(hAPP(hAPP(c_member(X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X30)),c_Int_Oring__1__class_OInts(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__power) ).

fof(fact_Collect__mem__eq,axiom,
    ! [X12,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__mem__eq) ).

fof(fact_nat__one__le__power,axiom,
    ! [X25,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X44))
     => 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),X44),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__one__le__power) ).

fof(fact_all__interval__nat__def,axiom,
    ! [X60,X61,X42] :
      ( c_List_Oall__interval__nat(X42,X61,X60)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X61),X60)))
         => hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__interval__nat__def) ).

fof(fact_one__less__power,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__power) ).

fof(fact_divide__neg__neg,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__neg__neg) ).

fof(fact_mult__neg__neg,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Olinordered__ring__strict(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__neg__neg) ).

fof(fact_divide__nonpos__neg,axiom,
    ! [X34,X26,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__nonpos__neg) ).

fof(fact_mult__nonpos__nonpos,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oordered__ring(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),c_Groups_Ozero__class_Ozero(X27)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__nonpos__nonpos) ).

fof(fact_setsum__lessThan__Suc,axiom,
    ! [X30,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30))),hAPP(X2,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__lessThan__Suc) ).

fof(fact_posDivAlg__div__mod,axiom,
    ! [X45,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_Divides_OposDivAlg(X33,X45) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),X45)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,X45)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__div__mod) ).

fof(fact_pos__imp__zdiv__pos__iff,axiom,
    ! [X61,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32))
     => ( 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),X61),X32)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__imp__zdiv__pos__iff) ).

fof(fact_lex__def,axiom,
    ! [X110,X10] : c_List_Olex(X10,X110) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lex__def) ).

fof(fact_less__max__iff__disj,axiom,
    ! [X16,X11,X19,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),X16)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X11))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__max__iff__disj) ).

fof(fact_le__max__iff__disj,axiom,
    ! [X16,X11,X19,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X19),hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),X16)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X19),X11))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X19),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__max__iff__disj) ).

fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
    ! [X13,X14] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),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),X13),X14)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X13),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,
    ! [X10,X200] :
      ( X200 != c_List_Olist_ONil(X10)
     => c_Random_Oselect__weight(X10,hAPP(hAPP(c_List_Omap(X10,tc_prod(tc_Code__Numeral_Ocode__numeral,X10)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X10),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X200)) = c_Random_Oselect(X10,X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_select__weigth__select) ).

fof(fact_finite__Inter,axiom,
    ! [X143,X10] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),X143))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X3)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X143))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Inter) ).

fof(fact_abs__eq__mult,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oordered__ring__abs(X27)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Ozero__class_Ozero(X27))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),c_Groups_Ozero__class_Ozero(X27))) ) )
       => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__mult) ).

fof(fact_butlast__take,axiom,
    ! [X202,X27,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => c_List_Obutlast(X27,hAPP(hAPP(c_List_Otake(X27),X25),X202)) = hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__take) ).

fof(fact_single__Diff__lessThan,axiom,
    ! [X32,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X32),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X32)) = hAPP(hAPP(c_Set_Oinsert(X10),X32),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__Diff__lessThan) ).

fof(fact_disjoint__iff__not__equal,axiom,
    ! [X15,X12,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => ! [X66] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X66),X15))
             => X3 != X66 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).

fof(fact_insort__remove1,axiom,
    ! [X200,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_List_Oset(X10),X200)))
       => ( c_List_Olinorder__class_Osorted(X10,X200)
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X13),c_List_Oremove1(X10,X13,X200)) = X200 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__remove1) ).

fof(fact_negDivAlg__div__mod,axiom,
    ! [X45,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),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)),X45))
       => c_Divides_OnegDivAlg(X33,X45) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),X45)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,X45)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__div__mod) ).

fof(fact_Inf__fin_Osubset__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
           => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X15)),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)) = c_Big__Operators_Olattice__class_OInf__fin(X10,X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Osubset__idem) ).

fof(fact_Sup__fin_Osubset__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
           => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X15)),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)) = c_Big__Operators_Olattice__class_OSup__fin(X10,X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Osubset__idem) ).

fof(fact_Max_Osubset__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,X15)),c_Big__Operators_Olinorder__class_OMax(X10,X12)) = c_Big__Operators_Olinorder__class_OMax(X10,X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Osubset__idem) ).

fof(fact_Min_Osubset__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,X15)),c_Big__Operators_Olinorder__class_OMin(X10,X12)) = c_Big__Operators_Olinorder__class_OMin(X10,X12) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Osubset__idem) ).

fof(fact_zpower__zmod,axiom,
    ! [X34,X24,X26] : 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,X26,X24)),X34),X24) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X34),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zmod) ).

fof(fact_zdiff__zmod__left,axiom,
    ! [X34,X24,X26] : 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,X26,X24)),X34),X24) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X34),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__left) ).

fof(fact_le__Inf__iff,axiom,
    ! [X12,X14,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),c_Complete__Lattice_OInf__class_OInf(X10,X12)))
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X3)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Inf__iff) ).

fof(fact_take__Cons_H,axiom,
    ! [X202,X26,X27,X25] :
      ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X27),X25),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = c_List_Olist_ONil(X27) )
      & ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(X27),X25),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Cons_H) ).

fof(fact_inf1I,axiom,
    ! [X10,X15,X11,X12] :
      ( hBOOL(hAPP(X12,X11))
     => ( hBOOL(hAPP(X15,X11))
       => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf1I) ).

fof(fact_list__ex__iff__raw,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__ex(X10,X42,X200)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
          & hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__raw) ).

fof(fact_Bex__set__list__ex,axiom,
    ! [X42,X200,X10] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
          & hBOOL(hAPP(X42,X3)) )
    <=> c_List_Olist__ex(X10,X42,X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bex__set__list__ex) ).

fof(fact_list__ex__iff,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__ex(X10,X42,X200)
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
          & hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff) ).

fof(fact_Rep__Integ,axiom,
    ! [X11] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X11)),c_Int_OInteg)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ) ).

fof(fact_folding__one__idem_Ounion__idem,axiom,
    ! [X15,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one__idem(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => hAPP(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(X2,hAPP(X9,X12)),hAPP(X9,X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Ounion__idem) ).

fof(fact_in__listsp__conv__set,axiom,
    ! [X200,X12,X10] :
      ( hBOOL(hAPP(c_List_Olistsp(X10,X12),X200))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X12,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listsp__conv__set) ).

fof(fact_add__strict__increasing2,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing2) ).

fof(fact_add__strict__increasing,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__strict__increasing) ).

fof(fact_pos__add__strict,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__add__strict) ).

fof(fact_add__increasing,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X35))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing) ).

fof(fact_add__increasing2,axiom,
    ! [X37,X36,X35,X27] :
      ( class_Groups_Oordered__comm__monoid__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X35))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X37))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__increasing2) ).

fof(fact_zmod__zdiv__equality,axiom,
    ! [X36,X37] : X37 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality) ).

fof(fact_less__infI1,axiom,
    ! [X36,X26,X37,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI1) ).

fof(fact_less__infI2,axiom,
    ! [X37,X26,X36,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__infI2) ).

fof(fact_min__max_Oless__infI1,axiom,
    ! [X36,X26,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__infI1) ).

fof(fact_min__max_Oless__infI2,axiom,
    ! [X37,X26,X36,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__infI2) ).

fof(fact_le__infI1,axiom,
    ! [X36,X26,X37,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI1) ).

fof(fact_le__infI2,axiom,
    ! [X37,X26,X36,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI2) ).

fof(fact_min__max_Ole__infI1,axiom,
    ! [X36,X26,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI1) ).

fof(fact_min__max_Ole__infI2,axiom,
    ! [X37,X26,X36,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI2) ).

fof(fact_listrel__Nil,axiom,
    ! [X110,X10] : hAPP(c_Relation_OImage(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Olistrel(X10,X110)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__Nil) ).

fof(fact_setsum__eq__0__iff,axiom,
    ! [X2,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X9))
           => 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,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,tc_Nat_Onat),X2),X9) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      <=> ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X9))
           => 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_Babs__def,axiom,
    ! [X31,X8,X148,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X148))
     => hAPP(c_Quotient_OBabs(X10,X8,X148,X31),X11) = hAPP(X31,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Babs__def) ).

fof(fact_nat__diff__split,axiom,
    ! [X14,X13,X42] :
      ( hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13),X14)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X14))
         => hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
        & ! [X75] :
            ( X13 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X75)
           => hBOOL(hAPP(X42,X75)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).

fof(fact_dvd__div__mult,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X36))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X36),X37)),X35) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)),X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult) ).

fof(fact_finite__compl,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__compl) ).

fof(fact_less__nat__number__of,axiom,
    ! [X119,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)))
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),X119))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X119)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X93),X119)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__number__of) ).

fof(fact_Un__insert__left,axiom,
    ! [X17,X15,X13,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)),X17) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__left) ).

fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
    ! [X11,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm__idem(X10,X8,X2)
     => hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X2,X11)),hAPP(X2,X11)) = hAPP(X2,X11) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem_Ofun__comp__idem) ).

fof(fact_divmod__int__rel__mod,axiom,
    ! [X80,X114,X36,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)))
     => ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = X80 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__mod) ).

fof(fact_snd__def,axiom,
    ! [X148,X10,X8] : hAPP(c_Product__Type_Osnd(X8,X10),X148) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X10,X10),hAPP(c_COMBK(tc_fun(X10,X10),X8),c_COMBI(X10))),X148),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__def) ).

fof(fact_Ints__odd__nonzero,axiom,
    ! [X13,X10] :
      ( class_Int_Oring__char__0(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Int_Oring__1__class_OInts(X10)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),c_Groups_Oone__class_Oone(X10)),X13)),X13) != c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__odd__nonzero) ).

fof(fact_finite__Int,axiom,
    ! [X4,X9,X10] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X4)) )
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X9),X4))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Int) ).

fof(fact_finite__Diff,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Diff) ).

fof(fact_sorted__many,axiom,
    ! [X215,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => ( c_List_Olinorder__class_Osorted(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X34),X215))
         => c_List_Olinorder__class_Osorted(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),hAPP(hAPP(c_List_Olist_OCons(X27),X34),X215))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__many) ).

fof(fact_sorted__many__eq,axiom,
    ! [X206,X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X206)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
          & c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X16),X206)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__many__eq) ).

fof(fact_mod__eq,axiom,
    ! [X80,X114,X25,X24] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X24,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X114),X80)))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = X80 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq) ).

fof(fact_pos__mod__conj,axiom,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => ( 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,X37,X36)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__conj) ).

fof(fact_pos__mod__bound,axiom,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__bound) ).

fof(fact_mod__less__divisor,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).

fof(fact_zmod__le__nonneg__dividend,axiom,
    ! [X33,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24,X33)),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__le__nonneg__dividend) ).

fof(fact_mod__le__divisor,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__le__divisor) ).

fof(fact_length__remdups__leq,axiom,
    ! [X202,X27] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),c_List_Oremdups(X27,X202))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__leq) ).

fof(fact_card__length,axiom,
    ! [X200,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(c_List_Oset(X10),X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__length) ).

fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
    ! [X16,X11,X10] :
      ( ( class_Divides_Osemiring__div(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X11)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)))
      <=> c_Divides_Odiv__class_Omod(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),X16),hAPP(c_Int_Onumber__class_Onumber__of(X10),X11)) = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0__number__of) ).

fof(fact_image__Pow__surj,axiom,
    ! [X15,X12,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),X12) = X15
     => hAPP(c_Set_Oimage(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool),c_Set_Oimage(X8,X10,X2)),hAPP(c_Set_OPow(X8),X12)) = hAPP(c_Set_OPow(X10),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Pow__surj) ).

fof(fact_surj__image__vimage__eq,axiom,
    ! [X12,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))
     => hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_Set_Ovimage(X8,X10,X2),X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__image__vimage__eq) ).

fof(fact_divmod__int__rel__div,axiom,
    ! [X80,X114,X36,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)))
     => ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = X114 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__div) ).

fof(fact_minus__less__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),X14))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__less__iff) ).

fof(fact_abs__le__D2,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D2) ).

fof(fact_minus__le__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),X14))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__iff) ).

fof(fact_neg__mod__conj,axiom,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),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,X37,X36)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__conj) ).

fof(fact_neg__mod__sign,axiom,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),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,X37,X36)),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,
    ! [X42,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(c_Set_OCollect(X8),X42)) = hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(X8,tc_HOL_Obool,X10),X42),X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Collect__eq) ).

fof(fact_div__eq,axiom,
    ! [X80,X114,X25,X24] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X24,X25),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X114),X80)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = X114 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__eq) ).

fof(fact_card__image,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => hAPP(c_Finite__Set_Ocard(X8),hAPP(c_Set_Oimage(X10,X8,X2),X12)) = hAPP(c_Finite__Set_Ocard(X10),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__image) ).

fof(fact_take__drop,axiom,
    ! [X202,X24,X25,X27] : hAPP(hAPP(c_List_Otake(X27),X25),hAPP(hAPP(c_List_Odrop(X27),X24),X202)) = hAPP(hAPP(c_List_Odrop(X27),X24),hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__drop) ).

fof(fact_sorted__filter,axiom,
    ! [X42,X200,X2,X8,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200))
       => c_List_Olinorder__class_Osorted(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(c_List_Ofilter(X8,X42),X200))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__filter) ).

fof(fact_nat__mod__eq__lemma,axiom,
    ! [X34,X25,X26] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X34,X25)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X34),X26))
       => ? [X138] : X26 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X138)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mod__eq__lemma) ).

fof(fact_takeWhile__eq__all__conv,axiom,
    ! [X200,X42,X10] :
      ( c_List_OtakeWhile(X10,X42,X200) = X200
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,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,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ),
    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,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__double__add__iff__zero__le__single__add) ).

fof(fact_Ball__set__list__all,axiom,
    ! [X42,X200,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,X3)) )
    <=> c_List_Olist__all(X10,X42,X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ball__set__list__all) ).

fof(fact_list__all__iff__raw,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__all(X10,X42,X200)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__raw) ).

fof(fact_list__all__iff,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__all(X10,X42,X200)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff) ).

fof(fact_add__gr__0,axiom,
    ! [X30,X31] :
      ( 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),X31),X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).

fof(fact_mod__mult__cong,axiom,
    ! [X113,X36,X127,X35,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( c_Divides_Odiv__class_Omod(X27,X37,X35) = c_Divides_Odiv__class_Omod(X27,X127,X35)
       => ( c_Divides_Odiv__class_Omod(X27,X36,X35) = c_Divides_Odiv__class_Omod(X27,X113,X35)
         => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X127),X113),X35) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__cong) ).

fof(fact_mod__add__cong,axiom,
    ! [X113,X36,X127,X35,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( c_Divides_Odiv__class_Omod(X27,X37,X35) = c_Divides_Odiv__class_Omod(X27,X127,X35)
       => ( c_Divides_Odiv__class_Omod(X27,X36,X35) = c_Divides_Odiv__class_Omod(X27,X113,X35)
         => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X127),X113),X35) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__cong) ).

fof(fact_mod__diff__cong,axiom,
    ! [X113,X36,X127,X35,X37,X27] :
      ( class_Divides_Oring__div(X27)
     => ( c_Divides_Odiv__class_Omod(X27,X37,X35) = c_Divides_Odiv__class_Omod(X27,X127,X35)
       => ( c_Divides_Odiv__class_Omod(X27,X36,X35) = c_Divides_Odiv__class_Omod(X27,X113,X35)
         => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X127),X113),X35) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__cong) ).

fof(fact_dvd__mod,axiom,
    ! [X25,X24,X33,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X33),X24))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X33),X25))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X33),c_Divides_Odiv__class_Omod(X27,X24,X25))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mod) ).

fof(fact_power__diff,axiom,
    ! [X24,X25,X37,X27] :
      ( class_Fields_Ofield(X27)
     => ( X37 != c_Groups_Ozero__class_Ozero(X27)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__diff) ).

fof(fact_divmod__int__rel__neg,axiom,
    ! [X151,X36,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)),X151))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(c_Divides_OnegateSnd,X151))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__rel__neg) ).

fof(fact_insert__Diff1,axiom,
    ! [X12,X15,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),X15) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Diff1) ).

fof(fact_Nat_Odiff__diff__eq,axiom,
    ! [X25,X24,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X25))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X33)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Odiff__diff__eq) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [X200,X42,X10] : c_List_OtakeWhile(X10,X42,X200) = hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200))),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [X42,X30] :
      ( ? [X74] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X74),X30))
          & hBOOL(hAPP(X42,X74)) )
    <=> ? [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)),X30)))
          & hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_Suc__diff__diff,axiom,
    ! [X33,X25,X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25)),hAPP(c_Nat_OSuc,X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__diff) ).

fof(fact_power__inject__base,axiom,
    ! [X36,X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(c_Nat_OSuc,X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),hAPP(c_Nat_OSuc,X25))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X36))
           => X37 = X36 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__base) ).

fof(fact_bex__reg__eqv,axiom,
    ! [X42,X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => ( ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),c_Quotient_ORespects(X10,X29)))
            & hBOOL(hAPP(X42,X3)) )
      <=> ? [X136] : hBOOL(hAPP(X42,X136)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__reg__eqv) ).

fof(fact_int__zle__neg,axiom,
    ! [X31,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31))))
    <=> ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__zle__neg) ).

fof(fact_wf,axiom,
    ! [X10] :
      ( class_Orderings_Owellorder(X10)
     => c_Wellfounded_Owf(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X10)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf) ).

fof(fact_dvd__add,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X35))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X35))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__add) ).

fof(fact_dvd__diff,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Rings_Ocomm__ring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X26),X38))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X26),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X34),X38))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff) ).

fof(fact_min__less__iff__conj,axiom,
    ! [X16,X11,X19,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),X16)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X11))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X19),X16)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__less__iff__conj) ).

fof(fact_inf__greatest,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X38))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X38))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__greatest) ).

fof(fact_le__infI,axiom,
    ! [X36,X37,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__infI) ).

fof(fact_le__inf__iff,axiom,
    ! [X19,X16,X11,X10] :
      ( class_Lattices_Osemilattice__inf(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X16),X19)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__inf__iff) ).

fof(fact_min__max_Oinf__greatest,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X38))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),X38))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__greatest) ).

fof(fact_min__max_Ole__infI,axiom,
    ! [X36,X37,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__infI) ).

fof(fact_min__max_Ole__inf__iff,axiom,
    ! [X19,X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X16),X19)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__inf__iff) ).

fof(fact_self__quotient__aux2,axiom,
    ! [X114,X80,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
     => ( X37 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X80),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X114))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X80))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X114),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,
    ! [X200,X42,X10] :
      ( hAPP(c_List_Ofilter(X10,X42),X200) = X200
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__id__conv) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => 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,X26,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_nth__append__length__plus,axiom,
    ! [X25,X201,X202,X27] : hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X25)) = hAPP(hAPP(c_List_Onth(X27),X201),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__append__length__plus) ).

fof(fact_list_Osimps_I5_J,axiom,
    ! [X204,X13,X49,X50,X8,X10] : hAPP(c_List_Olist_Olist__case(X10,X8,X50,X49),hAPP(hAPP(c_List_Olist_OCons(X8),X13),X204)) = hAPP(hAPP(X49,X13),X204),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I5_J) ).

fof(fact_sup1I1,axiom,
    ! [X15,X10,X11,X12] :
      ( hBOOL(hAPP(X12,X11))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1I1) ).

fof(fact_sup1I2,axiom,
    ! [X12,X10,X11,X15] :
      ( hBOOL(hAPP(X15,X11))
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup1I2) ).

fof(fact_zero__le__power__abs,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power__abs) ).

fof(fact_diff__Suc__diff__eq1,axiom,
    ! [X24,X43,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X43))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X33))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X33)),hAPP(c_Nat_OSuc,X43)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__diff__eq1) ).

fof(fact_subset__empty,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
    <=> X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__empty) ).

fof(fact_wfP__acyclicP,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_OwfP(X10,X110)
     => c_Wellfounded_Oacyclic(X10,hAPP(c_Set_OCollect(tc_prod(X10,X10)),hAPP(c_Product__Type_Oprod_Oprod__case(X10,X10,tc_HOL_Obool),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).

fof(fact_rel__comp__empty1,axiom,
    ! [X29,X8,X18,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X18),tc_HOL_Obool))),X29) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__empty1) ).

fof(fact_zdiv__zminus1__eq__if,axiom,
    ! [X37,X36] :
      ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = 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),X37)),X36) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) != 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),X37)),X36) = 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),X37),X36))),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,
    ! [X13,X14,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__iff__less) ).

fof(fact_compl__le__compl__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Lattices_Oboolean__algebra(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__le__compl__iff) ).

fof(fact_neg__le__iff__le,axiom,
    ! [X13,X14,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__iff__le) ).

fof(fact_all__nat__less__eq,axiom,
    ! [X42,X30] :
      ( ! [X74] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X74),X30))
         => hBOOL(hAPP(X42,X74)) )
    <=> ! [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)),X30)))
         => hBOOL(hAPP(X42,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).

fof(fact_power__gt1,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(c_Nat_OSuc,X25)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__gt1) ).

fof(fact__05,axiom,
    ! [X2,X232,X10,X8] : hAPP(c_Lazy__Sequence_Obind(X8,X10,X232),X2) = c_Lazy__Sequence_Oflat(X10,c_Lazy__Sequence_Omap(X8,tc_Lazy__Sequence_Olazy__sequence(X10),X2,X232)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__05) ).

fof(fact_self__quotient__aux1,axiom,
    ! [X114,X80,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37))
     => ( X37 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X80),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X114))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X80),X37))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X114)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient__aux1) ).

fof(fact_conversep_Ointros,axiom,
    ! [X8,X10,X14,X13,X110] :
      ( hBOOL(hAPP(hAPP(X110,X13),X14))
     => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X10,X8,X110),X14),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep_Ointros) ).

fof(fact_less__number__of,axiom,
    ! [X16,X11,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X11)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of) ).

fof(fact_le__number__of,axiom,
    ! [X16,X11,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X11)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__number__of) ).

fof(fact_zdvd__antisym__nonneg,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X24),X25))
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X25),X24))
           => X24 = X25 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__antisym__nonneg) ).

fof(fact_list__update__beyond,axiom,
    ! [X26,X44,X202,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X44))
     => hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26) = X202 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__beyond) ).

fof(fact_le__cube,axiom,
    ! [X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X24)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__cube) ).

fof(fact_in__set__butlastD,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Obutlast(X10,X200))))
     => hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__butlastD) ).

fof(fact_insert__image,axiom,
    ! [X2,X8,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => hAPP(hAPP(c_Set_Oinsert(X8),hAPP(X2,X11)),hAPP(c_Set_Oimage(X10,X8,X2),X12)) = hAPP(c_Set_Oimage(X10,X8,X2),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).

fof(fact_self__quotient,axiom,
    ! [X80,X114,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X37),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)))
     => ( X37 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => X114 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__quotient) ).

fof(fact_self__remainder,axiom,
    ! [X80,X114,X37] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X37),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)))
     => ( X37 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => X80 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__remainder) ).

fof(fact_wf__exp,axiom,
    ! [X29,X30,X10] :
      ( c_Wellfounded_Owf(X10,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29))
     => c_Wellfounded_Owf(X10,X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__exp) ).

fof(fact_of__int__less__iff,axiom,
    ! [X19,X90,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X90)),hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__less__iff) ).

fof(fact_of__nat__less__iff,axiom,
    ! [X30,X31,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X31)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__iff) ).

fof(fact_of__nat__less__imp__less,axiom,
    ! [X25,X24,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25)))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__imp__less) ).

fof(fact_of__int__le__iff,axiom,
    ! [X19,X90,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X90)),hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__le__iff) ).

fof(fact_of__nat__le__iff,axiom,
    ! [X30,X31,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X31)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__le__iff) ).

fof(fact_nonzero__power__divide,axiom,
    ! [X25,X37,X36,X27] :
      ( class_Fields_Ofield(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36)),X25) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__power__divide) ).

fof(fact_zless__imp__add1__zle,axiom,
    ! [X38,X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X92),X38))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X92),c_Groups_Oone__class_Oone(tc_Int_Oint))),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__imp__add1__zle) ).

fof(fact_Inf__fin_Ounion__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)),c_Big__Operators_Olattice__class_OInf__fin(X10,X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Ounion__idem) ).

fof(fact_Sup__fin_Ounion__idem,axiom,
    ! [X15,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)),c_Big__Operators_Olattice__class_OSup__fin(X10,X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Ounion__idem) ).

fof(fact_Max__Un,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),c_Big__Operators_Olinorder__class_OMax(X10,X12)),c_Big__Operators_Olinorder__class_OMax(X10,X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__Un) ).

fof(fact_Min__Un,axiom,
    ! [X15,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
           => ( X15 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
             => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),c_Big__Operators_Olinorder__class_OMin(X10,X12)),c_Big__Operators_Olinorder__class_OMin(X10,X15)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__Un) ).

fof(fact_splice_Osimps_I3_J,axiom,
    ! [X201,X34,X202,X26,X27] : c_List_Osplice(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202),hAPP(hAPP(c_List_Olist_OCons(X27),X34),X201)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),hAPP(hAPP(c_List_Olist_OCons(X27),X34),c_List_Osplice(X27,X202,X201))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I3_J) ).

fof(fact_code__numeral_Oof__nat__inject,axiom,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X11),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
       => ( hAPP(c_Code__Numeral_Oof__nat,X11) = hAPP(c_Code__Numeral_Oof__nat,X16)
        <=> X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Oof__nat__inject) ).

fof(fact_nat__mono__iff,axiom,
    ! [X90,X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X90)),hAPP(c_Int_Onat,X19)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mono__iff) ).

fof(fact_nat__less__eq__zless,axiom,
    ! [X19,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X90)),hAPP(c_Int_Onat,X19)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__eq__zless) ).

fof(fact_nat__le__eq__zle,axiom,
    ! [X19,X90] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X90)),hAPP(c_Int_Onat,X19)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__eq__zle) ).

fof(fact_funpow__swap1,axiom,
    ! [X11,X30,X10,X2] : hAPP(X2,hAPP(hAPP(hAPP(c_Nat_Ocompow(X10,X10),X30),X2),X11)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X10,X10),X30),X2),hAPP(X2,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__swap1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
    ! [X36,X24,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).

fof(fact_inf__sup__distrib2,axiom,
    ! [X26,X38,X34,X27] :
      ( class_Lattices_Odistrib__lattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X38)),X26) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X26)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X38),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).

fof(fact_sup__inf__distrib2,axiom,
    ! [X26,X38,X34,X27] :
      ( class_Lattices_Odistrib__lattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X38)),X26) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X26)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X38),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).

fof(fact_min__max_Osup__inf__distrib2,axiom,
    ! [X26,X38,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),X38)),X26) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),X26)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X38),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).

fof(fact_add__divide__distrib,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Odivision__ring(X27)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X35)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__divide__distrib) ).

fof(fact_diff__divide__distrib,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Odivision__ring(X27)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36)),X35) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X35)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__divide__distrib) ).

fof(fact_min__max_Oinf__sup__distrib2,axiom,
    ! [X26,X38,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),X38)),X26) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),X26)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X38),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).

fof(fact_power__divide,axiom,
    ! [X25,X36,X37,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36)),X25) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__divide) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
    ! [X114,X34,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X34)),X114) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X114)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X34),X114)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) ).

fof(fact_power__mult__distrib,axiom,
    ! [X25,X36,X37,X27] :
      ( class_Groups_Ocomm__monoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X36),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult__distrib) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).

fof(fact_comm__semiring__class_Odistrib,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__class_Odistrib) ).

fof(fact_max__add__distrib__left,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34)),X38) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),X38)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__add__distrib__left) ).

fof(fact_min__add__distrib__left,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)),X38) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),X38)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__add__distrib__left) ).

fof(fact_max__diff__distrib__left,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Groups_Oordered__ab__group__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34)),X38) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X26),X38)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__diff__distrib__left) ).

fof(fact_min__diff__distrib__left,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Groups_Oordered__ab__group__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)),X38) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X26),X38)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__diff__distrib__left) ).

fof(fact_set__insort,axiom,
    ! [X200,X11,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X11),X200)) = hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(c_List_Oset(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__insort) ).

fof(fact_nat__0__less__mult__iff,axiom,
    ! [X30,X31] :
      ( 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),X31),X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X31))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__less__mult__iff) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => 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),X26),X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => 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),X26),X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => 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),X26),X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) ).

fof(fact_dvd__div__div__eq__mult,axiom,
    ! [X20,X14,X6,X13,X10] :
      ( class_Divides_Osemiring__div(X10)
     => ( X13 != c_Groups_Ozero__class_Ozero(X10)
       => ( X6 != c_Groups_Ozero__class_Ozero(X10)
         => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X13),X14))
           => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X6),X20))
             => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X14),X13) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X20),X6)
              <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X20) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__div__eq__mult) ).

fof(fact_ivl__disj__un_I1_J,axiom,
    ! [X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X83),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X83)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X83) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I1_J) ).

fof(fact_finite__converse,axiom,
    ! [X110,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X8)),hAPP(c_Relation_Oconverse(X8,X10),X110)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X8,X10)),X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__converse) ).

fof(fact_finite__UNIV__card__ge__0,axiom,
    ! [X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,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(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV__card__ge__0) ).

fof(fact_set__remove1__eq,axiom,
    ! [X11,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X11,X200)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remove1__eq) ).

fof(fact_Int__Union,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X15),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__Union) ).

fof(fact_Un__Inter,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X15)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X15),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Inter) ).

fof(fact_length__insort,axiom,
    ! [X200,X11,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X11),X200)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__insort) ).

fof(fact_nat__less__iff,axiom,
    ! [X31,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X90)),X31))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__iff) ).

fof(fact_remove1__insort,axiom,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_List_Oremove1(X10,X11,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X11),X200)) = X200 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__insort) ).

fof(fact_Powp__def,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Predicate_OPowp(X10,X12),X15))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),X15))
         => hBOOL(hAPP(X12,X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).

fof(fact_split__curry,axiom,
    ! [X2,X18,X8,X10] : hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),c_Product__Type_Ocurry(X10,X8,X18,X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__curry) ).

fof(fact_eq__number__of__eq,axiom,
    ! [X16,X11,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X11) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)
      <=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X16)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__eq) ).

fof(fact_append__eq__conv__conj,axiom,
    ! [X206,X199,X200,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X200),X199) = X206
    <=> ( X200 = hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),X206)
        & X199 = hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),X206) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__conv__conj) ).

fof(fact_zdiv__zminus2__eq__if,axiom,
    ! [X37,X36] :
      ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)) = 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),X37),X36))),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,
    ! [X13,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv) ).

fof(fact_insert__is__Un,axiom,
    ! [X12,X13,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X13),X12) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__is__Un) ).

fof(fact_nat__of__induct,axiom,
    ! [X42,X16] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ( ! [X3] : hBOOL(hAPP(X42,hAPP(c_Code__Numeral_Onat__of,X3)))
       => hBOOL(hAPP(X42,X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__induct) ).

fof(fact_less__imp__diff__less,axiom,
    ! [X25,X33,X43] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X33))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X25)),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_add__diff__assoc2,axiom,
    ! [X44,X43,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X43))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X33)),X44) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X44)),X33) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc2) ).

fof(fact_diff__add__assoc2,axiom,
    ! [X44,X43,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X43))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X44)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X33)),X44) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_Int__absorb2,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb2) ).

fof(fact_Int__absorb1,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb1) ).

fof(fact_Un__absorb1,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15) = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb1) ).

fof(fact_subset__Un__eq,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
    <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15) = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__Un__eq) ).

fof(fact_Un__absorb2,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb2) ).

fof(fact_Collect__neg__eq,axiom,
    ! [X42,X10] : hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X42)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OCollect(X10),X42)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__neg__eq) ).

fof(fact_drop__all,axiom,
    ! [X25,X202,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X25))
     => hAPP(hAPP(c_List_Odrop(X27),X25),X202) = c_List_Olist_ONil(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__all) ).

fof(fact_drop__eq__Nil,axiom,
    ! [X200,X30,X10] :
      ( hAPP(hAPP(c_List_Odrop(X10),X30),X200) = c_List_Olist_ONil(X10)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__eq__Nil) ).

fof(fact_insert__iff,axiom,
    ! [X12,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),X12)))
    <=> ( X13 = X14
        | hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).

fof(fact_insertE,axiom,
    ! [X12,X14,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),X12)))
     => ( X13 != X14
       => hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).

fof(fact_take__all,axiom,
    ! [X25,X202,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X25))
     => hAPP(hAPP(c_List_Otake(X27),X25),X202) = X202 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__all) ).

fof(fact_ivl__diff,axiom,
    ! [X31,X30,X61,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X61),X30))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X61),X31)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X61),X30)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X30),X31) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__diff) ).

fof(fact_accp_Osimps,axiom,
    ! [X13,X110,X10] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X110),X13))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(X110,X3),X13))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X110),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).

fof(fact_accp_Oequations,axiom,
    ! [X13,X110,X10] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X110),X13))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(X110,X3),X13))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X110),X3)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).

fof(fact_Times__empty,axiom,
    ! [X15,X12,X8,X10] :
      ( hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X15)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),tc_HOL_Obool))
    <=> ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        | X15 = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Times__empty) ).

fof(fact_ivl__disj__un_I13_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X77)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X77)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X83) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I13_J) ).

fof(fact_ivl__disj__un_I11_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X77)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X77)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X83) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I11_J) ).

fof(fact_ivl__disj__un_I12_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X77)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X77)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X83) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I12_J) ).

fof(fact_Sup__set__fold,axiom,
    ! [X200,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OSup__class_OSup(X10,hAPP(c_List_Oset(X10),X200)) = hAPP(c_List_Ofoldl(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10),c_Orderings_Obot__class_Obot(X10)),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__set__fold) ).

fof(fact_Inf__set__fold,axiom,
    ! [X200,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OInf__class_OInf(X10,hAPP(c_List_Oset(X10),X200)) = hAPP(c_List_Ofoldl(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10),c_Orderings_Otop__class_Otop(X10)),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__set__fold) ).

fof(fact_card__atLeastAtMost__int,axiom,
    ! [X77,X83] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X83,X77)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X77),X83)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).

fof(fact_finite__imageI,axiom,
    ! [X7,X8,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_Oimage(X10,X8,X7),X9))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).

fof(fact_dvd_OatMost__iff,axiom,
    ! [X32,X61] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X61),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X61),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatMost__iff) ).

fof(fact_dvd_OatLeast__iff,axiom,
    ! [X32,X61] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X61),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeast__iff) ).

fof(fact_Sup__binary,axiom,
    ! [X14,X13,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OSup__class_OSup(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X13),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__binary) ).

fof(fact_Inf__binary,axiom,
    ! [X14,X13,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OInf__class_OInf(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X13),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__binary) ).

fof(fact_div__mult__swap,axiom,
    ! [X37,X36,X35,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X35),X36))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X36),X35)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__swap) ).

fof(fact_ord_OlessThan__iff,axiom,
    ! [X32,X84,X61,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X61),c_SetInterval_Oord_OlessThan(X10,X84,X32)))
    <=> hBOOL(hAPP(hAPP(X84,X61),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).

fof(fact_ord_OatMost__iff,axiom,
    ! [X32,X85,X61,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X61),c_SetInterval_Oord_OatMost(X10,X85,X32)))
    <=> hBOOL(hAPP(hAPP(X85,X61),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).

fof(fact_ord_OgreaterThan__iff,axiom,
    ! [X32,X84,X61,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X61),c_SetInterval_Oord_OgreaterThan(X10,X84,X32)))
    <=> hBOOL(hAPP(hAPP(X84,X32),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).

fof(fact_ord_OatLeast__iff,axiom,
    ! [X32,X85,X61,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X61),c_SetInterval_Oord_OatLeast(X10,X85,X32)))
    <=> hBOOL(hAPP(hAPP(X85,X32),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).

fof(fact_partition__set,axiom,
    ! [X233,X234,X200,X42,X10] :
      ( c_List_Opartition(X10,X42,X200) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X234),X233)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X234)),hAPP(c_List_Oset(X10),X233)) = hAPP(c_List_Oset(X10),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__set) ).

fof(fact_nth__Cons__number__of,axiom,
    ! [X202,X26,X27,X68] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = X26 )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(hAPP(c_List_Onth(X27),X202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),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,
    ! [X110,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X110),c_Transitive__Closure_Ortrancl(X10,X110)) = hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Ortrancl(X10,X110)),X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_r__comp__rtrancl__eq) ).

fof(help_c__COMBS__1,axiom,
    ! [X29,X41,X42,X10,X18,X8] : hAPP(hAPP(hAPP(c_COMBS(X8,X18,X10),X42),X41),X29) = hAPP(hAPP(X42,X29),hAPP(X41,X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBS__1) ).

fof(fact_abs__minus__le__zero,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37))),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__le__zero) ).

fof(fact_Un__insert__right,axiom,
    ! [X15,X13,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__insert__right) ).

fof(fact_sum__squares__eq__zero__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Rings_Olinordered__ring__strict(X10)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X16),X16)) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X11 = c_Groups_Ozero__class_Ozero(X10)
          & X16 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__squares__eq__zero__iff) ).

fof(fact_union__fold__insert,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15) = hAPP(hAPP(c_Finite__Set_Ofold(X10,tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10)),X15),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_union__fold__insert) ).

fof(fact_eq__special_I3_J,axiom,
    ! [X11,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X11) = c_Groups_Ozero__class_Ozero(X10)
      <=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),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,
    ! [X16,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( c_Groups_Ozero__class_Ozero(X10) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)
      <=> c_Int_Oiszero(X10,hAPP(c_Int_Onumber__class_Onumber__of(X10),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X16)))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I1_J) ).

fof(fact_trans__lex__prod,axiom,
    ! [X149,X8,X150,X10] :
      ( c_Relation_Otrans(X10,X150)
     => ( c_Relation_Otrans(X8,X149)
       => c_Relation_Otrans(tc_prod(X10,X8),c_Wellfounded_Olex__prod(X10,X8,X150,X149)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__lex__prod) ).

fof(fact_wf__lex__prod,axiom,
    ! [X192,X8,X193,X10] :
      ( c_Wellfounded_Owf(X10,X193)
     => ( c_Wellfounded_Owf(X8,X192)
       => c_Wellfounded_Owf(tc_prod(X10,X8),c_Wellfounded_Olex__prod(X10,X8,X193,X192)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex__prod) ).

fof(fact_distinct__zipI1,axiom,
    ! [X201,X10,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(X27,X10)),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__zipI1) ).

fof(fact_distinct__zipI2,axiom,
    ! [X202,X10,X201,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X201))
     => hBOOL(hAPP(c_List_Odistinct(tc_prod(X10,X27)),hAPP(hAPP(c_List_Ozip(X10,X27),X202),X201))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__zipI2) ).

fof(fact_vimage__Union,axiom,
    ! [X12,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,tc_HOL_Obool),X12)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X12),c_Set_Ovimage(X10,X8,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Union) ).

fof(fact_image__Union,axiom,
    ! [X28,X2,X10,X8] : hAPP(c_Set_Oimage(X8,X10,X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,tc_HOL_Obool),X28)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X8,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X28),c_Set_Oimage(X8,X10,X2)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Union) ).

fof(fact_Pow__bottom,axiom,
    ! [X15,X10] : hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),hAPP(c_Set_OPow(X10),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__bottom) ).

fof(fact_listsum__0,axiom,
    ! [X200,X8,X10] :
      ( class_Groups_Omonoid__add(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(X8,X10),hAPP(c_COMBK(X10,X8),c_Groups_Ozero__class_Ozero(X10))),X200)) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__0) ).

fof(fact_Int__left__absorb,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__left__absorb) ).

fof(fact_Un__left__absorb,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__left__absorb) ).

fof(fact_Un__Diff__cancel,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__Diff__cancel) ).

fof(fact_rotate1__length01,axiom,
    ! [X202,X27] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate1(X27),X202) = X202 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__length01) ).

fof(fact_fold__image__empty,axiom,
    ! [X19,X1,X2,X8,X10] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X8,X2),X1),X19),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__image__empty) ).

fof(fact_dvd__diff__nat,axiom,
    ! [X25,X24,X33] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X24))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X25))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__diff__nat) ).

fof(fact_mult__eq__if,axiom,
    ! [X25,X24] :
      ( ( X24 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X24 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__if) ).

fof(fact_listsp__inf__eq,axiom,
    ! [X15,X12,X10] : c_List_Olistsp(X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),c_List_Olistsp(X10,X12)),c_List_Olistsp(X10,X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp__inf__eq) ).

fof(fact_RangeP_Oequations,axiom,
    ! [X56,X110,X8,X10] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(X10,X8,X110),X56))
    <=> ? [X46] : hBOOL(hAPP(hAPP(X110,X46),X56)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).

fof(fact_nat__mult__distrib__neg,axiom,
    ! [X100,X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X100)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X100))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__distrib__neg) ).

fof(fact_pair__box_Osize_I2_J,axiom,
    ! [X36,X37,X10,X27] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X27,X10)),c_Nitpick_Opair__box_OPairBox(X27,X10,X37,X36)) = 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,
    ! [X26,X202,X27,X33] :
      ( ( X33 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(X27,hAPP(hAPP(c_List_Olist__update(X27,X202),X33),X26)) = c_List_Obutlast(X27,X202) )
      & ( X33 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(X27,hAPP(hAPP(c_List_Olist__update(X27,X202),X33),X26)) = hAPP(hAPP(c_List_Olist__update(X27,c_List_Obutlast(X27,X202)),X33),X26) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__list__update) ).

fof(fact_image__insert,axiom,
    ! [X15,X13,X2,X10,X8] : hAPP(c_Set_Oimage(X8,X10,X2),hAPP(hAPP(c_Set_Oinsert(X8),X13),X15)) = hAPP(hAPP(c_Set_Oinsert(X10),hAPP(X2,X13)),hAPP(c_Set_Oimage(X8,X10,X2),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).

fof(fact_finite__subset,axiom,
    ! [X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [X12,X15,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X15))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_neg__less__0__iff__less,axiom,
    ! [X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__0__iff__less) ).

fof(fact_neg__le__0__iff__le,axiom,
    ! [X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__le__0__iff__le) ).

fof(fact_length__sort,axiom,
    ! [X200,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Olinorder__class_Osort__key(X10,X8,X2,X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sort) ).

fof(fact_zip__rev,axiom,
    ! [X201,X10,X202,X27] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X201)
     => hAPP(hAPP(c_List_Ozip(X27,X10),hAPP(c_List_Orev(X27),X202)),hAPP(c_List_Orev(X10),X201)) = hAPP(c_List_Orev(tc_prod(X27,X10)),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__rev) ).

fof(fact_nat__zero__less__power__iff,axiom,
    ! [X30,X11] :
      ( 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),X11),X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X11))
        | X30 = 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,
    ! [X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X6)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),X6),X14) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL2) ).

fof(fact_Int__atLeastAtMostL1,axiom,
    ! [X20,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X20)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X14),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostL1) ).

fof(fact_list__update__code_I2_J,axiom,
    ! [X34,X202,X26,X27] : hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X34) = hAPP(hAPP(c_List_Olist_OCons(X27),X34),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I2_J) ).

fof(help_c__COMBC__1,axiom,
    ! [X29,X41,X42,X10,X18,X8] : hAPP(hAPP(hAPP(c_COMBC(X8,X18,X10),X42),X41),X29) = hAPP(hAPP(X42,X29),X41),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBB__1,axiom,
    ! [X29,X41,X42,X18,X10,X8] : hAPP(hAPP(hAPP(c_COMBB(X8,X10,X18),X42),X41),X29) = hAPP(X42,hAPP(X41,X29)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBB__1) ).

fof(fact_vimage__Compl,axiom,
    ! [X12,X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),X12)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X10,X8,X2),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__Compl) ).

fof(fact_mod__mult__self3,axiom,
    ! [X24,X25,X33] : 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),X33),X25)),X24),X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self3) ).

fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X34)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X34)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X34)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J) ).

fof(fact_nat__add__distrib,axiom,
    ! [X100,X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X100))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X38),X100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X38)),hAPP(c_Int_Onat,X100)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__distrib) ).

fof(fact_length__zip,axiom,
    ! [X201,X202,X10,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X27,X10))),hAPP(hAPP(c_List_Ozip(X27,X10),X202),X201)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__zip) ).

fof(fact_Union__image__eq,axiom,
    ! [X12,X15,X8,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X8,tc_fun(X10,tc_HOL_Obool),X15),X12)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__image__eq) ).

fof(fact_Inter__image__eq,axiom,
    ! [X12,X15,X8,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X8,tc_fun(X10,tc_HOL_Obool),X15),X12)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__image__eq) ).

fof(fact_INTER__eq__Inter__image,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X8,tc_fun(X10,tc_HOL_Obool),X15),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INTER__eq__Inter__image) ).

fof(fact_UNION__eq__Union__image,axiom,
    ! [X15,X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_Oimage(X8,tc_fun(X10,tc_HOL_Obool),X15),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNION__eq__Union__image) ).

fof(fact_of__nat__aux_Osimps_I2_J,axiom,
    ! [X61,X30,X125,X10] :
      ( class_Rings_Osemiring__1(X10)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X10,X125,hAPP(c_Nat_OSuc,X30),X61) = c_Nat_Osemiring__1__class_Oof__nat__aux(X10,X125,X30,hAPP(X125,X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).

fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X26),hAPP(c_Int_Onat,X34)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__nat__int__functions_I2_J) ).

fof(fact_nat__mod__distrib,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X34)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X26),hAPP(c_Int_Onat,X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mod__distrib) ).

fof(fact_zmod__zdiv__equality_H,axiom,
    ! [X25,X24] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X24,X25) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24),X25)),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__equality_H) ).

fof(fact_Divides_Omod__div__equality_H,axiom,
    ! [X25,X24] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25)),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Omod__div__equality_H) ).

fof(fact_zero__less__power,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__power) ).

fof(fact_zero__le__power,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__power) ).

fof(fact_one__le__power,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Oone__class_Oone(X27)),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Oone__class_Oone(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__le__power) ).

fof(fact_image__constant,axiom,
    ! [X6,X8,X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => hAPP(c_Set_Oimage(X10,X8,hAPP(c_COMBK(X8,X10),X6)),X12) = hAPP(hAPP(c_Set_Oinsert(X8),X6),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__constant) ).

fof(fact_zless__nat__conj,axiom,
    ! [X19,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X90)),hAPP(c_Int_Onat,X19)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__conj) ).

fof(fact_UNIV__Times__UNIV,axiom,
    ! [X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Times__UNIV) ).

fof(fact_zless__add1__eq,axiom,
    ! [X19,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X19))
        | X90 = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).

fof(fact_neg__less__nonneg,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),X13))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__less__nonneg) ).

fof(fact_minus__le__self__iff,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),X13))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__le__self__iff) ).

fof(fact_append__in__listsp__conv,axiom,
    ! [X199,X200,X12,X10] :
      ( hBOOL(hAPP(c_List_Olistsp(X10,X12),hAPP(hAPP(c_List_Oappend(X10),X200),X199)))
    <=> ( hBOOL(hAPP(c_List_Olistsp(X10,X12),X200))
        & hBOOL(hAPP(c_List_Olistsp(X10,X12),X199)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__in__listsp__conv) ).

fof(fact_funpow__mult,axiom,
    ! [X2,X31,X30,X10] : hAPP(hAPP(c_Nat_Ocompow(X10,X10),X30),hAPP(hAPP(c_Nat_Ocompow(X10,X10),X31),X2)) = hAPP(hAPP(c_Nat_Ocompow(X10,X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X30)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow__mult) ).

fof(fact_less__number__of__int__code,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_zless__int,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__int) ).

fof(fact_transfer__int__nat__relations_I2_J,axiom,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I2_J) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [X83,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X32)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X83)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X32),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_zle__int,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__int) ).

fof(fact_transfer__int__nat__relations_I3_J,axiom,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I3_J) ).

fof(fact_zero__less__diff,axiom,
    ! [X31,X30] :
      ( 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),X30),X31)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__diff) ).

fof(fact_zle__diff1__eq,axiom,
    ! [X19,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__diff1__eq) ).

fof(fact_zle__add1__eq__le,axiom,
    ! [X19,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__add1__eq__le) ).

fof(fact_minus__number__of__mult,axiom,
    ! [X38,X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92))),X38) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92))),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__number__of__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
    ! [X24,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X24)),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),c_Groups_Oone__class_Oone(X27))),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).

fof(fact_list__update__same__conv,axiom,
    ! [X11,X200,X10,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X61),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => ( hAPP(hAPP(c_List_Olist__update(X10,X200),X61),X11) = X200
      <=> hAPP(hAPP(c_List_Onth(X10),X200),X61) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__same__conv) ).

fof(fact_negative__zle,axiom,
    ! [X24,X25] : 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),X25))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle) ).

fof(fact_zero__le__zpower__abs,axiom,
    ! [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_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26)),X25))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__zpower__abs) ).

fof(fact_min__diff,axiom,
    ! [X25,X44,X24] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X44)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X44)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X24),X25)),X44),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__diff) ).

fof(fact_zadd__zmult__distrib,axiom,
    ! [X92,X97,X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),X97)),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X98),X92)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib) ).

fof(fact_zdiff__zmult__distrib,axiom,
    ! [X92,X97,X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X98),X97)),X92) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X98),X92)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib) ).

fof(fact_add__mult__distrib,axiom,
    ! [X33,X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib) ).

fof(fact_diff__mult__distrib,axiom,
    ! [X33,X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X33)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib) ).

fof(fact_nth_Osimps,axiom,
    ! [X30,X200,X11,X10] : hAPP(hAPP(c_List_Onth(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)),X30) = c_Nat_Onat_Onat__case(X10,X11,hAPP(c_List_Onth(X10),X200),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth_Osimps) ).

fof(fact_replicate__length__filter,axiom,
    ! [X200,X11,X10] : c_List_Oreplicate(X10,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,hAPP(c_fequal,X11)),X200)),X11) = hAPP(c_List_Ofilter(X10,hAPP(c_fequal,X11)),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__length__filter) ).

fof(fact_Plus__eq__empty__conv,axiom,
    ! [X15,X12,X8,X10] :
      ( c_Sum__Type_OPlus(X10,X8,X12,X15) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X10,X8),tc_HOL_Obool))
    <=> ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        & X15 = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Plus__eq__empty__conv) ).

fof(fact_set__sort,axiom,
    ! [X200,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => hAPP(c_List_Oset(X10),c_List_Olinorder__class_Osort__key(X10,X8,X2,X200)) = hAPP(c_List_Oset(X10),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__sort) ).

fof(fact_replicate__append__same,axiom,
    ! [X26,X44,X27] : hAPP(hAPP(c_List_Oappend(X27),c_List_Oreplicate(X27,X44,X26)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Olist_ONil(X27))) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Oreplicate(X27,X44,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__append__same) ).

fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
    ! [X6,X14,X13] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X6),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    <=> ( X13 = X14
        & X14 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton__iff) ).

fof(fact_Union__insert,axiom,
    ! [X15,X13,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X13),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X13),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__insert) ).

fof(fact_Inter__insert,axiom,
    ! [X15,X13,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X13),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X13),c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__insert) ).

fof(fact_wf__no__loop,axiom,
    ! [X29,X10] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),X29),X29) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
     => c_Wellfounded_Owf(X10,X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__no__loop) ).

fof(fact_add__eq__if,axiom,
    ! [X25,X24] :
      ( ( X24 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25) = X25 )
      & ( X24 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__if) ).

fof(fact_setsum__constant,axiom,
    ! [X12,X16,X8,X10] :
      ( class_Rings_Osemiring__1(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(c_COMBK(X10,X8),X16)),X12) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),hAPP(c_Finite__Set_Ocard(X8),X12))),X16) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__constant) ).

fof(fact_of__int__less__0__iff,axiom,
    ! [X19,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19),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,
    ! [X19,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19),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,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),c_Divides_Odiv__class_Omod(X27,X36,X35)),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I2_J) ).

fof(fact_mod__mult__right__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),c_Divides_Odiv__class_Omod(X27,X36,X35)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__right__eq) ).

fof(fact_mod__add__right__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),c_Divides_Odiv__class_Omod(X27,X36,X35)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__right__eq) ).

fof(fact_mod__diff__right__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Oring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36),X35) = c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),c_Divides_Odiv__class_Omod(X27,X36,X35)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__diff__right__eq) ).

fof(fact_predicate1D,axiom,
    ! [X11,X41,X42,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X42),X41))
     => ( hBOOL(hAPP(X42,X11))
       => hBOOL(hAPP(X41,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_predicate1D) ).

fof(fact_rev__predicate1D,axiom,
    ! [X41,X10,X11,X42] :
      ( hBOOL(hAPP(X42,X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X42),X41))
       => hBOOL(hAPP(X41,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_nat__diff__distrib,axiom,
    ! [X38,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),X100),X38))
       => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X38),X100)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X38)),hAPP(c_Int_Onat,X100)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__distrib) ).

fof(fact_listsp_Oequations_I2_J,axiom,
    ! [X56,X57,X12,X10] :
      ( hBOOL(hAPP(c_List_Olistsp(X10,X12),hAPP(hAPP(c_List_Olist_OCons(X10),X57),X56)))
    <=> ( hBOOL(hAPP(X12,X57))
        & hBOOL(hAPP(c_List_Olistsp(X10,X12),X56)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I2_J) ).

fof(fact_ivl__disj__un_I14_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X77)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X77)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X83) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I14_J) ).

fof(fact_less__special_I3_J,axiom,
    ! [X11,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X11)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X11),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I3_J) ).

fof(fact_le__special_I3_J,axiom,
    ! [X11,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X11)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X11),c_Int_OPls)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I3_J) ).

fof(fact_map__fst__zip,axiom,
    ! [X199,X8,X200,X10] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)
     => hAPP(hAPP(c_List_Omap(tc_prod(X10,X8),X10),c_Product__Type_Ofst(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199)) = X200 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__fst__zip) ).

fof(fact_map__snd__zip,axiom,
    ! [X199,X8,X200,X10] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X199)
     => hAPP(hAPP(c_List_Omap(tc_prod(X10,X8),X8),c_Product__Type_Osnd(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199)) = X199 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__snd__zip) ).

fof(fact_div__add__self1,axiom,
    ! [X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X37)),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36)),c_Groups_Oone__class_Oone(X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self1) ).

fof(fact_div__add__self2,axiom,
    ! [X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36)),c_Groups_Oone__class_Oone(X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add__self2) ).

fof(fact_mod__mult__mult2,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Divides_Odiv__class_Omod(X27,X37,X36)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult2) ).

fof(fact_nat__abs__mult__distrib,axiom,
    ! [X38,X92] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X38))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X92))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X38))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__abs__mult__distrib) ).

fof(fact_nat__mult__div__cancel1,axiom,
    ! [X25,X24,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X25)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel1) ).

fof(fact_zdiv__zmult2__eq,axiom,
    ! [X36,X37,X35] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X35))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X35)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zmult2__eq) ).

fof(fact_split__def,axiom,
    ! [X148,X6,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X6),X148) = hAPP(hAPP(X6,hAPP(c_Product__Type_Ofst(X8,X18),X148)),hAPP(c_Product__Type_Osnd(X8,X18),X148)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__def) ).

fof(fact_prod__case__beta,axiom,
    ! [X148,X2,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X2),X148) = hAPP(hAPP(X2,hAPP(c_Product__Type_Ofst(X8,X18),X148)),hAPP(c_Product__Type_Osnd(X8,X18),X148)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__case__beta) ).

fof(fact_split__beta,axiom,
    ! [X19,X42,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X42),X19) = hAPP(hAPP(X42,hAPP(c_Product__Type_Ofst(X8,X18),X19)),hAPP(c_Product__Type_Osnd(X8,X18),X19)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__beta) ).

fof(fact_sorted__sort,axiom,
    ! [X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_List_Olinorder__class_Osorted(X10,c_List_Olinorder__class_Osort__key(X10,X10,c_COMBI(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__sort) ).

fof(fact_append1__eq__conv,axiom,
    ! [X16,X199,X11,X200,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X200),hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10))) = hAPP(hAPP(c_List_Oappend(X10),X199),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10)))
    <=> ( X200 = X199
        & X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append1__eq__conv) ).

fof(fact_dvd__reduce,axiom,
    ! [X30,X32] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X32)))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__reduce) ).

fof(fact_hd__drop__conv__nth,axiom,
    ! [X25,X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(c_List_Ohd(X27),hAPP(hAPP(c_List_Odrop(X27),X25),X202)) = hAPP(hAPP(c_List_Onth(X27),X202),X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__drop__conv__nth) ).

fof(fact_abs__add__abs,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__add__abs) ).

fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
    ! [X13,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one__idem(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,X2),X13),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).

fof(fact_inf__le1,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le1) ).

fof(fact_inf__sup__ord_I1_J,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).

fof(fact_inf__le2,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__le2) ).

fof(fact_inf__sup__ord_I2_J,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).

fof(fact_min__max_Oinf__le1,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le1) ).

fof(fact_min__max_Oinf__le2,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__le2) ).

fof(fact_expand__Suc,axiom,
    ! [X68] :
      ( 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),X68)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),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,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X83)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X77)) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X77) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I9_J) ).

fof(fact_ivl__disj__un_I7_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X83)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X77)) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),X77) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I7_J) ).

fof(fact_ivl__disj__un_I10_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X83)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X77)) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X77) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I10_J) ).

fof(fact_minus__dvd__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Rings_Ocomm__ring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)),X16))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__dvd__iff) ).

fof(fact_abs__dvd__iff,axiom,
    ! [X32,X31,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),X31)),X32))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X31),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__dvd__iff) ).

fof(fact_abs__le__D1,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__D1) ).

fof(fact_inf__sup__distrib1,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Odistrib__lattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).

fof(fact_sup__inf__distrib1,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Odistrib__lattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).

fof(fact_min__max_Osup__inf__distrib1,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),X38)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).

fof(fact_min__max_Oinf__sup__distrib1,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),X38)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X38)) ),
    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,
    ! [X38,X34,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X34),X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X34)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
    ! [X87,X88,X89,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X88)),X87) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X87)),X88) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(fact_id__o,axiom,
    ! [X1,X10,X8] : hAPP(c_Fun_Ocomp(X8,X8,X10,c_Fun_Oid(X8)),X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__o) ).

fof(fact_length__pos__if__in__set,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => 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(X10)),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__pos__if__in__set) ).

fof(fact_single__valued__rel__pow,axiom,
    ! [X30,X29,X10] :
      ( c_Relation_Osingle__valued(X10,X10,X29)
     => c_Relation_Osingle__valued(X10,X10,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__rel__pow) ).

fof(fact_Random__Sequence_Osingle__def,axiom,
    ! [X243,X244,X11,X10] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X10),X11),X244),X243) = 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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X10),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random__Sequence_Osingle__def) ).

fof(fact_DomainP_Oequations,axiom,
    ! [X57,X110,X8,X10] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(X10,X8,X110),X57))
    <=> ? [X136] : hBOOL(hAPP(hAPP(X110,X57),X136)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).

fof(fact_inj__eq,axiom,
    ! [X16,X11,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hAPP(X2,X11) = hAPP(X2,X16)
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__eq) ).

fof(fact_injD,axiom,
    ! [X16,X11,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
     => ( hAPP(X2,X11) = hAPP(X2,X16)
       => X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_injD) ).

fof(fact_replicate__add,axiom,
    ! [X26,X24,X25,X27] : c_List_Oreplicate(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24),X26) = hAPP(hAPP(c_List_Oappend(X27),c_List_Oreplicate(X27,X25,X26)),c_List_Oreplicate(X27,X24,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__add) ).

fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
    ! [X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X13),X12) ) ),
    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,
    ! [X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X13),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oeq__fold__idem_H) ).

fof(fact_foldl__Nil,axiom,
    ! [X13,X2,X8,X10] : hAPP(c_List_Ofoldl(X10,X8,X2,X13),c_List_Olist_ONil(X8)) = X13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Nil) ).

fof(fact_list_Osimps_I4_J,axiom,
    ! [X49,X50,X8,X10] : hAPP(c_List_Olist_Olist__case(X10,X8,X50,X49),c_List_Olist_ONil(X8)) = X50,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).

fof(fact_o__id,axiom,
    ! [X2,X8,X10] : hAPP(c_Fun_Ocomp(X10,X8,X10,X2),c_Fun_Oid(X10)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__id) ).

fof(fact_add__nonneg__eq__0__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Groups_Oordered__comm__monoid__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X16))
         => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X11),X16) = c_Groups_Ozero__class_Ozero(X10)
          <=> ( X11 = c_Groups_Ozero__class_Ozero(X10)
              & X16 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__nonneg__eq__0__iff) ).

fof(fact_diff__add__assoc,axiom,
    ! [X44,X43,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X43))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__assoc) ).

fof(fact_add__diff__assoc,axiom,
    ! [X44,X43,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X43))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),X33) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__assoc) ).

fof(fact_diff__diff__right,axiom,
    ! [X44,X43,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X43))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X43),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X33)),X43) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__right) ).

fof(fact_compl__mono,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X34)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__mono) ).

fof(fact_le__imp__neg__le,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__neg__le) ).

fof(fact_one__less__nat__eq,axiom,
    ! [X19] :
      ( 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,X19)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__less__nat__eq) ).

fof(fact_mod__less__eq__dividend,axiom,
    ! [X25,X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).

fof(fact_greaterThan__Suc,axiom,
    ! [X32] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X32)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),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,
    ! [X114,X124,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X124)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X114)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X124),X114)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).

fof(fact_power__add,axiom,
    ! [X25,X24,X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X24)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__add) ).

fof(fact_fold1__eq__fold__idem,axiom,
    ! [X13,X12,X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Groups_Otimes__class_Otimes(X10)),X13),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__eq__fold__idem) ).

fof(fact_add__scale__eq__noteq,axiom,
    ! [X58,X35,X36,X37,X80,X27] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X27)
     => ( X80 != c_Groups_Ozero__class_Ozero(X27)
       => ( ( X37 = X36
            & X35 != X58 )
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X80),X35)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X80),X58)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__scale__eq__noteq) ).

fof(fact_some__eq__trivial,axiom,
    ! [X11,X10] : c_Hilbert__Choice_OEps(X10,hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__trivial) ).

fof(fact_the__eq__trivial,axiom,
    ! [X13,X10] : c_HOL_OThe(X10,hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13)) = X13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__eq__trivial) ).

fof(fact_diff__less__Suc,axiom,
    ! [X25,X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),hAPP(c_Nat_OSuc,X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).

fof(fact_less__add__Suc1,axiom,
    ! [X24,X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X24)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).

fof(fact_less__add__Suc2,axiom,
    ! [X24,X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X44)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).

fof(fact_ivl__disj__int_I16_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X31)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X31,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I16_J) ).

fof(fact_ivl__disj__int_I12_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X31)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X31,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I12_J) ).

fof(fact_ivl__disj__int_I14_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X31)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X31,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I14_J) ).

fof(fact_ivl__disj__int_I10_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X31)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X31,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I10_J) ).

fof(fact_ivl__disj__int_I13_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X31)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X31,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I13_J) ).

fof(fact_empty__subsetI,axiom,
    ! [X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__subsetI) ).

fof(fact_equiv__comp__eq,axiom,
    ! [X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),hAPP(c_Relation_Oconverse(X10,X10),X110)),X110) = X110 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__comp__eq) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X26,X34))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).

fof(fact_subset__insertI,axiom,
    ! [X13,X15,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__insertI) ).

fof(fact_zmod__simps_I3_J,axiom,
    ! [X35,X36,X37] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X35)),X35) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X36),X35),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__simps_I3_J) ).

fof(fact_zdiff__zmod__right,axiom,
    ! [X24,X34,X26] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),c_Divides_Odiv__class_Omod(tc_Int_Oint,X34,X24)),X24) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X34),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmod__right) ).

fof(fact_zmod__zmult1__eq,axiom,
    ! [X35,X36,X37] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),X36),X35) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X37),c_Divides_Odiv__class_Omod(tc_Int_Oint,X36,X35)),X35),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zmult1__eq) ).

fof(fact_ivl__disj__un_I8_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X77))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X83)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X77)) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),X77) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I8_J) ).

fof(fact_atLeastAtMostSuc__conv,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30)))
     => c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMostSuc__conv) ).

fof(fact_finite__option__UNIV,axiom,
    ! [X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X10)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X10),tc_HOL_Obool))))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__option__UNIV) ).

fof(fact_less__imp__of__nat__less,axiom,
    ! [X25,X24,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__of__nat__less) ).

fof(fact_Int__atLeastAtMostR2,axiom,
    ! [X20,X6,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X13)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X6,X20)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),X6),X20) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_Int__atLeastAtMostR1,axiom,
    ! [X20,X6,X14,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X14)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X6,X20)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X6,hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X14),X20)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__atLeastAtMostR1) ).

fof(fact_zless__nat__eq__int__zless,axiom,
    ! [X19,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(c_Int_Onat,X19)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__nat__eq__int__zless) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X34)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X26,X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J) ).

fof(fact_drop__take,axiom,
    ! [X202,X24,X25,X27] : hAPP(hAPP(c_List_Odrop(X27),X25),hAPP(hAPP(c_List_Otake(X27),X24),X202)) = hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),hAPP(hAPP(c_List_Odrop(X27),X25),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__take) ).

fof(fact_rel__comp__empty2,axiom,
    ! [X29,X8,X18,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X29),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X18,X8),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__comp__empty2) ).

fof(fact_curry__split,axiom,
    ! [X2,X18,X8,X10] : c_Product__Type_Ocurry(X10,X8,X18,hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X18),X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__split) ).

fof(fact_mod__pos__pos__1__number__of,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
     => 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),X92)) = 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),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos__1__number__of) ).

fof(fact_mod__mult__distrib,axiom,
    ! [X33,X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)),X33) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X33),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib) ).

fof(fact_dvd__power,axiom,
    ! [X26,X25,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
          | X26 = c_Groups_Oone__class_Oone(X27) )
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X26),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X25))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__power) ).

fof(fact_dvd__mult2,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X36))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult2) ).

fof(fact_dvd__mult,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X35))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult) ).

fof(fact_less__supI1,axiom,
    ! [X36,X37,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__supI1) ).

fof(fact_less__supI2,axiom,
    ! [X37,X36,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__supI2) ).

fof(fact_min__max_Oless__supI1,axiom,
    ! [X36,X37,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__supI1) ).

fof(fact_min__max_Oless__supI2,axiom,
    ! [X37,X36,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oless__supI2) ).

fof(fact_le__supI1,axiom,
    ! [X36,X37,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI1) ).

fof(fact_le__supI2,axiom,
    ! [X37,X36,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__supI2) ).

fof(fact_min__max_Ole__supI1,axiom,
    ! [X36,X37,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI1) ).

fof(fact_min__max_Ole__supI2,axiom,
    ! [X37,X36,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X36))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__supI2) ).

fof(fact_negative__zle__0,axiom,
    ! [X25] : 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),X25))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle__0) ).

fof(fact_transpose__empty,axiom,
    ! [X200,X10] :
      ( c_List_Otranspose(X10,X200) = c_List_Olist_ONil(tc_List_Olist(X10))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),X3),hAPP(c_List_Oset(tc_List_Olist(X10)),X200)))
         => X3 = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__empty) ).

fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
    ! [X32,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X10)
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X32)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0__upt) ).

fof(fact_UN__empty2,axiom,
    ! [X12,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X8,tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X8),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__empty2) ).

fof(fact_less__trans__Suc,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X43),X33))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__trans__Suc) ).

fof(fact_div__pos__pos__1__number__of,axiom,
    ! [X92] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
     => 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),X92)) = 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),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__1__number__of) ).

fof(fact_pos__mod__sign,axiom,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => 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,X37,X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__mod__sign) ).

fof(fact_greaterThanLessThan__upto,axiom,
    ! [X60,X61] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X61,X60) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X60),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,
    ! [X200,X11,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(hAPP(c_List_Olist_OCons(X8),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),hAPP(X2,X11)),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I2_J) ).

fof(fact_power__one__over,axiom,
    ! [X25,X37,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),c_Groups_Oone__class_Oone(X27)),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),c_Groups_Oone__class_Oone(X27)),X37)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__over) ).

fof(fact_le__imp__0__less,axiom,
    ! [X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
     => 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)),X38))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__0__less) ).

fof(fact_insertI2,axiom,
    ! [X14,X15,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X15))
     => hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),X15))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).

fof(fact_less__minus__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__iff) ).

fof(fact_le__minus__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__iff) ).

fof(fact_last__list__update,axiom,
    ! [X26,X33,X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => ( ( X33 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(X27,hAPP(hAPP(c_List_Olist__update(X27,X202),X33),X26)) = X26 )
        & ( X33 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(X27,hAPP(hAPP(c_List_Olist__update(X27,X202),X33),X26)) = c_List_Olast(X27,X202) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__list__update) ).

fof(fact_sgn__less,axiom,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Osgn__class_Osgn(X10,X13)),c_Groups_Ozero__class_Ozero(X10)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__less) ).

fof(fact_take__butlast,axiom,
    ! [X202,X27,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => hAPP(hAPP(c_List_Otake(X27),X25),c_List_Obutlast(X27,X202)) = hAPP(hAPP(c_List_Otake(X27),X25),X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__butlast) ).

fof(fact_last__drop,axiom,
    ! [X202,X27,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
     => c_List_Olast(X27,hAPP(hAPP(c_List_Odrop(X27),X25),X202)) = c_List_Olast(X27,X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__drop) ).

fof(fact_prod_Osimps_I2_J,axiom,
    ! [X14,X13,X50,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X50),hAPP(hAPP(c_Product__Type_OPair(X8,X18),X13),X14)) = hAPP(hAPP(X50,X13),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Osimps_I2_J) ).

fof(fact_split__conv,axiom,
    ! [X14,X13,X2,X10,X18,X8] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,X10),X2),hAPP(hAPP(c_Product__Type_OPair(X8,X18),X13),X14)) = hAPP(hAPP(X2,X13),X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__conv) ).

fof(fact_min__max_OSup__fin_Oin__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)) = c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).

fof(fact_min__max_OInf__fin_Oin__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)) = c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),X20))
         => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X6),X20)
          <=> ( X13 = X6
              & X14 = X20 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X6),X20)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),X20))
           => X13 = X6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X6),X20)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),X20))
           => X14 = X20 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_posDivAlg__correct,axiom,
    ! [X36,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(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),c_Divides_OposDivAlg(X37,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_posDivAlg__correct) ).

fof(fact_nth__list__update__neq,axiom,
    ! [X26,X202,X27,X43,X44] :
      ( X44 != X43
     => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)),X43) = hAPP(hAPP(c_List_Onth(X27),X202),X43) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__list__update__neq) ).

fof(fact_ivl__disj__int_I9_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X31)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X31),X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I9_J) ).

fof(fact_converse__inv__image,axiom,
    ! [X2,X29,X8,X10] : hAPP(c_Relation_Oconverse(X10,X10),hAPP(hAPP(c_Relation_Oinv__image(X8,X10),X29),X2)) = hAPP(hAPP(c_Relation_Oinv__image(X8,X10),hAPP(c_Relation_Oconverse(X8,X8),X29)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__inv__image) ).

fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
    ! [X13,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X13),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oeq__fold__idem_H) ).

fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
    ! [X13,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X13),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oeq__fold__idem_H) ).

fof(fact_Max_Oeq__fold__idem_H,axiom,
    ! [X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X13),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oeq__fold__idem_H) ).

fof(fact_Min_Oeq__fold__idem_H,axiom,
    ! [X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X13),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oeq__fold__idem_H) ).

fof(fact_log_Osimps,axiom,
    ! [X44,X36] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X36),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X44),X36)) )
       => c_Random_Olog(X36,X44) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X36),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X44),X36)) )
       => c_Random_Olog(X36,X44) = 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(X36,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X44),X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_log_Osimps) ).

fof(fact_Ints__minus,axiom,
    ! [X13,X10] :
      ( class_Rings_Oring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Int_Oring__1__class_OInts(X10)))
       => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)),c_Int_Oring__1__class_OInts(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__minus) ).

fof(fact_bot__empty__eq,axiom,
    ! [X11,X10] :
      ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X11))
    <=> hBOOL(hAPP(hAPP(c_member(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__empty__eq) ).

fof(fact_abs__div__pos,axiom,
    ! [X26,X34,X27] :
      ( class_Fields_Olinordered__field__inverse__zero(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X34))
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X26)),X34) = hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__div__pos) ).

fof(fact_abs__mult__pos,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X34)),X26) = hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__pos) ).

fof(fact_Pow__empty,axiom,
    ! [X10] : hAPP(c_Set_OPow(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__empty) ).

fof(fact_setsum__shift__lb__Suc0__0,axiom,
    ! [X32,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)),X32)) = 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),X32)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__shift__lb__Suc0__0) ).

fof(fact_inf__apply,axiom,
    ! [X11,X1,X2,X8,X10] :
      ( class_Lattices_Olattice(X10)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,X10)),X2),X1),X11) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),hAPP(X2,X11)),hAPP(X1,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__apply) ).

fof(fact_inf__fun__def,axiom,
    ! [X11,X1,X2,X8,X10] :
      ( class_Lattices_Olattice(X10)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,X10)),X2),X1),X11) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),hAPP(X2,X11)),hAPP(X1,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__fun__def) ).

fof(fact_sup__apply,axiom,
    ! [X11,X1,X2,X8,X10] :
      ( class_Lattices_Olattice(X10)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,X10)),X2),X1),X11) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),hAPP(X2,X11)),hAPP(X1,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__apply) ).

fof(fact_sup__fun__def,axiom,
    ! [X11,X1,X2,X8,X10] :
      ( class_Lattices_Olattice(X10)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,X10)),X2),X1),X11) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),hAPP(X2,X11)),hAPP(X1,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__fun__def) ).

fof(fact_minus__apply,axiom,
    ! [X11,X15,X12,X8,X10] :
      ( class_Groups_Ominus(X10)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,X10)),X12),X15),X11) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(X12,X11)),hAPP(X15,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__apply) ).

fof(fact_fun__diff__def,axiom,
    ! [X11,X15,X12,X8,X10] :
      ( class_Groups_Ominus(X10)
     => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,X10)),X12),X15),X11) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(X12,X11)),hAPP(X15,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__diff__def) ).

fof(fact_negDivAlg__correct,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),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)),X36))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),c_Divides_OnegDivAlg(X37,X36))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__correct) ).

fof(fact_neg__mod__bound,axiom,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__mod__bound) ).

fof(fact_folding_Oempty,axiom,
    ! [X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => hAPP(X9,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Fun_Oid(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding_Oempty) ).

fof(fact_less__code__numeral__def,axiom,
    ! [X31,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30),X31))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30)),hAPP(c_Code__Numeral_Onat__of,X31))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__code__numeral__def) ).

fof(fact_less__code__numeral__code,axiom,
    ! [X31,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30)),hAPP(c_Code__Numeral_Oof__nat,X31)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__code__numeral__code) ).

fof(fact_Suc__less__SucD,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),hAPP(c_Nat_OSuc,X25)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__SucD) ).

fof(fact_Suc__less__eq,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X31)),hAPP(c_Nat_OSuc,X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__less__eq) ).

fof(fact_less__eq__code__numeral__def,axiom,
    ! [X31,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X30),X31))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30)),hAPP(c_Code__Numeral_Onat__of,X31))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__code__numeral__def) ).

fof(fact_less__eq__code__numeral__code,axiom,
    ! [X31,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30)),hAPP(c_Code__Numeral_Oof__nat,X31)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__code__numeral__code) ).

fof(fact_Suc__le__mono,axiom,
    ! [X31,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),hAPP(c_Nat_OSuc,X31)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__mono) ).

fof(fact_nth__take,axiom,
    ! [X202,X27,X25,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X25))
     => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Otake(X27),X25),X202)),X44) = hAPP(hAPP(c_List_Onth(X27),X202),X44) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__take) ).

fof(fact_Diff__disjoint,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X15),X12)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__disjoint) ).

fof(fact_rev__eq__Cons__iff,axiom,
    ! [X199,X16,X200,X10] :
      ( hAPP(c_List_Orev(X10),X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199)
    <=> X200 = hAPP(hAPP(c_List_Oappend(X10),hAPP(c_List_Orev(X10),X199)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),c_List_Olist_ONil(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__eq__Cons__iff) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
    ! [X25,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_div__le__dividend,axiom,
    ! [X25,X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25)),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).

fof(fact_diff__le__self,axiom,
    ! [X25,X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).

fof(fact_ivl__disj__un_I2_J,axiom,
    ! [X77,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X77)),hAPP(hAPP(c_Set_Oinsert(X10),X77),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X77) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__un_I2_J) ).

fof(fact_Min__le,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olinorder__class_OMin(X10,X12)),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__le) ).

fof(fact_zpower__zadd__distrib,axiom,
    ! [X38,X34,X26] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X34)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X38)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zadd__distrib) ).

fof(fact_zadd__zmult__distrib2,axiom,
    ! [X97,X98,X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),X97)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X97)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zmult__distrib2) ).

fof(fact_zdiff__zmult__distrib2,axiom,
    ! [X97,X98,X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X98),X97)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X98)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X97)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__zmult__distrib2) ).

fof(fact_add__mult__distrib2,axiom,
    ! [X25,X24,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__mult__distrib2) ).

fof(fact_diff__mult__distrib2,axiom,
    ! [X25,X24,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__mult__distrib2) ).

fof(fact_diff__commute,axiom,
    ! [X33,X43,X44] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),X43)),X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),X33)),X43),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__commute) ).

fof(fact_neg__0__less__iff__less,axiom,
    ! [X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__less__iff__less) ).

fof(fact_neg__0__le__iff__le,axiom,
    ! [X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__le__iff__le) ).

fof(fact_dvd__trans,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X36),X35))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X35)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__trans) ).

fof(fact_order__less__trans,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X38))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__trans) ).

fof(fact_order__le__less__trans,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X38))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less__trans) ).

fof(fact_order__less__le__trans,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X38))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le__trans) ).

fof(fact_xt1_I10_J,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X38),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X38),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I10_J) ).

fof(fact_xt1_I8_J,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X38),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X38),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I8_J) ).

fof(fact_xt1_I7_J,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X38),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X38),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I7_J) ).

fof(fact_order__trans,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X38))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X38)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__trans) ).

fof(fact_xt1_I6_J,axiom,
    ! [X38,X26,X34,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X38),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X38),X26)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I6_J) ).

fof(fact_divmod__int__rel__0,axiom,
    ! [X36] :
      ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36),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,
    ! [X36,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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X37,X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos) ).

fof(fact_diff__eq__diff__less,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X6),X20)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less) ).

fof(fact_diff__eq__diff__less__eq,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X6),X20)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X20)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__less__eq) ).

fof(fact_eq__diff__iff,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X31))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32),X30))
       => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),X32) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30),X32)
        <=> X31 = X30 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__diff__iff) ).

fof(fact_Sigma__empty2,axiom,
    ! [X12,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),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,
    ! [X200,X2,X8,X10] : c_List_Oremdups(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_Oremdups(X8,X200))) = c_List_Oremdups(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__map__remdups) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
    ! [X37,X24,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X24)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),c_Groups_Oone__class_Oone(X27))),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).

fof(fact_div__pos__pos,axiom,
    ! [X36,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__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X37,X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos) ).

fof(fact_ivl__disj__int_I15_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X31)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X31,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I15_J) ).

fof(fact_of__int__0__less__iff,axiom,
    ! [X19,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__less__iff) ).

fof(fact_of__nat__0__less__iff,axiom,
    ! [X30,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__less__iff) ).

fof(fact_of__int__0__le__iff,axiom,
    ! [X19,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0__le__iff) ).

fof(fact_abs__le__zero__iff,axiom,
    ! [X13,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Groups_Oabs__class_Oabs(X10),X13)),c_Groups_Ozero__class_Ozero(X10)))
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__le__zero__iff) ).

fof(fact_mod__neg__pos,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),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)),X36))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X37,X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__pos) ).

fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).

fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).

fof(fact_dvd__div__mult__self,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X36))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X36),X37)),X37) = X36 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__mult__self) ).

fof(fact_of__nat__diff,axiom,
    ! [X24,X25,X27] :
      ( class_Rings_Oring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__diff) ).

fof(fact_div__neg__pos,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),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)),X36))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X37,X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__neg__pos) ).

fof(fact_assms_I1_J,axiom,
    ! [X4,X5] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X5),X4))
     => v_P(X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I1_J) ).

fof(fact_finite__insert,axiom,
    ! [X12,X13,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).

fof(fact_inf__Inf__fold__inf,axiom,
    ! [X15,X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X15),c_Complete__Lattice_OInf__class_OInf(X10,X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X15),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Inf__fold__inf) ).

fof(fact_sup__Sup__fold__sup,axiom,
    ! [X15,X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X15),c_Complete__Lattice_OSup__class_OSup(X10,X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X15),X12) ) ),
    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,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)),X12) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__disjoint2) ).

fof(fact_Compl__partition2,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)),X12) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__partition2) ).

fof(fact_UNIV__Plus__UNIV,axiom,
    ! [X8,X10] : c_Sum__Type_OPlus(X10,X8,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X10,X8),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__Plus__UNIV) ).

fof(fact_ivl__disj__int_I7_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X77)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I7_J) ).

fof(fact_ivl__disj__int_I5_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X77)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I5_J) ).

fof(fact_ivl__disj__int_I6_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X77)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I6_J) ).

fof(fact_less__special_I1_J,axiom,
    ! [X16,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__special_I1_J) ).

fof(fact_le__special_I1_J,axiom,
    ! [X16,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Rings_Olinordered__idom(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__special_I1_J) ).

fof(fact_finite__Domain,axiom,
    ! [X110,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X8)),X110))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Relation_ODomain(X10,X8),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Domain) ).

fof(fact_finite__Range,axiom,
    ! [X110,X8,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X8)),X110))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Relation_ORange(X10,X8),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Range) ).

fof(fact_fold1Set__nonempty,axiom,
    ! [X11,X12,X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,X12),X11))
     => X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set__nonempty) ).

fof(fact_Nitpick_Oint__gcd__def,axiom,
    ! [X34,X26] : hAPP(hAPP(c_Nitpick_Oint__gcd,X26),X34) = 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),X26)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X34)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Oint__gcd__def) ).

fof(fact_drop__map,axiom,
    ! [X200,X2,X8,X30,X10] : hAPP(hAPP(c_List_Odrop(X10),X30),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(hAPP(c_List_Odrop(X8),X30),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__map) ).

fof(fact_take__map,axiom,
    ! [X200,X2,X8,X30,X10] : hAPP(hAPP(c_List_Otake(X10),X30),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(hAPP(c_List_Otake(X8),X30),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__map) ).

fof(fact_filter__append,axiom,
    ! [X199,X200,X42,X10] : hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),hAPP(c_List_Ofilter(X10,X42),X200)),hAPP(c_List_Ofilter(X10,X42),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__append) ).

fof(fact_wf__acc__iff,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
    <=> ! [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),c_Wellfounded_Oacc(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acc__iff) ).

fof(fact_minus__Max__eq__Min,axiom,
    ! [X28,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( X28 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Big__Operators_Olinorder__class_OMax(X10,X28)) = c_Big__Operators_Olinorder__class_OMin(X10,hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),X28)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Max__eq__Min) ).

fof(fact_minus__Min__eq__Max,axiom,
    ! [X28,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( X28 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Big__Operators_Olinorder__class_OMin(X10,X28)) = c_Big__Operators_Olinorder__class_OMax(X10,hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),X28)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Min__eq__Max) ).

fof(fact_finite__UnionD,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X12)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UnionD) ).

fof(fact_Suc__times__mod__eq,axiom,
    ! [X24,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24)),X33) = 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,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),c_Groups_Osgn__class_Osgn(X10,X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__greater) ).

fof(fact_dvd__neg__div,axiom,
    ! [X26,X34,X27] :
      ( class_Divides_Oring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X34),X26))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)),X34) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__neg__div) ).

fof(fact_mod__mult__mult1,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),c_Divides_Odiv__class_Omod(X27,X37,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__mult1) ).

fof(fact_INT__constant,axiom,
    ! [X6,X8,X10,X12] :
      ( ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X6)) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
      & ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X6)) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__constant) ).

fof(fact_UN__constant,axiom,
    ! [X6,X8,X10,X12] :
      ( ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X6)) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) )
      & ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_HOL_Obool)),X12),hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X10),X6)) = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UN__constant) ).

fof(fact_Random__Sequence_Oempty__def,axiom,
    ! [X243,X244,X10] : c_Random__Sequence_Oempty(X10,X244,X243) = 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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Random__Sequence_Oempty__def) ).

fof(fact_div__mult__mult1__if,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( ( X35 = c_Groups_Ozero__class_Ozero(X27)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)) = c_Groups_Ozero__class_Ozero(X27) )
        & ( X35 != c_Groups_Ozero__class_Ozero(X27)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1__if) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => ( X35 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => ( X35 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_div__mult__mult1,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X35 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X37)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult1) ).

fof(fact_div__mult__mult2,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X35 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__mult2) ).

fof(fact_nat__rec__Suc,axiom,
    ! [X40,X49,X50,X10] : hAPP(c_Nat_Onat_Onat__rec(X10,X50,X49),hAPP(c_Nat_OSuc,X40)) = hAPP(hAPP(X49,X40),hAPP(c_Nat_Onat_Onat__rec(X10,X50,X49),X40)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).

fof(fact_trans__less__add1,axiom,
    ! [X24,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X24))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).

fof(fact_termination__basic__simps_I1_J,axiom,
    ! [X38,X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X34))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X38))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).

fof(fact_trans__less__add2,axiom,
    ! [X24,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).

fof(fact_termination__basic__simps_I2_J,axiom,
    ! [X34,X38,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X38))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X38))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).

fof(fact_trans__le__add1,axiom,
    ! [X24,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X24))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).

fof(fact_termination__basic__simps_I3_J,axiom,
    ! [X38,X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26),X34))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X38))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).

fof(fact_trans__le__add2,axiom,
    ! [X24,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X43))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).

fof(fact_termination__basic__simps_I4_J,axiom,
    ! [X34,X38,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26),X38))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X38))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).

fof(fact_mod__mult__self2,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)),X36) = c_Divides_Odiv__class_Omod(X27,X37,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2) ).

fof(fact_mod__mult__self1,axiom,
    ! [X36,X35,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X35),X36)),X36) = c_Divides_Odiv__class_Omod(X27,X37,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1) ).

fof(fact_less__Suc__eq__0__disj,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30)))
    <=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [X73] :
            ( X31 = hAPP(c_Nat_OSuc,X73)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X73),X30)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__0__disj) ).

fof(fact_bex__UNIV,axiom,
    ! [X42,X10] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
          & hBOOL(hAPP(X42,X3)) )
    <=> ? [X136] : hBOOL(hAPP(X42,X136)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__UNIV) ).

fof(fact_rotate1__hd__tl,axiom,
    ! [X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => hAPP(c_List_Orotate1(X27),X202) = hAPP(hAPP(c_List_Oappend(X27),hAPP(c_List_Otl(X27),X202)),hAPP(hAPP(c_List_Olist_OCons(X27),hAPP(c_List_Ohd(X27),X202)),c_List_Olist_ONil(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__hd__tl) ).

fof(fact_setsum__set__upto__conv__listsum__int,axiom,
    ! [X60,X61,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X61,X60))) = hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X10),X2),c_List_Oupto(X61,X60))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).

fof(fact_interv__listsum__conv__setsum__set__int,axiom,
    ! [X83,X32,X2,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X10),X2),c_List_Oupto(X32,X83))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X10),X2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X32,X83))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).

fof(fact_inf_Oassoc,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)),X35) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oassoc) ).

fof(fact_inf__assoc,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__assoc) ).

fof(fact_inf__sup__aci_I2_J,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).

fof(fact_inf__sup__aci_I6_J,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).

fof(fact_sup_Oassoc,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36)),X35) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oassoc) ).

fof(fact_sup__assoc,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34)),X38) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__assoc) ).

fof(fact_min__max_Osup_Oassoc,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36)),X35) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oassoc) ).

fof(fact_min__max_Osup__assoc,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34)),X38) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__assoc) ).

fof(fact_min__max_Oinf__assoc,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)),X38) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__assoc) ).

fof(fact_min__max_Oinf_Oassoc,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)),X35) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oassoc) ).

fof(fact_power__commutes,axiom,
    ! [X25,X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),X37) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__commutes) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [X87,X88,X89,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X88)),X87) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X88),X87)) ),
    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,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oab__semigroup__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),X35) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__mult__class_Omult__ac_I1_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Oab__semigroup__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(fact_times__divide__eq__right,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Rings_Odivision__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),X35) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__divide__eq__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
    ! [X86,X87,X89,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X87),X86)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X87)),X86) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
    ! [X58,X35,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)),X58) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(fact_last__conv__nth,axiom,
    ! [X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => c_List_Olast(X27,X202) = hAPP(hAPP(c_List_Onth(X27),X202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),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,
    ! [X90,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X90))
       => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Nat_Osemiring__1__class_ONats(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__number__of) ).

fof(fact_card__Pow,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(c_Finite__Set_Ocard(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X12)) = 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(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Pow) ).

fof(fact_atLeast__Suc,axiom,
    ! [X32] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X32)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X32),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,
    ! [X15,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__Compl) ).

fof(fact_Diff__eq,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__eq) ).

fof(fact_zero__less__two,axiom,
    ! [X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Oone__class_Oone(X27)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__two) ).

fof(fact_card__greaterThanLessThan__int,axiom,
    ! [X77,X83] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X83,X77)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X77),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X83),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanLessThan__int) ).

fof(fact_nth__replicate,axiom,
    ! [X26,X27,X25,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X25))
     => hAPP(hAPP(c_List_Onth(X27),c_List_Oreplicate(X27,X25,X26)),X44) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__replicate) ).

fof(fact_min__max_Osup__Inf__absorb,axiom,
    ! [X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X13),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)) = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).

fof(fact_min__max_Oinf__Sup__absorb,axiom,
    ! [X13,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X13),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)) = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).

fof(fact_less__minus__self__iff,axiom,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__minus__self__iff) ).

fof(fact_le__minus__self__iff,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__minus__self__iff) ).

fof(fact_Diff__triv,axiom,
    ! [X15,X12,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__triv) ).

fof(fact_insort__not__Nil,axiom,
    ! [X200,X13,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X13),X200) != c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__not__Nil) ).

fof(fact_setprod__constant,axiom,
    ! [X16,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(c_COMBK(X8,X10),X16)),X12) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X16),hAPP(c_Finite__Set_Ocard(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__constant) ).

fof(fact_fold1__insert__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__insert__idem) ).

fof(fact_ivl__disj__int_I11_J,axiom,
    ! [X77,X31,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X31)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X31),X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I11_J) ).

fof(fact_diff__Suc,axiom,
    ! [X30,X31] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30)) = 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),X31),X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc) ).

fof(fact_append__assoc,axiom,
    ! [X215,X201,X202,X27] : hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X215) = hAPP(hAPP(c_List_Oappend(X27),X202),hAPP(hAPP(c_List_Oappend(X27),X201),X215)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__assoc) ).

fof(fact_append__Cons,axiom,
    ! [X201,X202,X26,X27] : hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),X201) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Cons) ).

fof(fact_zdvd__imp__le,axiom,
    ! [X25,X38] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X38),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),X38),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__imp__le) ).

fof(fact_dvd__imp__le,axiom,
    ! [X25,X33] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__le) ).

fof(fact_take__Suc,axiom,
    ! [X25,X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => hAPP(hAPP(c_List_Otake(X27),hAPP(c_Nat_OSuc,X25)),X202) = hAPP(hAPP(c_List_Olist_OCons(X27),hAPP(c_List_Ohd(X27),X202)),hAPP(hAPP(c_List_Otake(X27),X25),hAPP(c_List_Otl(X27),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc) ).

fof(fact_image__atLeastZeroLessThan__int,axiom,
    ! [X77] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X77))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X77) = 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,X77))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__atLeastZeroLessThan__int) ).

fof(fact_nth__Cons_H,axiom,
    ! [X202,X26,X27,X25] :
      ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),X25) = X26 )
      & ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),X25) = hAPP(hAPP(c_List_Onth(X27),X202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),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,
    ! [X6,X8,X10,X12] :
      ( ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X10,X8,hAPP(c_COMBK(X8,X10),X6)),X12) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) )
      & ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(c_Set_Oimage(X10,X8,hAPP(c_COMBK(X8,X10),X6)),X12) = hAPP(hAPP(c_Set_Oinsert(X8),X6),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__constant__conv) ).

fof(fact_listsum__distinct__conv__setsum__set,axiom,
    ! [X2,X200,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(c_List_Oset(X10),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).

fof(fact_power__mult,axiom,
    ! [X25,X24,X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X24)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__mult) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
    ! [X114,X124,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X124)),X114) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X124),X114)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).

fof(fact_mod__minus__eq,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Oring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37),X36) = c_Divides_Odiv__class_Omod(X27,hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Divides_Odiv__class_Omod(X27,X37,X36)),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__eq) ).

fof(fact_tl__take,axiom,
    ! [X202,X25,X27] : hAPP(c_List_Otl(X27),hAPP(hAPP(c_List_Otake(X27),X25),X202)) = hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X27),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__take) ).

fof(fact_abs__power__minus,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X25)) = hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__power__minus) ).

fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(c_Finite__Set_Ocard(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))
       => X12 = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__UNIV__imp__eq__UNIV) ).

fof(fact_drop__Cons_H,axiom,
    ! [X202,X26,X27,X25] :
      ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X27),X25),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202) )
      & ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(X27),X25),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Odrop(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X202) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Cons_H) ).

fof(fact_neg__zminus__int,axiom,
    ! [X25] : 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,X25))))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zminus__int) ).

fof(fact_insert__code,axiom,
    ! [X11,X12,X16,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X10),X16),X12),X11))
    <=> ( X16 = X11
        | hBOOL(hAPP(X12,X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).

fof(fact_dvd__minus__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Rings_Ocomm__ring__1(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X11),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X11),X16)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__minus__iff) ).

fof(fact_dvd__abs__iff,axiom,
    ! [X32,X31,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X31),hAPP(c_Groups_Oabs__class_Oabs(X10),X32)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X31),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__abs__iff) ).

fof(fact_lessThan__iff,axiom,
    ! [X32,X61,X10] :
      ( class_Orderings_Oord(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X61),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X32)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X61),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__iff) ).

fof(fact_greaterThan__iff,axiom,
    ! [X32,X61,X10] :
      ( class_Orderings_Oord(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X61),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X32)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__iff) ).

fof(fact_atMost__iff,axiom,
    ! [X32,X61,X10] :
      ( class_Orderings_Oord(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X61),hAPP(c_SetInterval_Oord__class_OatMost(X10),X32)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X61),X32)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__iff) ).

fof(fact_atLeast__iff,axiom,
    ! [X32,X61,X10] :
      ( class_Orderings_Oord(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X61),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X32)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X32),X61)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__iff) ).

fof(fact_image__uminus__greaterThanAtMost,axiom,
    ! [X16,X11,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X11,X16)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThanAtMost) ).

fof(fact_folding__one__idem_Oin__idem,axiom,
    ! [X11,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one__idem(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(X2,X11),hAPP(X9,X12)) = hAPP(X9,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).

fof(fact_Max__ge,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),c_Big__Operators_Olinorder__class_OMax(X10,X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__ge) ).

fof(fact_listsum__setsum__nth,axiom,
    ! [X200,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X10),X200) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(c_List_Onth(X10),X200)),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(X10)),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__setsum__nth) ).

fof(fact_zdiff__int,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiff__int) ).

fof(fact_odd__nonzero,axiom,
    ! [X38] : 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)),X38)),X38) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_odd__nonzero) ).

fof(fact_Field__def,axiom,
    ! [X110,X10] : hAPP(c_Relation_OField(X10),X110) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X10,X10),X110)),hAPP(c_Relation_ORange(X10,X10),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__def) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
    ! [X30,X31] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30) = 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),X31),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_div__mult__self1__is__m,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X24)),X25) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__m) ).

fof(fact_div__mult__self__is__m,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)),X25) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self__is__m) ).

fof(fact_zmod__zminus2__eq__if,axiom,
    ! [X36,X37] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2__eq__if) ).

fof(fact_subset__UNIV,axiom,
    ! [X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).

fof(fact_dvd_Oorder__trans,axiom,
    ! [X38,X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X38))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X38)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__trans) ).

fof(fact_zle__trans,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X43),X33))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X44),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__trans) ).

fof(fact_le__trans,axiom,
    ! [X33,X43,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X43),X33))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).

fof(fact_mod__mod__cancel,axiom,
    ! [X37,X36,X35,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X35),X36))
       => c_Divides_Odiv__class_Omod(X27,c_Divides_Odiv__class_Omod(X27,X37,X36),X35) = c_Divides_Odiv__class_Omod(X27,X37,X35) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__cancel) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
    ! [X24,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X24),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Oone__class_Oone(X27))),X24) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).

fof(fact_less__add__eq__less,axiom,
    ! [X25,X24,X45,X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33),X45))
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X45) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X25)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).

fof(fact_dvd__div__neg,axiom,
    ! [X26,X34,X27] :
      ( class_Divides_Oring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X34),X26))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X34)) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__neg) ).

fof(fact_Suc__lessD,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessD) ).

fof(fact_Suc__le__lessD,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__lessD) ).

fof(fact_Suc__le__eq,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X31)),X30))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__le__eq) ).

fof(fact_less__eq__Suc__le,axiom,
    ! [X31,X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le) ).

fof(fact_Suc__leD,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leD) ).

fof(fact_drop__drop,axiom,
    ! [X202,X24,X25,X27] : hAPP(hAPP(c_List_Odrop(X27),X25),hAPP(hAPP(c_List_Odrop(X27),X24),X202)) = hAPP(hAPP(c_List_Odrop(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__drop) ).

fof(fact_take__take,axiom,
    ! [X202,X24,X25,X27] : hAPP(hAPP(c_List_Otake(X27),X25),hAPP(hAPP(c_List_Otake(X27),X24),X202)) = hAPP(hAPP(c_List_Otake(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25),X24)),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__take) ).

fof(fact_Inf__lower,axiom,
    ! [X12,X11,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Complete__Lattice_OInf__class_OInf(X10,X12)),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__lower) ).

fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [X42] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => hBOOL(hAPP(X42,X3)) )
    <=> ! [X3] : hBOOL(hAPP(X42,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,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X34)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),hAPP(c_Int_Onat,X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__div__distrib) ).

fof(fact_nat__mult__distrib,axiom,
    ! [X100,X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X100)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X38)),hAPP(c_Int_Onat,X100)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__distrib) ).

fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
    ! [X30,X31] :
      ( c_Nat__Transfer_Ois__nat(X31)
     => ( c_Nat__Transfer_Ois__nat(X30)
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X31,X30) = 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,X31),hAPP(c_Int_Onat,X30))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__functions) ).

fof(fact_transpose_Opsimps_I1_J,axiom,
    ! [X10] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X10)),c_List_Otranspose__rel(X10)),c_List_Olist_ONil(tc_List_Olist(X10))))
     => c_List_Otranspose(X10,c_List_Olist_ONil(tc_List_Olist(X10))) = c_List_Olist_ONil(tc_List_Olist(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Opsimps_I1_J) ).

fof(fact_mod__mult__distrib2,axiom,
    ! [X25,X24,X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__distrib2) ).

fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
    ! [X15,X12] :
      ( X12 = X15
    <=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,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)),X15) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__relations_I3_J) ).

fof(fact_set__append,axiom,
    ! [X199,X200,X10] : hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(c_List_Oset(X10),X199)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__append) ).

fof(fact_Suc__mono,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),hAPP(c_Nat_OSuc,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mono) ).

fof(fact_power__inject__exp,axiom,
    ! [X30,X31,X13,X10] :
      ( class_Rings_Olinordered__semidom(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Oone__class_Oone(X10)),X13))
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X31) = hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X30)
        <=> X31 = X30 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__inject__exp) ).

fof(fact_listset_Osimps_I2_J,axiom,
    ! [X216,X12,X10] : c_List_Olistset(X10,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X10,tc_HOL_Obool)),X12),X216)) = c_List_Oset__Cons(X10,X12,c_List_Olistset(X10,X216)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listset_Osimps_I2_J) ).

fof(fact_bex__empty,axiom,
    ! [X42,X10] :
      ~ ? [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
          & hBOOL(hAPP(X42,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__empty) ).

fof(fact_Sup__fold__sup,axiom,
    ! [X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Complete__Lattice_OSup__class_OSup(X10,X12) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),c_Orderings_Obot__class_Obot(X10)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fold__sup) ).

fof(fact_Inf__fold__inf,axiom,
    ! [X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Complete__Lattice_OInf__class_OInf(X10,X12) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),c_Orderings_Otop__class_Otop(X10)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fold__inf) ).

fof(fact_power__eq__if,axiom,
    ! [X124,X24] :
      ( ( X24 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X124),X24) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X24 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X124),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X124),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X124),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),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,
    ! [X16,X11,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X11,X16)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeastAtMost) ).

fof(fact_image__uminus__greaterThanLessThan,axiom,
    ! [X16,X11,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X11,X16)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X10,hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThanLessThan) ).

fof(fact_lessThan__Suc__eq__insert__0,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)) = 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),X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc__eq__insert__0) ).

fof(fact_div__mod__code__numeral__def,axiom,
    ! [X24,X25] : c_Code__Numeral_Odiv__mod__code__numeral(X25,X24) = 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),X25),X24)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X25,X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__code__numeral__def) ).

fof(fact_divmod__int__mod__div,axiom,
    ! [X114,X124] : c_Divides_Odivmod__int(X124,X114) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X124),X114)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X124,X114)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).

fof(fact_zminus__zmod,axiom,
    ! [X24,X26] : 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,X26,X24)),X24) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zmod) ).

fof(fact_eq__nat__nat__iff,axiom,
    ! [X137,X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X137))
       => ( hAPP(c_Int_Onat,X19) = hAPP(c_Int_Onat,X137)
        <=> X19 = X137 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__nat__iff) ).

fof(fact_transfer__nat__int__relations_I1_J,axiom,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
       => ( hAPP(c_Int_Onat,X11) = hAPP(c_Int_Onat,X16)
        <=> X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__relations_I1_J) ).

fof(fact_zless__iff__Suc__zadd,axiom,
    ! [X19,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X90),X19))
    <=> ? [X123] : X19 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X90),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X123))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__iff__Suc__zadd) ).

fof(fact_div__mod__equality_H,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25)),X25) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mod__equality_H) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X25) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_zero__less__int__conv,axiom,
    ! [X30] :
      ( 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),X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__int__conv) ).

fof(fact_int__eq__iff__number__of,axiom,
    ! [X93,X31] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93)
    <=> ( X31 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93))
        & 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),X93))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__iff__number__of) ).

fof(fact_finite__Pow__iff,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Set_OPow(X10),X12)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Pow__iff) ).

fof(fact_DomainP_Ointros,axiom,
    ! [X8,X10,X14,X13,X110] :
      ( hBOOL(hAPP(hAPP(X110,X13),X14))
     => hBOOL(hAPP(c_Predicate_ODomainP(X10,X8,X110),X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).

fof(fact_RangeP_Ointros,axiom,
    ! [X8,X10,X14,X13,X110] :
      ( hBOOL(hAPP(hAPP(X110,X13),X14))
     => hBOOL(hAPP(c_Predicate_ORangeP(X10,X8,X110),X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).

fof(fact_length__splice,axiom,
    ! [X201,X202,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),c_List_Osplice(X27,X202,X201)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__splice) ).

fof(fact_length__greater__0__conv,axiom,
    ! [X200,X10] :
      ( 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(X10)),X200)))
    <=> X200 != c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__greater__0__conv) ).

fof(fact_ivl__disj__int_I8_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X77)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I8_J) ).

fof(fact_le__less__Suc__eq,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_OSuc,X31)))
      <=> X30 = X31 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__less__Suc__eq) ).

fof(fact_mod__pos__pos__trivial,axiom,
    ! [X36,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(tc_Int_Oint),X37),X36))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__pos__pos__trivial) ).

fof(fact_atMost__Int__atLeast,axiom,
    ! [X30,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X30)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X30)) = hAPP(hAPP(c_Set_Oinsert(X10),X30),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__Int__atLeast) ).

fof(fact_length__append,axiom,
    ! [X201,X202,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X201)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__append) ).

fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
    ! [X15,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( c_Nat__Transfer_Onat__set(X15)
       => ( X12 = X15
        <=> hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X12) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X15) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__relations_I3_J) ).

fof(fact_setprod__zero,axiom,
    ! [X2,X12,X10,X8] :
      ( class_Rings_Ocomm__semiring__1(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
              & hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X8) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12) = c_Groups_Ozero__class_Ozero(X8) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__zero) ).

fof(fact_nat__mult__div__cancel__disj,axiom,
    ! [X25,X24,X33] :
      ( ( X33 = 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),X33),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X25)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X33 != 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),X33),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33),X25)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).

fof(fact_Pow__top,axiom,
    ! [X12,X10] : hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Set_OPow(X10),X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__top) ).

fof(fact_rev_Osimps_I2_J,axiom,
    ! [X202,X26,X27] : hAPP(c_List_Orev(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Oappend(X27),hAPP(c_List_Orev(X27),X202)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Olist_ONil(X27))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev_Osimps_I2_J) ).

fof(fact_div__pos__pos__trivial,axiom,
    ! [X36,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(tc_Int_Oint),X37),X36))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__pos__pos__trivial) ).

fof(fact_zdiv__eq__0__iff,axiom,
    ! [X32,X61] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X61),X32) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ( X32 = 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)),X61))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),X32)) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X61)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).

fof(fact_Inf__le__Sup,axiom,
    ! [X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)),c_Big__Operators_Olattice__class_OSup__fin(X10,X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__le__Sup) ).

fof(fact_map__replicate__const,axiom,
    ! [X249,X32,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),hAPP(c_COMBK(X10,X8),X32)),X249) = c_List_Oreplicate(X10,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X249),X32),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate__const) ).

fof(fact_part__equivp__transp,axiom,
    ! [X19,X16,X11,X29,X10] :
      ( c_Equiv__Relations_Opart__equivp(X10,X29)
     => ( hBOOL(hAPP(hAPP(X29,X11),X16))
       => ( hBOOL(hAPP(hAPP(X29,X16),X19))
         => hBOOL(hAPP(hAPP(X29,X11),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__transp) ).

fof(fact_transpE,axiom,
    ! [X19,X16,X11,X110,X10] :
      ( c_Predicate_Otransp(X10,X110)
     => ( hBOOL(hAPP(hAPP(X110,X11),X16))
       => ( hBOOL(hAPP(hAPP(X110,X16),X19))
         => hBOOL(hAPP(hAPP(X110,X11),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpE) ).

fof(fact_equivp__transp,axiom,
    ! [X19,X16,X11,X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => ( hBOOL(hAPP(hAPP(X29,X11),X16))
       => ( hBOOL(hAPP(hAPP(X29,X16),X19))
         => hBOOL(hAPP(hAPP(X29,X11),X19)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).

fof(fact_folding__one__idem_Oinsert__idem,axiom,
    ! [X11,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one__idem(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(X2,X11),hAPP(X9,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oinsert__idem) ).

fof(fact_mod__minus__cong,axiom,
    ! [X127,X36,X37,X27] :
      ( class_Divides_Oring__div(X27)
     => ( c_Divides_Odiv__class_Omod(X27,X37,X36) = c_Divides_Odiv__class_Omod(X27,X127,X36)
       => c_Divides_Odiv__class_Omod(X27,hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37),X36) = c_Divides_Odiv__class_Omod(X27,hAPP(c_Groups_Ouminus__class_Ouminus(X27),X127),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__minus__cong) ).

fof(fact_sublists__powset,axiom,
    ! [X200,X10] : hAPP(c_Set_Oimage(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),c_List_Oset(X10)),hAPP(c_List_Oset(tc_List_Olist(X10)),c_Enum_Osublists(X10,X200))) = hAPP(c_Set_OPow(X10),hAPP(c_List_Oset(X10),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublists__powset) ).

fof(fact_Union__def,axiom,
    ! [X28,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X28) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X28),c_COMBI(tc_fun(X10,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__def) ).

fof(fact_Inter__def,axiom,
    ! [X28,X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),X28) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X10,tc_HOL_Obool),tc_fun(X10,tc_HOL_Obool)),X28),c_COMBI(tc_fun(X10,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__def) ).

fof(fact_zabs__less__one__iff,axiom,
    ! [X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X19)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    <=> X19 = 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,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__le__0__conv) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
    ! [X25,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X26))
     => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X26)),X25) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J) ).

fof(fact_nat__power__eq,axiom,
    ! [X25,X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
     => hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X38),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X38)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__power__eq) ).

fof(fact_diff__cancel,axiom,
    ! [X25,X24,X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X24)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33),X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel) ).

fof(fact_diff__cancel2,axiom,
    ! [X25,X33,X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X33)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X33)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__cancel2) ).

fof(fact_zpower__zpower,axiom,
    ! [X38,X34,X26] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X34)),X38) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X34),X38)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__zpower) ).

fof(fact_zmult__assoc,axiom,
    ! [X99,X97,X98] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X98),X97)),X99) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X98),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__assoc) ).

fof(fact_nat__mult__assoc,axiom,
    ! [X33,X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__assoc) ).

fof(fact_zadd__assoc,axiom,
    ! [X99,X97,X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),X97)),X99) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X98),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),X99)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__assoc) ).

fof(fact_nat__add__assoc,axiom,
    ! [X33,X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).

fof(fact_diff__diff__left,axiom,
    ! [X33,X43,X44] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),X43)),X33) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__left) ).

fof(fact_div__mult2__eq,axiom,
    ! [X35,X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X36),X35)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X37),X36)),X35),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult2__eq) ).

fof(fact_ball__empty,axiom,
    ! [X42,X10,X3] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
     => hBOOL(hAPP(X42,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__empty) ).

fof(fact_ivl__disj__int_I3_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X83)),c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X83,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I3_J) ).

fof(fact_ivl__disj__int_I1_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X83)),c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X83,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I1_J) ).

fof(fact_ivl__disj__int_I4_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X83)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X83,X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I4_J) ).

fof(fact_mod__neg__neg__trivial,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X37))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__neg__neg__trivial) ).

fof(fact_set__map,axiom,
    ! [X200,X2,X8,X10] : hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_List_Oset(X8),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__map) ).

fof(fact_append__take__drop__id,axiom,
    ! [X202,X25,X27] : hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Otake(X27),X25),X202)),hAPP(hAPP(c_List_Odrop(X27),X25),X202)) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__take__drop__id) ).

fof(fact_mod__Suc__eq__Suc__mod,axiom,
    ! [X25,X24] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24),X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc__eq__Suc__mod) ).

fof(fact_less__0__number__of,axiom,
    ! [X93] :
      ( 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),X93)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X93)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__0__number__of) ).

fof(fact_list__ex__append,axiom,
    ! [X199,X200,X42,X10] :
      ( c_List_Olist__ex(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X199))
    <=> ( c_List_Olist__ex(X10,X42,X200)
        | c_List_Olist__ex(X10,X42,X199) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__append) ).

fof(fact_div__neg__neg__trivial,axiom,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X37))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = 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,
    ! [X202,X26,X25,X27] : hAPP(hAPP(c_List_Otake(X27),hAPP(c_Nat_OSuc,X25)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),hAPP(hAPP(c_List_Otake(X27),X25),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Suc__Cons) ).

fof(fact_small__lazy__prod__def,axiom,
    ! [X58,X10,X27] :
      ( ( class_Lazy__Sequence_Osmall__lazy(X27)
        & class_Lazy__Sequence_Osmall__lazy(X10) )
     => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X27,X10),X58) = c_Lazy__Sequence_Oproduct(X27,X10,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X27,X58),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X10,X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__prod__def) ).

fof(fact_map__eq__imp__length__eq,axiom,
    ! [X199,X1,X18,X200,X2,X10,X8] :
      ( hAPP(hAPP(c_List_Omap(X8,X10),X2),X200) = hAPP(hAPP(c_List_Omap(X18,X10),X1),X199)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X200) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X18)),X199) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__eq__imp__length__eq) ).

fof(fact_length__sublists,axiom,
    ! [X202,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X27))),c_Enum_Osublists(X27,X202)) = 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(X27)),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__sublists) ).

fof(fact_transfer__int__nat__set__return__embed,axiom,
    ! [X12] : 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)),X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).

fof(fact_fst__eqD,axiom,
    ! [X37,X34,X26,X10,X27] :
      ( hAPP(c_Product__Type_Ofst(X27,X10),hAPP(hAPP(c_Product__Type_OPair(X27,X10),X26),X34)) = X37
     => X26 = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__eqD) ).

fof(fact_snd__eqD,axiom,
    ! [X37,X34,X26,X27,X10] :
      ( hAPP(c_Product__Type_Osnd(X10,X27),hAPP(hAPP(c_Product__Type_OPair(X10,X27),X26),X34)) = X37
     => X34 = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__eqD) ).

fof(fact_transfer__nat__int__set__return__embed,axiom,
    ! [X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => 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),X12)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__set__return__embed) ).

fof(fact_finite__Field,axiom,
    ! [X110,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X110))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Relation_OField(X10),X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__Field) ).

fof(fact_image__uminus__atLeastLessThan,axiom,
    ! [X16,X11,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X11),X16)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeastLessThan) ).

fof(fact_Suc__lessI,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => ( hAPP(c_Nat_OSuc,X24) != X25
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__lessI) ).

fof(fact_finite__nat__set__iff__bounded,axiom,
    ! [X53] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X53))
    <=> ? [X74] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X53))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X74)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).

fof(fact_finite__nat__set__iff__bounded__le,axiom,
    ! [X53] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X53))
    <=> ? [X74] :
        ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),X53))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X74)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).

fof(fact_diff__number__of__eq,axiom,
    ! [X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__number__of__eq) ).

fof(fact_distinct__n__lists,axiom,
    ! [X25,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X27)),c_Enum_On__lists(X27,X25,X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__n__lists) ).

fof(fact_zero__less__nat__eq,axiom,
    ! [X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X19)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__nat__eq) ).

fof(fact_last__snoc,axiom,
    ! [X26,X202,X27] : c_List_Olast(X27,hAPP(hAPP(c_List_Oappend(X27),X202),hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Olist_ONil(X27)))) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__snoc) ).

fof(fact_butlast__snoc,axiom,
    ! [X26,X202,X27] : c_List_Obutlast(X27,hAPP(hAPP(c_List_Oappend(X27),X202),hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Olist_ONil(X27)))) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__snoc) ).

fof(fact_rtrancl__idemp__self__comp,axiom,
    ! [X29,X10] : hAPP(hAPP(c_Relation_Orel__comp(X10,X10,X10),c_Transitive__Closure_Ortrancl(X10,X29)),c_Transitive__Closure_Ortrancl(X10,X29)) = c_Transitive__Closure_Ortrancl(X10,X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp__self__comp) ).

fof(fact_fst__def,axiom,
    ! [X148,X8,X10] : hAPP(c_Product__Type_Ofst(X10,X8),X148) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,X10),c_COMBK(X10,X8)),X148),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__def) ).

fof(fact_finite__acyclic__wf__converse,axiom,
    ! [X110,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X110))
     => ( c_Wellfounded_Oacyclic(X10,X110)
       => c_Wellfounded_Owf(X10,hAPP(c_Relation_Oconverse(X10,X10),X110)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf__converse) ).

fof(fact_xt1_I5_J,axiom,
    ! [X26,X34,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
         => X26 = X34 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I5_J) ).

fof(fact_order__antisym,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
         => X26 = X34 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym) ).

fof(fact_order__antisym__conv,axiom,
    ! [X11,X16,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
        <=> X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__antisym__conv) ).

fof(fact_order__eq__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( X11 = X16
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).

fof(fact_le__mod__geq,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__mod__geq) ).

fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
    ! [X14,X13] :
      ( X13 = X14
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X13),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).

fof(fact_in__set__insert,axiom,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => c_List_Oinsert(X10,X11,X200) = X200 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__set__insert) ).

fof(fact_Suc__diff__le,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__le) ).

fof(fact_abs__ge__minus__self,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__minus__self) ).

fof(fact_zero__le__square,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__ring(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__square) ).

fof(fact_less__add__one,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),c_Groups_Oone__class_Oone(X27)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__one) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [X13,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Groups_Oabs__class_Oabs(X10),X13)))
      <=> X13 != c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__abs__iff) ).

fof(fact_accp__downward,axiom,
    ! [X13,X14,X110,X10] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X110),X14))
     => ( hBOOL(hAPP(hAPP(X110,X13),X14))
       => hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X110),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).

fof(fact_hd__in__set,axiom,
    ! [X10,X200] :
      ( X200 != c_List_Olist_ONil(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_List_Ohd(X10),X200)),hAPP(c_List_Oset(X10),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__in__set) ).

fof(fact_dvd_OatLeastAtMost__singleton,axiom,
    ! [X13] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X13) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X13),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton) ).

fof(fact_lazy__sequence_Osize_I4_J,axiom,
    ! [X252,X37,X27] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X27)),c_Lazy__Sequence_Olazy__sequence_OInsert(X27,X37,X252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X27)),X252)),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,
    ! [X114,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X114)),X26) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),hAPP(c_Nat_OSuc,X114)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) ).

fof(fact_power__Suc2,axiom,
    ! [X25,X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(c_Nat_OSuc,X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc2) ).

fof(fact_sorted__list__of__set__sort__remdups,axiom,
    ! [X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_List_Olinorder__class_Osorted__list__of__set(X10,hAPP(c_List_Oset(X10),X200)) = c_List_Olinorder__class_Osort__key(X10,X10,c_COMBI(X10),c_List_Oremdups(X10,X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__sort__remdups) ).

fof(fact_list_Osize_I4_J,axiom,
    ! [X205,X37,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(hAPP(c_List_Olist_OCons(X27),X37),X205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X205)),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,
    ! [X202,X25,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X27))),c_Enum_On__lists(X27,X25,X202)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__n__lists) ).

fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [X42] :
      ( ? [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
          & hBOOL(hAPP(X42,X3)) )
    <=> ? [X3] : hBOOL(hAPP(X42,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,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__leI) ).

fof(fact_Inf__fin_Oin__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)) = c_Big__Operators_Olattice__class_OInf__fin(X10,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oin__idem) ).

fof(fact_Sup__fin_Oin__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)) = c_Big__Operators_Olattice__class_OSup__fin(X10,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oin__idem) ).

fof(fact_Max_Oin__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olinorder__class_OMax(X10,X12)) = c_Big__Operators_Olinorder__class_OMax(X10,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oin__idem) ).

fof(fact_Min_Oin__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olinorder__class_OMin(X10,X12)) = c_Big__Operators_Olinorder__class_OMin(X10,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oin__idem) ).

fof(fact_Sup__upper,axiom,
    ! [X12,X11,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),c_Complete__Lattice_OSup__class_OSup(X10,X12))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__upper) ).

fof(fact_list__ex__simps_I1_J,axiom,
    ! [X200,X11,X42,X10] :
      ( c_List_Olist__ex(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))
    <=> ( hBOOL(hAPP(X42,X11))
        | c_List_Olist__ex(X10,X42,X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I1_J) ).

fof(fact_ivl__disj__int_I2_J,axiom,
    ! [X77,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X83)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X83),X77)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ivl__disj__int_I2_J) ).

fof(fact_card__gt__0__iff,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X12)))
    <=> ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).

fof(fact_nth__Cons__Suc,axiom,
    ! [X25,X202,X26,X27] : hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),hAPP(c_Nat_OSuc,X25)) = hAPP(hAPP(c_List_Onth(X27),X202),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__Suc) ).

fof(fact_map__tl,axiom,
    ! [X200,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(c_List_Otl(X8),X200)) = hAPP(c_List_Otl(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__tl) ).

fof(fact_rev__map,axiom,
    ! [X200,X2,X8,X10] : hAPP(c_List_Orev(X10),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(hAPP(c_List_Omap(X8,X10),X2),hAPP(c_List_Orev(X8),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__map) ).

fof(fact_in__respects,axiom,
    ! [X29,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),c_Quotient_ORespects(X10,X29)))
    <=> hBOOL(hAPP(hAPP(X29,X11),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__respects) ).

fof(fact_dvd__mult__div__cancel,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X36))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X36),X37)) = X36 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__mult__div__cancel) ).

fof(fact_ex__nat,axiom,
    ! [X42] :
      ( ? [X136] : hBOOL(hAPP(X42,X136))
    <=> ? [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
          & hBOOL(hAPP(X42,hAPP(c_Int_Onat,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat) ).

fof(fact_card__ge__0__finite,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X12)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__ge__0__finite) ).

fof(fact_list__all__append,axiom,
    ! [X199,X200,X42,X10] :
      ( c_List_Olist__all(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X199))
    <=> ( c_List_Olist__all(X10,X42,X200)
        & c_List_Olist__all(X10,X42,X199) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__append) ).

fof(fact_Suc__pred,axiom,
    ! [X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred) ).

fof(fact_singleton__inject,axiom,
    ! [X14,X13,X10] :
      ( hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))
     => X13 = X14 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__inject) ).

fof(fact_of__nat__inverse,axiom,
    ! [X16] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16),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,X16)) = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__inverse) ).

fof(fact_divide__eq__eq__number__of,axiom,
    ! [X90,X6,X14,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)
      <=> ( ( X6 != c_Groups_Ozero__class_Ozero(X10)
           => X14 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6) )
          & ( X6 = c_Groups_Ozero__class_Ozero(X10)
           => hAPP(c_Int_Onumber__class_Onumber__of(X10),X90) = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of) ).

fof(fact_eq__divide__eq__number__of,axiom,
    ! [X6,X14,X90,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X90) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)
      <=> ( ( X6 != c_Groups_Ozero__class_Ozero(X10)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6) = X14 )
          & ( X6 = c_Groups_Ozero__class_Ozero(X10)
           => hAPP(c_Int_Onumber__class_Onumber__of(X10),X90) = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of) ).

fof(fact_le__Suc__eq,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
        | X31 = hAPP(c_Nat_OSuc,X30) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__Suc__eq) ).

fof(fact_append__butlast__last__id,axiom,
    ! [X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => hAPP(hAPP(c_List_Oappend(X27),c_List_Obutlast(X27,X202)),hAPP(hAPP(c_List_Olist_OCons(X27),c_List_Olast(X27,X202)),c_List_Olist_ONil(X27))) = X202 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__butlast__last__id) ).

fof(fact_pair__collapse,axiom,
    ! [X124,X10,X27] : hAPP(hAPP(c_Product__Type_OPair(X27,X10),hAPP(c_Product__Type_Ofst(X27,X10),X124)),hAPP(c_Product__Type_Osnd(X27,X10),X124)) = X124,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__collapse) ).

fof(fact_surjective__pairing,axiom,
    ! [X10,X27,X54] : X54 = hAPP(hAPP(c_Product__Type_OPair(X27,X10),hAPP(c_Product__Type_Ofst(X27,X10),X54)),hAPP(c_Product__Type_Osnd(X27,X10),X54)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surjective__pairing) ).

fof(fact_insort__key_Osimps_I1_J,axiom,
    ! [X11,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X11),c_List_Olist_ONil(X10)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__key_Osimps_I1_J) ).

fof(fact_distinct__insert,axiom,
    ! [X26,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => hBOOL(hAPP(c_List_Odistinct(X27),c_List_Oinsert(X27,X26,X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insert) ).

fof(fact_distinct__takeWhile,axiom,
    ! [X42,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => hBOOL(hAPP(c_List_Odistinct(X10),c_List_OtakeWhile(X10,X42,X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).

fof(fact_distinct__remove1,axiom,
    ! [X26,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => hBOOL(hAPP(c_List_Odistinct(X27),c_List_Oremove1(X27,X26,X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1) ).

fof(fact_distinct__sublistI,axiom,
    ! [X161,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => hBOOL(hAPP(c_List_Odistinct(X10),c_List_Osublist(X10,X200,X161))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__sublistI) ).

fof(fact__01,axiom,
    ! [X253,X254,X26,X27] : c_Lazy__Sequence_Oappend(X27,c_Lazy__Sequence_Olazy__sequence_OInsert(X27,X26,X254),X253) = c_Lazy__Sequence_Olazy__sequence_OInsert(X27,X26,c_Lazy__Sequence_Oappend(X27,X254,X253)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__01) ).

fof(fact_remove1__commute,axiom,
    ! [X215,X34,X26,X27] : c_List_Oremove1(X27,X26,c_List_Oremove1(X27,X34,X215)) = c_List_Oremove1(X27,X34,c_List_Oremove1(X27,X26,X215)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__commute) ).

fof(fact_fun__left__comm_Ofun__left__comm,axiom,
    ! [X19,X16,X11,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => hAPP(hAPP(X2,X11),hAPP(hAPP(X2,X16),X19)) = hAPP(hAPP(X2,X16),hAPP(hAPP(X2,X11),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).

fof(fact_inf__Sup__absorb,axiom,
    ! [X13,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X13),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)) = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__Sup__absorb) ).

fof(fact_sup__Inf__absorb,axiom,
    ! [X13,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X13),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)) = X13 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__Inf__absorb) ).

fof(fact_wfP__empty,axiom,
    ! [X10] : c_Wellfounded_OwfP(X10,hAPP(c_COMBK(tc_fun(X10,tc_HOL_Obool),X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fFalse))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__empty) ).

fof(fact_of__nat__induct,axiom,
    ! [X11,X42] :
      ( ! [X51] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X51),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
         => hBOOL(hAPP(X42,hAPP(c_Code__Numeral_Oof__nat,X51))) )
     => hBOOL(hAPP(X42,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__induct) ).

fof(fact_dvd__triv__left,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__left) ).

fof(fact_dvd__triv__right,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__triv__right) ).

fof(fact_inf__sup__ord_I3_J,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).

fof(fact_sup__ge1,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__ge1) ).

fof(fact_inf__sup__ord_I4_J,axiom,
    ! [X26,X34,X27] :
      ( class_Lattices_Olattice(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).

fof(fact_sup__ge2,axiom,
    ! [X26,X34,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__ge2) ).

fof(fact_le__maxI1,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__maxI1) ).

fof(fact_le__maxI2,axiom,
    ! [X26,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__maxI2) ).

fof(fact_mem__Collect__eq,axiom,
    ! [X42,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Set_OCollect(X10),X42)))
    <=> hBOOL(hAPP(X42,X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__Collect__eq) ).

fof(fact_CollectD,axiom,
    ! [X42,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Set_OCollect(X10),X42)))
     => hBOOL(hAPP(X42,X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectD) ).

fof(fact_CollectE,axiom,
    ! [X42,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Set_OCollect(X10),X42)))
     => hBOOL(hAPP(X42,X13)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectE) ).

fof(fact_Suc__nat__eq__nat__zadd1,axiom,
    ! [X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
     => hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X38)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__eq__nat__zadd1) ).

fof(fact_remove1_Osimps_I2_J,axiom,
    ! [X202,X27,X34,X26] :
      ( ( X26 = X34
       => c_List_Oremove1(X27,X26,hAPP(hAPP(c_List_Olist_OCons(X27),X34),X202)) = X202 )
      & ( X26 != X34
       => c_List_Oremove1(X27,X26,hAPP(hAPP(c_List_Olist_OCons(X27),X34),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X34),c_List_Oremove1(X27,X26,X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).

fof(fact_dvd__div__eq__mult,axiom,
    ! [X6,X14,X13,X10] :
      ( class_Divides_Osemiring__div(X10)
     => ( X13 != c_Groups_Ozero__class_Ozero(X10)
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X13),X14))
         => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X10),X14),X13) = X6
          <=> X14 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X6),X13) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__div__eq__mult) ).

fof(fact_less__Suc__eq,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
        | X31 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq) ).

fof(fact_Image__Id__on,axiom,
    ! [X15,X12,X10] : hAPP(c_Relation_OImage(X10,X10,c_Relation_OId__on(X10,X12)),X15) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__Id__on) ).

fof(fact_inf_Oleft__commute,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X36),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X35)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).

fof(fact_inf__left__commute,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__commute) ).

fof(fact_inf__sup__aci_I3_J,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).

fof(fact_inf__sup__aci_I7_J,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).

fof(fact_sup_Oleft__commute,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X36),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X35)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).

fof(fact_sup__left__commute,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X38)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__left__commute) ).

fof(fact_min__max_Osup_Oleft__commute,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X36),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X35)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).

fof(fact_min__max_Osup__left__commute,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),X38)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__left__commute) ).

fof(fact_min__max_Oinf__left__commute,axiom,
    ! [X38,X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),X38)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__left__commute) ).

fof(fact_min__max_Oinf_Oleft__commute,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X36),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X35)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X36),X35)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__commute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
    ! [X86,X87,X89,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X87),X86)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X87),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X89),X86)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
    ! [X58,X35,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X58)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X58)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(fact_add__minus__cancel,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X36)) = X36 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__minus__cancel) ).

fof(fact_nat__mult__eq__cancel1,axiom,
    ! [X30,X31,X32] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X32))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)
      <=> X31 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel1) ).

fof(fact_less__Suc__eq__le,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,X30)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc__eq__le) ).

fof(fact_one__div__nat__number__of,axiom,
    ! [X120] : 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),X120)) = 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),X120))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__div__nat__number__of) ).

fof(fact_split__nat,axiom,
    ! [X61,X42] :
      ( hBOOL(hAPP(X42,hAPP(c_Int_Onat,X61)))
    <=> ( ! [X123] :
            ( X61 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X123)
           => hBOOL(hAPP(X42,X123)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X61),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__nat) ).

fof(fact_distinct__drop,axiom,
    ! [X44,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => hBOOL(hAPP(c_List_Odistinct(X27),hAPP(hAPP(c_List_Odrop(X27),X44),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__drop) ).

fof(fact_distinct__take,axiom,
    ! [X44,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => hBOOL(hAPP(c_List_Odistinct(X27),hAPP(hAPP(c_List_Otake(X27),X44),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__take) ).

fof(fact_finite_OinsertI,axiom,
    ! [X13,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).

fof(fact_image__Suc__atLeastAtMost,axiom,
    ! [X60,X61] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X61,X60)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X61),hAPP(c_Nat_OSuc,X60)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastAtMost) ).

fof(fact_INT__empty,axiom,
    ! [X15,X10,X8] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),X15) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__empty) ).

fof(fact_minus__numeral__code_I6_J,axiom,
    ! [X92,X68] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I6_J) ).

fof(fact_Compl__eq__Diff__UNIV,axiom,
    ! [X12,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).

fof(fact_map__butlast,axiom,
    ! [X200,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_Obutlast(X8,X200)) = c_List_Obutlast(X10,hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__butlast) ).

fof(fact_Max__in,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olinorder__class_OMax(X10,X12)),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__in) ).

fof(fact_Min__in,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_member(X10),c_Big__Operators_Olinorder__class_OMin(X10,X12)),X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__in) ).

fof(fact_nat__of__cases,axiom,
    ! [X16] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X16),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
     => ~ ! [X3] : X16 != hAPP(c_Code__Numeral_Onat__of,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__cases) ).

fof(fact_all__nat,axiom,
    ! [X42] :
      ( ! [X136] : hBOOL(hAPP(X42,X136))
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
         => hBOOL(hAPP(X42,hAPP(c_Int_Onat,X3))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat) ).

fof(fact_insertI1,axiom,
    ! [X15,X13,X10] : hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).

fof(fact_mod__Suc,axiom,
    ! [X25,X24] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)) = X25
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24),X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)) != X25
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24),X25) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__Suc) ).

fof(fact_inv__id,axiom,
    ! [X10] : c_Hilbert__Choice_Oinv__into(X10,X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Fun_Oid(X10)) = c_Fun_Oid(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inv__id) ).

fof(fact_insert__commute,axiom,
    ! [X12,X16,X11,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(hAPP(c_Set_Oinsert(X10),X16),X12)) = hAPP(hAPP(c_Set_Oinsert(X10),X16),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).

fof(fact_folding__one_Osingleton,axiom,
    ! [X11,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Osingleton) ).

fof(fact_diff__Suc__eq__diff__pred,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__eq__diff__pred) ).

fof(fact_fold__empty,axiom,
    ! [X19,X2,X10,X8] : hAPP(hAPP(c_Finite__Set_Ofold(X8,X10,X2),X19),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = X19,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__empty) ).

fof(fact_length__drop,axiom,
    ! [X202,X25,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(hAPP(c_List_Odrop(X27),X25),X202)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__drop) ).

fof(fact_length__take,axiom,
    ! [X202,X25,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(hAPP(c_List_Otake(X27),X25),X202)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__take) ).

fof(fact_inj__of__nat,axiom,
    ! [X10] :
      ( class_Nat_Osemiring__char__0(X10)
     => c_Fun_Oinj__on(tc_Nat_Onat,X10,c_Nat_Osemiring__1__class_Oof__nat(X10),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,
    ! [X202,X25,X27] : hAPP(hAPP(c_List_Otake(X27),X25),hAPP(c_List_Otl(X27),X202)) = hAPP(c_List_Otl(X27),hAPP(hAPP(c_List_Otake(X27),hAPP(c_Nat_OSuc,X25)),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__tl) ).

fof(fact_less__iff__Suc__add,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
    <=> ? [X59] : X30 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X59)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__iff__Suc__add) ).

fof(fact_drop__replicate,axiom,
    ! [X26,X33,X44,X27] : hAPP(hAPP(c_List_Odrop(X27),X44),c_List_Oreplicate(X27,X33,X26)) = c_List_Oreplicate(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33),X44),X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__replicate) ).

fof(fact_take__replicate,axiom,
    ! [X26,X33,X44,X27] : hAPP(hAPP(c_List_Otake(X27),X44),c_List_Oreplicate(X27,X33,X26)) = c_List_Oreplicate(X27,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X44),X33),X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__replicate) ).

fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30) = 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),X30))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_list__all__simps_I1_J,axiom,
    ! [X200,X11,X42,X10] :
      ( c_List_Olist__all(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))
    <=> ( hBOOL(hAPP(X42,X11))
        & c_List_Olist__all(X10,X42,X200) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I1_J) ).

fof(fact_nonzero__abs__divide,axiom,
    ! [X37,X36,X27] :
      ( class_Fields_Olinordered__field(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__abs__divide) ).

fof(fact_card_Oneutral,axiom,
    ! [X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
         => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => hAPP(c_Finite__Set_Ocard(X10),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oneutral) ).

fof(fact_Compl__disjoint,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__disjoint) ).

fof(fact_Compl__partition,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__partition) ).

fof(fact_inj__on__empty,axiom,
    ! [X2,X8,X10] : c_Fun_Oinj__on(X10,X8,X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__empty) ).

fof(fact_dvd_Oantisym,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X26))
       => X26 = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym) ).

fof(fact_dvd__antisym,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X24),X25))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24))
       => X24 = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__antisym) ).

fof(fact_dvd_Oantisym__conv,axiom,
    ! [X11,X16] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X11))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oantisym__conv) ).

fof(fact_dvd_Oeq__iff,axiom,
    ! [X16,X11] :
      ( X11 = X16
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__iff) ).

fof(fact_zle__antisym,axiom,
    ! [X92,X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),X92))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X92),X38))
       => X38 = X92 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__antisym) ).

fof(fact_le__antisym,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
       => X24 = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).

fof(fact_zmod__minus1,axiom,
    ! [X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X36) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X36),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__minus1) ).

fof(fact_babs__reg__eqv,axiom,
    ! [X42,X8,X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => c_Quotient_OBabs(X10,X8,c_Quotient_ORespects(X10,X29),X42) = X42 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_babs__reg__eqv) ).

fof(fact_Inf__fin_Oinsert__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oinsert__idem) ).

fof(fact_Sup__fin_Oinsert__idem,axiom,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oinsert__idem) ).

fof(fact_Max__insert,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olinorder__class_OMax(X10,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max__insert) ).

fof(fact_Min__insert,axiom,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olinorder__class_OMin(X10,X12)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min__insert) ).

fof(fact_Un__empty,axiom,
    ! [X15,X12,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        & X15 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty) ).

fof(fact_listsum__append,axiom,
    ! [X201,X202,X27] :
      ( class_Groups_Omonoid__add(X27)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_List_Omonoid__add__class_Olistsum(X27),X202)),hAPP(c_List_Omonoid__add__class_Olistsum(X27),X201)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__append) ).

fof(fact_abs__divide,axiom,
    ! [X36,X37,X27] :
      ( class_Fields_Olinordered__field__inverse__zero(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__divide) ).

fof(fact_abs__mult,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult) ).

fof(fact_compl__inf,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__inf) ).

fof(fact_compl__sup,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__sup) ).

fof(fact_minus__max__eq__min,axiom,
    ! [X34,X26,X27] :
      ( class_Groups_Olinordered__ab__group__add(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__max__eq__min) ).

fof(fact_minus__min__eq__max,axiom,
    ! [X34,X26,X27] :
      ( class_Groups_Olinordered__ab__group__add(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__min__eq__max) ).

fof(fact_minus__add__distrib,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oab__group__add(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__distrib) ).

fof(fact_minus__add,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add) ).

fof(fact_Cantors__paradox,axiom,
    ! [X12,X10] :
      ~ ? [X76] : hAPP(c_Set_Oimage(X10,tc_fun(X10,tc_HOL_Obool),X76),X12) = hAPP(c_Set_OPow(X10),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cantors__paradox) ).

fof(fact_equalityD1,axiom,
    ! [X10,X15,X12] :
      ( X12 = X15
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD1) ).

fof(fact_equalityD2,axiom,
    ! [X10,X15,X12] :
      ( X12 = X15
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityD2) ).

fof(fact_last__in__set,axiom,
    ! [X10,X230] :
      ( X230 != c_List_Olist_ONil(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),c_List_Olast(X10,X230)),hAPP(c_List_Oset(X10),X230))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__in__set) ).

fof(fact_Suc__mult__cancel1,axiom,
    ! [X30,X31,X32] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),X30)
    <=> X31 = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__mult__cancel1) ).

fof(fact_Pair__inject,axiom,
    ! [X113,X127,X36,X37,X10,X27] :
      ( hAPP(hAPP(c_Product__Type_OPair(X27,X10),X37),X36) = hAPP(hAPP(c_Product__Type_OPair(X27,X10),X127),X113)
     => ~ ( X37 = X127
         => X36 != X113 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).

fof(fact_Pair__eq,axiom,
    ! [X108,X109,X14,X13,X8,X10] :
      ( hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14) = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X109),X108)
    <=> ( X13 = X109
        & X14 = X108 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).

fof(fact_zmod__zminus1__eq__if,axiom,
    ! [X36,X37] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = 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),X37),X36) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) != 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),X37),X36) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X36),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus1__eq__if) ).

fof(fact_subset__refl,axiom,
    ! [X12,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [X60,X61] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X61),X60)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X61)),hAPP(c_Nat_OSuc,X60)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__Suc__atLeastLessThan) ).

fof(fact_rev__append,axiom,
    ! [X201,X202,X27] : hAPP(c_List_Orev(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(hAPP(c_List_Oappend(X27),hAPP(c_List_Orev(X27),X201)),hAPP(c_List_Orev(X27),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__append) ).

fof(fact_rotate__simps,axiom,
    ! [X202,X26,X10,X27] :
      ( hAPP(c_List_Orotate1(X27),c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27)
      & hAPP(c_List_Orotate1(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X26),X202)) = hAPP(hAPP(c_List_Oappend(X10),X202),hAPP(hAPP(c_List_Olist_OCons(X10),X26),c_List_Olist_ONil(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate__simps) ).

fof(fact_less__SucI,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__SucI) ).

fof(fact_le__imp__less__Suc,axiom,
    ! [X25,X24] :
      ( 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),X24),hAPP(c_Nat_OSuc,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__less__Suc) ).

fof(fact_le__SucI,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__SucI) ).

fof(fact_greaterThanAtMost__upto,axiom,
    ! [X60,X61] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X61,X60) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)),X60)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__upto) ).

fof(fact_Ints__double__eq__0__iff,axiom,
    ! [X13,X10] :
      ( class_Int_Oring__char__0(X10)
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),c_Int_Oring__1__class_OInts(X10)))
       => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X13) = c_Groups_Ozero__class_Ozero(X10)
        <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__double__eq__0__iff) ).

fof(fact_div__eq__minus1,axiom,
    ! [X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X36) = 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,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__commute) ).

fof(fact_Un__commute,axiom,
    ! [X15,X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X15),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__commute) ).

fof(fact_zero__less__imp__eq__int,axiom,
    ! [X33] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33))
     => ? [X123] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X123))
          & X33 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X123) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__imp__eq__int) ).

fof(fact_frac__eq__eq,axiom,
    ! [X90,X11,X19,X16,X10] :
      ( class_Fields_Ofield(X10)
     => ( X16 != c_Groups_Ozero__class_Ozero(X10)
       => ( X19 != c_Groups_Ozero__class_Ozero(X10)
         => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X11),X16) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X90),X19)
          <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X19) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X90),X16) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_zmult__div__cancel,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X24),X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24),c_Divides_Odiv__class_Omod(tc_Int_Oint,X24,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__div__cancel) ).

fof(fact_mult__div__cancel,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__div__cancel) ).

fof(fact_div__code__numeral__def,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X25),X24) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),hAPP(c_Code__Numeral_Onat__of,X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__code__numeral__def) ).

fof(fact_times__code__numeral__def,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X25),X24) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),hAPP(c_Code__Numeral_Onat__of,X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__code__numeral__def) ).

fof(fact_plus__code__numeral__def,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X25),X24) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),hAPP(c_Code__Numeral_Onat__of,X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__code__numeral__def) ).

fof(fact_minus__code__numeral__def,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X25),X24) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X25)),hAPP(c_Code__Numeral_Onat__of,X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__code__numeral__def) ).

fof(fact_le__add__diff__inverse,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add__diff__inverse) ).

fof(fact_diff__diff__cancel,axiom,
    ! [X25,X44] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X25))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X44)) = X44 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__diff__cancel) ).

fof(fact_nat__case__Suc,axiom,
    ! [X40,X49,X50,X10] : c_Nat_Onat_Onat__case(X10,X50,X49,hAPP(c_Nat_OSuc,X40)) = hAPP(X49,X40),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_listsum__eq__0__nat__iff__nat,axiom,
    ! [X209] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X209) = 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),X209)))
         => 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,
    ! [X37,X36,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X37))
       => ( X37 != X36
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I11_J) ).

fof(fact_order__le__neq__trans,axiom,
    ! [X36,X37,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
       => ( X37 != X36
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__neq__trans) ).

fof(fact_order__le__imp__less__or__eq,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
          | X26 = X34 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__imp__less__or__eq) ).

fof(fact_order__neq__le__trans,axiom,
    ! [X36,X37,X27] :
      ( class_Orderings_Oorder(X27)
     => ( X37 != X36
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X36))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__neq__le__trans) ).

fof(fact_order__le__less,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
          | X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__le__less) ).

fof(fact_order__less__le,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
          & X11 != X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__le) ).

fof(fact_xt1_I12_J,axiom,
    ! [X36,X37,X27] :
      ( class_Orderings_Oorder(X27)
     => ( X37 != X36
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X37))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_xt1_I12_J) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_add__number__of__eq,axiom,
    ! [X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__number__of__eq) ).

fof(fact_of__int__mult,axiom,
    ! [X38,X92,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Oring__1__class_Oof__int(X27),X92)),hAPP(c_Int_Oring__1__class_Oof__int(X27),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__mult) ).

fof(fact_of__int__add,axiom,
    ! [X38,X92,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X92),X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Oring__1__class_Oof__int(X27),X92)),hAPP(c_Int_Oring__1__class_Oof__int(X27),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__add) ).

fof(fact_of__int__diff,axiom,
    ! [X38,X92,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X92),X38)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Int_Oring__1__class_Oof__int(X27),X92)),hAPP(c_Int_Oring__1__class_Oof__int(X27),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__diff) ).

fof(fact_of__nat__mult,axiom,
    ! [X25,X24,X27] :
      ( class_Rings_Osemiring__1(X27)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__mult) ).

fof(fact_of__nat__add,axiom,
    ! [X25,X24,X27] :
      ( class_Rings_Osemiring__1(X27)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__add) ).

fof(fact_number__of__mult,axiom,
    ! [X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X92)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__mult) ).

fof(fact_number__of__add,axiom,
    ! [X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__add) ).

fof(fact_number__of__diff,axiom,
    ! [X92,X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X68),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X68)),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__diff) ).

fof(fact_product_Osimps_I1_J,axiom,
    ! [X236,X10,X27] : c_Enum_Oproduct(X27,X10,c_List_Olist_ONil(X27),X236) = c_List_Olist_ONil(tc_prod(X27,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product_Osimps_I1_J) ).

fof(fact_minus1__divide,axiom,
    ! [X26,X27] :
      ( ( class_Fields_Ofield__inverse__zero(X27)
        & class_Int_Onumber__ring(X27) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin)),X26) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),c_Groups_Oone__class_Oone(X27)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus1__divide) ).

fof(fact_setsum__0,axiom,
    ! [X12,X8,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),hAPP(c_COMBK(X10,X8),c_Groups_Ozero__class_Ozero(X10))),X12) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__0) ).

fof(fact_setprod__1,axiom,
    ! [X12,X8,X10] :
      ( class_Groups_Ocomm__monoid__mult(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),hAPP(c_COMBK(X10,X8),c_Groups_Oone__class_Oone(X10))),X12) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__1) ).

fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
    ! [X77,X83] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X83),c_Groups_Oone__class_Oone(tc_Int_Oint))),X77) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X83,X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastPlusOneLessThan__greaterThanLessThan__int) ).

fof(fact_order__less__imp__le,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__le) ).

fof(fact_tl__replicate,axiom,
    ! [X26,X27,X25] :
      ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Otl(X27),c_List_Oreplicate(X27,X25,X26)) = c_List_Oreplicate(X27,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__replicate) ).

fof(fact_negateSnd__eq,axiom,
    ! [X80,X114] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X80)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negateSnd__eq) ).

fof(fact_abs__power__minus__one,axiom,
    ! [X25,X27] :
      ( ( class_Int_Onumber__ring(X27)
        & class_Rings_Olinordered__idom(X27) )
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin)),X25)) = c_Groups_Oone__class_Oone(X27) ),
    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,
    ! [X15,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( c_Nat__Transfer_Onat__set(X15)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12),X15)) ) ),
    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,
    ! [X15,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( c_Nat__Transfer_Onat__set(X15)
       => c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X12),X15)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).

fof(fact_zle__iff__zadd,axiom,
    ! [X19,X90] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X90),X19))
    <=> ? [X123] : X19 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X90),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X123)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__iff__zadd) ).

fof(fact_map__replicate,axiom,
    ! [X11,X30,X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_Oreplicate(X8,X30,X11)) = c_List_Oreplicate(X10,X30,hAPP(X2,X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__replicate) ).

fof(fact_filter__remove1,axiom,
    ! [X200,X11,X41,X10] : hAPP(c_List_Ofilter(X10,X41),c_List_Oremove1(X10,X11,X200)) = c_List_Oremove1(X10,X11,hAPP(c_List_Ofilter(X10,X41),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter__remove1) ).

fof(fact_snoc__eq__iff__butlast,axiom,
    ! [X199,X11,X200,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X200),hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10))) = X199
    <=> ( X199 != c_List_Olist_ONil(X10)
        & c_List_Obutlast(X10,X199) = X200
        & c_List_Olast(X10,X199) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).

fof(fact_negD,axiom,
    ! [X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ? [X123] : X26 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X123))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negD) ).

fof(fact_Ints__of__int,axiom,
    ! [X19,X10] :
      ( class_Rings_Oring__1(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)),c_Int_Oring__1__class_OInts(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__of__int) ).

fof(fact_of__nat__in__Nats,axiom,
    ! [X30,X10] :
      ( class_Rings_Osemiring__1(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)),c_Nat_Osemiring__1__class_ONats(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__in__Nats) ).

fof(fact_Ints__of__nat,axiom,
    ! [X30,X10] :
      ( class_Rings_Oring__1(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)),c_Int_Oring__1__class_OInts(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__of__nat) ).

fof(fact_Ints__number__of,axiom,
    ! [X90,X10] :
      ( class_Int_Onumber__ring(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Int_Oring__1__class_OInts(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__number__of) ).

fof(fact_Suc__diff__1,axiom,
    ! [X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__diff__1) ).

fof(fact_Suc__pred_H,axiom,
    ! [X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => X25 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__pred_H) ).

fof(fact_nat__of,axiom,
    ! [X11] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X11)),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,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),c_Divides_Odiv__class_Omod(X27,X37,X36)),X36) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__div__trivial) ).

fof(fact_negDivAlg__minus1,axiom,
    ! [X36] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X36) = 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),X36),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negDivAlg__minus1) ).

fof(fact_set__replicate__Suc,axiom,
    ! [X11,X30,X10] : hAPP(c_List_Oset(X10),c_List_Oreplicate(X10,hAPP(c_Nat_OSuc,X30),X11)) = hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__replicate__Suc) ).

fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11))
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X11,X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).

fof(fact_min__max_OSup__fin_Osingleton,axiom,
    ! [X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).

fof(fact_min__max_OInf__fin_Osingleton,axiom,
    ! [X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).

fof(fact_int__one__le__iff__zero__less,axiom,
    ! [X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__one__le__iff__zero__less) ).

fof(fact_Int__empty__left,axiom,
    ! [X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X15) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__left) ).

fof(fact_Un__UNIV__left,axiom,
    ! [X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X15) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__UNIV__left) ).

fof(fact_empty__Diff,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X12) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Diff) ).

fof(fact_Sigma__empty1,axiom,
    ! [X15,X8,X10] : hAPP(hAPP(c_Product__Type_OSigma(X10,X8),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X15) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sigma__empty1) ).

fof(fact_le__square,axiom,
    ! [X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).

fof(fact_le__add1,axiom,
    ! [X24,X25] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).

fof(fact_le__add2,axiom,
    ! [X24,X25] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).

fof(fact_divide__eq__eq__number__of1,axiom,
    ! [X13,X90,X14,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)) = X13
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X90) != c_Groups_Ozero__class_Ozero(X10)
           => X14 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)) )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X90) = c_Groups_Ozero__class_Ozero(X10)
           => X13 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq__number__of1) ).

fof(fact_eq__divide__eq__number__of1,axiom,
    ! [X90,X14,X13,X10] :
      ( ( class_Fields_Ofield__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( X13 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))
      <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X90) != c_Groups_Ozero__class_Ozero(X10)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)) = X14 )
          & ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X90) = c_Groups_Ozero__class_Ozero(X10)
           => X13 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq__number__of1) ).

fof(fact_nat__less__cases,axiom,
    ! [X42,X30,X31] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
       => hBOOL(hAPP(hAPP(X42,X30),X31)) )
     => ( ( X31 = X30
         => hBOOL(hAPP(hAPP(X42,X30),X31)) )
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31))
           => hBOOL(hAPP(hAPP(X42,X30),X31)) )
         => hBOOL(hAPP(hAPP(X42,X30),X31)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
    ! [X12] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X12) = 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)),X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).

fof(fact_append__eq__appendI,axiom,
    ! [X219,X201,X215,X218,X202,X27] :
      ( hAPP(hAPP(c_List_Oappend(X27),X202),X218) = X215
     => ( X201 = hAPP(hAPP(c_List_Oappend(X27),X218),X219)
       => hAPP(hAPP(c_List_Oappend(X27),X202),X201) = hAPP(hAPP(c_List_Oappend(X27),X215),X219) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__eq__appendI) ).

fof(fact_Cons__eq__appendI,axiom,
    ! [X215,X202,X201,X218,X26,X27] :
      ( hAPP(hAPP(c_List_Olist_OCons(X27),X26),X218) = X201
     => ( X202 = hAPP(hAPP(c_List_Oappend(X27),X218),X215)
       => hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202) = hAPP(hAPP(c_List_Oappend(X27),X201),X215) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cons__eq__appendI) ).

fof(fact_zadd__left__commute,axiom,
    ! [X38,X34,X26] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X34),X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),X38)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__left__commute) ).

fof(fact_nat__add__left__commute,axiom,
    ! [X38,X34,X26] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X34),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),X38)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).

fof(fact_atLeastLessThan__upto,axiom,
    ! [X60,X61] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X61),X60) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X61,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X60),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,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)),X24) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__minus__add__max) ).

fof(fact_dual__min,axiom,
    ! [X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Orderings_Oord_Omin(X10,hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X10))) = c_Orderings_Oord__class_Omax(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dual__min) ).

fof(fact_dual__max,axiom,
    ! [X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Orderings_Oord_Omax(X10,hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X10))) = c_Orderings_Oord__class_Omin(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dual__max) ).

fof(fact_listsum__foldl,axiom,
    ! [X10] :
      ( class_Groups_Omonoid__add(X10)
     => c_List_Omonoid__add__class_Olistsum(X10) = c_List_Ofoldl(X10,X10,c_Groups_Oplus__class_Oplus(X10),c_Groups_Ozero__class_Ozero(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__foldl) ).

fof(fact_div__mult__self1__is__id,axiom,
    ! [X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X37)),X36) = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self1__is__id) ).

fof(fact_div__mult__self2__is__id,axiom,
    ! [X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)),X36) = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__mult__self2__is__id) ).

fof(fact_le__imp__diff__is__add,axiom,
    ! [X32,X60,X61] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X61),X60))
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X60),X61) = X32
      <=> X60 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X61) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_zmod__zminus2,axiom,
    ! [X36,X37] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)) = 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),X37),X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus2) ).

fof(fact_remove1__remdups,axiom,
    ! [X26,X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => c_List_Oremove1(X27,X26,c_List_Oremdups(X27,X202)) = c_List_Oremdups(X27,c_List_Oremove1(X27,X26,X202)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1__remdups) ).

fof(fact_Nitpick_Owf_H__def,axiom,
    ! [X110,X10] :
      ( c_Nitpick_Owf_H(X10,X110)
    <=> ( c_Wellfounded_Oacyclic(X10,X110)
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X110))
          | 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,
    ! [X110,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X110))
     => ( c_Wellfounded_Owf(X10,X110)
      <=> c_Wellfounded_Oacyclic(X10,X110) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__iff__acyclic__if__finite) ).

fof(fact_finite__acyclic__wf,axiom,
    ! [X110,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X10,X10)),X110))
     => ( c_Wellfounded_Oacyclic(X10,X110)
       => c_Wellfounded_Owf(X10,X110) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).

fof(fact_inj__on__rev,axiom,
    ! [X12,X10] : c_Fun_Oinj__on(tc_List_Olist(X10),tc_List_Olist(X10),c_List_Orev(X10),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__rev) ).

fof(fact_distinct__filter,axiom,
    ! [X42,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => hBOOL(hAPP(c_List_Odistinct(X10),hAPP(c_List_Ofilter(X10,X42),X200))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__filter) ).

fof(fact_equivp__def,axiom,
    ! [X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
    <=> ! [X3,X51] :
          ( hBOOL(hAPP(hAPP(X29,X3),X51))
        <=> hAPP(X29,X3) = hAPP(X29,X51) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).

fof(fact_diff__add__cancel,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36)),X36) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__cancel) ).

fof(fact_add__diff__cancel,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)),X36) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__diff__cancel) ).

fof(fact_sort__key__simps_I1_J,axiom,
    ! [X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => c_List_Olinorder__class_Osort__key(X10,X8,X2,c_List_Olist_ONil(X10)) = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__key__simps_I1_J) ).

fof(fact_fst__eq__Domain,axiom,
    ! [X29,X8,X10] : hAPP(c_Set_Oimage(tc_prod(X10,X8),X10,c_Product__Type_Ofst(X10,X8)),X29) = hAPP(c_Relation_ODomain(X10,X8),X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__eq__Domain) ).

fof(fact_snd__eq__Range,axiom,
    ! [X29,X10,X8] : hAPP(c_Set_Oimage(tc_prod(X8,X10),X10,c_Product__Type_Osnd(X8,X10)),X29) = hAPP(c_Relation_ORange(X8,X10),X29),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__eq__Range) ).

fof(fact_total__on__converse,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Ototal__on(X10,X12,hAPP(c_Relation_Oconverse(X10,X10),X110))
    <=> c_Relation_Ototal__on(X10,X12,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__converse) ).

fof(fact_refl__on__converse,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,hAPP(c_Relation_Oconverse(X10,X10),X110))
    <=> c_Relation_Orefl__on(X10,X12,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__converse) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
    ! [X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X12) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X12)) ),
    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,
    ! [X11,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11),X12))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) ).

fof(fact_nat__set__def,axiom,
    ! [X28] :
      ( c_Nat__Transfer_Onat__set(X28)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),X28))
         => 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,
    ! [X10] : c_Relation_Orefl__on(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__empty) ).

fof(fact_card__eq__setsum,axiom,
    ! [X12,X10] : hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__eq__setsum) ).

fof(fact_divmod__nat__rel__unique,axiom,
    ! [X153,X151,X25,X24] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X24,X25),X151))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X24,X25),X153))
       => X151 = X153 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).

fof(fact_inj__uminus,axiom,
    ! [X12,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => c_Fun_Oinj__on(X10,X10,c_Groups_Ouminus__class_Ouminus(X10),X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__uminus) ).

fof(fact_mod__code__numeral__def,axiom,
    ! [X24,X25] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X25,X24) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X25),hAPP(c_Code__Numeral_Onat__of,X24))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__code__numeral__def) ).

fof(fact_nth__Cons__0,axiom,
    ! [X202,X26,X27] : hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__Cons__0) ).

fof(fact_part__equivp__refl__symp__transp,axiom,
    ! [X29,X10] :
      ( c_Equiv__Relations_Opart__equivp(X10,X29)
    <=> ( ? [X3] : hBOOL(hAPP(hAPP(X29,X3),X3))
        & c_Predicate_Osymp(X10,X29)
        & c_Predicate_Otransp(X10,X29) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__refl__symp__transp) ).

fof(fact_image__is__empty,axiom,
    ! [X12,X2,X10,X8] :
      ( hAPP(c_Set_Oimage(X8,X10,X2),X12) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> X12 = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__is__empty) ).

fof(fact_empty__is__image,axiom,
    ! [X12,X2,X8,X10] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X8,X10,X2),X12)
    <=> X12 = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__is__image) ).

fof(fact_listrelp_ONil,axiom,
    ! [X110,X10] : c_List_Olistrelp(X10,X110,c_List_Olist_ONil(X10),c_List_Olist_ONil(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_ONil) ).

fof(fact_listrelp_Oequations_I1_J,axiom,
    ! [X110,X10] : c_List_Olistrelp(X10,X110,c_List_Olist_ONil(X10),c_List_Olist_ONil(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).

fof(fact_hd__map,axiom,
    ! [X2,X8,X10,X200] :
      ( X200 != c_List_Olist_ONil(X10)
     => hAPP(c_List_Ohd(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)) = hAPP(X2,hAPP(c_List_Ohd(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__map) ).

fof(fact_of__nat__aux_Osimps_I1_J,axiom,
    ! [X61,X125,X10] :
      ( class_Rings_Osemiring__1(X10)
     => c_Nat_Osemiring__1__class_Oof__nat__aux(X10,X125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X61) = X61 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).

fof(fact_atLeastAtMost__singleton__iff,axiom,
    ! [X6,X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14) = hAPP(hAPP(c_Set_Oinsert(X10),X6),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))
      <=> ( X13 = X14
          & X14 = X6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).

fof(fact_pos__single__def,axiom,
    ! [X242,X243,X244,X11,X10] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X10),X11),X244),X243),X242) = c_New__DSequence_Opos__single(X10,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__single__def) ).

fof(fact_neg__single__def,axiom,
    ! [X242,X243,X244,X11,X10] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X10),X11),X244),X243),X242) = c_New__DSequence_Oneg__single(X10,X11),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__single__def) ).

fof(fact_power__abs,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__abs) ).

fof(fact_minus__divide__left,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Odivision__ring(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__left) ).

fof(fact_minus__mult__left,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oring(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__left) ).

fof(fact_power_Opower_Opower__0,axiom,
    ! [X13,X128,X129,X10] : hAPP(hAPP(c_Power_Opower_Opower(X10,X129,X128),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X129,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).

fof(fact__07,axiom,
    ! [X2,X10,X8] : c_Lazy__Sequence_Omap(X8,X10,X2,c_Lazy__Sequence_Olazy__sequence_OEmpty(X8)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__07) ).

fof(fact_maps__simps_I2_J,axiom,
    ! [X2,X10,X8] : c_List_Omaps(X8,X10,X2,c_List_Olist_ONil(X8)) = c_List_Olist_ONil(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_maps__simps_I2_J) ).

fof(fact_atLeastatMost__empty,axiom,
    ! [X13,X14,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),X13))
       => c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__empty) ).

fof(fact_greaterThanAtMost__empty,axiom,
    ! [X32,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X32))
       => c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X32,X83) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanAtMost__empty) ).

fof(fact_greaterThanLessThan__empty,axiom,
    ! [X32,X83,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X83),X32))
       => c_SetInterval_Oord__class_OgreaterThanLessThan(X10,X32,X83) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThanLessThan__empty) ).

fof(fact_dvd__1__iff__1,axiom,
    ! [X31] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X31),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> X31 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__iff__1) ).

fof(fact_tl__append2,axiom,
    ! [X201,X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => hAPP(c_List_Otl(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(hAPP(c_List_Oappend(X27),hAPP(c_List_Otl(X27),X202)),X201) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__append2) ).

fof(fact_zmod__zdiv__trivial,axiom,
    ! [X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)),X36) = 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,
    ! [X8,X10,X154,X116] :
      ( X116 = X154
    <=> ( hAPP(c_Product__Type_Ofst(X10,X8),X116) = hAPP(c_Product__Type_Ofst(X10,X8),X154)
        & hAPP(c_Product__Type_Osnd(X10,X8),X116) = hAPP(c_Product__Type_Osnd(X10,X8),X154) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__fst__snd__eq) ).

fof(fact_prod__eqI,axiom,
    ! [X114,X124,X10,X27] :
      ( hAPP(c_Product__Type_Ofst(X27,X10),X124) = hAPP(c_Product__Type_Ofst(X27,X10),X114)
     => ( hAPP(c_Product__Type_Osnd(X27,X10),X124) = hAPP(c_Product__Type_Osnd(X27,X10),X114)
       => X124 = X114 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod__eqI) ).

fof(fact_inj__on__id,axiom,
    ! [X12,X10] : c_Fun_Oinj__on(X10,X10,c_Fun_Oid(X10),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id) ).

fof(fact_inj__on__id2,axiom,
    ! [X12,X10] : c_Fun_Oinj__on(X10,X10,c_COMBI(X10),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).

fof(fact_sgn__times,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => c_Groups_Osgn__class_Osgn(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Osgn__class_Osgn(X27,X37)),c_Groups_Osgn__class_Osgn(X27,X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__times) ).

fof(fact_sorted__distinct__set__unique,axiom,
    ! [X199,X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,X200)
       => ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
         => ( c_List_Olinorder__class_Osorted(X10,X199)
           => ( hBOOL(hAPP(c_List_Odistinct(X10),X199))
             => ( hAPP(c_List_Oset(X10),X200) = hAPP(c_List_Oset(X10),X199)
               => X200 = X199 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__distinct__set__unique) ).

fof(fact_drop__Suc__Cons,axiom,
    ! [X202,X26,X25,X27] : hAPP(hAPP(c_List_Odrop(X27),hAPP(c_Nat_OSuc,X25)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Odrop(X27),X25),X202),
    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,
    ! [X36,X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36)) = hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X36),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__commute) ).

fof(fact_code__numeral_Orecs_I1_J,axiom,
    ! [X49,X50,X10] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X10,X50,X49,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X50,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).

fof(fact_code__numeral_Osimps_I4_J,axiom,
    ! [X49,X50,X10] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X10,X50,X49,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X50,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).

fof(fact_nat__case__0,axiom,
    ! [X49,X50,X10] : c_Nat_Onat_Onat__case(X10,X50,X49,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X50,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).

fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X34,X26] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X26),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I1_J) ).

fof(fact_zmult__int,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__int) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X34,X26] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [X92,X68] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_zadd__int,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__int) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
    ! [X34,X26] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X26),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [X92,X68] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_zminus__zadd__distrib,axiom,
    ! [X92,X38] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X38),X92)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zadd__distrib) ).

fof(fact_zdiv__int,axiom,
    ! [X36,X37] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X37),X36)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X37)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__int) ).

fof(fact_int__mult,axiom,
    ! [X25,X24] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__mult) ).

fof(fact_Int__UNIV__left,axiom,
    ! [X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))),X15) = X15,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).

fof(fact_Un__empty__left,axiom,
    ! [X15,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X15) = X15,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__left) ).

fof(fact_pos__zmult__eq__1__iff,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X31))
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X30) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      <=> ( X31 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X30 = 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,
    ! [X13,X2,X10] : hAPP(c_Finite__Set_Ofold1(X10,X2),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X13,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__singleton) ).

fof(fact_length__map,axiom,
    ! [X200,X2,X8,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__map) ).

fof(fact_length__list__update,axiom,
    ! [X26,X44,X202,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(hAPP(c_List_Olist__update(X27,X202),X44),X26)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__list__update) ).

fof(fact_of__int__power,axiom,
    ! [X25,X38,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X38),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Int_Oring__1__class_Oof__int(X27),X38)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__power) ).

fof(fact_of__nat__power,axiom,
    ! [X25,X24,X27] :
      ( class_Rings_Osemiring__1(X27)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__power) ).

fof(fact_zless__le,axiom,
    ! [X90,X19] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19),X90))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19),X90))
        & X19 != X90 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).

fof(fact_le__neq__implies__less,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
     => ( X24 != X25
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).

fof(fact_le__eq__less__or__eq,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
        | X31 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).

fof(fact_nat__less__le,axiom,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
        & X31 != X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).

fof(fact_fold1__singleton__def,axiom,
    ! [X13,X2,X10,X1] :
      ( X1 = c_Finite__Set_Ofold1(X10,X2)
     => hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__singleton__def) ).

fof(fact_length__tl,axiom,
    ! [X202,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(c_List_Otl(X27),X202)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),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,
    ! [X19,X11,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm__idem(X10,X8,X2)
     => hAPP(hAPP(X2,X11),hAPP(hAPP(X2,X11),X19)) = hAPP(hAPP(X2,X11),X19) ),
    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,
    ! [X17] : 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)),X17)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).

fof(fact_finite__atLeastAtMost__int,axiom,
    ! [X77,X83] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X83,X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).

fof(fact_finite__greaterThanAtMost__int,axiom,
    ! [X77,X83] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X83,X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).

fof(fact_finite__greaterThanLessThan__int,axiom,
    ! [X77,X83] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X83,X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).

fof(fact_finite__atLeastAtMost,axiom,
    ! [X77,X83] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X83,X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).

fof(fact_finite__greaterThanAtMost,axiom,
    ! [X77,X83] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X83,X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).

fof(fact_finite__greaterThanLessThan,axiom,
    ! [X77,X83] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X83,X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).

fof(fact_less__Suc0,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).

fof(fact_inj__Suc,axiom,
    ! [X53] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X53),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).

fof(fact_termination__basic__simps_I5_J,axiom,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X34))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X26),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).

fof(fact_less__or__eq__imp__le,axiom,
    ! [X25,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
        | X24 = X25 )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).

fof(fact_less__imp__le__nat,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).

fof(fact_atLeastLessThan__empty,axiom,
    ! [X13,X14,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X13))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan__empty) ).

fof(fact_eq__mem,axiom,
    ! [X16,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_fequal,X16)))
    <=> X11 = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).

fof(fact_last__map,axiom,
    ! [X2,X8,X10,X200] :
      ( X200 != c_List_Olist_ONil(X10)
     => c_List_Olast(X8,hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)) = hAPP(X2,c_List_Olast(X10,X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__map) ).

fof(fact_minus__add__cancel,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36)) = X36 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__add__cancel) ).

fof(fact_ex__in__conv,axiom,
    ! [X12,X10] :
      ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
    <=> X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__in__conv) ).

fof(fact_of__nat__nat,axiom,
    ! [X38,X27] :
      ( class_Rings_Oring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onat,X38)) = hAPP(c_Int_Oring__1__class_Oof__int(X27),X38) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__nat) ).

fof(fact_zmod__zminus__zminus,axiom,
    ! [X36,X37] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zminus__zminus) ).

fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
    ! [X34,X26] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__functions_I2_J) ).

fof(fact_zmod__int,axiom,
    ! [X36,X37] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X37,X36)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X37),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__int) ).

fof(fact_distinct__listsum__conv__Setsum,axiom,
    ! [X200,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
       => hAPP(c_List_Omonoid__add__class_Olistsum(X10),X200) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X10),c_COMBI(X10)),hAPP(c_List_Oset(X10),X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
    ! [X114,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X114)) = hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),hAPP(c_Nat_OSuc,X114)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) ).

fof(fact_power__Suc,axiom,
    ! [X25,X37,X27] :
      ( class_Power_Opower(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(c_Nat_OSuc,X25)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
    ! [X114,X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),hAPP(c_Nat_OSuc,X114)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),X114)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) ).

fof(fact_image__uminus__greaterThan,axiom,
    ! [X11,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X11)) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__greaterThan) ).

fof(fact_image__uminus__atLeast,axiom,
    ! [X11,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X11)) = hAPP(c_SetInterval_Oord__class_OatMost(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atLeast) ).

fof(fact_image__uminus__atMost,axiom,
    ! [X11,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X11)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__atMost) ).

fof(fact_image__uminus__lessThan,axiom,
    ! [X11,X10] :
      ( class_Groups_Oordered__ab__group__add(X10)
     => hAPP(c_Set_Oimage(X10,X10,c_Groups_Ouminus__class_Ouminus(X10)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X11)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__uminus__lessThan) ).

fof(fact_replicate__Suc,axiom,
    ! [X26,X25,X27] : c_List_Oreplicate(X27,hAPP(c_Nat_OSuc,X25),X26) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Oreplicate(X27,X25,X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__Suc) ).

fof(fact_set__replicate__conv__if,axiom,
    ! [X11,X10,X30] :
      ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(X10),c_List_Oreplicate(X10,X30,X11)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) )
      & ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(c_List_Oset(X10),c_List_Oreplicate(X10,X30,X11)) = hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__replicate__conv__if) ).

fof(fact_set__replicate,axiom,
    ! [X11,X10,X30] :
      ( X30 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Oset(X10),c_List_Oreplicate(X10,X30,X11)) = hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__replicate) ).

fof(fact_abs__of__pos,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => hAPP(c_Groups_Oabs__class_Oabs(X27),X37) = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__pos) ).

fof(fact_abs__of__nonneg,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => hAPP(c_Groups_Oabs__class_Oabs(X27),X37) = X37 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonneg) ).

fof(fact_abs__of__neg,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => hAPP(c_Groups_Oabs__class_Oabs(X27),X37) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__neg) ).

fof(fact_abs__of__nonpos,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => hAPP(c_Groups_Oabs__class_Oabs(X27),X37) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nonpos) ).

fof(fact_sgn__neg,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
       => c_Groups_Osgn__class_Osgn(X27,X37) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__neg) ).

fof(fact_sgn__1__neg,axiom,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Groups_Osgn__class_Osgn(X10,X13) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Groups_Oone__class_Oone(X10))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__neg) ).

fof(fact_part__equivp__symp,axiom,
    ! [X16,X11,X29,X10] :
      ( c_Equiv__Relations_Opart__equivp(X10,X29)
     => ( hBOOL(hAPP(hAPP(X29,X11),X16))
       => hBOOL(hAPP(hAPP(X29,X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__symp) ).

fof(fact_sympE,axiom,
    ! [X16,X11,X110,X10] :
      ( c_Predicate_Osymp(X10,X110)
     => ( hBOOL(hAPP(hAPP(X110,X11),X16))
       => hBOOL(hAPP(hAPP(X110,X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sympE) ).

fof(fact_equivp__symp,axiom,
    ! [X16,X11,X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => ( hBOOL(hAPP(hAPP(X29,X11),X16))
       => hBOOL(hAPP(hAPP(X29,X16),X11)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).

fof(fact_dvd__imp__mod__0,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X36))
       => c_Divides_Odiv__class_Omod(X27,X36,X37) = c_Groups_Ozero__class_Ozero(X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__imp__mod__0) ).

fof(fact_dvd__eq__mod__eq__0,axiom,
    ! [X14,X13,X10] :
      ( class_Divides_Osemiring__div(X10)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X10),X13),X14))
      <=> c_Divides_Odiv__class_Omod(X10,X14,X13) = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__eq__mod__eq__0) ).

fof(fact_length__butlast,axiom,
    ! [X202,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),c_List_Obutlast(X27,X202)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__butlast) ).

fof(fact_lists_ONil,axiom,
    ! [X12,X10] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_List_Olists(X10,X12))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists_ONil) ).

fof(fact_sgn__pos,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => c_Groups_Osgn__class_Osgn(X27,X37) = c_Groups_Oone__class_Oone(X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__pos) ).

fof(fact_sgn__1__pos,axiom,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Groups_Osgn__class_Osgn(X10,X13) = c_Groups_Oone__class_Oone(X10)
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__1__pos) ).

fof(fact_nonzero__minus__divide__divide,axiom,
    ! [X37,X36,X27] :
      ( class_Rings_Odivision__ring(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__divide) ).

fof(fact_listset_Osimps_I1_J,axiom,
    ! [X10] : c_List_Olistset(X10,c_List_Olist_ONil(tc_fun(X10,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listset_Osimps_I1_J) ).

fof(fact_lists__empty,axiom,
    ! [X10] : c_List_Olists(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X10),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__empty) ).

fof(fact_CollectI,axiom,
    ! [X10,X13,X42] :
      ( hBOOL(hAPP(X42,X13))
     => hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Set_OCollect(X10),X42))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectI) ).

fof(fact_distinct__rev,axiom,
    ! [X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(c_List_Orev(X10),X200)))
    <=> hBOOL(hAPP(c_List_Odistinct(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__rev) ).

fof(fact_distinct1__rotate,axiom,
    ! [X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(c_List_Orotate1(X10),X200)))
    <=> hBOOL(hAPP(c_List_Odistinct(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct1__rotate) ).

fof(fact_quotient__empty,axiom,
    ! [X110,X10] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X110) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__empty) ).

fof(fact_split__Pair,axiom,
    ! [X8,X10] : hAPP(c_Product__Type_Oprod_Oprod__case(X10,X8,tc_prod(X10,X8)),c_Product__Type_OPair(X10,X8)) = c_Fun_Oid(tc_prod(X10,X8)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__Pair) ).

fof(fact_inf__absorb1,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34) = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb1) ).

fof(fact_le__iff__inf,axiom,
    ! [X16,X11,X10] :
      ( class_Lattices_Osemilattice__inf(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),X16) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__inf) ).

fof(fact_inf__absorb2,axiom,
    ! [X26,X34,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34) = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__absorb2) ).

fof(fact_le__iff__sup,axiom,
    ! [X16,X11,X10] :
      ( class_Lattices_Osemilattice__sup(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
      <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),X16) = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__sup) ).

fof(fact_sup__absorb2,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34) = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__absorb2) ).

fof(fact_sup__absorb1,axiom,
    ! [X26,X34,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34) = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__absorb1) ).

fof(fact_min__max_Ole__iff__sup,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),X16) = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__iff__sup) ).

fof(fact_min__max_Osup__absorb2,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34) = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__absorb2) ).

fof(fact_min__max_Osup__absorb1,axiom,
    ! [X26,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34) = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__absorb1) ).

fof(fact_min__max_Oinf__absorb1,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34) = X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb1) ).

fof(fact_min__max_Ole__iff__inf,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
      <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),X16) = X11 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ole__iff__inf) ).

fof(fact_min__max_Oinf__absorb2,axiom,
    ! [X26,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34) = X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__absorb2) ).

fof(fact_Sup__singleton,axiom,
    ! [X13,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OSup__class_OSup(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__singleton) ).

fof(fact_Inf__singleton,axiom,
    ! [X13,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OInf__class_OInf(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X13 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__singleton) ).

fof(fact_Inf__fin_Osingleton,axiom,
    ! [X11,X10] :
      ( class_Lattices_Olattice(X10)
     => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).

fof(fact_Sup__fin_Osingleton,axiom,
    ! [X11,X10] :
      ( class_Lattices_Olattice(X10)
     => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).

fof(fact_Max_Osingleton,axiom,
    ! [X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Osingleton) ).

fof(fact_Min_Osingleton,axiom,
    ! [X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Osingleton) ).

fof(fact_mult__Suc,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc) ).

fof(fact_diff__add__inverse,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)),X25) = X24,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).

fof(fact_diff__add__inverse2,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),X25) = X24,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).

fof(fact_New__DSequence_Opos__union__def,axiom,
    ! [X61,X250,X232,X10] : hAPP(c_New__DSequence_Opos__union(X10,X232,X250),X61) = c_Lazy__Sequence_Oappend(X10,hAPP(X232,X61),hAPP(X250,X61)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__union__def) ).

fof(fact_Union__quotient,axiom,
    ! [X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__quotient) ).

fof(fact_minus__divide__divide,axiom,
    ! [X36,X37,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__divide) ).

fof(fact_abs__mult__self,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__mult__self) ).

fof(fact_minus__mult__minus,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__minus) ).

fof(fact_minus__mult__commute,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__commute) ).

fof(fact_wfP__accp__iff,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_OwfP(X10,X110)
    <=> ! [X136] : hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X110),X136)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).

fof(fact_nonzero__minus__divide__right,axiom,
    ! [X37,X36,X27] :
      ( class_Rings_Odivision__ring(X27)
     => ( X36 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__minus__divide__right) ).

fof(fact_quotient__is__empty2,axiom,
    ! [X110,X12,X10] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)
    <=> X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).

fof(fact_quotient__is__empty,axiom,
    ! [X110,X12,X10] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))
    <=> X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_quotient__is__empty) ).

fof(fact_card__greaterThanAtMost__int,axiom,
    ! [X77,X83] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X83,X77)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X77),X83)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).

fof(fact_linorder__neq__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( X11 != X16
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).

fof(fact_linorder__less__linear,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
        | X26 = X34
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__less__linear) ).

fof(fact_mod__mod__trivial,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,c_Divides_Odiv__class_Omod(X27,X37,X36),X36) = c_Divides_Odiv__class_Omod(X27,X37,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mod__trivial) ).

fof(fact_Int__empty__right,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__empty__right) ).

fof(fact_Un__UNIV__right,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__UNIV__right) ).

fof(fact_Diff__UNIV,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__UNIV) ).

fof(fact_Domain__empty,axiom,
    ! [X8,X10] : hAPP(c_Relation_ODomain(X10,X8),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty) ).

fof(fact_Range__empty,axiom,
    ! [X10,X8] : hAPP(c_Relation_ORange(X8,X10),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X10),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty) ).

fof(fact_fst__conv,axiom,
    ! [X36,X37,X10,X27] : hAPP(c_Product__Type_Ofst(X27,X10),hAPP(hAPP(c_Product__Type_OPair(X27,X10),X37),X36)) = X37,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__conv) ).

fof(fact_snd__conv,axiom,
    ! [X36,X37,X27,X10] : hAPP(c_Product__Type_Osnd(X10,X27),hAPP(hAPP(c_Product__Type_OPair(X10,X27),X37),X36)) = X36,
    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,
    ! [X30,X31] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
    <=> ? [X59] : X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X59) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).

fof(fact_insert__absorb,axiom,
    ! [X12,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => hAPP(hAPP(c_Set_Oinsert(X10),X13),X12) = X12 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).

fof(fact_the__elem__eq,axiom,
    ! [X11,X10] : c_Set_Othe__elem(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__elem__eq) ).

fof(fact_linorder__le__less__linear,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__le__less__linear) ).

fof(fact_linorder__linear,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__linear) ).

fof(fact_listsum__simps_I2_J,axiom,
    ! [X202,X26,X27] :
      ( class_Groups_Omonoid__add(X27)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),hAPP(c_List_Omonoid__add__class_Olistsum(X27),X202)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__simps_I2_J) ).

fof(fact_minus__divide__right,axiom,
    ! [X36,X37,X27] :
      ( class_Fields_Ofield__inverse__zero(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X36)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__divide__right) ).

fof(fact_minus__mult__right,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Oring(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__mult__right) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [X42,X10] : c_List_Opartition(X10,X42,c_List_Olist_ONil(X10)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),c_List_Olist_ONil(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition_Osimps_I1_J) ).

fof(fact_take__1__Cons,axiom,
    ! [X202,X26,X27] : hAPP(hAPP(c_List_Otake(X27),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Olist_ONil(X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__1__Cons) ).

fof(fact_sym__inv__image,axiom,
    ! [X2,X8,X110,X10] :
      ( c_Relation_Osym(X10,X110)
     => c_Relation_Osym(X8,hAPP(hAPP(c_Relation_Oinv__image(X10,X8),X110),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__inv__image) ).

fof(fact_trans__inv__image,axiom,
    ! [X2,X8,X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => c_Relation_Otrans(X8,hAPP(hAPP(c_Relation_Oinv__image(X10,X8),X110),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__inv__image) ).

fof(fact_wf__inv__image,axiom,
    ! [X2,X8,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(X8,hAPP(hAPP(c_Relation_Oinv__image(X10,X8),X110),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__inv__image) ).

fof(fact_rp__inv__image__rp,axiom,
    ! [X2,X8,X42,X10] :
      ( c_FunDef_Oreduction__pair(X10,X42)
     => c_FunDef_Oreduction__pair(X8,hAPP(hAPP(c_FunDef_Orp__inv__image(X10,X8),X42),X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).

fof(fact_dvd__0__left,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),c_Groups_Ozero__class_Ozero(X27)),X37))
       => X37 = c_Groups_Ozero__class_Ozero(X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__left) ).

fof(fact_mod__add__self1,axiom,
    ! [X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X37),X36) = c_Divides_Odiv__class_Omod(X27,X37,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self1) ).

fof(fact_mod__add__self2,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36),X36) = c_Divides_Odiv__class_Omod(X27,X37,X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__add__self2) ).

fof(fact_nth__via__drop,axiom,
    ! [X201,X34,X202,X25,X27] :
      ( hAPP(hAPP(c_List_Odrop(X27),X25),X202) = hAPP(hAPP(c_List_Olist_OCons(X27),X34),X201)
     => hAPP(hAPP(c_List_Onth(X27),X202),X25) = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nth__via__drop) ).

fof(fact_max__Suc__Suc,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),hAPP(c_Nat_OSuc,X25)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__Suc__Suc) ).

fof(fact_min__Suc__Suc,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),hAPP(c_Nat_OSuc,X25)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__Suc__Suc) ).

fof(fact_times__code__numeral__code,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X25)),hAPP(c_Code__Numeral_Oof__nat,X24)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times__code__numeral__code) ).

fof(fact_plus__code__numeral__code,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X25)),hAPP(c_Code__Numeral_Oof__nat,X24)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__code__numeral__code) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
    ! [X25,X26] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)),X25) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X26),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J) ).

fof(fact_zpower__int,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)),X25) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zpower__int) ).

fof(fact_zmult__zminus,axiom,
    ! [X92,X38] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)),X92) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__zminus) ).

fof(fact_int__power,axiom,
    ! [X25,X24] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X24),X25)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__power) ).

fof(fact_List_Oset__insert,axiom,
    ! [X200,X11,X10] : hAPP(c_List_Oset(X10),c_List_Oinsert(X10,X11,X200)) = hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(c_List_Oset(X10),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset__insert) ).

fof(fact_splice_Osimps_I2_J,axiom,
    ! [X246,X68,X27] : c_List_Osplice(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X68),X246),c_List_Olist_ONil(X27)) = hAPP(hAPP(c_List_Olist_OCons(X27),X68),X246),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I2_J) ).

fof(fact_abs__ge__zero,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(c_Groups_Oabs__class_Oabs(X27),X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).

fof(fact_zero__le__imp__of__nat,axiom,
    ! [X24,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__imp__of__nat) ).

fof(fact_of__nat__0__le__iff,axiom,
    ! [X25,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).

fof(fact_inf_Oleft__idem,axiom,
    ! [X36,X37,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).

fof(fact_inf__left__idem,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__left__idem) ).

fof(fact_inf__sup__aci_I4_J,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).

fof(fact_inf__sup__aci_I8_J,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).

fof(fact_sup_Oleft__idem,axiom,
    ! [X36,X37,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).

fof(fact_sup__left__idem,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__left__idem) ).

fof(fact_min__max_Osup_Oleft__idem,axiom,
    ! [X36,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).

fof(fact_min__max_Osup__left__idem,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__left__idem) ).

fof(fact_min__max_Oinf__left__idem,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__left__idem) ).

fof(fact_min__max_Oinf_Oleft__idem,axiom,
    ! [X36,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oleft__idem) ).

fof(fact_mult__left__idem,axiom,
    ! [X36,X37,X27] :
      ( class_Lattices_Oab__semigroup__idem__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__left__idem) ).

fof(fact__03,axiom,
    ! [X276,X254,X27] : c_Lazy__Sequence_Oflat(X27,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X27),X254,X276)) = c_Lazy__Sequence_Oappend(X27,X254,c_Lazy__Sequence_Oflat(X27,X276)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__03) ).

fof(fact_finite__sorted__distinct__unique,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ? [X3] :
            ( hAPP(c_List_Oset(X10),X3) = X12
            & c_List_Olinorder__class_Osorted(X10,X3)
            & hBOOL(hAPP(c_List_Odistinct(X10),X3))
            & ! [X51] :
                ( ( hAPP(c_List_Oset(X10),X51) = X12
                  & c_List_Olinorder__class_Osorted(X10,X51)
                  & hBOOL(hAPP(c_List_Odistinct(X10),X51)) )
               => X51 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__sorted__distinct__unique) ).

fof(fact_drop__tl,axiom,
    ! [X202,X25,X27] : hAPP(hAPP(c_List_Odrop(X27),X25),hAPP(c_List_Otl(X27),X202)) = hAPP(c_List_Otl(X27),hAPP(hAPP(c_List_Odrop(X27),X25),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__tl) ).

fof(fact_tl__drop,axiom,
    ! [X202,X25,X27] : hAPP(c_List_Otl(X27),hAPP(hAPP(c_List_Odrop(X27),X25),X202)) = hAPP(hAPP(c_List_Odrop(X27),X25),hAPP(c_List_Otl(X27),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl__drop) ).

fof(fact_List_Oset_Osimps_I2_J,axiom,
    ! [X200,X11,X10] : hAPP(c_List_Oset(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(c_List_Oset(X10),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).

fof(fact_card__atLeastAtMost,axiom,
    ! [X77,X83] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X83,X77)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X77)),X83),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastAtMost) ).

fof(fact_surj__id,axiom,
    ! [X10] : hAPP(c_Set_Oimage(X10,X10,c_Fun_Oid(X10)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surj__id) ).

fof(fact_Respects__def,axiom,
    ! [X11,X29,X10] :
      ( hBOOL(hAPP(c_Quotient_ORespects(X10,X29),X11))
    <=> hBOOL(hAPP(hAPP(X29,X11),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Respects__def) ).

fof(fact_some__eq__ex,axiom,
    ! [X10,X42] :
      ( hBOOL(hAPP(X42,c_Hilbert__Choice_OEps(X10,X42)))
    <=> ? [X136] : hBOOL(hAPP(X42,X136)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).

fof(fact_partition__filter1,axiom,
    ! [X200,X42,X10] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Opartition(X10,X42,X200)) = hAPP(c_List_Ofilter(X10,X42),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_partition__filter1) ).

fof(fact_dvd__1__left,axiom,
    ! [X33] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).

fof(fact_iso__tuple__UNIV__I,axiom,
    ! [X11,X10] : hBOOL(hAPP(hAPP(c_member(X10),X11),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).

fof(fact_UNIV__I,axiom,
    ! [X11,X10] : hBOOL(hAPP(hAPP(c_member(X10),X11),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__I) ).

fof(fact_Compl__eq__Compl__iff,axiom,
    ! [X15,X12,X10] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X15)
    <=> X12 = X15 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__eq__Compl__iff) ).

fof(fact_uminus__apply,axiom,
    ! [X11,X12,X8,X10] :
      ( class_Groups_Ouminus(X10)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,X10)),X12),X11) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(X12,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_uminus__apply) ).

fof(fact_fun__Compl__def,axiom,
    ! [X11,X12,X8,X10] :
      ( class_Groups_Ouminus(X10)
     => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,X10)),X12),X11) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(X12,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__Compl__def) ).

fof(fact_nat__0__le,axiom,
    ! [X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X38)) = X38 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__le) ).

fof(fact_tsub__eq,axiom,
    ! [X26,X34] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34),X26))
     => c_Nat__Transfer_Otsub(X26,X34) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X34) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__eq) ).

fof(fact_subtract__code__numeral__code,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X25)),hAPP(c_Code__Numeral_Oof__nat,X24)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subtract__code__numeral__code) ).

fof(fact_int__eq__iff,axiom,
    ! [X19,X31] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) = X19
    <=> ( X31 = hAPP(c_Int_Onat,X19)
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__iff) ).

fof(fact_semilattice__big_OF__eq,axiom,
    ! [X12,X9,X2,X10] :
      ( c_Big__Operators_Osemilattice__big(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(X9,X12) = hAPP(c_Finite__Set_Ofold1(X10,X2),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).

fof(fact_folding__one_Oeq__fold,axiom,
    ! [X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(X9,X12) = hAPP(c_Finite__Set_Ofold1(X10,X2),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).

fof(fact_Union__UNIV,axiom,
    ! [X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__UNIV) ).

fof(fact_Union__empty,axiom,
    ! [X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__empty) ).

fof(fact_Inter__UNIV,axiom,
    ! [X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__UNIV) ).

fof(fact_Inter__empty,axiom,
    ! [X10] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X10,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inter__empty) ).

fof(fact_insert__absorb2,axiom,
    ! [X12,X11,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Set_Oinsert(X10),X11),X12),
    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,
    ! [X143,X10,X12,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,X8),X12),hAPP(c_COMBK(X8,X10),X143)) = X143 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INF__const) ).

fof(fact_SUP__const,axiom,
    ! [X143,X10,X12,X8] :
      ( class_Complete__Lattice_Ocomplete__lattice(X8)
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,X8),X12),hAPP(c_COMBK(X8,X10),X143)) = X143 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SUP__const) ).

fof(fact_compl__unique,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34) = c_Orderings_Obot__class_Obot(X27)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34) = c_Orderings_Otop__class_Otop(X27)
         => hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26) = X34 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__unique) ).

fof(fact_mult__Suc__right,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Suc__right) ).

fof(fact_finite__atLeastZeroLessThan__int,axiom,
    ! [X77] : 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)),X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastZeroLessThan__int) ).

fof(fact_transpose_Osimps_I2_J,axiom,
    ! [X238,X27] : c_List_Otranspose(X27,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X27)),c_List_Olist_ONil(X27)),X238)) = c_List_Otranspose(X27,X238),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Osimps_I2_J) ).

fof(fact_Field__empty,axiom,
    ! [X10] : hAPP(c_Relation_OField(X10),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__empty) ).

fof(fact_mod__less,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = X24 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).

fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [X77,X83] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X83),c_Groups_Oone__class_Oone(tc_Int_Oint)),X77) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X83,X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).

fof(fact_Sup__insert,axiom,
    ! [X12,X13,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OSup__class_OSup(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X13),c_Complete__Lattice_OSup__class_OSup(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__insert) ).

fof(fact_Inf__insert,axiom,
    ! [X12,X13,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OInf__class_OInf(X10,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X13),c_Complete__Lattice_OInf__class_OInf(X10,X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__insert) ).

fof(fact_infinite__UNIV__int,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__int) ).

fof(fact_infinite__UNIV__nat,axiom,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).

fof(fact_insert__remdups,axiom,
    ! [X202,X26,X27] : c_List_Oinsert(X27,X26,c_List_Oremdups(X27,X202)) = c_List_Oremdups(X27,c_List_Oinsert(X27,X26,X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__remdups) ).

fof(fact_list__all__rev,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__all(X10,X42,hAPP(c_List_Orev(X10),X200))
    <=> c_List_Olist__all(X10,X42,X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__rev) ).

fof(fact_list__ex__rev,axiom,
    ! [X200,X42,X10] :
      ( c_List_Olist__ex(X10,X42,hAPP(c_List_Orev(X10),X200))
    <=> c_List_Olist__ex(X10,X42,X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__rev) ).

fof(fact_butlast__append,axiom,
    ! [X202,X27,X201] :
      ( ( X201 = c_List_Olist_ONil(X27)
       => c_List_Obutlast(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = c_List_Obutlast(X27,X202) )
      & ( X201 != c_List_Olist_ONil(X27)
       => c_List_Obutlast(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(hAPP(c_List_Oappend(X27),X202),c_List_Obutlast(X27,X201)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__append) ).

fof(fact_butlast_Osimps_I2_J,axiom,
    ! [X26,X27,X202] :
      ( ( X202 = c_List_Olist_ONil(X27)
       => c_List_Obutlast(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = c_List_Olist_ONil(X27) )
      & ( X202 != c_List_Olist_ONil(X27)
       => c_List_Obutlast(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Obutlast(X27,X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I2_J) ).

fof(fact_vimage__UNIV,axiom,
    ! [X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__UNIV) ).

fof(fact_vimage__empty,axiom,
    ! [X2,X8,X10] : hAPP(c_Set_Ovimage(X10,X8,X2),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__empty) ).

fof(fact_Image__empty,axiom,
    ! [X29,X10,X8] : hAPP(c_Relation_OImage(X8,X10,X29),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Image__empty) ).

fof(fact_image__empty,axiom,
    ! [X2,X10,X8] : hAPP(c_Set_Oimage(X8,X10,X2),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__empty) ).

fof(fact_listrel__refl__on,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
     => c_Relation_Orefl__on(tc_List_Olist(X10),c_List_Olists(X10,X12),c_List_Olistrel(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__refl__on) ).

fof(fact_equiv__listrel,axiom,
    ! [X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => c_Equiv__Relations_Oequiv(tc_List_Olist(X10),c_List_Olists(X10,X12),c_List_Olistrel(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__listrel) ).

fof(fact_mem__def,axiom,
    ! [X12,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
    <=> hBOOL(hAPP(X12,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).

fof(fact_dvdI,axiom,
    ! [X33,X36,X37,X27] :
      ( class_Rings_Odvd(X27)
     => ( X37 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X33)
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X36),X37)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvdI) ).

fof(fact_div__less,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).

fof(fact_diff__is__0__eq_H,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25) = 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,
    ! [X30,X31] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31),X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__is__0__eq) ).

fof(fact_Int__UNIV__right,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).

fof(fact_Un__empty__right,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__right) ).

fof(fact_Diff__empty,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).

fof(fact_double__complement,axiom,
    ! [X12,X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).

fof(fact_rel__pow__1,axiom,
    ! [X29,X10] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X29) = X29,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__1) ).

fof(fact_list__update__id,axiom,
    ! [X44,X202,X27] : hAPP(hAPP(c_List_Olist__update(X27,X202),X44),hAPP(hAPP(c_List_Onth(X27),X202),X44)) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__id) ).

fof(fact_square__eq__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Oidom(X10)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X13) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X14),X14)
      <=> ( X13 = X14
          | X13 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__iff) ).

fof(fact_add__Suc,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc) ).

fof(fact_drop__butlast,axiom,
    ! [X202,X25,X27] : hAPP(hAPP(c_List_Odrop(X27),X25),c_List_Obutlast(X27,X202)) = c_List_Obutlast(X27,hAPP(hAPP(c_List_Odrop(X27),X25),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__butlast) ).

fof(fact_butlast__drop,axiom,
    ! [X202,X25,X27] : c_List_Obutlast(X27,hAPP(hAPP(c_List_Odrop(X27),X25),X202)) = hAPP(hAPP(c_List_Odrop(X27),X25),c_List_Obutlast(X27,X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast__drop) ).

fof(fact_code__numeral__not__eq__zero,axiom,
    ! [X61] :
      ( X61 != 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)),X61)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).

fof(fact_Domain__empty__iff,axiom,
    ! [X110,X8,X10] :
      ( hAPP(c_Relation_ODomain(X10,X8),X110) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> X110 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X8),tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).

fof(fact_Range__empty__iff,axiom,
    ! [X110,X10,X8] :
      ( hAPP(c_Relation_ORange(X8,X10),X110) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> X110 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X10),tc_HOL_Obool)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__empty__iff) ).

fof(fact_abs__zmult__eq__1,axiom,
    ! [X25,X24] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X25)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X24) = 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,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X26),X34))
      | X26 = X34
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__linear) ).

fof(fact_nat__neq__iff,axiom,
    ! [X30,X31] :
      ( X31 != X30
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).

fof(fact_card__atLeastLessThan__int,axiom,
    ! [X77,X83] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X83),X77)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X77),X83)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastLessThan__int) ).

fof(fact_abs__ge__self,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),hAPP(c_Groups_Oabs__class_Oabs(X27),X37))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).

fof(fact_card__greaterThanLessThan,axiom,
    ! [X77,X83] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X83,X77)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X77),hAPP(c_Nat_OSuc,X83)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanLessThan) ).

fof(fact_part__equivpI,axiom,
    ! [X10,X29] :
      ( ? [X3] : hBOOL(hAPP(hAPP(X29,X3),X3))
     => ( c_Predicate_Osymp(X10,X29)
       => ( c_Predicate_Otransp(X10,X29)
         => c_Equiv__Relations_Opart__equivp(X10,X29) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivpI) ).

fof(fact_zle__linear,axiom,
    ! [X92,X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),X92))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X92),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).

fof(fact_nat__le__linear,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).

fof(fact_zdiv__zminus__zminus,axiom,
    ! [X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus__zminus) ).

fof(fact_zdiv__zminus2,axiom,
    ! [X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37)),X36),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zminus2) ).

fof(fact_drop__Suc,axiom,
    ! [X202,X25,X27] : hAPP(hAPP(c_List_Odrop(X27),hAPP(c_Nat_OSuc,X25)),X202) = hAPP(hAPP(c_List_Odrop(X27),X25),hAPP(c_List_Otl(X27),X202)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Suc) ).

fof(fact_gr0__conv__Suc,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30))
    <=> ? [X74] : X30 = hAPP(c_Nat_OSuc,X74) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0__conv__Suc) ).

fof(fact_min__max_OSup__fin_OF__eq,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12) = hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omax(X10)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).

fof(fact_min__max_OInf__fin_OF__eq,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12) = hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).

fof(fact_fun__left__comm__insort,axiom,
    ! [X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Finite__Set_Ofun__left__comm(X10,tc_List_Olist(X10),c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__insort) ).

fof(fact_equiv__def,axiom,
    ! [X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
    <=> ( c_Relation_Orefl__on(X10,X12,X110)
        & c_Relation_Osym(X10,X110)
        & c_Relation_Otrans(X10,X110) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equiv__def) ).

fof(fact_equivI,axiom,
    ! [X110,X12,X10] :
      ( c_Relation_Orefl__on(X10,X12,X110)
     => ( c_Relation_Osym(X10,X110)
       => ( c_Relation_Otrans(X10,X110)
         => c_Equiv__Relations_Oequiv(X10,X12,X110) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivI) ).

fof(fact_distinct__tl,axiom,
    ! [X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => hBOOL(hAPP(c_List_Odistinct(X27),hAPP(c_List_Otl(X27),X202))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__tl) ).

fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
    ! [X77,X83] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X83),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X77),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X83,X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanPlusOne__atLeastAtMost__int) ).

fof(fact_neg__def,axiom,
    ! [X118] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X118))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X118),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__def) ).

fof(fact_card__distinct,axiom,
    ! [X200,X10] :
      ( hAPP(c_Finite__Set_Ocard(X10),hAPP(c_List_Oset(X10),X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)
     => hBOOL(hAPP(c_List_Odistinct(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__distinct) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [X34,X26] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X34)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X26),X34)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_assms_I4_J,axiom,
    ! [X23] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X23),v_U))
     => v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X23))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_assms_I4_J) ).

fof(fact_singleton__rev__conv,axiom,
    ! [X200,X11,X10] :
      ( hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)) = hAPP(c_List_Orev(X10),X200)
    <=> X200 = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__rev__conv) ).

fof(fact_rev__singleton__conv,axiom,
    ! [X11,X200,X10] :
      ( hAPP(c_List_Orev(X10),X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10))
    <=> X200 = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__singleton__conv) ).

fof(fact_listrel1__converse,axiom,
    ! [X110,X10] : c_List_Olistrel1(X10,hAPP(c_Relation_Oconverse(X10,X10),X110)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olistrel1(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel1__converse) ).

fof(fact_minus__diff__eq,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oab__group__add(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__diff__eq) ).

fof(fact_rev__replicate,axiom,
    ! [X26,X25,X27] : hAPP(c_List_Orev(X27),c_List_Oreplicate(X27,X25,X26)) = c_List_Oreplicate(X27,X25,X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__replicate) ).

fof(fact_acc__wfD,axiom,
    ! [X11,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => hBOOL(hAPP(hAPP(c_member(X10),X11),c_Wellfounded_Oacc(X10,X110))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acc__wfD) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
    ! [X26,X27] :
      ( class_Rings_Ocomm__ring__1(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27))),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).

fof(fact_finite__atLeastLessThan__int,axiom,
    ! [X77,X83] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X83),X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).

fof(fact_finite__atLeastLessThan,axiom,
    ! [X77,X83] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X83),X77))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).

fof(fact_list__all__iff__all__interval__int,axiom,
    ! [X60,X61,X42] :
      ( c_List_Olist__all(tc_Int_Oint,X42,c_List_Oupto(X61,X60))
    <=> c_List_Oall__interval__int(X42,X61,X60) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__int) ).

fof(fact_enum__all,axiom,
    ! [X42,X10] :
      ( class_Enum_Oenum(X10)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X10),X42))
      <=> ! [X136] : hBOOL(hAPP(X42,X136)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all) ).

fof(fact_all__code,axiom,
    ! [X42,X10] :
      ( class_Enum_Oenum(X10)
     => ( ! [X136] : hBOOL(hAPP(X42,X136))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X10),X42)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__code) ).

fof(fact_nat_Osize_I4_J,axiom,
    ! [X96] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X96)),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,
    ! [X34,X26,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => X34 != X26 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).

fof(fact_order__less__imp__not__eq,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => X26 != X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq) ).

fof(fact_less__imp__neq,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => X26 != X34 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__neq) ).

fof(fact_dvd__if__abs__eq,axiom,
    ! [X33,X45,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( hAPP(c_Groups_Oabs__class_Oabs(X27),X45) = hAPP(c_Groups_Oabs__class_Oabs(X27),X33)
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X45),X33)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__if__abs__eq) ).

fof(fact_replicate__eq__replicate,axiom,
    ! [X16,X30,X11,X31,X10] :
      ( c_List_Oreplicate(X10,X31,X11) = c_List_Oreplicate(X10,X30,X16)
    <=> ( X31 = X30
        & ( X31 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X11 = X16 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__eq__replicate) ).

fof(fact_diff__eq__diff__eq,axiom,
    ! [X20,X6,X14,X13,X10] :
      ( class_Groups_Oab__group__add(X10)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X6),X20)
       => ( X13 = X14
        <=> X6 = X20 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq__diff__eq) ).

fof(fact_rev__filter,axiom,
    ! [X200,X42,X10] : hAPP(c_List_Orev(X10),hAPP(c_List_Ofilter(X10,X42),X200)) = hAPP(c_List_Ofilter(X10,X42),hAPP(c_List_Orev(X10),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__filter) ).

fof(fact_zmod__zminus1__not__zero,axiom,
    ! [X45,X33] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33),X45) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,X45) != 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,
    ! [X45,X33] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X45)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,X45) != 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,
    ! [X30] :
      ( X30 != 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)),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).

fof(fact_n__lists__Nil,axiom,
    ! [X27,X25] :
      ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(X27,X25,c_List_Olist_ONil(X27)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X27)),c_List_Olist_ONil(X27)),c_List_Olist_ONil(tc_List_Olist(X27))) )
      & ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Enum_On__lists(X27,X25,c_List_Olist_ONil(X27)) = c_List_Olist_ONil(tc_List_Olist(X27)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists__Nil) ).

fof(fact_add__right__cancel,axiom,
    ! [X6,X13,X14,X10] :
      ( class_Groups_Ocancel__semigroup__add(X10)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X14),X13) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X6),X13)
      <=> X14 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__cancel) ).

fof(fact_add__right__imp__eq,axiom,
    ! [X35,X37,X36,X27] :
      ( class_Groups_Ocancel__semigroup__add(X27)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X36),X37) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X37)
       => X36 = X35 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__right__imp__eq) ).

fof(fact_add__imp__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Ocancel__ab__semigroup__add(X27)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)
       => X36 = X35 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__imp__eq) ).

fof(fact_add__left__cancel,axiom,
    ! [X6,X14,X13,X10] :
      ( class_Groups_Ocancel__semigroup__add(X10)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X14) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X6)
      <=> X14 = X6 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__cancel) ).

fof(fact_add__left__imp__eq,axiom,
    ! [X35,X36,X37,X27] :
      ( class_Groups_Ocancel__semigroup__add(X27)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35)
       => X36 = X35 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__left__imp__eq) ).

fof(fact_lazy__sequence_Oinject,axiom,
    ! [X255,X109,X256,X13,X10] :
      ( c_Lazy__Sequence_Olazy__sequence_OInsert(X10,X13,X256) = c_Lazy__Sequence_Olazy__sequence_OInsert(X10,X109,X255)
    <=> ( X13 = X109
        & X256 = X255 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Oinject) ).

fof(fact_nat__0__iff,axiom,
    ! [X61] :
      ( hAPP(c_Int_Onat,X61) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),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,
    ! [X38] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(c_Int_Onat,X38) = 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,
    ! [X11] :
      ( c_Nat__Transfer_Ois__nat(X11)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_is__nat__def) ).

fof(fact_add__Suc__right,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__right) ).

fof(fact_lexn_Osimps_I1_J,axiom,
    ! [X110,X10] : hAPP(c_List_Olexn(X10,X110),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10)),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexn_Osimps_I1_J) ).

fof(fact_zero__zle__int,axiom,
    ! [X25] : 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),X25))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__zle__int) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
    ! [X38] : 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),X38))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).

fof(fact_Diff__cancel,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X12) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).

fof(fact_antisym__empty,axiom,
    ! [X10] : c_Relation_Oantisym(X10,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__empty) ).

fof(fact_wf__empty,axiom,
    ! [X10] : c_Wellfounded_Owf(X10,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__empty) ).

fof(fact_atLeastAtMost__singleton_H,axiom,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( X13 = X14
       => c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14) = hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton_H) ).

fof(fact_sorted__list__of__set,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hAPP(c_List_Oset(X10),c_List_Olinorder__class_Osorted__list__of__set(X10,X12)) = X12
          & c_List_Olinorder__class_Osorted(X10,c_List_Olinorder__class_Osorted__list__of__set(X10,X12))
          & hBOOL(hAPP(c_List_Odistinct(X10),c_List_Olinorder__class_Osorted__list__of__set(X10,X12))) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set) ).

fof(fact_mod__mult__self1__is__0,axiom,
    ! [X37,X36,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X37),X36) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self1__is__0) ).

fof(fact_mod__mult__self2__is__0,axiom,
    ! [X36,X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36),X36) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__mult__self2__is__0) ).

fof(fact_distinct__butlast,axiom,
    ! [X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
       => hBOOL(hAPP(c_List_Odistinct(X27),c_List_Obutlast(X27,X202))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__butlast) ).

fof(fact_card__greaterThanAtMost,axiom,
    ! [X77,X83] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X83,X77)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X77),X83),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).

fof(fact_list_Oinject,axiom,
    ! [X203,X109,X204,X13,X10] :
      ( hAPP(hAPP(c_List_Olist_OCons(X10),X13),X204) = hAPP(hAPP(c_List_Olist_OCons(X10),X109),X203)
    <=> ( X13 = X109
        & X204 = X203 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Oinject) ).

fof(fact_append__same__eq,axiom,
    ! [X206,X200,X199,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X199),X200) = hAPP(hAPP(c_List_Oappend(X10),X206),X200)
    <=> X199 = X206 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__same__eq) ).

fof(fact_same__append__eq,axiom,
    ! [X206,X199,X200,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X200),X199) = hAPP(hAPP(c_List_Oappend(X10),X200),X206)
    <=> X199 = X206 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_same__append__eq) ).

fof(fact_atLeastAtMost__singleton,axiom,
    ! [X13,X10] :
      ( class_Orderings_Oorder(X10)
     => c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X13) = hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).

fof(fact_upto__empty,axiom,
    ! [X44,X43] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X43),X44))
     => c_List_Oupto(X44,X43) = 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,
    ! [X202,X27] : c_Enum_On__lists(X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X202) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X27)),c_List_Olist_ONil(X27)),c_List_Olist_ONil(tc_List_Olist(X27))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists_Osimps_I1_J) ).

fof(fact_atMost__Suc,axiom,
    ! [X32] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X32)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__Suc) ).

fof(fact_eq__number__of__0,axiom,
    ! [X93] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X93),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__0) ).

fof(fact_neg__imp__number__of__eq__0,axiom,
    ! [X68] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
     => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) = 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,
    ! [X93] :
      ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X93),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__0__number__of) ).

fof(fact_inf__sup__absorb,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).

fof(fact_sup__inf__absorb,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).

fof(fact_min__max_Osup__inf__absorb,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__inf__absorb) ).

fof(fact_min__max_Oinf__sup__absorb,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).

fof(fact_conversep__conversep,axiom,
    ! [X110,X10,X8] : c_Predicate_Oconversep(X8,X10,c_Predicate_Oconversep(X10,X8,X110)) = X110,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__conversep) ).

fof(fact_le__0__eq,axiom,
    ! [X30] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    <=> X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).

fof(fact_nat__dvd__1__iff__1,axiom,
    ! [X31] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X31),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    <=> X31 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).

fof(fact_drop__1__Cons,axiom,
    ! [X202,X26,X27] : hAPP(hAPP(c_List_Odrop(X27),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__1__Cons) ).

fof(fact_diff__Suc__Suc,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),hAPP(c_Nat_OSuc,X25)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__Suc) ).

fof(fact_add__Suc__shift,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24)),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Suc__shift) ).

fof(fact_fold1__def,axiom,
    ! [X12,X2,X10] : hAPP(c_Finite__Set_Ofold1(X10,X2),X12) = c_HOL_OThe(X10,c_Finite__Set_Ofold1Set(X10,X2,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__def) ).

fof(fact_zmod__eq__0__iff,axiom,
    ! [X20,X31] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X31,X20) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> ? [X138] : X31 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X138) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).

fof(fact_mod__eq__0__iff,axiom,
    ! [X20,X31] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X31,X20) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ? [X138] : X31 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X138) ),
    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,
    ! [X11,X12] :
      ( c_Nat__Transfer_Onat__set(X12)
     => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X11),X12))
       => c_Nat__Transfer_Ois__nat(X11) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).

fof(fact_sym__converse,axiom,
    ! [X110,X10] :
      ( c_Relation_Osym(X10,hAPP(c_Relation_Oconverse(X10,X10),X110))
    <=> c_Relation_Osym(X10,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__converse) ).

fof(fact_antisym__converse,axiom,
    ! [X110,X10] :
      ( c_Relation_Oantisym(X10,hAPP(c_Relation_Oconverse(X10,X10),X110))
    <=> c_Relation_Oantisym(X10,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__converse) ).

fof(fact_trans__converse,axiom,
    ! [X110,X10] :
      ( c_Relation_Otrans(X10,hAPP(c_Relation_Oconverse(X10,X10),X110))
    <=> c_Relation_Otrans(X10,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__converse) ).

fof(fact_acyclic__converse,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Oacyclic(X10,hAPP(c_Relation_Oconverse(X10,X10),X110))
    <=> c_Wellfounded_Oacyclic(X10,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__converse) ).

fof(fact_distinct__card,axiom,
    ! [X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => hAPP(c_Finite__Set_Ocard(X10),hAPP(c_List_Oset(X10),X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__card) ).

fof(fact_length__remdups__eq,axiom,
    ! [X200,X10] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremdups(X10,X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)
    <=> c_List_Oremdups(X10,X200) = X200 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__eq) ).

fof(fact_Domain__converse,axiom,
    ! [X110,X8,X10] : hAPP(c_Relation_ODomain(X10,X8),hAPP(c_Relation_Oconverse(X8,X10),X110)) = hAPP(c_Relation_ORange(X8,X10),X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__converse) ).

fof(fact_Range__converse,axiom,
    ! [X110,X10,X8] : hAPP(c_Relation_ORange(X8,X10),hAPP(c_Relation_Oconverse(X10,X8),X110)) = hAPP(c_Relation_ODomain(X10,X8),X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__converse) ).

fof(fact_remdups__filter,axiom,
    ! [X200,X42,X10] : c_List_Oremdups(X10,hAPP(c_List_Ofilter(X10,X42),X200)) = hAPP(c_List_Ofilter(X10,X42),c_List_Oremdups(X10,X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__filter) ).

fof(fact_rtrancl__converse,axiom,
    ! [X110,X10] : c_Transitive__Closure_Ortrancl(X10,hAPP(c_Relation_Oconverse(X10,X10),X110)) = hAPP(c_Relation_Oconverse(X10,X10),c_Transitive__Closure_Ortrancl(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__converse) ).

fof(fact_Range__def,axiom,
    ! [X110,X10,X8] : hAPP(c_Relation_ORange(X8,X10),X110) = hAPP(c_Relation_ODomain(X10,X8),hAPP(c_Relation_Oconverse(X8,X10),X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__def) ).

fof(fact_exists__code,axiom,
    ! [X42,X10] :
      ( class_Enum_Oenum(X10)
     => ( ? [X136] : hBOOL(hAPP(X42,X136))
      <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X10),X42)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists__code) ).

fof(fact_enum__ex,axiom,
    ! [X42,X10] :
      ( class_Enum_Oenum(X10)
     => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X10),X42))
      <=> ? [X136] : hBOOL(hAPP(X42,X136)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex) ).

fof(fact_list__update__nonempty,axiom,
    ! [X11,X32,X200,X10] :
      ( hAPP(hAPP(c_List_Olist__update(X10,X200),X32),X11) = c_List_Olist_ONil(X10)
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__nonempty) ).

fof(fact_map__is__Nil__conv,axiom,
    ! [X200,X2,X10,X8] :
      ( hAPP(hAPP(c_List_Omap(X8,X10),X2),X200) = c_List_Olist_ONil(X10)
    <=> X200 = c_List_Olist_ONil(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__is__Nil__conv) ).

fof(fact_Nil__is__map__conv,axiom,
    ! [X200,X2,X8,X10] :
      ( c_List_Olist_ONil(X10) = hAPP(hAPP(c_List_Omap(X8,X10),X2),X200)
    <=> X200 = c_List_Olist_ONil(X8) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__map__conv) ).

fof(fact_diffs0__imp__equal,axiom,
    ! [X25,X24] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),X24) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => X24 = X25 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_setsum_Oempty,axiom,
    ! [X1,X8,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X1),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum_Oempty) ).

fof(fact_setsum__empty,axiom,
    ! [X2,X8,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,X10),X2),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__empty) ).

fof(fact_setprod__empty,axiom,
    ! [X2,X8,X10] :
      ( class_Groups_Ocomm__monoid__mult(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),X2),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod__empty) ).

fof(fact_setprod_Oempty,axiom,
    ! [X1,X8,X10] :
      ( class_Groups_Ocomm__monoid__mult(X10)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X8,X10),X1),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setprod_Oempty) ).

fof(fact_gr__implies__not0,axiom,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).

fof(fact_finite__UNIV,axiom,
    ! [X10] :
      ( class_Finite__Set_Ofinite(X10)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__UNIV) ).

fof(fact_divide__eq__eq,axiom,
    ! [X13,X6,X14,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6) = X13
      <=> ( ( X6 != c_Groups_Ozero__class_Ozero(X10)
           => X14 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6) )
          & ( X6 = c_Groups_Ozero__class_Ozero(X10)
           => X13 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_eq__divide__eq,axiom,
    ! [X6,X14,X13,X10] :
      ( class_Fields_Ofield__inverse__zero(X10)
     => ( X13 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)
      <=> ( ( X6 != c_Groups_Ozero__class_Ozero(X10)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6) = X14 )
          & ( X6 = c_Groups_Ozero__class_Ozero(X10)
           => X13 = c_Groups_Ozero__class_Ozero(X10) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__eq) ).

fof(fact_of__nat__Suc,axiom,
    ! [X24,X27] :
      ( class_Rings_Osemiring__1(X27)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Nat_OSuc,X24)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Oone__class_Oone(X27)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__Suc) ).

fof(fact_zero__less__Suc,axiom,
    ! [X25] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X25))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).

fof(fact_less__not__refl3,axiom,
    ! [X54,X55] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),X54))
     => X55 != X54 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).

fof(fact_less__not__refl2,axiom,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X24))
     => X24 != X25 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).

fof(fact_atLeastLessThan__singleton,axiom,
    ! [X31] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),hAPP(c_Nat_OSuc,X31)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X31),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,
    ! [X42,X200,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( c_List_Olinorder__class_Osorted(X10,X200)
       => c_List_Olinorder__class_Osorted(X10,c_List_OtakeWhile(X10,X42,X200)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_sorted__remove1,axiom,
    ! [X37,X202,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( c_List_Olinorder__class_Osorted(X27,X202)
       => c_List_Olinorder__class_Osorted(X27,c_List_Oremove1(X27,X37,X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__remove1) ).

fof(fact_mult__cancel2,axiom,
    ! [X30,X32,X31] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30),X32)
    <=> ( X31 = X30
        | X32 = 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,
    ! [X30,X31,X32] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)
    <=> ( X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X31 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).

fof(fact_mult__cancel1,axiom,
    ! [X30,X31,X32] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X31) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X32),X30)
    <=> ( X31 = X30
        | X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__cancel1) ).

fof(fact_hd__append,axiom,
    ! [X201,X27,X202] :
      ( ( X202 = c_List_Olist_ONil(X27)
       => hAPP(c_List_Ohd(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(c_List_Ohd(X27),X201) )
      & ( X202 != c_List_Olist_ONil(X27)
       => hAPP(c_List_Ohd(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(c_List_Ohd(X27),X202) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__append) ).

fof(fact_mult__sgn__abs,axiom,
    ! [X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Osgn__class_Osgn(X27,X26)),hAPP(c_Groups_Oabs__class_Oabs(X27),X26)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__sgn__abs) ).

fof(fact_zero__less__one,axiom,
    ! [X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),c_Groups_Oone__class_Oone(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).

fof(fact_Nats__0,axiom,
    ! [X10] :
      ( class_Rings_Osemiring__1(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Ozero__class_Ozero(X10)),c_Nat_Osemiring__1__class_ONats(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__0) ).

fof(fact_Ints__0,axiom,
    ! [X10] :
      ( class_Rings_Oring__1(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Ozero__class_Ozero(X10)),c_Int_Oring__1__class_OInts(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__0) ).

fof(fact_Nats__1,axiom,
    ! [X10] :
      ( class_Rings_Osemiring__1(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Oone__class_Oone(X10)),c_Nat_Osemiring__1__class_ONats(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__1) ).

fof(fact_Ints__1,axiom,
    ! [X10] :
      ( class_Rings_Oring__1(X10)
     => hBOOL(hAPP(hAPP(c_member(X10),c_Groups_Oone__class_Oone(X10)),c_Int_Oring__1__class_OInts(X10))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__1) ).

fof(fact_zero__le__one,axiom,
    ! [X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Ozero__class_Ozero(X27)),c_Groups_Oone__class_Oone(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).

fof(fact_divide__eq__imp,axiom,
    ! [X37,X36,X35,X27] :
      ( class_Rings_Odivision__ring(X27)
     => ( X35 != c_Groups_Ozero__class_Ozero(X27)
       => ( X36 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35) = X37 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__eq__imp) ).

fof(fact_nonzero__divide__eq__eq,axiom,
    ! [X13,X14,X6,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X6 != c_Groups_Ozero__class_Ozero(X10)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6) = X13
        <=> X14 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__divide__eq__eq) ).

fof(fact_nonzero__eq__divide__eq,axiom,
    ! [X14,X13,X6,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X6 != c_Groups_Ozero__class_Ozero(X10)
       => ( X13 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)
        <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6) = X14 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__eq__divide__eq) ).

fof(fact_eq__divide__imp,axiom,
    ! [X36,X37,X35,X27] :
      ( class_Rings_Odivision__ring(X27)
     => ( X35 != c_Groups_Ozero__class_Ozero(X27)
       => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X35) = X36
         => X37 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X36),X35) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__divide__imp) ).

fof(fact_diff__minus__eq__add,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__minus__eq__add) ).

fof(fact_diff__eq,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X26),X34) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__eq) ).

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [X34,X26,X27] :
      ( class_Rings_Ocomm__ring__1(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X26),X34) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_diff__def,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__def) ).

fof(fact_ab__diff__minus,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Oab__group__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X36) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X36)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__diff__minus) ).

fof(fact_mult__minus1,axiom,
    ! [X38,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin)),X38) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),X38) ),
    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,
    ! [X201,X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => hAPP(c_List_Ohd(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = hAPP(c_List_Ohd(X27),X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__append2) ).

fof(fact_nat__add__right__cancel,axiom,
    ! [X30,X32,X31] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X32) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),X32)
    <=> X31 = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).

fof(fact_nat__add__left__cancel,axiom,
    ! [X30,X31,X32] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X31) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32),X30)
    <=> X31 = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).

fof(fact_singleton__conv2,axiom,
    ! [X13,X10] : hAPP(c_Set_OCollect(X10),hAPP(c_fequal,X13)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv2) ).

fof(fact_sorted__drop,axiom,
    ! [X25,X202,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( c_List_Olinorder__class_Osorted(X27,X202)
       => c_List_Olinorder__class_Osorted(X27,hAPP(hAPP(c_List_Odrop(X27),X25),X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__drop) ).

fof(fact_sorted__take,axiom,
    ! [X25,X202,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( c_List_Olinorder__class_Osorted(X27,X202)
       => c_List_Olinorder__class_Osorted(X27,hAPP(hAPP(c_List_Otake(X27),X25),X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__take) ).

fof(fact_finite_Oequations_I1_J,axiom,
    ! [X10] : hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).

fof(fact_finite_OemptyI,axiom,
    ! [X10] : hBOOL(hAPP(c_Finite__Set_Ofinite(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OemptyI) ).

fof(fact_Pow__not__empty,axiom,
    ! [X12,X10] : hAPP(c_Set_OPow(X10),X12) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__not__empty) ).

fof(fact_Compl__UNIV__eq,axiom,
    ! [X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).

fof(fact_Compl__empty__eq,axiom,
    ! [X10] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).

fof(fact_Pow__UNIV,axiom,
    ! [X10] : hAPP(c_Set_OPow(X10),c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__UNIV) ).

fof(fact_Id__on__empty,axiom,
    ! [X10] : c_Relation_OId__on(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Id__on__empty) ).

fof(fact_Int__absorb,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X12) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).

fof(fact_Un__absorb,axiom,
    ! [X12,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X12) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb) ).

fof(fact_wf__in__rel,axiom,
    ! [X29,X10] :
      ( c_Wellfounded_Owf(X10,X29)
     => c_Wellfounded_OwfP(X10,c_FunDef_Oin__rel(X10,X10,X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__in__rel) ).

fof(fact_wf__mlex,axiom,
    ! [X2,X29,X10] :
      ( c_Wellfounded_Owf(X10,X29)
     => c_Wellfounded_Owf(X10,c_Wellfounded_Omlex__prod(X10,X2,X29)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__mlex) ).

fof(fact_Inf__fin_OF__eq,axiom,
    ! [X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olattice__class_OInf__fin(X10,X12) = hAPP(c_Finite__Set_Ofold1(X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_OF__eq) ).

fof(fact_Sup__fin_OF__eq,axiom,
    ! [X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olattice__class_OSup__fin(X10,X12) = hAPP(c_Finite__Set_Ofold1(X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_OF__eq) ).

fof(fact_Max_OF__eq,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olinorder__class_OMax(X10,X12) = hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omax(X10)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_OF__eq) ).

fof(fact_Min_OF__eq,axiom,
    ! [X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Big__Operators_Olinorder__class_OMin(X10,X12) = hAPP(c_Finite__Set_Ofold1(X10,c_Orderings_Oord__class_Omin(X10)),X12) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_OF__eq) ).

fof(fact_lessI,axiom,
    ! [X25] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_OSuc,X25))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).

fof(fact_length__replicate,axiom,
    ! [X26,X25,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),c_List_Oreplicate(X27,X25,X26)) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__replicate) ).

fof(fact_compl__inf__bot,axiom,
    ! [X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)),X26) = c_Orderings_Obot__class_Obot(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__inf__bot) ).

fof(fact_compl__sup__top,axiom,
    ! [X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)),X26) = c_Orderings_Otop__class_Otop(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__sup__top) ).

fof(fact_left__minus,axiom,
    ! [X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).

fof(fact_ab__left__minus,axiom,
    ! [X37,X27] :
      ( class_Groups_Oab__group__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)),X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).

fof(fact_last__appendL,axiom,
    ! [X202,X27,X201] :
      ( X201 = c_List_Olist_ONil(X27)
     => c_List_Olast(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = c_List_Olast(X27,X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendL) ).

fof(fact_last__append,axiom,
    ! [X202,X27,X201] :
      ( ( X201 = c_List_Olist_ONil(X27)
       => c_List_Olast(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = c_List_Olast(X27,X202) )
      & ( X201 != c_List_Olist_ONil(X27)
       => c_List_Olast(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = c_List_Olast(X27,X201) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__append) ).

fof(fact_diff__add__0,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24)) = 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,
    ! [X30,X83,X10] : c_List_Osublist(X10,X83,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30)) = hAPP(hAPP(c_List_Otake(X10),X30),X83),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__upt__eq__take) ).

fof(fact_one__dvd,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),c_Groups_Oone__class_Oone(X27)),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).

fof(fact_bot__least,axiom,
    ! [X26,X27] :
      ( class_Orderings_Obot(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Orderings_Obot__class_Obot(X27)),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__least) ).

fof(fact_divmod__int__correct,axiom,
    ! [X37,X36] :
      ( X36 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),c_Divides_Odivmod__int(X37,X36))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__int__correct) ).

fof(fact_pdivmod__posDivAlg,axiom,
    ! [X33,X45] :
      ( ( X45 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(X33,X45) = 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),X33)) )
      & ( X45 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Opdivmod(X33,X45) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X33),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X45)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pdivmod__posDivAlg) ).

fof(fact_sorted__single,axiom,
    ! [X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => c_List_Olinorder__class_Osorted(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Olist_ONil(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__single) ).

fof(fact_last__appendR,axiom,
    ! [X202,X27,X201] :
      ( X201 != c_List_Olist_ONil(X27)
     => c_List_Olast(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)) = c_List_Olast(X27,X201) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__appendR) ).

fof(fact_last__ConsR,axiom,
    ! [X26,X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => c_List_Olast(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = c_List_Olast(X27,X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsR) ).

fof(fact_last_Osimps,axiom,
    ! [X26,X27,X202] :
      ( ( X202 = c_List_Olist_ONil(X27)
       => c_List_Olast(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = X26 )
      & ( X202 != c_List_Olist_ONil(X27)
       => c_List_Olast(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = c_List_Olast(X27,X202) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last_Osimps) ).

fof(fact_nat__gcd_Osimps,axiom,
    ! [X26,X34] :
      ( ( X34 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(X26,X34) = X26 )
      & ( X34 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => c_Nitpick_Onat__gcd(X26,X34) = c_Nitpick_Onat__gcd(X34,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26,X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).

fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [X77,X83] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X83)),X77) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X83,X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_card__atLeastLessThan,axiom,
    ! [X77,X83] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X83),X77)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X77),X83),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastLessThan) ).

fof(fact_rel__simps_I7_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I7_J) ).

fof(fact_rel__simps_I3_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).

fof(fact_rel__simps_I2_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I2_J) ).

fof(fact_rel__simps_I20_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).

fof(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,
    ! [X201,X10,X27] : hAPP(hAPP(c_List_Ozip(X27,X10),c_List_Olist_ONil(X27)),X201) = c_List_Olist_ONil(tc_prod(X27,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Nil) ).

fof(fact_top1I,axiom,
    ! [X11,X10] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),X11)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).

fof(fact_vimage__id,axiom,
    ! [X12,X10] : hAPP(c_Set_Ovimage(X10,X10,c_Fun_Oid(X10)),X12) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__id) ).

fof(fact_vimage__ident,axiom,
    ! [X65,X10] : hAPP(c_Set_Ovimage(X10,X10,c_COMBI(X10)),X65) = X65,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__ident) ).

fof(fact_image__id,axiom,
    ! [X65,X10] : hAPP(c_Set_Oimage(X10,X10,c_Fun_Oid(X10)),X65) = X65,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__id) ).

fof(fact_image__ident,axiom,
    ! [X65,X10] : hAPP(c_Set_Oimage(X10,X10,c_COMBI(X10)),X65) = X65,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).

fof(fact_refl__rtrancl,axiom,
    ! [X110,X10] : c_Relation_Orefl__on(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__rtrancl) ).

fof(fact_hd__replicate,axiom,
    ! [X26,X27,X25] :
      ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Ohd(X27),c_List_Oreplicate(X27,X25,X26)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__replicate) ).

fof(fact_Compl__greaterThan,axiom,
    ! [X32,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X32)) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__greaterThan) ).

fof(fact_Compl__atLeast,axiom,
    ! [X32,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X10),X32)) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__atLeast) ).

fof(fact_Compl__atMost,axiom,
    ! [X32,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X10),X32)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__atMost) ).

fof(fact_Compl__lessThan,axiom,
    ! [X32,X10] :
      ( class_Orderings_Olinorder(X10)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X10),X32)) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X32) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__lessThan) ).

fof(fact_Sup__fin__Sup,axiom,
    ! [X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OSup__fin(X10,X12) = c_Complete__Lattice_OSup__class_OSup(X10,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin__Sup) ).

fof(fact_Inf__fin__Inf,axiom,
    ! [X12,X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
         => c_Big__Operators_Olattice__class_OInf__fin(X10,X12) = c_Complete__Lattice_OInf__class_OInf(X10,X12) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin__Inf) ).

fof(fact_add__numeral__0,axiom,
    ! [X37,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OPls)),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).

fof(fact_add__is__1,axiom,
    ! [X30,X31] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( ( X31 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X30 = 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,
    ! [X30,X31] :
      ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30)
    <=> ( ( X31 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & X30 = 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,
    ! [X10,X194] :
      ( ? [X3] : hBOOL(hAPP(X194,X3))
     => hBOOL(hAPP(X194,c_Hilbert__Choice_OEps(X10,X194))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).

fof(fact_someI,axiom,
    ! [X10,X11,X42] :
      ( hBOOL(hAPP(X42,X11))
     => hBOOL(hAPP(X42,c_Hilbert__Choice_OEps(X10,X42))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).

fof(fact_someI__ex,axiom,
    ! [X10,X42] :
      ( ? [X136] : hBOOL(hAPP(X42,X136))
     => hBOOL(hAPP(X42,c_Hilbert__Choice_OEps(X10,X42))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).

fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
    ! [X77,X83] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X83),X77) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X83,X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).

fof(fact_square__eq__1__iff,axiom,
    ! [X11,X10] :
      ( class_Rings_Oring__1__no__zero__divisors(X10)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),X11) = c_Groups_Oone__class_Oone(X10)
      <=> ( X11 = c_Groups_Oone__class_Oone(X10)
          | X11 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),c_Groups_Oone__class_Oone(X10)) ) ) ),
    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,
    ! [X202,X10,X27] : hAPP(hAPP(c_List_Ozip(X27,X10),X202),c_List_Olist_ONil(X10)) = c_List_Olist_ONil(tc_prod(X27,X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).

fof(fact_folding__one__idem_Oidem,axiom,
    ! [X11,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one__idem(X10,X2,X9)
     => hAPP(hAPP(X2,X11),X11) = X11 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).

fof(fact_sublists_Osimps_I1_J,axiom,
    ! [X27] : c_Enum_Osublists(X27,c_List_Olist_ONil(X27)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X27)),c_List_Olist_ONil(X27)),c_List_Olist_ONil(tc_List_Olist(X27))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublists_Osimps_I1_J) ).

fof(fact_dvd__0__right,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),c_Groups_Ozero__class_Ozero(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).

fof(fact_top__greatest,axiom,
    ! [X26,X27] :
      ( class_Orderings_Otop(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),c_Orderings_Otop__class_Otop(X27))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).

fof(fact_last__ConsL,axiom,
    ! [X26,X27,X202] :
      ( X202 = c_List_Olist_ONil(X27)
     => c_List_Olast(X27,hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__ConsL) ).

fof(fact_last__replicate,axiom,
    ! [X26,X27,X25] :
      ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => c_List_Olast(X27,c_List_Oreplicate(X27,X25,X26)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__replicate) ).

fof(fact_nat__rec__0,axiom,
    ! [X49,X50,X10] : hAPP(c_Nat_Onat_Onat__rec(X10,X50,X49),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X50,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__0) ).

fof(fact_insert__not__empty,axiom,
    ! [X12,X13,X10] : hAPP(hAPP(c_Set_Oinsert(X10),X13),X12) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__not__empty) ).

fof(fact_empty__not__insert,axiom,
    ! [X12,X13,X10] : c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X10),X13),X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__not__insert) ).

fof(fact_int__Suc,axiom,
    ! [X24] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X24)) = 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),X24)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc) ).

fof(fact_diff__int__def__symmetric,axiom,
    ! [X92,X38] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X38),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X38),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).

fof(fact_diff__int__def,axiom,
    ! [X92,X38] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X38),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X38),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def) ).

fof(fact_tl_Osimps_I2_J,axiom,
    ! [X202,X26,X27] : hAPP(c_List_Otl(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).

fof(fact_hd_Osimps,axiom,
    ! [X202,X26,X27] : hAPP(c_List_Ohd(X27),hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202)) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd_Osimps) ).

fof(fact_power__eq__0__iff,axiom,
    ! [X30,X13,X10] :
      ( ( class_Power_Opower(X10)
        & class_Rings_Omult__zero(X10)
        & class_Rings_Ono__zero__divisors(X10)
        & class_Rings_Ozero__neq__one(X10) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(X10),X13),X30) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X13 = c_Groups_Ozero__class_Ozero(X10)
          & X30 != 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,
    ! [X34,X26] :
      ( c_Nat__Transfer_Ois__nat(X26)
     => ( c_Nat__Transfer_Ois__nat(X34)
       => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_divide__minus1,axiom,
    ! [X26,X27] :
      ( ( class_Fields_Ofield__inverse__zero(X27)
        & class_Int_Onumber__ring(X27) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__minus1) ).

fof(fact_wf__lexn,axiom,
    ! [X30,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(tc_List_Olist(X10),hAPP(c_List_Olexn(X10,X110),X30)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lexn) ).

fof(fact_list__update_Osimps_I1_J,axiom,
    ! [X68,X44,X27] : hAPP(hAPP(c_List_Olist__update(X27,c_List_Olist_ONil(X27)),X44),X68) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update_Osimps_I1_J) ).

fof(fact_list__update__code_I1_J,axiom,
    ! [X34,X44,X27] : hAPP(hAPP(c_List_Olist__update(X27,c_List_Olist_ONil(X27)),X44),X34) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).

fof(fact_power__Suc__0,axiom,
    ! [X25] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X25) = 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,
    ! [X26,X27] : c_List_Oinsert(X27,X26,c_List_Olist_ONil(X27)) = hAPP(hAPP(c_List_Olist_OCons(X27),X26),c_List_Olist_ONil(X27)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Nil) ).

fof(fact_finite__set,axiom,
    ! [X200,X10] : hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_List_Oset(X10),X200))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__set) ).

fof(fact_converse__converse,axiom,
    ! [X110,X10,X8] : hAPP(c_Relation_Oconverse(X8,X10),hAPP(c_Relation_Oconverse(X10,X8),X110)) = X110,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).

fof(fact_lessThan__Suc,axiom,
    ! [X32] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X32),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc) ).

fof(fact_Field__converse,axiom,
    ! [X110,X10] : hAPP(c_Relation_OField(X10),hAPP(c_Relation_Oconverse(X10,X10),X110)) = hAPP(c_Relation_OField(X10),X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__converse) ).

fof(fact_of__int__minus,axiom,
    ! [X38,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Int_Oring__1__class_Oof__int(X27),X38)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__minus) ).

fof(fact_number__of__minus,axiom,
    ! [X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [X92,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_nat__power__eq__Suc__0__iff,axiom,
    ! [X31,X11] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X11),X31) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X11 = 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,
    ! [X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( X26 = X34
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__refl) ).

fof(fact_minus__unique,axiom,
    ! [X36,X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X36) = c_Groups_Ozero__class_Ozero(X27)
       => hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37) = X36 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__unique) ).

fof(fact_eq__neg__iff__add__eq__0,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( X13 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)
      <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X14) = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).

fof(fact_length__remdups__card__conv,axiom,
    ! [X200,X10] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremdups(X10,X200)) = hAPP(c_Finite__Set_Ocard(X10),hAPP(c_List_Oset(X10),X200)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__remdups__card__conv) ).

fof(fact_UNIV__def,axiom,
    ! [X10] : c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fTrue)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).

fof(fact_empty__def,axiom,
    ! [X10] : c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),hAPP(c_COMBK(tc_HOL_Obool,X10),c_fFalse)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).

fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
    ! [X16,X11] :
      ( c_Nat__Transfer_Ois__nat(X11)
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X11,X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).

fof(fact_mult__minus1__right,axiom,
    ! [X38,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X38),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),X38) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__minus1__right) ).

fof(fact_mult__eq__1__iff,axiom,
    ! [X30,X31] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X30) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( X31 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        & X30 = 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,
    ! [X96] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X96)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X96)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).

fof(fact_dvd__refl,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X27),X37),X37)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).

fof(fact_order__refl,axiom,
    ! [X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X26)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).

fof(fact_card__atLeastZeroLessThan__int,axiom,
    ! [X77] : 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)),X77)) = hAPP(c_Int_Onat,X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).

fof(fact_zadd__zminus__inverse2,axiom,
    ! [X38] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)),X38) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).

fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [X77,X83] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X83),hAPP(c_Nat_OSuc,X77)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X83,X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_mod__int__def,axiom,
    ! [X36,X37] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X36) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X37,X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__int__def) ).

fof(fact_inf_Ocommute,axiom,
    ! [X36,X37,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Ocommute) ).

fof(fact_inf__commute,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__commute) ).

fof(fact_inf__sup__aci_I1_J,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X34) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X34),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).

fof(fact_inf__sup__aci_I5_J,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).

fof(fact_sup_Ocommute,axiom,
    ! [X36,X37,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Ocommute) ).

fof(fact_sup__commute,axiom,
    ! [X34,X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X34) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X34),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__commute) ).

fof(fact_min__max_Osup_Ocommute,axiom,
    ! [X36,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Ocommute) ).

fof(fact_min__max_Osup__commute,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X34) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X34),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup__commute) ).

fof(fact_min__max_Oinf__commute,axiom,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X34) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X34),X26) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf__commute) ).

fof(fact_min__max_Oinf_Ocommute,axiom,
    ! [X36,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Ocommute) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X36),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
    ! [X35,X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),X35) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X35),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(fact_nat__zminus__int,axiom,
    ! [X25] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zminus__int) ).

fof(fact_gr0I,axiom,
    ! [X25] :
      ( X25 != 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)),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).

fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [X34,X26] :
      ( c_Nat__Transfer_Ois__nat(X26)
     => ( c_Nat__Transfer_Ois__nat(X34)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
    ! [X34,X26] :
      ( c_Nat__Transfer_Ois__nat(X26)
     => ( c_Nat__Transfer_Ois__nat(X34)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
    ! [X34,X26] :
      ( c_Nat__Transfer_Ois__nat(X26)
     => ( c_Nat__Transfer_Ois__nat(X34)
       => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X26),X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).

fof(fact_negative__eq__positive,axiom,
    ! [X31,X30] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31)
    <=> ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X31 = 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,
    ! [X25] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).

fof(fact_le0,axiom,
    ! [X25] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).

fof(fact_total__on__empty,axiom,
    ! [X110,X10] : c_Relation_Ototal__on(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__empty) ).

fof(fact_mult__eq__0__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Rings_Oring__no__zero__divisors(X10)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X14) = c_Groups_Ozero__class_Ozero(X10)
      <=> ( X13 = c_Groups_Ozero__class_Ozero(X10)
          | X14 = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).

fof(fact_no__zero__divisors,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Ono__zero__divisors(X27)
     => ( X37 != c_Groups_Ozero__class_Ozero(X27)
       => ( X36 != c_Groups_Ozero__class_Ozero(X27)
         => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36) != c_Groups_Ozero__class_Ozero(X27) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_no__zero__divisors) ).

fof(fact_divisors__zero,axiom,
    ! [X36,X37,X27] :
      ( class_Rings_Ono__zero__divisors(X27)
     => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X36) = c_Groups_Ozero__class_Ozero(X27)
       => ( X37 = c_Groups_Ozero__class_Ozero(X27)
          | X36 = c_Groups_Ozero__class_Ozero(X27) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divisors__zero) ).

fof(fact_posDivAlg__0,axiom,
    ! [X36] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36) = 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,
    ! [X36,X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X36) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X37,X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__int__def) ).

fof(fact_power__0__Suc,axiom,
    ! [X25,X27] :
      ( ( class_Power_Opower(X27)
        & class_Rings_Osemiring__0(X27) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),c_Groups_Ozero__class_Ozero(X27)),hAPP(c_Nat_OSuc,X25)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__Suc) ).

fof(fact_divide__Numeral0,axiom,
    ! [X26,X27] :
      ( ( class_Fields_Ofield__inverse__zero(X27)
        & class_Int_Onumber__ring(X27) )
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X26),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__Numeral0) ).

fof(fact_abs__sgn,axiom,
    ! [X33,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),X33) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X33),c_Groups_Osgn__class_Osgn(X27,X33)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__sgn) ).

fof(fact_lists__UNIV,axiom,
    ! [X10] : c_List_Olists(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lists__UNIV) ).

fof(fact_map__ident,axiom,
    ! [X200,X10] : hAPP(hAPP(c_List_Omap(X10,X10),c_COMBI(X10)),X200) = X200,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map__ident) ).

fof(fact_accp__wfPD,axiom,
    ! [X11,X110,X10] :
      ( c_Wellfounded_OwfP(X10,X110)
     => hBOOL(hAPP(c_Wellfounded_Oaccp(X10,X110),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__wfPD) ).

fof(fact_reflpE,axiom,
    ! [X11,X110,X10] :
      ( c_Predicate_Oreflp(X10,X110)
     => hBOOL(hAPP(hAPP(X110,X11),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).

fof(fact_equivp__reflp,axiom,
    ! [X11,X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => hBOOL(hAPP(hAPP(X29,X11),X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).

fof(fact_sublist__empty,axiom,
    ! [X200,X10] : c_List_Osublist(X10,X200,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__empty) ).

fof(fact_right__inverse__eq,axiom,
    ! [X13,X14,X10] :
      ( class_Rings_Odivision__ring(X10)
     => ( X14 != c_Groups_Ozero__class_Ozero(X10)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X13),X14) = c_Groups_Oone__class_Oone(X10)
        <=> X13 = X14 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_length__rev,axiom,
    ! [X202,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(c_List_Orev(X27),X202)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rev) ).

fof(fact_length__rotate1,axiom,
    ! [X202,X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),hAPP(c_List_Orotate1(X27),X202)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate1) ).

fof(fact_exE__some,axiom,
    ! [X10,X6,X42] :
      ( ? [X136] : hBOOL(hAPP(X42,X136))
     => ( X6 = c_Hilbert__Choice_OEps(X10,X42)
       => hBOOL(hAPP(X42,X6)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).

fof(fact_funpow_Osimps_I1_J,axiom,
    ! [X2,X10] : hAPP(hAPP(c_Nat_Ocompow(X10,X10),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_Fun_Oid(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).

fof(fact_map_Osimps_I1_J,axiom,
    ! [X2,X10,X8] : hAPP(hAPP(c_List_Omap(X8,X10),X2),c_List_Olist_ONil(X8)) = c_List_Olist_ONil(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).

fof(fact_inf__compl__bot,axiom,
    ! [X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)) = c_Orderings_Obot__class_Obot(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__compl__bot) ).

fof(fact_sup__compl__top,axiom,
    ! [X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)) = c_Orderings_Otop__class_Otop(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__compl__top) ).

fof(fact_right__minus,axiom,
    ! [X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
    ! [X25,X26] :
      ( c_Nat__Transfer_Ois__nat(X26)
     => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X26),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).

fof(fact_zmult__eq__1__iff,axiom,
    ! [X30,X31] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X30) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    <=> ( ( X31 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & X30 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | ( X31 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & X30 = 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,
    ! [X16,X11,X10] :
      ( class_Lattices_Obounded__lattice__top(X10)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),X16) = c_Orderings_Otop__class_Otop(X10)
      <=> ( X11 = c_Orderings_Otop__class_Otop(X10)
          & X16 = c_Orderings_Otop__class_Otop(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__eq__top__iff) ).

fof(fact_sup__eq__bot__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Lattices_Obounded__lattice__bot(X10)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),X16) = c_Orderings_Obot__class_Obot(X10)
      <=> ( X11 = c_Orderings_Obot__class_Obot(X10)
          & X16 = c_Orderings_Obot__class_Obot(X10) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).

fof(fact_field__power__not__zero,axiom,
    ! [X25,X37,X27] :
      ( class_Rings_Oring__1__no__zero__divisors(X27)
     => ( X37 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),X25) != c_Groups_Ozero__class_Ozero(X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_field__power__not__zero) ).

fof(fact_double__eq__0__iff,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X13) = c_Groups_Ozero__class_Ozero(X10)
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__eq__0__iff) ).

fof(fact_double__zero__sym,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( c_Groups_Ozero__class_Ozero(X10) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X13),X13)
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).

fof(fact_finite__atMost,axiom,
    ! [X32] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X32))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atMost) ).

fof(fact_finite__lessThan,axiom,
    ! [X32] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X32))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lessThan) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [X92] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_right__minus__eq,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14) = c_Groups_Ozero__class_Ozero(X10)
      <=> X13 = X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus__eq) ).

fof(fact_eq__iff__diff__eq__0,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Oab__group__add(X10)
     => ( X13 = X14
      <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),X13),X14) = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).

fof(fact_dvd_Oeq__refl,axiom,
    ! [X34,X26] :
      ( X26 = X34
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oeq__refl) ).

fof(fact_eq__imp__le,axiom,
    ! [X25,X24] :
      ( X24 = X25
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).

fof(fact_take__eq__Nil,axiom,
    ! [X200,X30,X10] :
      ( hAPP(hAPP(c_List_Otake(X10),X30),X200) = c_List_Olist_ONil(X10)
    <=> ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X200 = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__eq__Nil) ).

fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
    ! [X25,X24] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X24),X25) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => ( X24 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X24 = 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,
    ! [X13,X14,X10] :
      ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X10)
     => ( X14 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),X14),X13)
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).

fof(fact_replicate__empty,axiom,
    ! [X11,X30,X10] :
      ( c_List_Oreplicate(X10,X30,X11) = c_List_Olist_ONil(X10)
    <=> X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__empty) ).

fof(fact_empty__replicate,axiom,
    ! [X11,X30,X10] :
      ( c_List_Olist_ONil(X10) = c_List_Oreplicate(X10,X30,X11)
    <=> X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__replicate) ).

fof(fact_diff__Suc__1,axiom,
    ! [X25] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).

fof(fact_set__upto,axiom,
    ! [X60,X61] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X61,X60)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X61,X60),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__upto) ).

fof(fact_atLeastAtMost__upto,axiom,
    ! [X60,X61] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X61,X60) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X61,X60)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__upto) ).

fof(fact_add__numeral__0__right,axiom,
    ! [X37,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OPls)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_dvd_Oorder__refl,axiom,
    ! [X26] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X26)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(fact_zle__refl,axiom,
    ! [X92] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X92),X92)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).

fof(fact_le__refl,axiom,
    ! [X25] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X25),X25)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).

fof(fact_listsp_Oequations_I1_J,axiom,
    ! [X12,X10] : hBOOL(hAPP(c_List_Olistsp(X10,X12),c_List_Olist_ONil(X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_Oequations_I1_J) ).

fof(fact_listsp_ONil,axiom,
    ! [X12,X10] : hBOOL(hAPP(c_List_Olistsp(X10,X12),c_List_Olist_ONil(X10))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_ONil) ).

fof(fact_distinct__remdups,axiom,
    ! [X202,X27] : hBOOL(hAPP(c_List_Odistinct(X27),c_List_Oremdups(X27,X202))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remdups) ).

fof(fact_append__is__Nil__conv,axiom,
    ! [X199,X200,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X200),X199) = c_List_Olist_ONil(X10)
    <=> ( X200 = c_List_Olist_ONil(X10)
        & X199 = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).

fof(fact_Nil__is__append__conv,axiom,
    ! [X199,X200,X10] :
      ( c_List_Olist_ONil(X10) = hAPP(hAPP(c_List_Oappend(X10),X200),X199)
    <=> ( X200 = c_List_Olist_ONil(X10)
        & X199 = c_List_Olist_ONil(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__append__conv) ).

fof(fact_Domain__rtrancl,axiom,
    ! [X29,X10] : hAPP(c_Relation_ODomain(X10,X10),c_Transitive__Closure_Ortrancl(X10,X29)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).

fof(fact_Range__rtrancl,axiom,
    ! [X29,X10] : hAPP(c_Relation_ORange(X10,X10),c_Transitive__Closure_Ortrancl(X10,X29)) = c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__rtrancl) ).

fof(help_c__COMBK__1,axiom,
    ! [X280,X279,X10,X27] : hAPP(hAPP(c_COMBK(X27,X10),X279),X280) = X279,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).

fof(fact_lazy__sequence_Osimps_I3_J,axiom,
    ! [X259,X127,X27] : c_Lazy__Sequence_Olazy__sequence_OInsert(X27,X127,X259) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I3_J) ).

fof(fact_lazy__sequence_Osimps_I2_J,axiom,
    ! [X259,X127,X27] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X27) != c_Lazy__Sequence_Olazy__sequence_OInsert(X27,X127,X259),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I2_J) ).

fof(fact_zdiv__minus1__right,axiom,
    ! [X37] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).

fof(fact_zmult__commute,axiom,
    ! [X92,X38] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),X92) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X92),X38),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).

fof(fact_nat__mult__commute,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).

fof(fact_zadd__commute,axiom,
    ! [X92,X38] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X38),X92) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X92),X38),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).

fof(fact_nat__add__commute,axiom,
    ! [X25,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).

fof(fact_Nitpick_Ofrac__def,axiom,
    ! [X36,X37,X27] : hAPP(hAPP(c_Nitpick_Ofrac(X27),X37),X36) = c_Nitpick_OAbs__Frac(X27,c_Nitpick_Onorm__frac(X37,X36)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ofrac__def) ).

fof(fact_diff__0,axiom,
    ! [X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),c_Groups_Ozero__class_Ozero(X27)),X37) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).

fof(fact_append__self__conv2,axiom,
    ! [X199,X200,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X200),X199) = X199
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv2) ).

fof(fact_append__self__conv,axiom,
    ! [X199,X200,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X200),X199) = X200
    <=> X199 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv) ).

fof(fact_self__append__conv,axiom,
    ! [X199,X10,X200] :
      ( X200 = hAPP(hAPP(c_List_Oappend(X10),X200),X199)
    <=> X199 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv) ).

fof(fact_self__append__conv2,axiom,
    ! [X200,X10,X199] :
      ( X199 = hAPP(hAPP(c_List_Oappend(X10),X200),X199)
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_self__append__conv2) ).

fof(fact_power__0__left,axiom,
    ! [X25,X27] :
      ( ( class_Power_Opower(X27)
        & class_Rings_Osemiring__0(X27) )
     => ( ( X25 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(X27),c_Groups_Ozero__class_Ozero(X27)),X25) = c_Groups_Oone__class_Oone(X27) )
        & ( X25 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(X27),c_Groups_Ozero__class_Ozero(X27)),X25) = c_Groups_Ozero__class_Ozero(X27) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0__left) ).

fof(fact_list_Osimps_I3_J,axiom,
    ! [X214,X127,X27] : hAPP(hAPP(c_List_Olist_OCons(X27),X127),X214) != c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I3_J) ).

fof(fact_list_Osimps_I2_J,axiom,
    ! [X214,X127,X27] : c_List_Olist_ONil(X27) != hAPP(hAPP(c_List_Olist_OCons(X27),X127),X214),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).

fof(fact_distinct__upto,axiom,
    ! [X43,X44] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X44,X43))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upto) ).

fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [X110,X10] : c_List_Olistrel(X10,c_Transitive__Closure_Ortrancl(X10,X110)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X10),c_List_Olistrel1(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).

fof(fact_max__ext__wf,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(tc_fun(X10,tc_HOL_Obool),c_Wellfounded_Omax__ext(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__wf) ).

fof(fact_min__ext__wf,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(tc_fun(X10,tc_HOL_Obool),c_Wellfounded_Omin__ext(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__wf) ).

fof(fact_listsum__rev,axiom,
    ! [X202,X27] :
      ( class_Groups_Ocomm__monoid__add(X27)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X27),hAPP(c_List_Orev(X27),X202)) = hAPP(c_List_Omonoid__add__class_Olistsum(X27),X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__rev) ).

fof(fact_abs__idempotent,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)) = hAPP(c_Groups_Oabs__class_Oabs(X27),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).

fof(fact_abs__minus__cancel,axiom,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)) = hAPP(c_Groups_Oabs__class_Oabs(X27),X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).

fof(fact_abs__of__nat,axiom,
    ! [X25,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__of__nat) ).

fof(fact_UNIV__not__empty,axiom,
    ! [X10] : c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).

fof(fact_zmod__minus1__right,axiom,
    ! [X37] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,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,
    ! [X24] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,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,
    ! [X30,X31] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X30 = 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,
    ! [X202,X26,X27] : hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202) != X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).

fof(fact_not__Cons__self,axiom,
    ! [X26,X27,X202] : X202 != hAPP(hAPP(c_List_Olist_OCons(X27),X26),X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self) ).

fof(fact_fun__left__comm__idem__insert,axiom,
    ! [X10] : c_Finite__Set_Ofun__left__comm__idem(X10,tc_fun(X10,tc_HOL_Obool),c_Set_Oinsert(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).

fof(fact_top__apply,axiom,
    ! [X11,X8,X10] :
      ( class_Orderings_Otop(X10)
     => hAPP(c_Orderings_Otop__class_Otop(tc_fun(X8,X10)),X11) = c_Orderings_Otop__class_Otop(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).

fof(fact_bot__apply,axiom,
    ! [X11,X8,X10] :
      ( class_Orderings_Obot(X10)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X8,X10)),X11) = c_Orderings_Obot__class_Obot(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).

fof(fact_bot__fun__def,axiom,
    ! [X11,X8,X10] :
      ( class_Orderings_Obot(X10)
     => hAPP(c_Orderings_Obot__class_Obot(tc_fun(X8,X10)),X11) = c_Orderings_Obot__class_Obot(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__fun__def) ).

fof(fact_minus__code__numeral__code,axiom,
    ! [X24,X25] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X25),X24) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X25),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__code__numeral__code) ).

fof(fact_equivpI,axiom,
    ! [X29,X10] :
      ( c_Predicate_Oreflp(X10,X29)
     => ( c_Predicate_Osymp(X10,X29)
       => ( c_Predicate_Otransp(X10,X29)
         => c_Equiv__Relations_Oequivp(X10,X29) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivpI) ).

fof(fact_equivp__reflp__symp__transp,axiom,
    ! [X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
    <=> ( c_Predicate_Oreflp(X10,X29)
        & c_Predicate_Osymp(X10,X29)
        & c_Predicate_Otransp(X10,X29) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp__symp__transp) ).

fof(fact_sorted__tl,axiom,
    ! [X202,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( c_List_Olinorder__class_Osorted(X27,X202)
       => c_List_Olinorder__class_Osorted(X27,hAPP(c_List_Otl(X27),X202)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__tl) ).

fof(fact_remdups__id__iff__distinct,axiom,
    ! [X200,X10] :
      ( c_List_Oremdups(X10,X200) = X200
    <=> hBOOL(hAPP(c_List_Odistinct(X10),X200)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__id__iff__distinct) ).

fof(fact_distinct__remdups__id,axiom,
    ! [X202,X27] :
      ( hBOOL(hAPP(c_List_Odistinct(X27),X202))
     => c_List_Oremdups(X27,X202) = X202 ),
    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,
    ! [X25,X24] :
      ( X24 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X25)
     => ( X25 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X24 = 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,
    ! [X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => hAPP(c_List_Ohd(X27),X202) = hAPP(hAPP(c_List_Onth(X27),X202),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,
    ! [X41,X42] :
      ( hBOOL(X42)
      | hBOOL(hAPP(hAPP(c_fimplies,X42),X41)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).

fof(fact_single__valued__Id__on,axiom,
    ! [X12,X10] : c_Relation_Osingle__valued(X10,X10,c_Relation_OId__on(X10,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).

fof(fact_refl__on__Id__on,axiom,
    ! [X12,X10] : c_Relation_Orefl__on(X10,X12,c_Relation_OId__on(X10,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).

fof(fact_add__is__0,axiom,
    ! [X30,X31] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31),X30) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & X30 = 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,
    ! [X30,X31] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X30) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    <=> ( X31 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X30 = 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,
    ! [X30,X31] :
      ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X31),X30)
    <=> ( X31 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        & X30 = 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,
    ! [X16,X11,X10] :
      ( ( class_Int_Onumber__ring(X10)
        & class_Int_Oring__char__0(X10) )
     => ( hAPP(c_Int_Onumber__class_Onumber__of(X10),X11) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X16)
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of) ).

fof(fact_converse__Id__on,axiom,
    ! [X12,X10] : hAPP(c_Relation_Oconverse(X10,X10),c_Relation_OId__on(X10,X12)) = c_Relation_OId__on(X10,X12),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__Id__on) ).

fof(help_c__fequal__2,axiom,
    ! [X16,X11] :
      ( X11 != X16
      | hBOOL(hAPP(hAPP(c_fequal,X11),X16)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).

fof(fact_of__int__of__nat__eq,axiom,
    ! [X25,X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X25) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).

fof(fact_of__int__number__of__eq,axiom,
    ! [X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),X68) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__number__of__eq) ).

fof(fact_set__empty2,axiom,
    ! [X200,X10] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_List_Oset(X10),X200)
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__empty2) ).

fof(fact_set__empty,axiom,
    ! [X200,X10] :
      ( hAPP(c_List_Oset(X10),X200) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__empty) ).

fof(fact_sym__conv__converse__eq,axiom,
    ! [X110,X10] :
      ( c_Relation_Osym(X10,X110)
    <=> hAPP(c_Relation_Oconverse(X10,X10),X110) = X110 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__conv__converse__eq) ).

fof(fact_set__rev,axiom,
    ! [X200,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_Orev(X10),X200)) = hAPP(c_List_Oset(X10),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev) ).

fof(fact_set__rotate1,axiom,
    ! [X200,X10] : hAPP(c_List_Oset(X10),hAPP(c_List_Orotate1(X10),X200)) = hAPP(c_List_Oset(X10),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rotate1) ).

fof(fact_power__power__power,axiom,
    ! [X10] :
      ( class_Power_Opower(X10)
     => c_Power_Opower__class_Opower(X10) = c_Power_Opower_Opower(X10,c_Groups_Oone__class_Oone(X10),c_Groups_Otimes__class_Otimes(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).

fof(fact_add__eq__self__zero,axiom,
    ! [X25,X24] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X25) = X24
     => X25 = 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,
    ! [X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => hAPP(c_List_Ohd(X27),hAPP(c_List_Orev(X27),X202)) = c_List_Olast(X27,X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd__rev) ).

fof(fact_last__rev,axiom,
    ! [X27,X202] :
      ( X202 != c_List_Olist_ONil(X27)
     => c_List_Olast(X27,hAPP(c_List_Orev(X27),X202)) = hAPP(c_List_Ohd(X27),X202) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last__rev) ).

fof(fact_sorted__list__of__set__empty,axiom,
    ! [X10] :
      ( class_Orderings_Olinorder(X10)
     => c_List_Olinorder__class_Osorted__list__of__set(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__empty) ).

fof(fact_Sup__UNIV,axiom,
    ! [X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OSup__class_OSup(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__UNIV) ).

fof(fact_Sup__empty,axiom,
    ! [X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OSup__class_OSup(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__empty) ).

fof(fact_Inf__UNIV,axiom,
    ! [X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OInf__class_OInf(X10,c_Orderings_Otop__class_Otop(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__UNIV) ).

fof(fact_Inf__empty,axiom,
    ! [X10] :
      ( class_Complete__Lattice_Ocomplete__lattice(X10)
     => c_Complete__Lattice_OInf__class_OInf(X10,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__empty) ).

fof(fact_div__1,axiom,
    ! [X24] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X24,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).

fof(fact_Union__Pow__eq,axiom,
    ! [X12,X10] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),hAPP(c_Set_OPow(X10),X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).

fof(fact_inf__bot__left,axiom,
    ! [X26,X27] :
      ( class_Lattices_Obounded__lattice__bot(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),c_Orderings_Obot__class_Obot(X27)),X26) = c_Orderings_Obot__class_Obot(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__left) ).

fof(fact_sup__top__left,axiom,
    ! [X26,X27] :
      ( class_Lattices_Obounded__lattice__top(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),c_Orderings_Otop__class_Otop(X27)),X26) = c_Orderings_Otop__class_Otop(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__left) ).

fof(fact_divide__zero__left,axiom,
    ! [X37,X27] :
      ( class_Rings_Odivision__ring(X27)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),c_Groups_Ozero__class_Ozero(X27)),X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero__left) ).

fof(fact_div__0,axiom,
    ! [X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),c_Groups_Ozero__class_Ozero(X27)),X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).

fof(fact_power__one,axiom,
    ! [X25,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),c_Groups_Oone__class_Oone(X27)),X25) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Ozero__class_Ozero(X27)),X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).

fof(fact_mult__zero__left,axiom,
    ! [X37,X27] :
      ( class_Rings_Omult__zero(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Ozero__class_Ozero(X27)),X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).

fof(fact_sorted__butlast,axiom,
    ! [X202,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( X202 != c_List_Olist_ONil(X27)
       => ( c_List_Olinorder__class_Osorted(X27,X202)
         => c_List_Olinorder__class_Osorted(X27,c_List_Obutlast(X27,X202)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__butlast) ).

fof(fact_of__int__m1,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__m1) ).

fof(fact_card_Oempty,axiom,
    ! [X10] : hAPP(c_Finite__Set_Ocard(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,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,
    ! [X27] :
      ( ( class_Int_Onumber__ring(X27)
        & class_Rings_Olinordered__idom(X27) )
     => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__one) ).

fof(fact_atLeast0AtMost,axiom,
    ! [X30] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).

fof(fact_greaterThan__eq__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X11) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X10),X16)
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_greaterThan__eq__iff) ).

fof(fact_atLeast__eq__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hAPP(c_SetInterval_Oord__class_OatLeast(X10),X11) = hAPP(c_SetInterval_Oord__class_OatLeast(X10),X16)
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__eq__iff) ).

fof(fact_atMost__eq__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hAPP(c_SetInterval_Oord__class_OatMost(X10),X11) = hAPP(c_SetInterval_Oord__class_OatMost(X10),X16)
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__eq__iff) ).

fof(fact_lessThan__eq__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hAPP(c_SetInterval_Oord__class_OlessThan(X10),X11) = hAPP(c_SetInterval_Oord__class_OlessThan(X10),X16)
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__eq__iff) ).

fof(fact_of__int__eq__iff,axiom,
    ! [X19,X90,X10] :
      ( class_Int_Oring__char__0(X10)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(X10),X90) = hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)
      <=> X90 = X19 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__iff) ).

fof(fact_compl__eq__compl__iff,axiom,
    ! [X16,X11,X10] :
      ( class_Lattices_Oboolean__algebra(X10)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X11) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X16)
      <=> X11 = X16 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__eq__compl__iff) ).

fof(fact_neg__equal__iff__equal,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)
      <=> X13 = X14 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__iff__equal) ).

fof(fact_of__nat__eq__iff,axiom,
    ! [X30,X31,X10] :
      ( class_Nat_Osemiring__char__0(X10)
     => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X31) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X10),X30)
      <=> X31 = X30 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__eq__iff) ).

fof(fact_inf__top__left,axiom,
    ! [X26,X27] :
      ( class_Lattices_Obounded__lattice__top(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),c_Orderings_Otop__class_Otop(X27)),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__left) ).

fof(fact_sup__bot__left,axiom,
    ! [X26,X27] :
      ( class_Lattices_Obounded__lattice__bot(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),c_Orderings_Obot__class_Obot(X27)),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Oone__class_Oone(X27)),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

fof(fact_mult__1,axiom,
    ! [X37,X27] :
      ( class_Groups_Ocomm__monoid__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Oone__class_Oone(X27)),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).

fof(fact_mult__1__left,axiom,
    ! [X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),c_Groups_Oone__class_Oone(X27)),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Ozero__class_Ozero(X27)),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(fact_add__0,axiom,
    ! [X37,X27] :
      ( class_Groups_Ocomm__monoid__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Ozero__class_Ozero(X27)),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).

fof(fact_add__0__left,axiom,
    ! [X37,X27] :
      ( class_Groups_Omonoid__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),c_Groups_Ozero__class_Ozero(X27)),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).

fof(fact_divide__self__if,axiom,
    ! [X37,X27] :
      ( class_Rings_Odivision__ring__inverse__zero(X27)
     => ( ( X37 = c_Groups_Ozero__class_Ozero(X27)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X37) = c_Groups_Ozero__class_Ozero(X27) )
        & ( X37 != c_Groups_Ozero__class_Ozero(X27)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X37) = c_Groups_Oone__class_Oone(X27) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self__if) ).

fof(fact_mod__0,axiom,
    ! [X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,c_Groups_Ozero__class_Ozero(X27),X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).

fof(fact_mod__by__1,axiom,
    ! [X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,X37,c_Groups_Oone__class_Oone(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).

fof(fact_sorted__remdups,axiom,
    ! [X45,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( c_List_Olinorder__class_Osorted(X27,X45)
       => c_List_Olinorder__class_Osorted(X27,c_List_Oremdups(X27,X45)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__remdups) ).

fof(fact_inf__bot__right,axiom,
    ! [X26,X27] :
      ( class_Lattices_Obounded__lattice__bot(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),c_Orderings_Obot__class_Obot(X27)) = c_Orderings_Obot__class_Obot(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__right) ).

fof(fact_sup__top__right,axiom,
    ! [X26,X27] :
      ( class_Lattices_Obounded__lattice__top(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),c_Orderings_Otop__class_Otop(X27)) = c_Orderings_Otop__class_Otop(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__right) ).

fof(fact_divide__zero,axiom,
    ! [X37,X27] :
      ( class_Rings_Odivision__ring__inverse__zero(X27)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),c_Groups_Ozero__class_Ozero(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__zero) ).

fof(fact_div__by__0,axiom,
    ! [X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),c_Groups_Ozero__class_Ozero(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),c_Groups_Ozero__class_Ozero(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).

fof(fact_mult__zero__right,axiom,
    ! [X37,X27] :
      ( class_Rings_Omult__zero(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),c_Groups_Ozero__class_Ozero(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).

fof(fact_listrel__sym,axiom,
    ! [X110,X10] :
      ( c_Relation_Osym(X10,X110)
     => c_Relation_Osym(tc_List_Olist(X10),c_List_Olistrel(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__sym) ).

fof(fact_listrel__trans,axiom,
    ! [X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => c_Relation_Otrans(tc_List_Olist(X10),c_List_Olistrel(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__trans) ).

fof(fact_lexord__transI,axiom,
    ! [X110,X10] :
      ( c_Relation_Otrans(X10,X110)
     => c_Relation_Otrans(tc_List_Olist(X10),c_List_Olexord(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__transI) ).

fof(fact_wf__lex,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(tc_List_Olist(X10),c_List_Olex(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lex) ).

fof(fact_wf__lenlex,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Owf(tc_List_Olist(X10),c_List_Olenlex(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lenlex) ).

fof(fact_eq__Nil__appendI,axiom,
    ! [X27,X201,X202] :
      ( X202 = X201
     => X202 = hAPP(hAPP(c_List_Oappend(X27),c_List_Olist_ONil(X27)),X201) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__Nil__appendI) ).

fof(fact_divide__self,axiom,
    ! [X37,X27] :
      ( class_Rings_Odivision__ring(X27)
     => ( X37 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),X37) = c_Groups_Oone__class_Oone(X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__self) ).

fof(fact_div__self,axiom,
    ! [X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => ( X37 != c_Groups_Ozero__class_Ozero(X27)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),X37) = c_Groups_Oone__class_Oone(X27) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__self) ).

fof(fact_mod__by__0,axiom,
    ! [X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,X37,c_Groups_Ozero__class_Ozero(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).

fof(fact_fun__left__comm,axiom,
    ! [X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => c_Finite__Set_Ofun__left__comm(X10,X10,c_Groups_Otimes__class_Otimes(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm) ).

fof(fact_fun__left__comm__idem__inf,axiom,
    ! [X10] :
      ( class_Lattices_Osemilattice__inf(X10)
     => c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).

fof(fact_fun__left__comm__idem__sup,axiom,
    ! [X10] :
      ( class_Lattices_Osemilattice__sup(X10)
     => c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__sup) ).

fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
    ! [X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Orderings_Oord__class_Omax(X10)) ),
    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,
    ! [X10] :
      ( class_Orderings_Olinorder(X10)
     => c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Orderings_Oord__class_Omin(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).

fof(fact_fun__left__comm__idem,axiom,
    ! [X10] :
      ( class_Lattices_Oab__semigroup__idem__mult(X10)
     => c_Finite__Set_Ofun__left__comm__idem(X10,X10,c_Groups_Otimes__class_Otimes(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem) ).

fof(fact_Domain__Id__on,axiom,
    ! [X12,X10] : hAPP(c_Relation_ODomain(X10,X10),c_Relation_OId__on(X10,X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__Id__on) ).

fof(fact_Range__Id__on,axiom,
    ! [X12,X10] : hAPP(c_Relation_ORange(X10,X10),c_Relation_OId__on(X10,X12)) = X12,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__Id__on) ).

fof(fact_power__0,axiom,
    ! [X37,X27] :
      ( class_Power_Opower(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
    ! [X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).

fof(fact_inf__top__right,axiom,
    ! [X26,X27] :
      ( class_Lattices_Obounded__lattice__top(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),c_Orderings_Otop__class_Otop(X27)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__right) ).

fof(fact_sup__bot__right,axiom,
    ! [X26,X27] :
      ( class_Lattices_Obounded__lattice__bot(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),c_Orderings_Obot__class_Obot(X27)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__right) ).

fof(fact_divide__1,axiom,
    ! [X37,X27] :
      ( class_Rings_Odivision__ring(X27)
     => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X27),X37),c_Groups_Oone__class_Oone(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divide__1) ).

fof(fact_div__by__1,axiom,
    ! [X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(X27),X37),c_Groups_Oone__class_Oone(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),c_Groups_Oone__class_Oone(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).

fof(fact_mult_Ocomm__neutral,axiom,
    ! [X37,X27] :
      ( class_Groups_Ocomm__monoid__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),c_Groups_Oone__class_Oone(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).

fof(fact_mult__1__right,axiom,
    ! [X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),c_Groups_Oone__class_Oone(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
    ! [X37,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),c_Groups_Ozero__class_Ozero(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(fact_add_Ocomm__neutral,axiom,
    ! [X37,X27] :
      ( class_Groups_Ocomm__monoid__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),c_Groups_Ozero__class_Ozero(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).

fof(fact_add__0__right,axiom,
    ! [X37,X27] :
      ( class_Groups_Omonoid__add(X27)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),X37),c_Groups_Ozero__class_Ozero(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).

fof(fact_diff__0__right,axiom,
    ! [X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),c_Groups_Ozero__class_Ozero(X27)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).

fof(fact_double__compl,axiom,
    ! [X26,X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X26)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).

fof(fact_minus__minus,axiom,
    ! [X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).

fof(fact_abs__int__eq,axiom,
    ! [X24] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__int__eq) ).

fof(fact_of__int__int__eq,axiom,
    ! [X25] : hAPP(c_Int_Oring__1__class_Oof__int(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),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__int__eq) ).

fof(fact_set__remdups,axiom,
    ! [X200,X10] : hAPP(c_List_Oset(X10),c_List_Oremdups(X10,X200)) = hAPP(c_List_Oset(X10),X200),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remdups) ).

fof(fact_mod__self,axiom,
    ! [X37,X27] :
      ( class_Divides_Osemiring__div(X27)
     => c_Divides_Odiv__class_Omod(X27,X37,X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).

fof(fact_rev__is__rev__conv,axiom,
    ! [X199,X200,X10] :
      ( hAPP(c_List_Orev(X10),X200) = hAPP(c_List_Orev(X10),X199)
    <=> X200 = X199 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).

fof(fact_inc__shift__def,axiom,
    ! [X33,X68] :
      ( ( X68 = X33
       => c_Random_Oinc__shift(X68,X33) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( X68 != X33
       => c_Random_Oinc__shift(X68,X33) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X33),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,
    ! [X201,X27] : hAPP(hAPP(c_List_Oappend(X27),c_List_Olist_ONil(X27)),X201) = X201,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil) ).

fof(fact_Suc__eq__plus1__left,axiom,
    ! [X25] : hAPP(c_Nat_OSuc,X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).

fof(fact_sublist__nil,axiom,
    ! [X12,X10] : c_List_Osublist(X10,c_List_Olist_ONil(X10),X12) = c_List_Olist_ONil(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sublist__nil) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [X42,X10] : c_List_OtakeWhile(X10,X42,c_List_Olist_ONil(X10)) = c_List_Olist_ONil(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).

fof(fact_remove1_Osimps_I1_J,axiom,
    ! [X26,X27] : c_List_Oremove1(X27,X26,c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).

fof(fact_atLeastLessThan0,axiom,
    ! [X31] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),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,
    ! [X26,X27] :
      ( class_Rings_Ocomm__semiring__1(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).

fof(fact_power__one__right,axiom,
    ! [X37,X27] :
      ( class_Groups_Omonoid__mult(X27)
     => hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).

fof(fact_diff__self,axiom,
    ! [X37,X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(X27),X37),X37) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).

fof(fact_list_Osize_I1_J,axiom,
    ! [X95,X10] : c_List_Olist_Olist__size(X10,X95,c_List_Olist_ONil(X10)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).

fof(fact_sym__rtrancl,axiom,
    ! [X110,X10] :
      ( c_Relation_Osym(X10,X110)
     => c_Relation_Osym(X10,c_Transitive__Closure_Ortrancl(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__rtrancl) ).

fof(fact_acyclic__impl__antisym__rtrancl,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Oacyclic(X10,X110)
     => c_Relation_Oantisym(X10,c_Transitive__Closure_Ortrancl(X10,X110)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).

fof(fact_take__0,axiom,
    ! [X202,X27] : hAPP(hAPP(c_List_Otake(X27),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X202) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__0) ).

fof(fact_drop__Nil,axiom,
    ! [X25,X27] : hAPP(hAPP(c_List_Odrop(X27),X25),c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Nil) ).

fof(fact_take__Nil,axiom,
    ! [X25,X27] : hAPP(hAPP(c_List_Otake(X27),X25),c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Nil) ).

fof(fact_minus__equation__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13) = X14
      <=> hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14) = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__equation__iff) ).

fof(fact_equation__minus__iff,axiom,
    ! [X14,X13,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( X13 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X14)
      <=> X14 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equation__minus__iff) ).

fof(fact_nat__list__def,axiom,
    ! [X83] :
      ( c_List_Onat__list(X83)
    <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X83)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__list__def) ).

fof(fact_card__atMost,axiom,
    ! [X77] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X77)) = hAPP(c_Nat_OSuc,X77),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atMost) ).

fof(fact_nat__of__number,axiom,
    ! [X33] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X33)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__number) ).

fof(fact_nat__number__of,axiom,
    ! [X92] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of) ).

fof(fact_nat__number__of__def,axiom,
    ! [X68] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__def) ).

fof(fact_Suc__eq__plus1,axiom,
    ! [X25] : hAPP(c_Nat_OSuc,X25) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).

fof(fact_replicate__0,axiom,
    ! [X26,X27] : c_List_Oreplicate(X27,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X26) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_replicate__0) ).

fof(fact__02,axiom,
    ! [X253,X27] : c_Lazy__Sequence_Oappend(X27,c_Lazy__Sequence_Olazy__sequence_OEmpty(X27),X253) = X253,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__02) ).

fof(fact_splice_Osimps_I1_J,axiom,
    ! [X201,X27] : c_List_Osplice(X27,c_List_Olist_ONil(X27),X201) = X201,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).

fof(fact_splice__Nil2,axiom,
    ! [X202,X27] : c_List_Osplice(X27,X202,c_List_Olist_ONil(X27)) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).

fof(fact_sgn__sgn,axiom,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => c_Groups_Osgn__class_Osgn(X27,c_Groups_Osgn__class_Osgn(X27,X37)) = c_Groups_Osgn__class_Osgn(X27,X37) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).

fof(fact_list__all__simps_I2_J,axiom,
    ! [X42,X10] : c_List_Olist__all(X10,X42,c_List_Olist_ONil(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I2_J) ).

fof(fact_inf_Oidem,axiom,
    ! [X37,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).

fof(fact_inf__idem,axiom,
    ! [X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__idem) ).

fof(fact_Inf__fin_Oidem,axiom,
    ! [X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X26),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).

fof(fact_Sup__fin_Oidem,axiom,
    ! [X26,X27] :
      ( class_Lattices_Olattice(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).

fof(fact_sup_Oidem,axiom,
    ! [X37,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oidem) ).

fof(fact_sup__idem,axiom,
    ! [X26,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X26),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__idem) ).

fof(fact_Max_Oidem,axiom,
    ! [X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X26),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oidem) ).

fof(fact_min__max_Osup_Oidem,axiom,
    ! [X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Osup_Oidem) ).

fof(fact_Min_Oidem,axiom,
    ! [X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X26),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Oidem) ).

fof(fact_min__max_Oinf_Oidem,axiom,
    ! [X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oidem) ).

fof(fact_mult__idem,axiom,
    ! [X26,X27] :
      ( class_Lattices_Oab__semigroup__idem__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X26) = X26 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__idem) ).

fof(fact_times_Oidem,axiom,
    ! [X37,X27] :
      ( class_Lattices_Oab__semigroup__idem__mult(X27)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X37) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_times_Oidem) ).

fof(fact_length__0__conv,axiom,
    ! [X200,X10] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__0__conv) ).

fof(fact_mult__Min,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X33) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Min) ).

fof(fact_atLeast0LessThan,axiom,
    ! [X30] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X30),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).

fof(fact_New__DSequence_Opos__single__def,axiom,
    ! [X245,X26,X27] : hAPP(c_New__DSequence_Opos__single(X27,X26),X245) = hAPP(c_Lazy__Sequence_Osingle(X27),X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).

fof(fact_drop__0,axiom,
    ! [X202,X27] : hAPP(hAPP(c_List_Odrop(X27),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X202) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__0) ).

fof(fact_append__Nil2,axiom,
    ! [X202,X27] : hAPP(hAPP(c_List_Oappend(X27),X202),c_List_Olist_ONil(X27)) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil2) ).

fof(fact_rev__rev__ident,axiom,
    ! [X202,X27] : hAPP(c_List_Orev(X27),hAPP(c_List_Orev(X27),X202)) = X202,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).

fof(fact_small__lazy__int__def,axiom,
    ! [X58] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X58) = c_Lazy__Sequence_Osmall__lazy_H(X58,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X58)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__int__def) ).

fof(fact_zmod__zero,axiom,
    ! [X36] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X36) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).

fof(fact_neg__nat,axiom,
    ! [X38] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X38))
     => hAPP(c_Int_Onat,X38) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__nat) ).

fof(fact_atLeast__Suc__greaterThan,axiom,
    ! [X32] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X32),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).

fof(fact_lessThan__Suc__atMost,axiom,
    ! [X32] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X32)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X32),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).

fof(fact_less__eq__Suc__le__raw,axiom,
    ! [X30] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_DIVISION__BY__ZERO,axiom,
    ! [X37] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X37 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).

fof(fact_iszero__Numeral0,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => c_Int_Oiszero(X27,hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OPls)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).

fof(fact_List_Omap_Oid,axiom,
    ! [X10] : hAPP(c_List_Omap(X10,X10),c_Fun_Oid(X10)) = c_Fun_Oid(tc_List_Olist(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).

fof(fact_List_Omap_Oidentity,axiom,
    ! [X10] : hAPP(c_List_Omap(X10,X10),c_COMBI(X10)) = c_Fun_Oid(tc_List_Olist(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).

fof(fact_transfer__int__nat__relations_I1_J,axiom,
    ! [X16,X11] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X11) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X16)
    <=> X11 = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__relations_I1_J) ).

fof(fact_int__int__eq,axiom,
    ! [X30,X31] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)
    <=> X31 = X30 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__int__eq) ).

fof(fact_zmod__self,axiom,
    ! [X37] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X37,X37) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).

fof(fact_rev__swap,axiom,
    ! [X199,X200,X10] :
      ( hAPP(c_List_Orev(X10),X200) = X199
    <=> X200 = hAPP(c_List_Orev(X10),X199) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__swap) ).

fof(fact_min__0L,axiom,
    ! [X25] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__0L) ).

fof(fact_zdiv__zero,axiom,
    ! [X36] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).

fof(fact_mult__0,axiom,
    ! [X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25) = 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,
    ! [X25] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25) = 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,
    ! [X27] : hBOOL(hAPP(c_List_Odistinct(X27),c_List_Olist_ONil(X27))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).

fof(fact_New__DSequence_Oneg__single__def,axiom,
    ! [X245,X26,X27] : hAPP(c_New__DSequence_Oneg__single(X27,X26),X245) = c_Lazy__Sequence_Ohb__single(X27,X26),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).

fof(fact_remdups__remdups,axiom,
    ! [X202,X27] : c_List_Oremdups(X27,c_List_Oremdups(X27,X202)) = c_List_Oremdups(X27,X202),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__remdups) ).

fof(fact_rtrancl__idemp,axiom,
    ! [X110,X10] : c_Transitive__Closure_Ortrancl(X10,c_Transitive__Closure_Ortrancl(X10,X110)) = c_Transitive__Closure_Ortrancl(X10,X110),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).

fof(fact_List_Oset_Osimps_I1_J,axiom,
    ! [X10] : hAPP(c_List_Oset(X10),c_List_Olist_ONil(X10)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).

fof(fact_max__0L,axiom,
    ! [X25] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__0L) ).

fof(fact_zmult__1,axiom,
    ! [X38] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X38) = X38,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).

fof(fact_nat__mult__1,axiom,
    ! [X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).

fof(fact_zadd__0,axiom,
    ! [X38] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38) = X38,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0) ).

fof(fact_plus__nat_Oadd__0,axiom,
    ! [X25] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).

fof(fact_conversep__eq,axiom,
    ! [X10] : c_Predicate_Oconversep(X10,X10,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,
    ! [X37] :
      ( X37 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X37),X37) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).

fof(fact_arith__simps_I31_J,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).

fof(fact_number__of__Min,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Min) ).

fof(fact_min__0R,axiom,
    ! [X25] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X25),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,
    ! [X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),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,
    ! [X13,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( c_Groups_Ozero__class_Ozero(X10) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)
      <=> c_Groups_Ozero__class_Ozero(X10) = X13 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__0__equal__iff__equal) ).

fof(fact_abs__eq__0,axiom,
    ! [X13,X10] :
      ( class_Groups_Oordered__ab__group__add__abs(X10)
     => ( hAPP(c_Groups_Oabs__class_Oabs(X10),X13) = c_Groups_Ozero__class_Ozero(X10)
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).

fof(fact_neg__equal__0__iff__equal,axiom,
    ! [X13,X10] :
      ( class_Groups_Ogroup__add(X10)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13) = c_Groups_Ozero__class_Ozero(X10)
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).

fof(fact_max__0R,axiom,
    ! [X25] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__0R) ).

fof(fact_zmult__1__right,axiom,
    ! [X38] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X38),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X38,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).

fof(fact_nat__mult__1__right,axiom,
    ! [X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).

fof(fact_zadd__0__right,axiom,
    ! [X38] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X38),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X38,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__0__right) ).

fof(fact_Nat_Oadd__0__right,axiom,
    ! [X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_zminus__zminus,axiom,
    ! [X38] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X38)) = X38,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).

fof(fact_card__lessThan,axiom,
    ! [X77] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X77)) = X77,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__lessThan) ).

fof(fact_filter_Osimps_I1_J,axiom,
    ! [X42,X10] : hAPP(c_List_Ofilter(X10,X42),c_List_Olist_ONil(X10)) = c_List_Olist_ONil(X10),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).

fof(fact_finite,axiom,
    ! [X12,X10] :
      ( class_Finite__Set_Ofinite(X10)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).

fof(fact_finite__code,axiom,
    ! [X12,X10] :
      ( class_Finite__Set_Ofinite(X10)
     => hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__code) ).

fof(fact_of__int__eq__0__iff,axiom,
    ! [X19,X10] :
      ( class_Int_Oring__char__0(X10)
     => ( hAPP(c_Int_Oring__1__class_Oof__int(X10),X19) = c_Groups_Ozero__class_Ozero(X10)
      <=> X19 = 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,
    ! [X19,X10] :
      ( class_Int_Oring__char__0(X10)
     => ( c_Groups_Ozero__class_Ozero(X10) = hAPP(c_Int_Oring__1__class_Oof__int(X10),X19)
      <=> X19 = 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,
    ! [X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X24) = 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,
    ! [X95,X10] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X10,X95),c_Lazy__Sequence_Olazy__sequence_OEmpty(X10)) = 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,
    ! [X33,X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),X33) = hAPP(c_Int_Oring__1__class_Oof__int(X27),X33) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__eq) ).

fof(fact_neg__equal__zero,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13) = X13
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__zero) ).

fof(fact_equal__neg__zero,axiom,
    ! [X13,X10] :
      ( class_Groups_Olinordered__ab__group__add(X10)
     => ( X13 = hAPP(c_Groups_Ouminus__class_Ouminus(X10),X13)
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).

fof(fact_add__Pls__right,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X33),c_Int_OPls) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X33),c_Int_OPls) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_nat__int,axiom,
    ! [X25] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__int) ).

fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
    ! [X278,X277] :
      ( ( class_Lazy__Sequence_Osmall__lazy(X277)
        & class_Lazy__Sequence_Osmall__lazy(X278) )
     => class_Lazy__Sequence_Osmall__lazy(tc_prod(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Lazy__Sequence_Osmall__lazy) ).

fof(arity_prod__Enum_Oenum,axiom,
    ! [X278,X277] :
      ( ( class_Enum_Oenum(X277)
        & class_Enum_Oenum(X278) )
     => class_Enum_Oenum(tc_prod(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Enum_Oenum) ).

fof(arity_sum__Enum_Oenum,axiom,
    ! [X278,X277] :
      ( ( class_Enum_Oenum(X277)
        & class_Enum_Oenum(X278) )
     => class_Enum_Oenum(tc_sum(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Enum_Oenum) ).

fof(arity_fun__Enum_Oenum,axiom,
    ! [X278,X277] :
      ( ( class_Enum_Oenum(X277)
        & class_Enum_Oenum(X278) )
     => class_Enum_Oenum(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
    ! [X34,X26] :
      ( c_Nat__Transfer_Ois__nat(X26)
     => ( c_Nat__Transfer_Ois__nat(X34)
       => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X26,X34)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).

fof(arity_prod__Finite__Set_Ofinite,axiom,
    ! [X278,X277] :
      ( ( class_Finite__Set_Ofinite(X277)
        & class_Finite__Set_Ofinite(X278) )
     => class_Finite__Set_Ofinite(tc_prod(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).

fof(arity_sum__Finite__Set_Ofinite,axiom,
    ! [X278,X277] :
      ( ( class_Finite__Set_Ofinite(X277)
        & class_Finite__Set_Ofinite(X278) )
     => class_Finite__Set_Ofinite(tc_sum(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).

fof(arity_fun__Finite__Set_Ofinite,axiom,
    ! [X278,X277] :
      ( ( class_Finite__Set_Ofinite(X277)
        & class_Finite__Set_Ofinite(X278) )
     => class_Finite__Set_Ofinite(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).

fof(fact_add__Pls,axiom,
    ! [X33] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X33) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).

fof(fact_rev__is__Nil__conv,axiom,
    ! [X200,X10] :
      ( hAPP(c_List_Orev(X10),X200) = c_List_Olist_ONil(X10)
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).

fof(fact_rotate1__is__Nil__conv,axiom,
    ! [X200,X10] :
      ( hAPP(c_List_Orotate1(X10),X200) = c_List_Olist_ONil(X10)
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).

fof(fact_Nil__is__rev__conv,axiom,
    ! [X200,X10] :
      ( c_List_Olist_ONil(X10) = hAPP(c_List_Orev(X10),X200)
    <=> X200 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).

fof(fact_mult__Pls,axiom,
    ! [X92] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X92) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).

fof(fact_trans__finite__psubset,axiom,
    ! [X10] : c_Relation_Otrans(tc_fun(X10,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__finite__psubset) ).

fof(fact_wf__finite__psubset,axiom,
    ! [X10] : c_Wellfounded_Owf(tc_fun(X10,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X10)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__finite__psubset) ).

fof(fact_transpose_Osimps_I1_J,axiom,
    ! [X27] : c_List_Otranspose(X27,c_List_Olist_ONil(tc_List_Olist(X27))) = c_List_Olist_ONil(tc_List_Olist(X27)),
    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,
    ! [X16,X11] :
      ( hAPP(c_Code__Numeral_Onat__of,X11) = hAPP(c_Code__Numeral_Onat__of,X16)
    <=> X11 = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Onat__of__inject,axiom,
    ! [X83,X32] :
      ( hAPP(c_Code__Numeral_Onat__of,X32) = hAPP(c_Code__Numeral_Onat__of,X83)
    <=> X32 = X83 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).

fof(fact_Code__Numeral_Oof__nat__inject,axiom,
    ! [X31,X30] :
      ( hAPP(c_Code__Numeral_Oof__nat,X30) = hAPP(c_Code__Numeral_Oof__nat,X31)
    <=> X30 = X31 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).

fof(fact_Rep__Integ__inject,axiom,
    ! [X16,X11] :
      ( hAPP(c_Int_ORep__Integ,X11) = hAPP(c_Int_ORep__Integ,X16)
    <=> X11 = X16 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).

fof(fact_Suc__inject,axiom,
    ! [X34,X26] :
      ( hAPP(c_Nat_OSuc,X26) = hAPP(c_Nat_OSuc,X34)
     => X26 = X34 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).

fof(fact_nat_Oinject,axiom,
    ! [X39,X40] :
      ( hAPP(c_Nat_OSuc,X40) = hAPP(c_Nat_OSuc,X39)
    <=> X40 = X39 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).

fof(fact_sgn__0__0,axiom,
    ! [X13,X10] :
      ( class_Rings_Olinordered__idom(X10)
     => ( c_Groups_Osgn__class_Osgn(X10,X13) = c_Groups_Ozero__class_Ozero(X10)
      <=> X13 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).

fof(fact_lazy__sequence_Osize_I3_J,axiom,
    ! [X27] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X27)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X27)) = 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,
    ! [X27] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),c_List_Olist_ONil(X27)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).

fof(fact_sym__Id__on,axiom,
    ! [X12,X10] : c_Relation_Osym(X10,c_Relation_OId__on(X10,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Id__on) ).

fof(fact_antisym__Id__on,axiom,
    ! [X12,X10] : c_Relation_Oantisym(X10,c_Relation_OId__on(X10,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id__on) ).

fof(fact_trans__rtrancl,axiom,
    ! [X110,X10] : c_Relation_Otrans(X10,c_Transitive__Closure_Ortrancl(X10,X110)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__rtrancl) ).

fof(fact_trans__Id__on,axiom,
    ! [X12,X10] : c_Relation_Otrans(X10,c_Relation_OId__on(X10,X12)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__Id__on) ).

fof(fact_wf__measures,axiom,
    ! [X241,X10] : c_Wellfounded_Owf(X10,c_List_Omeasures(X10,X241)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measures) ).

fof(fact_sorted__upto,axiom,
    ! [X43,X44] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X44,X43)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__upto) ).

fof(fact_some__sym__eq__trivial,axiom,
    ! [X11,X10] : c_Hilbert__Choice_OEps(X10,hAPP(c_fequal,X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).

fof(fact_the__sym__eq__trivial,axiom,
    ! [X11,X10] : c_HOL_OThe(X10,hAPP(c_fequal,X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).

fof(fact_listsum__simps_I1_J,axiom,
    ! [X27] :
      ( class_Groups_Omonoid__add(X27)
     => hAPP(c_List_Omonoid__add__class_Olistsum(X27),c_List_Olist_ONil(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).

fof(fact_abs__zero,axiom,
    ! [X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),c_Groups_Ozero__class_Ozero(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).

fof(fact_abs__one,axiom,
    ! [X27] :
      ( class_Rings_Olinordered__idom(X27)
     => hAPP(c_Groups_Oabs__class_Oabs(X27),c_Groups_Oone__class_Oone(X27)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).

fof(fact_compl__top__eq,axiom,
    ! [X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Orderings_Otop__class_Otop(X27)) = c_Orderings_Obot__class_Obot(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__top__eq) ).

fof(fact_minus__zero,axiom,
    ! [X27] :
      ( class_Groups_Ogroup__add(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Ozero__class_Ozero(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).

fof(fact_compl__bot__eq,axiom,
    ! [X27] :
      ( class_Lattices_Oboolean__algebra(X27)
     => hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Orderings_Obot__class_Obot(X27)) = c_Orderings_Otop__class_Otop(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__bot__eq) ).

fof(arity_fun__Lattices_Obounded__lattice,axiom,
    ! [X277,X278] :
      ( class_Lattices_Obounded__lattice(X278)
     => class_Lattices_Obounded__lattice(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).

fof(arity_fun__Orderings_Otop,axiom,
    ! [X277,X278] :
      ( class_Orderings_Otop(X278)
     => class_Orderings_Otop(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).

fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
    ! [X277,X278] :
      ( class_Lattices_Obounded__lattice(X278)
     => class_Lattices_Obounded__lattice__top(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).

fof(arity_fun__Lattices_Osemilattice__inf,axiom,
    ! [X277,X278] :
      ( class_Lattices_Olattice(X278)
     => class_Lattices_Osemilattice__inf(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).

fof(arity_fun__Lattices_Odistrib__lattice,axiom,
    ! [X277,X278] :
      ( class_Lattices_Odistrib__lattice(X278)
     => class_Lattices_Odistrib__lattice(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).

fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
    ! [X277,X278] :
      ( class_Complete__Lattice_Ocomplete__lattice(X278)
     => class_Complete__Lattice_Ocomplete__lattice(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).

fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
    ! [X277,X278] :
      ( class_Lattices_Obounded__lattice(X278)
     => class_Lattices_Obounded__lattice__bot(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).

fof(arity_fun__Lattices_Olattice,axiom,
    ! [X277,X278] :
      ( class_Lattices_Olattice(X278)
     => class_Lattices_Olattice(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).

fof(arity_fun__Lattices_Osemilattice__sup,axiom,
    ! [X277,X278] :
      ( class_Lattices_Olattice(X278)
     => class_Lattices_Osemilattice__sup(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).

fof(arity_fun__Lattices_Oboolean__algebra,axiom,
    ! [X277,X278] :
      ( class_Lattices_Oboolean__algebra(X278)
     => class_Lattices_Oboolean__algebra(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).

fof(arity_fun__Groups_Ouminus,axiom,
    ! [X277,X278] :
      ( class_Groups_Ouminus(X278)
     => class_Groups_Ouminus(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).

fof(arity_fun__Groups_Ominus,axiom,
    ! [X277,X278] :
      ( class_Groups_Ominus(X278)
     => class_Groups_Ominus(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).

fof(arity_fun__Orderings_Oord,axiom,
    ! [X277,X278] :
      ( class_Orderings_Oord(X278)
     => class_Orderings_Oord(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).

fof(arity_fun__Orderings_Oorder,axiom,
    ! [X277,X278] :
      ( class_Orderings_Oorder(X278)
     => class_Orderings_Oorder(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).

fof(arity_fun__Orderings_Obot,axiom,
    ! [X277,X278] :
      ( class_Orderings_Obot(X278)
     => class_Orderings_Obot(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).

fof(arity_fun__Orderings_Opreorder,axiom,
    ! [X277,X278] :
      ( class_Orderings_Opreorder(X278)
     => class_Orderings_Opreorder(tc_fun(X277,X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).

fof(fact_equivp__implies__part__equivp,axiom,
    ! [X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => c_Equiv__Relations_Opart__equivp(X10,X29) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__implies__part__equivp) ).

fof(fact_wf__acyclic,axiom,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => c_Wellfounded_Oacyclic(X10,X110) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acyclic) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
    ! [X38] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X38)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).

fof(fact__04,axiom,
    ! [X27] : c_Lazy__Sequence_Oflat(X27,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X27))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__04) ).

fof(fact_nat__of__of__nat,axiom,
    ! [X25] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X25)) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).

fof(fact_of__nat__nat__of,axiom,
    ! [X33] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X33)) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__nat__of) ).

fof(fact_nat__of__inverse,axiom,
    ! [X26] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X26)) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__inverse) ).

fof(fact_Rep__Integ__inverse,axiom,
    ! [X11] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X11)) = X11,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).

fof(fact_iszero__def,axiom,
    ! [X19,X10] :
      ( class_Rings_Osemiring__1(X10)
     => ( c_Int_Oiszero(X10,X19)
      <=> X19 = c_Groups_Ozero__class_Ozero(X10) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__def) ).

fof(fact_int__eq__0__conv,axiom,
    ! [X30] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    <=> X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).

fof(fact_of__int__0,axiom,
    ! [X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0) ).

fof(fact_of__int__1,axiom,
    ! [X27] :
      ( class_Rings_Oring__1(X27)
     => hAPP(c_Int_Oring__1__class_Oof__int(X27),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__1) ).

fof(fact_of__nat__0,axiom,
    ! [X27] :
      ( class_Rings_Osemiring__1(X27)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).

fof(fact_of__nat__1,axiom,
    ! [X27] :
      ( class_Rings_Osemiring__1(X27)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).

fof(fact_int__number__of__def,axiom,
    ! [X92] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X92),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__number__of__def) ).

fof(fact_remdups__eq__nil__iff,axiom,
    ! [X11,X10] :
      ( c_List_Oremdups(X10,X11) = c_List_Olist_ONil(X10)
    <=> X11 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__eq__nil__iff) ).

fof(fact_remdups__eq__nil__right__iff,axiom,
    ! [X11,X10] :
      ( c_List_Olist_ONil(X10) = c_List_Oremdups(X10,X11)
    <=> X11 = c_List_Olist_ONil(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__eq__nil__right__iff) ).

fof(fact_sgn0,axiom,
    ! [X27] :
      ( class_Groups_Osgn__if(X27)
     => c_Groups_Osgn__class_Osgn(X27,c_Groups_Ozero__class_Ozero(X27)) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).

fof(fact_max__ord__max,axiom,
    ! [X10] :
      ( class_Orderings_Oord(X10)
     => c_Orderings_Oord__class_Omax(X10) = c_Orderings_Oord_Omax(X10,c_Orderings_Oord__class_Oless__eq(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ord__max) ).

fof(fact_min__ord__min,axiom,
    ! [X10] :
      ( class_Orderings_Oord(X10)
     => c_Orderings_Oord__class_Omin(X10) = c_Orderings_Oord_Omin(X10,c_Orderings_Oord__class_Oless__eq(X10)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ord__min) ).

fof(fact_rev_Osimps_I1_J,axiom,
    ! [X27] : hAPP(c_List_Orev(X27),c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).

fof(fact_tl_Osimps_I1_J,axiom,
    ! [X27] : hAPP(c_List_Otl(X27),c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).

fof(arity_prod__Nat_Osize,axiom,
    ! [X278,X277] : class_Nat_Osize(tc_prod(X277,X278)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Nat_Osize) ).

fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
    ! [X278,X277] : class_Nat_Osize(tc_Nitpick_Opair__box(X277,X278)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nitpick__Opair____box__Nat_Osize) ).

fof(arity_sum__Nat_Osize,axiom,
    ! [X278,X277] : class_Nat_Osize(tc_sum(X277,X278)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Nat_Osize) ).

fof(fact_number__of__Pls,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => c_Groups_Ozero__class_Ozero(X27) = hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OPls) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_sorted_Oequations_I1_J,axiom,
    ! [X27] :
      ( class_Orderings_Olinorder(X27)
     => c_List_Olinorder__class_Osorted(X27,c_List_Olist_ONil(X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Oequations_I1_J) ).

fof(fact_sorted_ONil,axiom,
    ! [X27] :
      ( class_Orderings_Olinorder(X27)
     => c_List_Olinorder__class_Osorted(X27,c_List_Olist_ONil(X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_ONil) ).

fof(fact_iszero__0,axiom,
    ! [X27] :
      ( class_Rings_Osemiring__1(X27)
     => c_Int_Oiszero(X27,c_Groups_Ozero__class_Ozero(X27)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__0) ).

fof(fact_New__DSequence_Opos__empty__def,axiom,
    ! [X245,X27] : hAPP(c_New__DSequence_Opos__empty(X27),X245) = c_Lazy__Sequence_Oempty(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).

fof(fact_remdups_Osimps_I1_J,axiom,
    ! [X27] : c_List_Oremdups(X27,c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I1_J) ).

fof(fact_butlast_Osimps_I1_J,axiom,
    ! [X27] : c_List_Obutlast(X27,c_List_Olist_ONil(X27)) = c_List_Olist_ONil(X27),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_butlast_Osimps_I1_J) ).

fof(fact_Suc__neq__Zero,axiom,
    ! [X24] : hAPP(c_Nat_OSuc,X24) != 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,
    ! [X71] : hAPP(c_Nat_OSuc,X71) != 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,
    ! [X24] : hAPP(c_Nat_OSuc,X24) != 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,
    ! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__neq__Suc) ).

fof(fact_nat_Osimps_I2_J,axiom,
    ! [X70] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X70),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).

fof(fact_Zero__not__Suc,axiom,
    ! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X24),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Zero__not__Suc) ).

fof(fact_inf__min,axiom,
    ! [X10] :
      ( ( class_Lattices_Osemilattice__inf(X10)
        & class_Orderings_Olinorder(X10) )
     => c_Lattices_Osemilattice__inf__class_Oinf(X10) = c_Orderings_Oord__class_Omin(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__min) ).

fof(fact_sup__max,axiom,
    ! [X10] :
      ( ( class_Lattices_Osemilattice__sup(X10)
        & class_Orderings_Olinorder(X10) )
     => c_Lattices_Osemilattice__sup__class_Osup(X10) = c_Orderings_Oord__class_Omax(X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__max) ).

fof(fact_Suc__n__not__n,axiom,
    ! [X25] : hAPP(c_Nat_OSuc,X25) != X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).

fof(fact_n__not__Suc__n,axiom,
    ! [X25] : X25 != hAPP(c_Nat_OSuc,X25),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).

fof(fact_id__apply,axiom,
    ! [X26,X27] : hAPP(c_Fun_Oid(X27),X26) = X26,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__apply) ).

fof(fact_id__def,axiom,
    ! [X190,X27] : hAPP(c_Fun_Oid(X27),X190) = X190,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__def) ).

fof(fact_Collect__def,axiom,
    ! [X42,X10] : hAPP(c_Set_OCollect(X10),X42) = X42,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).

fof(help_c__COMBI__1,axiom,
    ! [X279,X27] : hAPP(c_COMBI(X27),X279) = X279,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).

fof(fact_one__neq__zero,axiom,
    ! [X27] :
      ( class_Rings_Ozero__neq__one(X27)
     => c_Groups_Oone__class_Oone(X27) != c_Groups_Ozero__class_Ozero(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).

fof(fact_zero__neq__one,axiom,
    ! [X27] :
      ( class_Rings_Ozero__neq__one(X27)
     => c_Groups_Ozero__class_Ozero(X27) != c_Groups_Oone__class_Oone(X27) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__neq__one) ).

fof(fact_beyond__zero,axiom,
    ! [X33] : c_Quickcheck_Obeyond(X33,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_beyond__zero) ).

fof(fact_wf__int__ge__less__than2,axiom,
    ! [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_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_nat__size,axiom,
    ! [X25] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X25) = X25,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).

fof(fact_number__of__is__id,axiom,
    ! [X33] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X33) = X33,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).

fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
    ! [X278] :
      ( class_Lazy__Sequence_Osmall__lazy(X278)
     => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Lazy__Sequence_Osmall__lazy) ).

fof(arity_Option__Ooption__Enum_Oenum,axiom,
    ! [X278] :
      ( class_Enum_Oenum(X278)
     => class_Enum_Oenum(tc_Option_Ooption(X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).

fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
    ! [X278] :
      ( class_Finite__Set_Ofinite(X278)
     => class_Finite__Set_Ofinite(tc_Option_Ooption(X278)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).

fof(fact_identity__equivp,axiom,
    ! [X10] : c_Equiv__Relations_Oequivp(X10,c_fequal),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).

fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
    ! [X278] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X278)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).

fof(arity_List__Olist__Nat_Osize,axiom,
    ! [X278] : class_Nat_Osize(tc_List_Olist(X278)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Nat_Osize) ).

fof(arity_Option__Ooption__Nat_Osize,axiom,
    ! [X278] : class_Nat_Osize(tc_Option_Ooption(X278)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).

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(conj_3,hypothesis,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,v_n)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).

fof(conj_4,hypothesis,
    hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Nat_OSuc,v_n)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

fof(conj_2,hypothesis,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

fof(fact_wf__less,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less) ).

fof(fact_int__of__def,axiom,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__of__def) ).

fof(fact_number__of__code__numeral__def,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__code__numeral__def) ).

fof(fact_Integ__def,axiom,
    c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Int_Ointrel),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Integ__def) ).

fof(fact_transfer__morphism__int__nat,axiom,
    c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__morphism__int__nat) ).

fof(fact_inj__int,axiom,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__int) ).

fof(fact_INT__greaterThan__UNIV,axiom,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_INT__greaterThan__UNIV) ).

fof(fact_UN__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(conj_6,hypothesis,
    hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).

fof(fact_number__of2,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of2) ).

fof(fact_atMost__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atMost__0) ).

fof(fact_int__0__less__1,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__less__1) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).

fof(fact_bin__less__0__simps_I2_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).

fof(fact_rel__simps_I6_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).

fof(conj_5,hypothesis,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).

fof(fact_rel__simps_I24_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I24_J) ).

fof(fact_rel__simps_I23_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).

fof(fact_rel__simps_I19_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I19_J) ).

fof(fact_neg__number__of__Min,axiom,
    hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Min) ).

fof(fact_card__UNIV__unit,axiom,
    hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).

fof(fact_code__numeral__zero__minus__one,axiom,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__zero__minus__one) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
    c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).

fof(fact_eq__number__of__Pls__Min,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).

fof(fact_int__Suc0__eq__1,axiom,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).

fof(fact_atLeast__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__0) ).

fof(fact_lessThan__0,axiom,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__0) ).

fof(conj_0,hypothesis,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_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_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_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_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_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__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_nat__0,axiom,
    hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0) ).

fof(fact_zero__code__numeral__code,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__code) ).

fof(fact_zero__is__num__zero,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).

fof(fact_semiring__norm_I113_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).

fof(fact_zero__code__numeral__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__code__numeral__def) ).

fof(fact_transfer__nat__int__numerals_I1_J,axiom,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).

fof(fact_one__code__numeral__def,axiom,
    c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__code__numeral__def) ).

fof(fact_transfer__nat__int__numerals_I2_J,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).

fof(fact_One__nat__def,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).

fof(fact_minus__Pls,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls) ).

fof(fact_trans__less__than,axiom,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__than) ).

fof(fact_wf__pred__nat,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).

fof(fact_wf__less__than,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less__than) ).

fof(fact_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_inf__nat__def,axiom,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__nat__def) ).

fof(fact_sup__nat__def,axiom,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__nat__def) ).

fof(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__Rings_Ocomm__ring,axiom,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).

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fof(arity_Int__Oint__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).

fof(arity_Nat__Onat__Rings_Odvd,axiom,
    class_Rings_Odvd(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).

fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
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    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy) ).

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_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_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_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
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fof(arity_Com__Ocom__Nat_Osize,axiom,
    class_Nat_Osize(tc_Com_Ocom),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).

fof(arity_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_Product____Type__Ounit__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).

fof(arity_HOL__Obool__Enum_Oenum,axiom,
    class_Enum_Oenum(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
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fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).

fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).

fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
    class_Orderings_Owellorder(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).

fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
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fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
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    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
    class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).

fof(arity_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_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_Int__Oint__Groups_Oabs__if,axiom,
    class_Groups_Oabs__if(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).

fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
    class_Rings_Oordered__ring__abs(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).

fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
    class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).

fof(arity_Int__Oint__Groups_Osgn__if,axiom,
    class_Groups_Osgn__if(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).

fof(arity_Int__Oint__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_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_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_Int__Oint__Rings_Ocomm__ring__1,axiom,
    class_Rings_Ocomm__ring__1(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).

fof(arity_Int__Oint__Rings_Oidom,axiom,
    class_Rings_Oidom(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).

fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).

fof(arity_Int__Oint__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).

fof(arity_HOL__Obool__Groups_Ouminus,axiom,
    class_Groups_Ouminus(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).

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) ).

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    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).

fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
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    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) ).

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fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
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    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).

fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
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fof(arity_Int__Oint__Power_Opower,axiom,
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fof(arity_Nat__Onat__Power_Opower,axiom,
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fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
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fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
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fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
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fof(arity_Int__Oint__Int_Onumber__ring,axiom,
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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(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).

fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).

fof(help_c__fTrue__1,axiom,
    hBOOL(c_fTrue),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).

fof(fact_subtract__code__numeral__def,axiom,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subtract__code__numeral__def) ).

fof(fact_Code__Numeral_Oof__nat__code,axiom,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).

fof(fact_rel__simps_I40_J,axiom,
    c_Int_OMin != c_Int_OPls,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).

fof(fact_rel__simps_I37_J,axiom,
    c_Int_OPls != c_Int_OMin,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).

fof(i_0_5180,plain,
    ! [X32,X10] :
      ( class_Rings_Oring__1(X10)
     => ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(c_Int_Oring__1__class_Oof__int(X10),X32) = c_Groups_Ozero__class_Ozero(X10) )
        & ( X32 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X10),X32) = hAPP(c_Groups_Ouminus__class_Ouminus(X10),hAPP(c_Int_Oring__1__class_Oof__int(X10),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X32))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
             => hAPP(c_Int_Oring__1__class_Oof__int(X10),X32) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X10),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X10,X10)),tc_fun(tc_Int_Oint,X10)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X10,X10),X10),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X10,X10)),tc_fun(tc_Int_Oint,X10)),tc_Int_Oint),c_COMBB(tc_fun(X10,X10),X10,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_fun(X10,X10),X10),tc_Int_Oint),c_HOL_OLet(X10,X10)),c_Int_Oring__1__class_Oof__int(X10)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X10,X10),tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,X10)),tc_fun(tc_fun(X10,X10),tc_fun(X10,X10)),tc_Int_Oint),c_COMBS(X10,X10,X10)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X10,X10),tc_fun(X10,tc_fun(X10,X10))),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_fun(X10,X10)),tc_fun(tc_fun(X10,X10),tc_fun(X10,tc_fun(X10,X10))),tc_Int_Oint),c_COMBB(X10,tc_fun(X10,X10),X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),tc_Int_Oint),c_If(X10)),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(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_COMBI(X10))))),hAPP(hAPP(c_COMBC(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Oplus__class_Oplus(X10)),hAPP(hAPP(c_COMBS(X10,X10,X10),c_Groups_Oplus__class_Oplus(X10)),c_COMBI(X10)))),c_Groups_Oone__class_Oone(X10))))),c_Divides_Odivmod__int(X32,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_5181,plain,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X26),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(X27),X34),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X27))) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__power2__lt__zero]) ).

fof(i_0_5182,plain,
    ! [X37,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Power_Opower__class_Opower(X27),X37),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X27))) ),
    inference(fof_simplification,[status(thm)],[fact_power2__less__0]) ).

fof(i_0_5183,plain,
    ! [X68,X92] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = 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),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))),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),X92)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = 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),X68)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zmod__number__of__Bit1]) ).

fof(i_0_5184,plain,
    ! [X92,X68] :
      ( 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),X68)))
     => ( ( 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),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = 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),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68))) )
        & ( ~ 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),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68))))
         => c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),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),X68)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__number__of]) ).

fof(i_0_5185,plain,
    ! [X92] :
      ( 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),X92)))
     => ( ( 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),X92))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = 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),X92))) )
        & ( ~ 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),X92))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),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),X92)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn__1__number__of]) ).

fof(i_0_5186,plain,
    ! [X92,X68] :
      ( 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),X68)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = 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),X92)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
         => c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92),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),X68)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__number__of]) ).

fof(i_0_5187,plain,
    ! [X92] :
      ( 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),X92)))
     => ( ( 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),X92)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = 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),X92)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)),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),X92)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn__1__number__of]) ).

fof(i_0_5188,plain,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => ( ( 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),X37),X36)))
         => c_Divides_OnegDivAlg(X37,X36) = 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),X37),X36)) )
        & ( ~ 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),X37),X36)))
         => c_Divides_OnegDivAlg(X37,X36) = hAPP(c_Divides_Oadjust(X36),c_Divides_OnegDivAlg(X37,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)))),X36))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_negDivAlg__eqn]) ).

fof(i_0_5189,plain,
    ! [X37,X36] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),X36))
         => c_Divides_OposDivAlg(X37,X36) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X37) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X37),X36))
         => c_Divides_OposDivAlg(X37,X36) = hAPP(c_Divides_Oadjust(X36),c_Divides_OposDivAlg(X37,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)))),X36))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_posDivAlg__eqn]) ).

fof(i_0_5190,plain,
    ! [X200,X42,X10] :
      ( c_List_OdropWhile(X10,X42,X200) != c_List_Olist_ONil(X10)
     => ~ hBOOL(hAPP(X42,hAPP(c_List_Ohd(X10),c_List_OdropWhile(X10,X42,X200)))) ),
    inference(fof_simplification,[status(thm)],[fact_hd__dropWhile]) ).

fof(i_0_5191,plain,
    ! [X93,X90,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( ( 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),X90)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),hAPP(hAPP(c_COMBS(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)))),c_COMBI(X10))) )
        & ( ~ 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),X90)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = c_Groups_Oone__class_Oone(X10) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__number__of__odd__number__of]) ).

fof(i_0_5192,plain,
    ! [X200,X42,X10] :
      ( ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),c_List_OdropWhile(X10,X42,X200))))
         => ~ hBOOL(hAPP(X42,X3)) )
     => c_List_OtakeWhile(X10,X42,X200) = hAPP(c_List_Ofilter(X10,X42),X200) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__filter]) ).

fof(i_0_5193,plain,
    ! [X19,X90,X10] :
      ( class_Int_Onumber__ring(X10)
     => ( ( 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),X90)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = hAPP(hAPP(c_HOL_OLet(X10,X10),hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),hAPP(hAPP(c_COMBS(X10,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),X10),c_Groups_Otimes__class_Otimes(X10)),hAPP(c_Groups_Otimes__class_Otimes(X10),X19))),c_COMBI(X10))) )
        & ( ~ 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),X90)))
         => hAPP(hAPP(c_Power_Opower__class_Opower(X10),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = c_Groups_Oone__class_Oone(X10) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__number__of__odd]) ).

fof(i_0_5194,plain,
    ! [X19,X90] :
      ( ( 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),X90)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90))),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),X19))),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),X90)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_zpower__number__of__odd]) ).

fof(i_0_5195,plain,
    ! [X11,X110,X10] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X10,X10),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X10,X10),X110)),c_Transitive__Closure_Ortrancl(X10,X110)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X10,X10),tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X11)),c_Transitive__Closure_Otrancl(X10,X110))) ),
    inference(fof_simplification,[status(thm)],[fact_irrefl__tranclI]) ).

fof(i_0_5196,plain,
    ! [X199,X42,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ( ~ hBOOL(hAPP(X42,X11))
       => c_List_OdropWhile(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),c_List_OdropWhile(X10,X42,X200)),X199) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile__append1]) ).

fof(i_0_5197,plain,
    ! [X20,X6,X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X20)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14))
          | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X13))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X20))
            & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X13))
                & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X6)) )
              | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X20))
                & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X20),X14)) ) ) ) )
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X20)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__psubset__iff]) ).

fof(i_0_5198,plain,
    ! [X110,X10] :
      ( c_Wellfounded_Oacyclic(X10,X110)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),c_Transitive__Closure_Otrancl(X10,X110))) ),
    inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).

fof(i_0_5199,plain,
    ! [X68,X92] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X68))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X68))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X92))) = 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),X68)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X92)) ) ),
    inference(fof_simplification,[status(thm)],[fact_zdiv__number__of__Bit1]) ).

fof(i_0_5200,plain,
    ! [X110,X10] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),c_Transitive__Closure_Otrancl(X10,X110)))
     => c_Wellfounded_Oacyclic(X10,X110) ),
    inference(fof_simplification,[status(thm)],[fact_acyclicI]) ).

fof(i_0_5201,plain,
    ! [X200,X10,X11,X42] :
      ( ( hBOOL(hAPP(X42,X11))
       => c_List_OdropWhile(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = c_List_OdropWhile(X10,X42,X200) )
      & ( ~ hBOOL(hAPP(X42,X11))
       => c_List_OdropWhile(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(i_0_5202,plain,
    ! [X90] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X90)))
       => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X90)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X90)),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_5203,plain,
    ! [X60,X61,X42] :
      ( c_List_Olist__ex(tc_Nat_Onat,X42,c_List_Oupt(X61,X60))
    <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X42),X61,X60) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex__iff__not__all__inverval__nat]) ).

fof(i_0_5204,plain,
    ! [X25,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25)))
       => c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X25)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__rec__number__of]) ).

fof(i_0_5205,plain,
    ! [X92,X27] :
      ( ( class_Int_Onumber__ring(X27)
        & class_Int_Oring__char__0(X27) )
     => ~ c_Int_Oiszero(X27,hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(X92))) ),
    inference(fof_simplification,[status(thm)],[fact_iszero__number__of__Bit1]) ).

fof(i_0_5206,plain,
    ! [X199,X16,X200,X42,X10] :
      ( c_List_OdropWhile(X10,X42,X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199)
    <=> ( X200 = hAPP(hAPP(c_List_Oappend(X10),c_List_OtakeWhile(X10,X42,X200)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199))
        & ~ hBOOL(hAPP(X42,X16)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).

fof(i_0_5207,plain,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => ~ c_Int_Oiszero(X27,hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OBit1(c_Int_OPls))) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__Numeral1]) ).

fof(i_0_5208,plain,
    ! [X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => hAPP(c_List_OremoveAll(X10,X11),X200) = X200 ),
    inference(fof_simplification,[status(thm)],[fact_removeAll__id]) ).

fof(i_0_5209,plain,
    ! [X200,X10,X11,X42] :
      ( ~ hBOOL(hAPP(X42,X11))
     => hAPP(c_List_OremoveAll(X10,X11),hAPP(c_List_Ofilter(X10,X42),X200)) = hAPP(c_List_Ofilter(X10,X42),X200) ),
    inference(fof_simplification,[status(thm)],[fact_removeAll__filter__not]) ).

fof(i_0_5210,plain,
    ! [X25,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X25) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X25)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X68))),X25) ) ),
    inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of__add]) ).

fof(i_0_5211,plain,
    ! [X43,X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
       => c_List_Oupt(X44,hAPP(c_Nat_OSuc,X43)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X44,X43)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X43),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X43))
       => c_List_Oupt(X44,hAPP(c_Nat_OSuc,X43)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__Suc]) ).

fof(i_0_5212,plain,
    ! [X43,X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
       => c_List_Oupt(X44,X43) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X44),c_List_Oupt(hAPP(c_Nat_OSuc,X44),X43)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X43))
       => c_List_Oupt(X44,X43) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_upt__rec]) ).

fof(i_0_5213,plain,
    ! [X30,X32,X42] :
      ( epred2_3(X42,X32,X30)
    <=> ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X42,X30)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32))
         => ! [X91,X73] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X32))
                & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
             => hBOOL(hAPP(X42,X73)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X91,X73] :
              ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X73))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
             => hBOOL(hAPP(X42,X73)) ) ) ) ),
    introduced(definition) ).

fof(i_0_5214,plain,
    ! [X30,X32,X42] :
      ( epred1_3(X42,X32,X30)
    <=> ( ( X32 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(X42,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)),X32))
         => ! [X91] :
              ( ? [X73] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X73))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X73),X32))
                  & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
             => hBOOL(hAPP(X42,X91)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ! [X91] :
              ( ? [X73] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32),X73))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X73),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & X30 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X91)),X73) )
             => hBOOL(hAPP(X42,X91)) ) ) ) ),
    introduced(definition) ).

fof(i_0_5215,plain,
    ! [X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),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),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X68)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__1]) ).

fof(i_0_5216,plain,
    ! [X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),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),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X68)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__diff__1]) ).

fof(i_0_5217,plain,
    ! [X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),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),X68)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),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),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X68)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__1__add__number__of]) ).

fof(i_0_5218,plain,
    ! [X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X68)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Suc__nat__number__of]) ).

fof(i_0_5219,plain,
    ! [X34,X27] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X27),c_List_Olist_ONil(X27)),X34)),
    inference(fof_simplification,[status(thm)],[fact_member__rec_I2_J]) ).

fof(i_0_5220,plain,
    ! [X22040] : c_Divides_Oadjust(X22040) = 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)),X22040))))),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)),X22040))))),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_5221,plain,
    ! [X20454] : c_Int_Osucc(c_Int_OBit0(X20454)) = c_Int_OBit1(X20454),
    inference(variable_rename,[status(thm)],[fact_succ__Bit0]) ).

fof(i_0_5222,plain,
    ! [X20386] : c_Int_OBit0(X20386) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20386),X20386),
    inference(variable_rename,[status(thm)],[fact_Bit0__def]) ).

fof(i_0_5223,plain,
    ! [X20844] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20844),c_Int_OMin) = c_Int_Osucc(X20844),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I2_J]) ).

fof(i_0_5224,plain,
    ! [X29,X1,X2,X102,X18,X6,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X6),hAPP(c_Set_Oimage(tc_prod(X18,X102),tc_prod(X10,X8),c_Product__Type_Omap__pair(X18,X10,X102,X8,X2,X1)),X29)))
     => ~ ! [X3,X51] :
            ( X6 = hAPP(hAPP(c_Product__Type_OPair(X10,X8),hAPP(X2,X3)),hAPP(X1,X51))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X102)),hAPP(hAPP(c_Product__Type_OPair(X18,X102),X3),X51)),X29)) ) ),
    inference(fof_simplification,[status(thm)],[fact_prod__fun__imageE]) ).

fof(i_0_5225,plain,
    ! [X110,X263,X264,X265,X159,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X159),X265)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X264),X263))),c_Transitive__Closure_Ortrancl(tc_prod(X10,X8),X110)))
     => ( hAPP(hAPP(c_Product__Type_OPair(X10,X8),X159),X265) != hAPP(hAPP(c_Product__Type_OPair(X10,X8),X264),X263)
       => ~ ! [X46,X81] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X159),X265)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81))),X110))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X10,X8),tc_prod(X10,X8))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X10,X8),tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X46),X81)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X264),X263))),c_Transitive__Closure_Ortrancl(tc_prod(X10,X8),X110))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_converse__rtranclE2]) ).

fof(i_0_5226,plain,
    ! [X25987,X25988] :
      ( ( X25988 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X25988,X25987) = 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)) )
      & ( X25987 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X25988,X25987) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25988)
        | X25988 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X25987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X25988,X25987) = 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,X25987))),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)),X25987)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25988))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25988),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(X25988,X25987)),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),X25987))))),c_Divides_Opdivmod(X25988,X25987))))
        | X25988 = 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_5227,plain,
    ! [X27833,X27834,X27835,X27836] : c_Product__Type_Oapsnd(X27836,X27835,X27834,X27833) = c_Product__Type_Omap__pair(X27834,X27834,X27836,X27835,c_Fun_Oid(X27834),X27833),
    inference(variable_rename,[status(thm)],[fact_apsnd__def]) ).

fof(i_0_5228,plain,
    ! [X25991,X25992] :
      ( ( X25992 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X25992,X25991) = 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)) )
      & ( X25991 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X25992,X25991) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25992)
        | X25992 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X25991 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X25992,X25991) = 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,X25991))),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,X25992)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,X25991))),c_Divides_Opdivmod(X25992,X25991)),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),X25991))))),c_Divides_Opdivmod(X25992,X25991))))
        | X25992 = 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_5229,plain,
    ! [X29142,X29143,X29144] : c_Nitpick_Oplus__frac(X29144,X29143,X29142) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X29144),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(X29144),X29143),hAPP(c_Nitpick_Odenom(X29144),X29142))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,X29144),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,X29144),tc_Int_Oint),c_Nitpick_Ofrac(X29144)),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(X29144),X29143))),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(X29144),X29143))))),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(X29144),X29142))),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(X29144),X29142)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oplus__frac__def]) ).

fof(i_0_5230,plain,
    ! [X29166] : c_Nitpick_Odenom(X29166) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X29166,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X29166)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Odenom__def]) ).

fof(i_0_5231,plain,
    ! [X29167] : c_Nitpick_Onum(X29167) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,X29167,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(X29167)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Onum__def]) ).

fof(i_0_5232,plain,
    ! [X28592,X28593,X28594,X28595] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28595,tc_fun(X28595,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X28595,tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_fun(X28595,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28595,tc_fun(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_fun(X28595,tc_HOL_Obool)),X28595),c_COMBC(X28595,tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28595,tc_prod(X28595,X28595)),tc_fun(X28595,tc_fun(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_HOL_Obool)),X28595),hAPP(c_COMBB(tc_prod(X28595,X28595),tc_fun(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_HOL_Obool),X28595),c_member(tc_prod(X28595,X28595)))),c_Product__Type_OPair(X28595,X28595)))),X28594)),c_fequal),X28593),X28592))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28595,X28595)),hAPP(hAPP(c_Product__Type_OPair(X28595,X28595),X28593),X28592)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool)),X28594),c_Relation_OId(X28595)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28595,X28595)),hAPP(hAPP(c_Product__Type_OPair(X28595,X28595),X28593),X28592)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool)),X28594),c_Relation_OId(X28595))))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28595,tc_fun(X28595,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X28595,tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_fun(X28595,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28595,tc_fun(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_fun(X28595,tc_HOL_Obool)),X28595),c_COMBC(X28595,tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28595,tc_prod(X28595,X28595)),tc_fun(X28595,tc_fun(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_HOL_Obool)),X28595),hAPP(c_COMBB(tc_prod(X28595,X28595),tc_fun(tc_fun(tc_prod(X28595,X28595),tc_HOL_Obool),tc_HOL_Obool),X28595),c_member(tc_prod(X28595,X28595)))),c_Product__Type_OPair(X28595,X28595)))),X28594)),c_fequal),X28593),X28592)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflcl__set__eq])]) ).

fof(i_0_5233,plain,
    ! [X28620] : c_Transitive__Closure_Ortrancl(X28620,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28620,X28620),tc_HOL_Obool))) = c_Relation_OId(X28620),
    inference(variable_rename,[status(thm)],[fact_rtrancl__empty]) ).

fof(i_0_5234,plain,
    ! [X21845,X21846,X21847] : hAPP(c_Divides_Oadjust(X21847),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21846),X21845)) = 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),X21845),X21847)),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)))),X21846)),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)))),X21846)),X21845))),
    inference(variable_rename,[status(thm)],[fact_adjust__eq]) ).

fof(i_0_5235,plain,
    ! [X28588,X28589,X28590,X28591] : c_Transitive__Closure_Otrancl(X28591,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28591,X28591)),hAPP(hAPP(c_Product__Type_OPair(X28591,X28591),X28590),X28589)),X28588)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28591,X28591),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28591,X28588)),hAPP(c_Set_OCollect(tc_prod(X28591,X28591)),hAPP(c_Product__Type_Oprod_Oprod__case(X28591,X28591,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28591,tc_fun(X28591,tc_HOL_Obool),tc_fun(X28591,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28591,tc_HOL_Obool),tc_fun(X28591,tc_HOL_Obool)),X28591),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28591)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28591),c_fconj),hAPP(hAPP(c_COMBC(X28591,tc_fun(tc_prod(X28591,X28591),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X28591,X28591),tc_fun(tc_fun(tc_prod(X28591,X28591),tc_HOL_Obool),tc_HOL_Obool),X28591),c_member(tc_prod(X28591,X28591))),hAPP(hAPP(c_COMBC(X28591,X28591,tc_prod(X28591,X28591)),c_Product__Type_OPair(X28591,X28591)),X28590))),c_Transitive__Closure_Ortrancl(X28591,X28588))))),hAPP(hAPP(c_COMBC(X28591,tc_fun(tc_prod(X28591,X28591),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X28591,X28591),tc_fun(tc_fun(tc_prod(X28591,X28591),tc_HOL_Obool),tc_HOL_Obool),X28591),c_member(tc_prod(X28591,X28591))),hAPP(c_Product__Type_OPair(X28591,X28591),X28589))),c_Transitive__Closure_Ortrancl(X28591,X28588)))))),
    inference(variable_rename,[status(thm)],[fact_trancl__insert]) ).

fof(i_0_5236,plain,
    ! [X28616,X28617] : c_Transitive__Closure_Otrancl(X28617,X28616) = hAPP(hAPP(c_Relation_Orel__comp(X28617,X28617,X28617),X28616),c_Transitive__Closure_Ortrancl(X28617,X28616)),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold__left]) ).

fof(i_0_5237,plain,
    ! [X21723,X21724] :
      ( ( X21723 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(X21724),X21723) = c_Groups_Ozero__class_Ozero(X21724)
        | ~ class_Rings_Oring__1(X21724) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21723),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X21724),X21723) = hAPP(c_Groups_Ouminus__class_Ouminus(X21724),hAPP(c_Int_Oring__1__class_Oof__int(X21724),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21723)))
        | X21723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Rings_Oring__1(X21724) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21723),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X21724),X21723) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,X21724),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(X21724,X21724)),tc_fun(tc_Int_Oint,X21724)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X21724,X21724),X21724),tc_fun(tc_fun(tc_Int_Oint,tc_fun(X21724,X21724)),tc_fun(tc_Int_Oint,X21724)),tc_Int_Oint),c_COMBB(tc_fun(X21724,X21724),X21724,tc_Int_Oint)),hAPP(hAPP(c_COMBB(X21724,tc_fun(tc_fun(X21724,X21724),X21724),tc_Int_Oint),c_HOL_OLet(X21724,X21724)),c_Int_Oring__1__class_Oof__int(X21724)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X21724,X21724),tc_fun(X21724,X21724)),hAPP(hAPP(c_COMBB(tc_fun(X21724,tc_fun(X21724,X21724)),tc_fun(tc_fun(X21724,X21724),tc_fun(X21724,X21724)),tc_Int_Oint),c_COMBS(X21724,X21724,X21724)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(X21724,X21724),tc_fun(X21724,tc_fun(X21724,X21724))),hAPP(hAPP(c_COMBB(tc_fun(X21724,tc_fun(X21724,X21724)),tc_fun(tc_fun(X21724,X21724),tc_fun(X21724,tc_fun(X21724,X21724))),tc_Int_Oint),c_COMBB(X21724,tc_fun(X21724,X21724),X21724)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21724,tc_fun(X21724,X21724)),tc_Int_Oint),c_If(X21724)),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(X21724,X21724,X21724),c_Groups_Oplus__class_Oplus(X21724)),c_COMBI(X21724))))),hAPP(hAPP(c_COMBC(X21724,X21724,X21724),hAPP(hAPP(c_COMBB(X21724,tc_fun(X21724,X21724),X21724),c_Groups_Oplus__class_Oplus(X21724)),hAPP(hAPP(c_COMBS(X21724,X21724,X21724),c_Groups_Oplus__class_Oplus(X21724)),c_COMBI(X21724)))),c_Groups_Oone__class_Oone(X21724))))),c_Divides_Odivmod__int(X21723,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
        | X21723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Rings_Oring__1(X21724) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5180])])]) ).

fof(i_0_5238,plain,
    ! [X6,X14,X15,X12,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
           => ~ hBOOL(hAPP(hAPP(hAPP(X15,X3),X14),X6)) ) ),
    inference(fof_simplification,[status(thm)],[fact_SUP2__E]) ).

fof(i_0_5239,plain,
    ! [X20598,X20599,X20600] :
      ( ( X20599 = c_Groups_Ozero__class_Ozero(X20600)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20600),hAPP(hAPP(c_Power_Opower__class_Opower(X20600),X20599),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(X20600),X20598),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X20600)))
        | ~ class_Rings_Olinordered__idom(X20600) )
      & ( X20598 = c_Groups_Ozero__class_Ozero(X20600)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20600),hAPP(hAPP(c_Power_Opower__class_Opower(X20600),X20599),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(X20600),X20598),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X20600)))
        | ~ class_Rings_Olinordered__idom(X20600) )
      & ( X20599 != c_Groups_Ozero__class_Ozero(X20600)
        | X20598 != c_Groups_Ozero__class_Ozero(X20600)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20600),hAPP(hAPP(c_Power_Opower__class_Opower(X20600),X20599),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(X20600),X20598),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X20600)))
        | ~ class_Rings_Olinordered__idom(X20600) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__le__zero__iff])])]) ).

fof(i_0_5240,plain,
    ! [X20604,X20605,X20606] :
      ( ~ class_Rings_Olinordered__idom(X20606)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20606),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20606),hAPP(hAPP(c_Power_Opower__class_Opower(X20606),X20605),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(X20606),X20604),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Ozero__class_Ozero(X20606))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5181])]) ).

fof(i_0_5241,plain,
    ! [X31516,X31517,X31518,X31519] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31519)),c_List_Otranspose__rel(X31519)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31519)),hAPP(hAPP(c_List_Olist_OCons(X31519),X31518),X31517)),X31516)))
      | c_List_Otranspose(X31519,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31519)),hAPP(hAPP(c_List_Olist_OCons(X31519),X31518),X31517)),X31516)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31519)),hAPP(hAPP(c_List_Olist_OCons(X31519),X31518),c_List_Oconcat(X31519,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31519),tc_List_Olist(X31519)),c_List_Olist_Olist__case(tc_List_Olist(X31519),X31519,c_List_Olist_ONil(X31519),hAPP(hAPP(c_COMBB(tc_List_Olist(X31519),tc_fun(tc_List_Olist(X31519),tc_List_Olist(X31519)),X31519),c_COMBK(tc_List_Olist(X31519),tc_List_Olist(X31519))),hAPP(hAPP(c_COMBC(X31519,tc_List_Olist(X31519),tc_List_Olist(X31519)),c_List_Olist_OCons(X31519)),c_List_Olist_ONil(X31519))))),X31516)))),c_List_Otranspose(X31519,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31519)),X31517),c_List_Oconcat(tc_List_Olist(X31519),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31519),tc_List_Olist(tc_List_Olist(X31519))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31519)),X31519,c_List_Olist_ONil(tc_List_Olist(X31519)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31519),tc_List_Olist(tc_List_Olist(X31519))),X31519),hAPP(hAPP(c_COMBC(tc_List_Olist(X31519),tc_List_Olist(tc_List_Olist(X31519)),tc_List_Olist(tc_List_Olist(X31519))),c_List_Olist_OCons(tc_List_Olist(X31519))),c_List_Olist_ONil(tc_List_Olist(X31519)))))),X31516))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I3_J])]) ).

fof(i_0_5242,plain,
    ! [X31315,X31316] : c_List_Oconcat(X31316,X31315) = hAPP(c_List_Ofoldl(tc_List_Olist(X31316),tc_List_Olist(X31316),c_List_Oappend(X31316),c_List_Olist_ONil(X31316)),X31315),
    inference(variable_rename,[status(thm)],[fact_concat__conv__foldl]) ).

fof(i_0_5243,plain,
    ! [X31384,X31385,X31386,X31387] : c_List_Otranspose(X31387,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31387)),hAPP(hAPP(c_List_Olist_OCons(X31387),X31386),X31385)),X31384)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31387)),hAPP(hAPP(c_List_Olist_OCons(X31387),X31386),c_List_Oconcat(X31387,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31387),tc_List_Olist(X31387)),c_List_Olist_Olist__case(tc_List_Olist(X31387),X31387,c_List_Olist_ONil(X31387),hAPP(hAPP(c_COMBB(tc_List_Olist(X31387),tc_fun(tc_List_Olist(X31387),tc_List_Olist(X31387)),X31387),c_COMBK(tc_List_Olist(X31387),tc_List_Olist(X31387))),hAPP(hAPP(c_COMBC(X31387,tc_List_Olist(X31387),tc_List_Olist(X31387)),c_List_Olist_OCons(X31387)),c_List_Olist_ONil(X31387))))),X31384)))),c_List_Otranspose(X31387,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31387)),X31385),c_List_Oconcat(tc_List_Olist(X31387),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31387),tc_List_Olist(tc_List_Olist(X31387))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31387)),X31387,c_List_Olist_ONil(tc_List_Olist(X31387)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31387),tc_List_Olist(tc_List_Olist(X31387))),X31387),hAPP(hAPP(c_COMBC(tc_List_Olist(X31387),tc_List_Olist(tc_List_Olist(X31387)),tc_List_Olist(tc_List_Olist(X31387))),c_List_Olist_OCons(tc_List_Olist(X31387))),c_List_Olist_ONil(tc_List_Olist(X31387)))))),X31384))))),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I3_J]) ).

fof(i_0_5244,plain,
    ! [X20356,X20357,X20358] :
      ( ~ class_Rings_Olinordered__idom(X20358)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20358),X20357),c_Groups_Ozero__class_Ozero(X20358)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20358),hAPP(hAPP(c_Power_Opower__class_Opower(X20358),X20357),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)))),X20356)))),c_Groups_Ozero__class_Ozero(X20358))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero])]) ).

fof(i_0_5245,plain,
    ! [X116,X110,X18,X197,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X197),hAPP(hAPP(c_Relation_Orel__comp(X10,X18,X8),X110),X116)))
     => ~ ! [X3,X51,X177] :
            ( X197 = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X3),X177)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X18)),hAPP(hAPP(c_Product__Type_OPair(X10,X18),X3),X51)),X110))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X18,X8)),hAPP(hAPP(c_Product__Type_OPair(X18,X8),X51),X177)),X116)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__compE]) ).

fof(i_0_5246,plain,
    ! [X20359,X20360,X20361] :
      ( ~ class_Rings_Olinordered__idom(X20361)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20361),c_Groups_Ozero__class_Ozero(X20361)),hAPP(hAPP(c_Power_Opower__class_Opower(X20361),X20360),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)))),X20359)))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20361),c_Groups_Ozero__class_Ozero(X20361)),X20360)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le])]) ).

fof(i_0_5247,plain,
    ! [X199,X42,X200,X11,X10] :
      ( hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) = hAPP(c_List_Ofilter(X10,X42),X199)
    <=> ? [X220,X225] :
          ( X199 = hAPP(hAPP(c_List_Oappend(X10),X220),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X225))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X220)))
             => ~ hBOOL(hAPP(X42,X3)) )
          & hBOOL(hAPP(X42,X11))
          & X200 = hAPP(c_List_Ofilter(X10,X42),X225) ) ),
    inference(fof_simplification,[status(thm)],[fact_Cons__eq__filter__iff]) ).

fof(i_0_5248,plain,
    ! [X200,X11,X199,X42,X10] :
      ( hAPP(c_List_Ofilter(X10,X42),X199) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)
    <=> ? [X220,X225] :
          ( X199 = hAPP(hAPP(c_List_Oappend(X10),X220),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X225))
          & ! [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X220)))
             => ~ hBOOL(hAPP(X42,X3)) )
          & hBOOL(hAPP(X42,X11))
          & X200 = hAPP(c_List_Ofilter(X10,X42),X225) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__eq__Cons__iff]) ).

fof(i_0_5249,plain,
    ! [X20610,X20611,X20612] :
      ( ~ class_Int_Onumber__ring(X20612)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20612),X20611),X20610)),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(X20612),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20612),hAPP(hAPP(c_Power_Opower__class_Opower(X20612),X20611),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(X20612),X20610),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(X20612),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20612),hAPP(c_Int_Onumber__class_Onumber__of(X20612),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X20611)),X20610)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__sum])]) ).

fof(i_0_5250,plain,
    ! [X20362,X20363,X20364] :
      ( ~ class_Int_Onumber__ring(X20364)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20364),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20364),X20363),X20362)),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(X20364),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20364),hAPP(hAPP(c_Power_Opower__class_Opower(X20364),X20363),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(X20364),X20362),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(X20364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20364),hAPP(c_Int_Onumber__class_Onumber__of(X20364),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X20363)),X20362)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__diff])]) ).

fof(i_0_5251,plain,
    ! [X32,X61] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X61),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32)))
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X61))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X61),X32)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThan__iff]) ).

fof(i_0_5252,plain,
    ! [X32,X61] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X61),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32)))
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X61),X32))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X61)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OlessThan__iff]) ).

fof(i_0_5253,plain,
    ! [X2,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => c_Nitpick_Osetsum_H(X10,X8,X2,X12) = hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),c_Hilbert__Choice_OEps(tc_List_Olist(X10),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_List_Oset(X10))),X12))),c_List_Odistinct(X10))))) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => c_Nitpick_Osetsum_H(X10,X8,X2,X12) = c_Groups_Ozero__class_Ozero(X8) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Nitpick_Osetsum_H__def]) ).

fof(i_0_5254,plain,
    ! [X20607,X20608,X20609] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20609),c_Groups_Ozero__class_Ozero(X20609)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20609),hAPP(hAPP(c_Power_Opower__class_Opower(X20609),X20608),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(X20609),X20607),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | X20608 != c_Groups_Ozero__class_Ozero(X20609)
        | X20607 != c_Groups_Ozero__class_Ozero(X20609)
        | ~ class_Rings_Olinordered__idom(X20609) )
      & ( X20608 = c_Groups_Ozero__class_Ozero(X20609)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20609),c_Groups_Ozero__class_Ozero(X20609)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20609),hAPP(hAPP(c_Power_Opower__class_Opower(X20609),X20608),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(X20609),X20607),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ class_Rings_Olinordered__idom(X20609) )
      & ( X20607 = c_Groups_Ozero__class_Ozero(X20609)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20609),c_Groups_Ozero__class_Ozero(X20609)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20609),hAPP(hAPP(c_Power_Opower__class_Opower(X20609),X20608),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(X20609),X20607),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ class_Rings_Olinordered__idom(X20609) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__gt__zero__iff])])]) ).

fof(i_0_5255,plain,
    ! [X31533,X31534,X31535,X31536] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31536)),X31535))),c_List_Ofoldr(tc_List_Olist(X31534),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31534)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31534))),X31533,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(X31536)),X31535)),c_List_Ofoldr(tc_List_Olist(X31534),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31534)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(X31534),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31534)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31534)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(X31534),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31534)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31534),tc_List_Olist(X31534),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31534)))),X31533),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__max]) ).

fof(i_0_5256,plain,
    ! [X31840,X31841,X31842,X31843,X31844] : c_List_Ofoldr(X31844,X31843,X31842,X31841,X31840) = hAPP(c_List_Ofoldl(X31843,X31844,hAPP(c_COMBC(X31844,X31843,X31843),X31842),X31840),hAPP(c_List_Orev(X31844),X31841)),
    inference(variable_rename,[status(thm)],[fact_foldr__foldl]) ).

fof(i_0_5257,plain,
    ! [X31573,X31574,X31575,X31576] : hAPP(hAPP(c_List_Omap(tc_prod(X31576,tc_Nat_Onat),X31576),c_Product__Type_Ofst(X31576,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31576,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31576,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(X31576,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X31576,tc_Nat_Onat))),X31575)),hAPP(hAPP(c_List_Ozip(X31576,tc_Nat_Onat),X31574),c_List_Oupt(X31573,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31573),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31576)),X31574)))))) = hAPP(hAPP(c_List_Omap(tc_prod(X31576,tc_Nat_Onat),X31576),c_Product__Type_Ofst(X31576,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31576,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31576,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(X31576,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X31576,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(X31576,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(X31576,tc_Nat_Onat))),X31573))),X31575)),hAPP(hAPP(c_List_Ozip(X31576,tc_Nat_Onat),X31574),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31576)),X31574))))),
    inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma]) ).

fof(i_0_5258,plain,
    ! [X31600,X31601] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31601),X31600)) = c_List_Oupt(X31601,X31600),
    inference(variable_rename,[status(thm)],[fact_sorted__list__of__set__range]) ).

fof(i_0_5259,plain,
    ! [X243,X1,X10,X244] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X244),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X10,X1,X244,X243) = 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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X10)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X244),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(X10,X1,X244,X243) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X10,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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X1,X243)),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(X10)))),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(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X10,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(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X10,X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X244),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X243))),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(X10)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),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(X10)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X10,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(X10)))),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(X10)))),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(X10))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),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(X10)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10))))),tc_prod(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X10)),hAPP(hAPP(c_COMBB(X10,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X10)))),tc_prod(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X10)),c_Product__Type_Ofst(X10,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_Random_Osimps]) ).

fof(i_0_5260,plain,
    ! [X20997,X20998] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X20998)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20997)) = 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)))),X20998)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20997)),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div__number__of]) ).

fof(i_0_5261,plain,
    ! [X20995,X20996] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X20996)))),X20995) = 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)))),X20996)),X20995),
    inference(variable_rename,[status(thm)],[fact_Suc__div__eq__add3__div]) ).

fof(i_0_5262,plain,
    ! [X31008,X31009] : hAPP(c_New__DSequence_Opos__not__seq(X31009),X31008) = c_Lazy__Sequence_Ohb__not__seq(hAPP(X31009,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)))),X31008))),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__not__seq__def]) ).

fof(i_0_5263,plain,
    ! [X148,X6,X18,X8,X19,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X19),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X18,tc_fun(X10,tc_HOL_Obool)),X6),X148)))
     => ~ ! [X3,X51] :
            ( X148 = hAPP(hAPP(c_Product__Type_OPair(X8,X18),X3),X51)
           => ~ hBOOL(hAPP(hAPP(c_member(X10),X19),hAPP(hAPP(X6,X3),X51))) ) ),
    inference(fof_simplification,[status(thm)],[fact_mem__splitE]) ).

fof(i_0_5264,plain,
    ! [X93,X12,X11,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),X93))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ~ ! [X51] :
                ( X93 = hAPP(hAPP(X2,X11),X51)
               => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X51)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__graph__insertE]) ).

fof(i_0_5265,plain,
    ! [X21427] :
      ( ( X21427 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Code__Numeral_Oint__of,X21427) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21427,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,X21427) = 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),X21427),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X21427 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X21427,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,X21427) = 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),X21427),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))
        | X21427 = 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_5266,plain,
    ! [X20601,X20602,X20603] :
      ( ~ class_Rings_Olinordered__idom(X20603)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20603),c_Groups_Ozero__class_Ozero(X20603)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20603),hAPP(hAPP(c_Power_Opower__class_Opower(X20603),X20602),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(X20603),X20601),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_5267,plain,
    ! [X2,X8,X12,X10] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => ? [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
            & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),X12))),hAPP(hAPP(c_COMBC(X10,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X8,tc_fun(X8,tc_HOL_Obool),X10),c_fequal),X2)),hAPP(X2,X3)))))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole__infinite]) ).

fof(i_0_5268,plain,
    ! [X31373,X31374,X31375] :
      ( ( c_List_Oconcat(X31375,X31374) != c_List_Oconcat(X31375,X31373)
        | X31374 = X31373
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31375))),X31374) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31375))),X31373)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31375),tc_List_Olist(X31375))),esk423_3(X31373,X31374,X31375)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31375),tc_List_Olist(X31375))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31375),tc_List_Olist(X31375)),X31374),X31373)))) )
      & ( X31374 != X31373
        | c_List_Oconcat(X31375,X31374) = c_List_Oconcat(X31375,X31373)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31375))),X31374) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31375))),X31373)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31375),tc_List_Olist(X31375))),esk423_3(X31373,X31374,X31375)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31375),tc_List_Olist(X31375))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31375),tc_List_Olist(X31375)),X31374),X31373)))) )
      & ( c_List_Oconcat(X31375,X31374) != c_List_Oconcat(X31375,X31373)
        | X31374 = X31373
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31375))),X31374) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31375))),X31373)
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31375),tc_List_Olist(X31375),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31375),tc_fun(tc_List_Olist(X31375),tc_Nat_Onat),tc_fun(tc_List_Olist(X31375),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31375),tc_Nat_Onat),tc_fun(tc_List_Olist(X31375),tc_HOL_Obool)),tc_List_Olist(X31375)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31375))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31375)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31375))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31375)))),esk423_3(X31373,X31374,X31375))) )
      & ( X31374 != X31373
        | c_List_Oconcat(X31375,X31374) = c_List_Oconcat(X31375,X31373)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31375))),X31374) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31375))),X31373)
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31375),tc_List_Olist(X31375),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31375),tc_fun(tc_List_Olist(X31375),tc_Nat_Onat),tc_fun(tc_List_Olist(X31375),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31375),tc_Nat_Onat),tc_fun(tc_List_Olist(X31375),tc_HOL_Obool)),tc_List_Olist(X31375)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31375))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31375)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31375))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31375)))),esk423_3(X31373,X31374,X31375))) ) ),
    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_5269,plain,
    ! [X31369,X31370,X31371] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X31371),tc_List_Olist(X31371))),esk422_3(X31369,X31370,X31371)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(X31371),tc_List_Olist(X31371))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(X31371),tc_List_Olist(X31371)),X31370),X31369))))
        | X31370 = X31369
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31371))),X31370) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31371))),X31369)
        | c_List_Oconcat(X31371,X31370) != c_List_Oconcat(X31371,X31369) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31371),tc_List_Olist(X31371),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X31371),tc_fun(tc_List_Olist(X31371),tc_Nat_Onat),tc_fun(tc_List_Olist(X31371),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X31371),tc_Nat_Onat),tc_fun(tc_List_Olist(X31371),tc_HOL_Obool)),tc_List_Olist(X31371)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31371))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31371)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31371))))),c_Nat_Osize__class_Osize(tc_List_Olist(X31371)))),esk422_3(X31369,X31370,X31371)))
        | X31370 = X31369
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31371))),X31370) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31371))),X31369)
        | c_List_Oconcat(X31371,X31370) != c_List_Oconcat(X31371,X31369) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_concat__injective])])])]) ).

fof(i_0_5270,plain,
    ! [X21079,X21080,X21081,X21082,X21083] : hAPP(c_Nat_Onat_Onat__rec(X21083,X21082,X21081),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21080)),X21079)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21083),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21080))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21083,X21083),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21083,tc_fun(X21083,X21083)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21083,tc_fun(X21083,X21083)),tc_Int_Oint),c_If(X21083)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(X21083,X21082,X21081),X21079))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21083,X21083),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21083,X21083),tc_Int_Oint),X21081),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)),X21079))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21083,tc_Int_Oint),c_Nat_Onat_Onat__rec(X21083,X21082,X21081)),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)),X21079))))),
    inference(variable_rename,[status(thm)],[fact_nat__rec__add__eq__if]) ).

fof(i_0_5271,plain,
    ! [X20840] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20840),c_Int_OMin) = c_Int_Opred(X20840),
    inference(variable_rename,[status(thm)],[fact_add__Min__right]) ).

fof(i_0_5272,plain,
    ! [X20622,X20623] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20623),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)))),X20622)),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)))),X20623)) = 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),X20622),c_Groups_Oone__class_Oone(tc_Int_Oint)),X20623))),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_5273,plain,
    ! [X20539,X20540] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20540),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)))),X20539))),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)))),X20540)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20539),c_Groups_Oone__class_Oone(tc_Int_Oint))),X20540) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__zdiv__mult__2])]) ).

fof(i_0_5274,plain,
    ! [X20537,X20538] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20538))
      | 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)))),X20537))),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)))),X20538)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20537),X20538) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zdiv__mult__2])]) ).

fof(i_0_5275,plain,
    ! [X21035,X21036] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21036) != hAPP(c_Nat_OSuc,X21035)
        | 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(X21036))),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)),X21035))))) )
      & ( ~ 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(X21036))),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)),X21035)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21036) = hAPP(c_Nat_OSuc,X21035) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__Suc])]) ).

fof(i_0_5276,plain,
    ! [X21033,X21034] :
      ( ( hAPP(c_Nat_OSuc,X21034) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21033)
        | 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(X21033))),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)),X21034))))) )
      & ( ~ 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(X21033))),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)),X21034)))))
        | hAPP(c_Nat_OSuc,X21034) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21033) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__eq__number__of])]) ).

fof(i_0_5277,plain,
    ! [X12,X10] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Nitpick_Ocard_H(X10,X12) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_Hilbert__Choice_OEps(tc_List_Olist(X10),hAPP(hAPP(c_COMBS(tc_List_Olist(X10),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X10)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X10),tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X10,tc_HOL_Obool),tc_fun(tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X10)),c_fequal),c_List_Oset(X10))),X12))),c_List_Odistinct(X10)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => c_Nitpick_Ocard_H(X10,X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_Nitpick_Ocard_H__def]) ).

fof(i_0_5278,plain,
    ! [X61,X143] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X143))
     => 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)),X143))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X61)))) = 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)),X143))),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,X61))))) ),
    inference(fof_simplification,[status(thm)],[fact_card__less__Suc2]) ).

fof(i_0_5279,plain,
    ! [X20595,X20596,X20597] :
      ( ~ class_Rings_Olinordered__semidom(X20597)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20597),hAPP(hAPP(c_Power_Opower__class_Opower(X20597),X20596),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(X20597),X20595),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(X20597),c_Groups_Ozero__class_Ozero(X20597)),X20595))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20597),X20596),X20595)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__less__imp__less])]) ).

fof(i_0_5280,plain,
    ! [X20577,X20578,X20579] :
      ( ~ class_Rings_Olinordered__semidom(X20579)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20579),hAPP(hAPP(c_Power_Opower__class_Opower(X20579),X20578),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(X20579),X20577),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(X20579),c_Groups_Ozero__class_Ozero(X20579)),X20577))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20579),X20578),X20577)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__le__imp__le])]) ).

fof(i_0_5281,plain,
    ! [X15,X8,X20,X12,X6,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X20),X12))
           => hAPP(c_Set_Ovimage(X8,X10,hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBC(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))),X6)),X20)),X12) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X20),X12))
           => hAPP(c_Set_Ovimage(X8,X10,hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBC(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))),X6)),X20)),X12) = X15 ) ) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X20),X12))
           => hAPP(c_Set_Ovimage(X8,X10,hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBC(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))),X6)),X20)),X12) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),X15) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X20),X12))
           => hAPP(c_Set_Ovimage(X8,X10,hAPP(hAPP(c_COMBC(X8,X10,X10),hAPP(hAPP(c_COMBC(X8,X10,tc_fun(X10,X10)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X10,tc_fun(X10,X10)),X8),c_If(X10)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15))),X6)),X20)),X12) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_vimage__if]) ).

fof(i_0_5282,plain,
    ! [X20626,X20627] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20627))
      | 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)))),X20626)),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)))),X20627)) = 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,X20626,X20627))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmod__mult__2])]) ).

fof(i_0_5283,plain,
    ! [X21396,X21397] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21397))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21396)) = 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)))),X21397),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21396)),
    inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod__number__of]) ).

fof(i_0_5284,plain,
    ! [X20613,X20614,X20615] :
      ( ~ class_Rings_Olinordered__idom(X20615)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20615),c_Groups_Ozero__class_Ozero(X20615)),hAPP(hAPP(c_Power_Opower__class_Opower(X20615),X20614),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)))),X20613)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H])]) ).

fof(i_0_5285,plain,
    ! [X21398,X21399] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21399))),X21398) = 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)))),X21399),X21398),
    inference(variable_rename,[status(thm)],[fact_Suc__mod__eq__add3__mod]) ).

fof(i_0_5286,plain,
    ! [X21400,X21401] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21401,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21400)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21401,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)))),X21400)),
    inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__mod__add3]) ).

fof(i_0_5287,plain,
    ! [X20993,X20994] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20994),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X20993)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20994),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)))),X20993)),
    inference(variable_rename,[status(thm)],[fact_div__Suc__eq__div__add3]) ).

fof(i_0_5288,plain,
    ! [X28541,X28542,X28543] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28543,X28543),tc_HOL_Obool)),X28542),X28541))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28543,X28543),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28543,X28543,X28543),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28543,X28543),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28543,X28542)),X28541)),X28542)),X28541))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28543,X28543),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28543,X28542)),X28541)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__Int__subset])]) ).

fof(i_0_5289,plain,
    ! [X6,X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),X6)),X28) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X14,X13)),hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X28)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),X6)),X28) = hAPP(hAPP(c_Power_Opower__class_Opower(X8),X6),hAPP(c_Finite__Set_Ocard(X10),X28)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__gen__delta]) ).

fof(i_0_5290,plain,
    ! [X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),c_Groups_Ozero__class_Ozero(X8))),X28) = hAPP(X14,X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),c_Groups_Ozero__class_Ozero(X8))),X28) = c_Groups_Ozero__class_Ozero(X8) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__delta]) ).

fof(i_0_5291,plain,
    ! [X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),c_Groups_Oone__class_Oone(X8))),X28) = hAPP(X14,X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X14)),c_Groups_Oone__class_Oone(X8))),X28) = c_Groups_Oone__class_Oone(X8) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__delta]) ).

fof(i_0_5292,plain,
    ! [X21061,X21062] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21062)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21061)))
        | 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(X21061))),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),X21062)),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(X21061))),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),X21062)),c_Int_Onat)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21062)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21061))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__number__of])]) ).

fof(i_0_5293,plain,
    ! [X21067,X21068] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21068)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21067)))
        | 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(X21067))),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),X21068)),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(X21067))),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),X21068)),c_Int_Onat)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21068)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21067))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__number__of])]) ).

fof(i_0_5294,plain,
    ! [X26082,X26083,X26084,X26085,X26086,X26087,X26088] : hAPP(c_Product__Type_Oapsnd(X26088,X26087,X26086,X26085),hAPP(c_Product__Type_Oapfst(X26084,X26086,X26088,X26083),X26082)) = hAPP(c_Product__Type_Oapfst(X26084,X26086,X26087,X26083),hAPP(c_Product__Type_Oapsnd(X26088,X26087,X26084,X26085),X26082)),
    inference(variable_rename,[status(thm)],[fact_apsnd__apfst__commute]) ).

fof(i_0_5295,plain,
    ! [X27837,X27838,X27839,X27840] : c_Product__Type_Oapfst(X27840,X27839,X27838,X27837) = c_Product__Type_Omap__pair(X27840,X27839,X27838,X27838,X27837,c_Fun_Oid(X27838)),
    inference(variable_rename,[status(thm)],[fact_apfst__def]) ).

fof(i_0_5296,plain,
    ! [X110,X93,X77,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Oappend(X10),X11),X77)),hAPP(hAPP(c_List_Oappend(X10),X11),X93))),c_List_Olexord(X10,X110)))
     => ( ! [X46] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X46),X46)),X110))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X77),X93)),c_List_Olexord(X10,X110))) ) ),
    inference(fof_simplification,[status(thm)],[fact_lexord__append__leftD]) ).

fof(i_0_5297,plain,
    ! [X20584,X20585] :
      ( ~ class_Rings_Olinordered__idom(X20585)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20585),hAPP(hAPP(c_Power_Opower__class_Opower(X20585),X20584),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(X20585))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5182])]) ).

fof(i_0_5298,plain,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
     => ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X11 != X19 )
       => ~ ! [X51,X74] :
              ( X30 = hAPP(c_Nat_OSuc,X74)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),X29))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X74),X29))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__E2]) ).

fof(i_0_5299,plain,
    ! [X14,X13] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X13)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff]) ).

fof(i_0_5300,plain,
    ! [X83,X32] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32,X83) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X83))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X83),X32)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff]) ).

fof(i_0_5301,plain,
    ! [X14,X13] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X13,X14)
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X13)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastLessThan__empty__iff2]) ).

fof(i_0_5302,plain,
    ! [X83,X32] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X32,X83)
    <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X32),X83))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X83),X32)) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty__iff2]) ).

fof(i_0_5303,plain,
    ! [X16,X11,X2,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X10,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
       => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
            & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X11)) )
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(X2,X11)),hAPP(X2,X16))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Ostrict__monoD]) ).

fof(i_0_5304,plain,
    ! [X20616,X20617,X20618] :
      ( ~ class_Groups_Omonoid__mult(X20618)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20618),X20617),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)))),X20616))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20618),X20617),hAPP(hAPP(c_Power_Opower__class_Opower(X20618),hAPP(hAPP(c_Power_Opower__class_Opower(X20618),X20617),X20616)),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_5305,plain,
    ! [X31964,X31965,X31966] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31966),X31965))
      | ~ hBOOL(hAPP(hAPP(c_member(X31966),X31964),hAPP(c_List_Oset(X31966),X31965)))
      | c_List_OtakeWhile(X31966,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31966),c_fNot),hAPP(hAPP(c_COMBC(X31966,X31966,tc_HOL_Obool),c_fequal),X31964)),hAPP(c_List_Orev(X31966),X31965)) = hAPP(c_List_Orev(X31966),hAPP(c_List_Otl(X31966),c_List_OdropWhile(X31966,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31966),c_fNot),hAPP(hAPP(c_COMBC(X31966,X31966,tc_HOL_Obool),c_fequal),X31964)),X31965))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev])]) ).

fof(i_0_5306,plain,
    ! [X32014,X32015,X32016] : c_List_OdropWhile(X32016,X32015,X32014) = hAPP(hAPP(c_List_Odrop(X32016),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32016)),c_List_OtakeWhile(X32016,X32015,X32014))),X32014),
    inference(variable_rename,[status(thm)],[fact_dropWhile__eq__drop]) ).

fof(i_0_5307,plain,
    ! [X25999,X26000,X26001,X26002,X26003,X26004,X26005] : hAPP(c_Product__Type_Oapsnd(X26005,X26004,X26003,X26002),hAPP(c_Product__Type_Oapsnd(X26001,X26005,X26003,X26000),X25999)) = hAPP(c_Product__Type_Oapsnd(X26001,X26004,X26003,hAPP(c_Fun_Ocomp(X26005,X26004,X26001,X26002),X26000)),X25999),
    inference(variable_rename,[status(thm)],[fact_apsnd__compose]) ).

fof(i_0_5308,plain,
    ! [X26053,X26054,X26055,X26056,X26057,X26058,X26059] : hAPP(c_Product__Type_Oapfst(X26059,X26058,X26057,X26056),hAPP(c_Product__Type_Oapfst(X26055,X26059,X26057,X26054),X26053)) = hAPP(c_Product__Type_Oapfst(X26055,X26058,X26057,hAPP(c_Fun_Ocomp(X26059,X26058,X26055,X26056),X26054)),X26053),
    inference(variable_rename,[status(thm)],[fact_apfst__compose]) ).

fof(i_0_5309,plain,
    ! [X20586,X20587,X20588] :
      ( ( X20587 = c_Groups_Ozero__class_Ozero(X20588)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20588),hAPP(hAPP(c_Power_Opower__class_Opower(X20588),X20587),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(X20588),X20586),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X20588)
        | ~ class_Rings_Olinordered__idom(X20588) )
      & ( X20586 = c_Groups_Ozero__class_Ozero(X20588)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20588),hAPP(hAPP(c_Power_Opower__class_Opower(X20588),X20587),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(X20588),X20586),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(X20588)
        | ~ class_Rings_Olinordered__idom(X20588) )
      & ( X20587 != c_Groups_Ozero__class_Ozero(X20588)
        | X20586 != c_Groups_Ozero__class_Ozero(X20588)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20588),hAPP(hAPP(c_Power_Opower__class_Opower(X20588),X20587),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(X20588),X20586),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(X20588)
        | ~ class_Rings_Olinordered__idom(X20588) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__power2__eq__zero__iff])])]) ).

fof(i_0_5310,plain,
    ! [X31647,X31648,X31649] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk427_3(X31647,X31648,X31649)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31648))),X31649)))
        | c_List_Otranspose(X31648,X31649) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31648)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31648)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31648),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31648)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31648)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31648),hAPP(hAPP(c_COMBB(tc_List_Olist(X31648),tc_fun(tc_Nat_Onat,X31648),tc_Nat_Onat),c_List_Onth(X31648)),hAPP(c_List_Onth(tc_List_Olist(X31648)),X31649))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31648))),X31649)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31647))
        | X31649 = c_List_Olist_ONil(tc_List_Olist(X31648)) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31648)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31648)),X31649),esk427_3(X31647,X31648,X31649))) != X31647
        | c_List_Otranspose(X31648,X31649) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31648)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31648)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31648),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31648)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31648)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31648),hAPP(hAPP(c_COMBB(tc_List_Olist(X31648),tc_fun(tc_Nat_Onat,X31648),tc_Nat_Onat),c_List_Onth(X31648)),hAPP(c_List_Onth(tc_List_Olist(X31648)),X31649))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31648))),X31649)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31647))
        | X31649 = c_List_Olist_ONil(tc_List_Olist(X31648)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk427_3(X31647,X31648,X31649)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31648))),X31649)))
        | c_List_Otranspose(X31648,X31649) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31648)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31648)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31648),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31648)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31648)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31648),hAPP(hAPP(c_COMBB(tc_List_Olist(X31648),tc_fun(tc_Nat_Onat,X31648),tc_Nat_Onat),c_List_Onth(X31648)),hAPP(c_List_Onth(tc_List_Olist(X31648)),X31649))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31648))),X31649)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31647))
        | X31647 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31648)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31648)),X31649),esk427_3(X31647,X31648,X31649))) != X31647
        | c_List_Otranspose(X31648,X31649) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(X31648)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31648)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,X31648),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(X31648)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,X31648)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,X31648),hAPP(hAPP(c_COMBB(tc_List_Olist(X31648),tc_fun(tc_Nat_Onat,X31648),tc_Nat_Onat),c_List_Onth(X31648)),hAPP(c_List_Onth(tc_List_Olist(X31648)),X31649))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31648))),X31649)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31647))
        | X31647 != 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_5311,plain,
    ! [X20624,X20625] :
      ( ( ~ 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),X20625)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X20624)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X20625))) = 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),X20624),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20625)))),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),X20625)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X20624)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X20625))) = 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),X20624)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20625)))),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5183])]) ).

fof(i_0_5312,plain,
    ! [X22248,X22249,X22250] :
      ( ( 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),esk93_3(X22248,X22249,X22250)),esk94_3(X22248,X22249,X22250))))
        | hBOOL(hAPP(hAPP(X22248,X22250),X22249))
        | ~ 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),X22250),X22249))) )
      & ( 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),esk93_3(X22248,X22249,X22250)),esk94_3(X22248,X22249,X22250))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk94_3(X22248,X22249,X22250)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X22248,esk93_3(X22248,X22249,X22250)),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)))),esk94_3(X22248,X22249,X22250))))
        | hBOOL(hAPP(hAPP(X22248,X22250),X22249))
        | ~ 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),X22250),X22249))) )
      & ( ~ hBOOL(hAPP(hAPP(X22248,esk93_3(X22248,X22249,X22250)),esk94_3(X22248,X22249,X22250)))
        | hBOOL(hAPP(hAPP(X22248,X22250),X22249))
        | ~ 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),X22250),X22249))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opinduct])])])]) ).

fof(i_0_5313,plain,
    ! [X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(c_fequal,X13))),X14)),c_Groups_Ozero__class_Ozero(X8))),X28) = hAPP(X14,X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(c_fequal,X13))),X14)),c_Groups_Ozero__class_Ozero(X8))),X28) = c_Groups_Ozero__class_Ozero(X8) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__delta_H]) ).

fof(i_0_5314,plain,
    ! [X14,X13,X28,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X28))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(c_fequal,X13))),X14)),c_Groups_Oone__class_Oone(X8))),X28) = hAPP(X14,X13) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X28))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),hAPP(hAPP(c_COMBC(X10,X8,X8),hAPP(hAPP(c_COMBS(X10,X8,tc_fun(X8,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X8,tc_fun(X8,X8)),X10),c_If(X8)),hAPP(c_fequal,X13))),X14)),c_Groups_Oone__class_Oone(X8))),X28) = c_Groups_Oone__class_Oone(X8) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__delta_H]) ).

fof(i_0_5315,plain,
    ! [X22253,X22254,X22255] :
      ( ( 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),esk95_3(X22253,X22254,X22255)),esk96_3(X22253,X22254,X22255))))
        | hBOOL(hAPP(hAPP(X22253,X22255),X22254))
        | ~ 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),X22255),X22254))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk95_3(X22253,X22254,X22255)),esk96_3(X22253,X22254,X22255)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk96_3(X22253,X22254,X22255)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X22253,esk95_3(X22253,X22254,X22255)),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)))),esk96_3(X22253,X22254,X22255))))
        | hBOOL(hAPP(hAPP(X22253,X22255),X22254))
        | ~ 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),X22255),X22254))) )
      & ( ~ hBOOL(hAPP(hAPP(X22253,esk95_3(X22253,X22254,X22255)),esk96_3(X22253,X22254,X22255)))
        | hBOOL(hAPP(hAPP(X22253,X22255),X22254))
        | ~ 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),X22255),X22254))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opinduct])])])]) ).

fof(i_0_5316,plain,
    ! [X110,X199,X16,X200,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199))),c_List_Olistrel(X10,X110)))
     => ~ ! [X3,X208] :
            ( X200 = hAPP(hAPP(c_List_Olist_OCons(X10),X3),X208)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X16)),X110))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X208),X199)),c_List_Olistrel(X10,X110))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_listrel__Cons2]) ).

fof(i_0_5317,plain,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30)),X29)))
     => ~ ! [X51] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),X29))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29))) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E2]) ).

fof(i_0_5318,plain,
    ! [X29150,X29151,X29152] : c_Nitpick_Otimes__frac(X29152,X29151,X29150) = hAPP(hAPP(c_Nitpick_Ofrac(X29152),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29152),X29151)),hAPP(c_Nitpick_Onum(X29152),X29150))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(X29152),X29151)),hAPP(c_Nitpick_Odenom(X29152),X29150))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Otimes__frac__def]) ).

fof(i_0_5319,plain,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
     => ( ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => X11 != X19 )
       => ~ ! [X51,X74] :
              ( X30 = hAPP(c_Nat_OSuc,X74)
             => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X74),X29)))
               => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),X29)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__E]) ).

fof(i_0_5320,plain,
    ! [X29,X30,X19,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X19)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),hAPP(c_Nat_OSuc,X30)),X29)))
     => ~ ! [X51] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X51)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X10,X10),tc_HOL_Obool),X30),X29)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X19)),X29)) ) ),
    inference(fof_simplification,[status(thm)],[fact_rel__pow__Suc__E]) ).

fof(i_0_5321,plain,
    ! [X22170,X22171] :
      ( ( ~ 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),X22170)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22171))))
        | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22170),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22171)) = 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),X22170)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22171)))
        | ~ 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),X22171))) )
      & ( 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),X22170)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22171))))
        | c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22170),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22171)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22171)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22170),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),X22171))))
        | ~ 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),X22171))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5184])])]) ).

fof(i_0_5322,plain,
    ! [X22203,X22204] :
      ( ( ~ 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),X22204),X22203)))
        | c_Divides_OnegDivAlg(X22204,X22203) = 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),X22204),X22203))
        | ~ 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),X22204),X22203))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22203),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X22204,X22203) = 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),X22204),X22203))
        | ~ 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),X22204),X22203))) )
      & ( 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),X22204),X22203)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22203),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X22204,X22203) = hAPP(c_Divides_Oadjust(X22203),c_Divides_OnegDivAlg(X22204,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)))),X22203)))
        | ~ 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),X22204),X22203))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Opsimps])])]) ).

fof(i_0_5323,plain,
    ! [X22050] :
      ( ( ~ 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),X22050))))
        | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22050)) = 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),X22050)))
        | ~ 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),X22050))) )
      & ( 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),X22050))))
        | c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22050)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22050)),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),X22050))))
        | ~ 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),X22050))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5185])])]) ).

fof(i_0_5324,plain,
    ! [X22209,X22210] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22210),X22209))
        | c_Divides_OposDivAlg(X22210,X22209) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22210)
        | ~ 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),X22210),X22209))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22209),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X22210,X22209) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22210)
        | ~ 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),X22210),X22209))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22210),X22209))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22209),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X22210,X22209) = hAPP(c_Divides_Oadjust(X22209),c_Divides_OposDivAlg(X22210,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)))),X22209)))
        | ~ 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),X22210),X22209))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Opsimps])])]) ).

fof(i_0_5325,plain,
    ! [X22197,X22198] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22197)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22198)))
        | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22197),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22198)) = 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),X22197))
        | ~ 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),X22198))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22197)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22198)))
        | c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22197),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22198)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22198)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22197),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),X22198))))
        | ~ 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),X22198))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5186])])]) ).

fof(i_0_5326,plain,
    ! [X20619,X20620,X20621] :
      ( ~ class_Rings_Ocomm__semiring__1(X20621)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20621),X20620),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)))),X20619))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20621),X20620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20621),hAPP(hAPP(c_Power_Opower__class_Opower(X20621),X20620),X20619)),hAPP(hAPP(c_Power_Opower__class_Opower(X20621),X20620),X20619))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J])]) ).

fof(i_0_5327,plain,
    ! [X24387,X24388,X24389] : 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),X24389)),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))),X24388))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24387))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24387)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24389),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24389),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),X24387),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X24388)))),
    inference(variable_rename,[status(thm)],[fact_arith__series__int]) ).

fof(i_0_5328,plain,
    ! [X21063,X21064] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21064)),hAPP(c_Nat_OSuc,X21063)))
        | 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(X21064))),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)),X21063)))) )
      & ( ~ 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(X21064))),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)),X21063))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21064)),hAPP(c_Nat_OSuc,X21063))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__Suc])]) ).

fof(i_0_5329,plain,
    ! [X21065,X21066] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21066)),hAPP(c_Nat_OSuc,X21065)))
        | 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(X21066))),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)),X21065)))) )
      & ( ~ 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(X21066))),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)),X21065))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21066)),hAPP(c_Nat_OSuc,X21065))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of__Suc])]) ).

fof(i_0_5330,plain,
    ! [X22187] :
      ( ( ~ 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),X22187)))
        | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22187)) = 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),X22187))) )
      & ( 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),X22187)))
        | c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22187)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22187)),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),X22187))))
        | ~ 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),X22187))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5187])])]) ).

fof(i_0_5331,plain,
    ! [X20628,X20629] :
      ( ~ class_Rings_Osemiring__1(X20629)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20628))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20629),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)))),X20628))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20629),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20629),hAPP(c_Int_Onat,X20628))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20629),hAPP(c_Int_Onat,X20628))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__double])]) ).

fof(i_0_5332,plain,
    ! [X22172,X22173] :
      ( ( ~ 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),X22172),X22173)))
        | c_Divides_OnegDivAlg(X22172,X22173) = 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),X22172),X22173))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22173)) )
      & ( 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),X22172),X22173)))
        | c_Divides_OnegDivAlg(X22172,X22173) = hAPP(c_Divides_Oadjust(X22173),c_Divides_OnegDivAlg(X22172,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)))),X22173)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22173)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5188])])]) ).

fof(i_0_5333,plain,
    ! [X22168,X22169] :
      ( ( ~ 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),X22169),X22168)))
        | c_Divides_OnegDivAlg(X22169,X22168) = 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),X22169),X22168)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22168),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X22169,X22168) = 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),X22169),X22168)) )
      & ( 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),X22169),X22168)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22168),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OnegDivAlg(X22169,X22168) = hAPP(c_Divides_Oadjust(X22168),c_Divides_OnegDivAlg(X22169,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)))),X22168))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg_Osimps])])]) ).

fof(i_0_5334,plain,
    ! [X22195,X22196] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22195),X22196))
        | c_Divides_OposDivAlg(X22195,X22196) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22195)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22196)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22195),X22196))
        | c_Divides_OposDivAlg(X22195,X22196) = hAPP(c_Divides_Oadjust(X22196),c_Divides_OposDivAlg(X22195,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)))),X22196)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22196)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5189])])]) ).

fof(i_0_5335,plain,
    ! [X22188,X22189] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22189),X22188))
        | c_Divides_OposDivAlg(X22189,X22188) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22189) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22188),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X22189,X22188) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22189) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22189),X22188))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22188),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Divides_OposDivAlg(X22189,X22188) = hAPP(c_Divides_Oadjust(X22188),c_Divides_OposDivAlg(X22189,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)))),X22188))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg_Osimps])])]) ).

fof(i_0_5336,plain,
    ! [X21425,X21426] :
      ( ~ class_Rings_Oring__1(X21426)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21426),hAPP(c_Groups_Ouminus__class_Ouminus(X21426),c_Groups_Oone__class_Oone(X21426))),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)))),X21425))) = hAPP(c_Groups_Ouminus__class_Ouminus(X21426),c_Groups_Oone__class_Oone(X21426)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__odd])]) ).

fof(i_0_5337,plain,
    ! [X21413,X21414,X21415] :
      ( ~ class_Rings_Oring__1(X21415)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21415),hAPP(c_Groups_Ouminus__class_Ouminus(X21415),X21414)),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)))),X21413)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21415),X21414),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)))),X21413)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus__even])]) ).

fof(i_0_5338,plain,
    ! [X20631,X20632] :
      ( ~ class_Int_Onumber__ring(X20632)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20632),hAPP(c_Int_Onumber__class_Onumber__of(X20632),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)))),X20631))) = hAPP(c_Int_Onumber__class_Onumber__of(X20632),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__odd])]) ).

fof(i_0_5339,plain,
    ! [X19978] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X19978))) = 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)))),X19978),
    inference(variable_rename,[status(thm)],[fact_Suc3__eq__add__3]) ).

fof(i_0_5340,plain,
    ! [X12,X110,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(c_Relation_OImage(X8,X10,X110),X12)))
     => ~ ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X3),X14)),X110))
           => ~ hBOOL(hAPP(hAPP(c_member(X8),X3),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_ImageE]) ).

fof(i_0_5341,plain,
    ! [X31381,X31382,X31383] : c_Enum_On__lists(X31383,hAPP(c_Nat_OSuc,X31382),X31381) = c_List_Oconcat(tc_List_Olist(X31383),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31383),tc_List_Olist(tc_List_Olist(X31383))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31383),tc_List_Olist(X31383),tc_List_Olist(tc_List_Olist(X31383))),hAPP(hAPP(c_COMBB(tc_fun(X31383,tc_List_Olist(X31383)),tc_fun(tc_List_Olist(X31383),tc_List_Olist(tc_List_Olist(X31383))),tc_List_Olist(X31383)),c_List_Omap(X31383,tc_List_Olist(X31383))),hAPP(c_COMBC(X31383,tc_List_Olist(X31383),tc_List_Olist(X31383)),c_List_Olist_OCons(X31383)))),X31381)),c_Enum_On__lists(X31383,X31382,X31381))),
    inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I2_J]) ).

fof(i_0_5342,plain,
    ! [X21070,X21071,X21072,X21073,X21074] : c_Nat_Onat_Onat__case(X21074,X21073,X21072,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21071)),X21070)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21074),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21071))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21074,X21074),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21074,tc_fun(X21074,X21074)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21074,tc_fun(X21074,X21074)),tc_Int_Oint),c_If(X21074)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(X21074,X21073,X21072,X21070))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21074,tc_Int_Oint),X21072),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)),X21070)))),
    inference(variable_rename,[status(thm)],[fact_nat__case__add__eq__if]) ).

fof(i_0_5343,plain,
    ! [X21422] :
      ( ( ~ 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,X21422,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,X21422,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,X21422,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,X21422,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_5344,plain,
    ! [X26011,X26012,X26013,X26014,X26015,X26016] :
      ( ( hAPP(c_Product__Type_Oapsnd(X26016,X26015,X26014,X26013),X26012) != hAPP(c_Product__Type_Oapsnd(X26016,X26015,X26014,X26011),X26012)
        | hAPP(X26013,hAPP(c_Product__Type_Osnd(X26014,X26016),X26012)) = hAPP(X26011,hAPP(c_Product__Type_Osnd(X26014,X26016),X26012)) )
      & ( hAPP(X26013,hAPP(c_Product__Type_Osnd(X26014,X26016),X26012)) != hAPP(X26011,hAPP(c_Product__Type_Osnd(X26014,X26016),X26012))
        | hAPP(c_Product__Type_Oapsnd(X26016,X26015,X26014,X26013),X26012) = hAPP(c_Product__Type_Oapsnd(X26016,X26015,X26014,X26011),X26012) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apsnd__eq__conv])]) ).

fof(i_0_5345,plain,
    ! [X26066,X26067,X26068,X26069,X26070,X26071] :
      ( ( hAPP(c_Product__Type_Oapfst(X26071,X26070,X26069,X26068),X26067) != hAPP(c_Product__Type_Oapfst(X26071,X26070,X26069,X26066),X26067)
        | hAPP(X26068,hAPP(c_Product__Type_Ofst(X26071,X26069),X26067)) = hAPP(X26066,hAPP(c_Product__Type_Ofst(X26071,X26069),X26067)) )
      & ( hAPP(X26068,hAPP(c_Product__Type_Ofst(X26071,X26069),X26067)) != hAPP(X26066,hAPP(c_Product__Type_Ofst(X26071,X26069),X26067))
        | hAPP(c_Product__Type_Oapfst(X26071,X26070,X26069,X26068),X26067) = hAPP(c_Product__Type_Oapfst(X26071,X26070,X26069,X26066),X26067) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_apfst__eq__conv])]) ).

fof(i_0_5346,plain,
    ! [X28745] : c_Relation_OId(X28745) = hAPP(c_Set_OCollect(tc_prod(X28745,X28745)),hAPP(hAPP(c_COMBB(tc_fun(X28745,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X28745,X28745)),c_HOL_OEx(X28745)),hAPP(hAPP(c_COMBC(tc_prod(X28745,X28745),tc_fun(X28745,tc_prod(X28745,X28745)),tc_fun(X28745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28745,X28745),tc_HOL_Obool),tc_fun(tc_fun(X28745,tc_prod(X28745,X28745)),tc_fun(X28745,tc_HOL_Obool)),tc_prod(X28745,X28745)),c_COMBB(tc_prod(X28745,X28745),tc_HOL_Obool,X28745)),c_fequal)),hAPP(hAPP(c_COMBS(X28745,X28745,tc_prod(X28745,X28745)),c_Product__Type_OPair(X28745,X28745)),c_COMBI(X28745))))),
    inference(variable_rename,[status(thm)],[fact_Id__def]) ).

fof(i_0_5347,plain,
    ! [X26039,X26040,X26041,X26042,X26043,X26044,X26045] : hAPP(c_Product__Type_Oapsnd(X26045,X26044,X26043,X26042),hAPP(c_Product__Type_Oapfst(X26041,X26043,X26045,X26040),X26039)) = hAPP(hAPP(c_Product__Type_OPair(X26043,X26044),hAPP(X26040,hAPP(c_Product__Type_Ofst(X26041,X26045),X26039))),hAPP(X26042,hAPP(c_Product__Type_Osnd(X26041,X26045),X26039))),
    inference(variable_rename,[status(thm)],[fact_apsnd__apfst]) ).

fof(i_0_5348,plain,
    ! [X26046,X26047,X26048,X26049,X26050,X26051,X26052] : hAPP(c_Product__Type_Oapfst(X26052,X26051,X26050,X26049),hAPP(c_Product__Type_Oapsnd(X26048,X26050,X26052,X26047),X26046)) = hAPP(hAPP(c_Product__Type_OPair(X26051,X26050),hAPP(X26049,hAPP(c_Product__Type_Ofst(X26052,X26048),X26046))),hAPP(X26047,hAPP(c_Product__Type_Osnd(X26052,X26048),X26046))),
    inference(variable_rename,[status(thm)],[fact_apfst__apsnd]) ).

fof(i_0_5349,plain,
    ! [X22750,X22751] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22751),c_Groups_Ozero__class_Ozero(X22751)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22751),X22750),hAPP(c_Int_Onumber__class_Onumber__of(X22751),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22751),c_Groups_Ozero__class_Ozero(X22751)),X22750))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22751)
        | ~ class_Int_Onumber__ring(X22751) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22751),c_Groups_Ozero__class_Ozero(X22751)),X22750))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22751),c_Groups_Ozero__class_Ozero(X22751)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22751),X22750),hAPP(c_Int_Onumber__class_Onumber__of(X22751),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22751)
        | ~ class_Int_Onumber__ring(X22751) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_half__gt__zero__iff])])]) ).

fof(i_0_5350,plain,
    ! [X22754,X22755] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22755)),hAPP(c_Nat_OSuc,X22754)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22755))),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,X22754))),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)),X22754)))),
    inference(variable_rename,[status(thm)],[fact_max__Suc__number__of]) ).

fof(i_0_5351,plain,
    ! [X20582,X20583] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20583),c_Groups_Ozero__class_Ozero(X20583)),hAPP(hAPP(c_Power_Opower__class_Opower(X20583),X20582),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | X20582 != c_Groups_Ozero__class_Ozero(X20583)
        | ~ class_Rings_Olinordered__idom(X20583) )
      & ( X20582 = c_Groups_Ozero__class_Ozero(X20583)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20583),c_Groups_Ozero__class_Ozero(X20583)),hAPP(hAPP(c_Power_Opower__class_Opower(X20583),X20582),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ class_Rings_Olinordered__idom(X20583) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power2])])]) ).

fof(i_0_5352,plain,
    ! [X21480,X21481] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21481)),hAPP(c_Nat_OSuc,X21480)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21481))),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)),X21480)))),
    inference(variable_rename,[status(thm)],[fact_min__Suc__number__of]) ).

fof(i_0_5353,plain,
    ! [X21084,X21085,X21086,X21087] : hAPP(c_Nat_Onat_Onat__rec(X21087,X21086,X21085),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21084)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21087),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21084))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21087,X21087),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21087,tc_fun(X21087,X21087)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21087,tc_fun(X21087,X21087)),tc_Int_Oint),c_If(X21087)),c_Nat__Numeral_Oneg)),X21086)),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21087,X21087),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21087,X21087),tc_Int_Oint),X21085),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21087,tc_Int_Oint),c_Nat_Onat_Onat__rec(X21087,X21086,X21085)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_nat__rec__number__of]) ).

fof(i_0_5354,plain,
    ! [X31388,X31389] : c_List_Oconcat(X31389,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31389),tc_List_Olist(X31389)),c_List_Olist_Olist__case(tc_List_Olist(X31389),X31389,c_List_Olist_ONil(X31389),hAPP(hAPP(c_COMBB(tc_List_Olist(X31389),tc_fun(tc_List_Olist(X31389),tc_List_Olist(X31389)),X31389),c_COMBK(tc_List_Olist(X31389),tc_List_Olist(X31389))),hAPP(hAPP(c_COMBC(X31389,tc_List_Olist(X31389),tc_List_Olist(X31389)),c_List_Olist_OCons(X31389)),c_List_Olist_ONil(X31389))))),X31388)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31389),X31389),c_List_Ohd(X31389)),hAPP(c_List_Ofilter(tc_List_Olist(X31389),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31389)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31389),tc_List_Olist(X31389),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31389)))),X31388)),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__head]) ).

fof(i_0_5355,plain,
    ! [X31514,X31515] : c_List_Oconcat(tc_List_Olist(X31515),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31515),tc_List_Olist(tc_List_Olist(X31515))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(X31515)),X31515,c_List_Olist_ONil(tc_List_Olist(X31515)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X31515),tc_List_Olist(tc_List_Olist(X31515))),X31515),hAPP(hAPP(c_COMBC(tc_List_Olist(X31515),tc_List_Olist(tc_List_Olist(X31515)),tc_List_Olist(tc_List_Olist(X31515))),c_List_Olist_OCons(tc_List_Olist(X31515))),c_List_Olist_ONil(tc_List_Olist(X31515)))))),X31514)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31515),tc_List_Olist(X31515)),c_List_Otl(X31515)),hAPP(c_List_Ofilter(tc_List_Olist(X31515),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31515)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31515),tc_List_Olist(X31515),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31515)))),X31514)),
    inference(variable_rename,[status(thm)],[fact_transpose__aux__filter__tail]) ).

fof(i_0_5356,plain,
    ! [X28621,X28622,X28623] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28623,X28623),tc_HOL_Obool)),c_Relation_OId(X28623)),X28622))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28623,X28623),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28623,X28623,X28623),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28623,X28623),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28623,X28621)),X28622)),X28621)),X28622))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28623,X28623),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28623,X28621)),X28622)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__Int__subset])]) ).

fof(i_0_5357,plain,
    ! [X110,X200,X199,X16,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),hAPP(hAPP(c_List_Olist_OCons(X10),X16),X199)),X200)),c_List_Olistrel(X10,X110)))
     => ~ ! [X51,X207] :
            ( X200 = hAPP(hAPP(c_List_Olist_OCons(X10),X51),X207)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X51)),X110))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X199),X207)),c_List_Olistrel(X10,X110))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_listrel__Cons1]) ).

fof(i_0_5358,plain,
    ! [X20571,X20572,X20573] :
      ( ~ class_Groups_Omonoid__mult(X20573)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20573),X20572),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)))),X20571)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20573),hAPP(hAPP(c_Power_Opower__class_Opower(X20573),X20572),X20571)),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_5359,plain,
    ! [X31570,X31571,X31572] : c_List_Osublist(X31572,X31571,X31570) = hAPP(hAPP(c_List_Omap(tc_prod(X31572,tc_Nat_Onat),X31572),c_Product__Type_Ofst(X31572,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31572,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(X31572,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(X31572,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(X31572,tc_Nat_Onat))),X31570)),hAPP(hAPP(c_List_Ozip(X31572,tc_Nat_Onat),X31571),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31572)),X31571))))),
    inference(variable_rename,[status(thm)],[fact_sublist__def]) ).

fof(i_0_5360,plain,
    ! [X64,X56,X57,X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X57),X56)),X64))
    <=> ? [X46,X52] :
          ( hAPP(hAPP(c_Set_Oinsert(X10),X57),X56) = hAPP(hAPP(c_Set_Oinsert(X10),X46),X52)
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X46,X52),X64))
          & ~ hBOOL(hAPP(hAPP(c_member(X10),X46),X52)) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1Set_Oequations]) ).

fof(i_0_5361,plain,
    ! [X29158,X29159] : c_Nitpick_Ouminus__frac(X29159,X29158) = c_Nitpick_OAbs__Frac(X29159,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(X29159),X29158))),hAPP(c_Nitpick_Odenom(X29159),X29158))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Ouminus__frac__def]) ).

fof(i_0_5362,plain,
    ! [X26017,X26018,X26019,X26020,X26021] : hAPP(c_Product__Type_Osnd(X26021,X26020),hAPP(c_Product__Type_Oapsnd(X26019,X26020,X26021,X26018),X26017)) = hAPP(X26018,hAPP(c_Product__Type_Osnd(X26021,X26019),X26017)),
    inference(variable_rename,[status(thm)],[fact_snd__apsnd]) ).

fof(i_0_5363,plain,
    ! [X26072,X26073,X26074,X26075,X26076] : hAPP(c_Product__Type_Ofst(X26076,X26075),hAPP(c_Product__Type_Oapfst(X26074,X26076,X26075,X26073),X26072)) = hAPP(X26073,hAPP(c_Product__Type_Ofst(X26074,X26075),X26072)),
    inference(variable_rename,[status(thm)],[fact_fst__apfst]) ).

fof(i_0_5364,plain,
    ! [X26006,X26007,X26008,X26009,X26010] : hAPP(c_Product__Type_Ofst(X26010,X26009),hAPP(c_Product__Type_Oapsnd(X26008,X26009,X26010,X26007),X26006)) = hAPP(c_Product__Type_Ofst(X26010,X26008),X26006),
    inference(variable_rename,[status(thm)],[fact_fst__apsnd]) ).

fof(i_0_5365,plain,
    ! [X26077,X26078,X26079,X26080,X26081] : hAPP(c_Product__Type_Osnd(X26081,X26080),hAPP(c_Product__Type_Oapfst(X26079,X26081,X26080,X26078),X26077)) = hAPP(c_Product__Type_Osnd(X26079,X26080),X26077),
    inference(variable_rename,[status(thm)],[fact_snd__apfst]) ).

fof(i_0_5366,plain,
    ! [X21037,X21038,X21039,X21040] : c_Nat_Onat_Onat__case(X21040,X21039,X21038,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21037)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,X21040),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21037))),hAPP(hAPP(c_COMBS(tc_Int_Oint,X21040,X21040),hAPP(hAPP(c_COMBC(tc_Int_Oint,X21040,tc_fun(X21040,X21040)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21040,tc_fun(X21040,X21040)),tc_Int_Oint),c_If(X21040)),c_Nat__Numeral_Oneg)),X21039)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21040,tc_Int_Oint),X21038),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[fact_nat__case__number__of]) ).

fof(i_0_5367,plain,
    ! [X22453,X22454] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22454)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X22453)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X22453))),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,X22454))),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),X22454)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_max__number__of__Suc]) ).

fof(i_0_5368,plain,
    ! [X21478,X21479] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21479)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21478)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X21478))),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),X21479)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_min__number__of__Suc]) ).

fof(i_0_5369,plain,
    ! [X21075] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21075))
      | 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),X21075),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_5370,plain,
    ! [X22752,X22753] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X22753)
      | ~ class_Int_Onumber__ring(X22753)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22753),c_Groups_Ozero__class_Ozero(X22753)),X22752))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22753),c_Groups_Ozero__class_Ozero(X22753)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22753),X22752),hAPP(c_Int_Onumber__class_Onumber__of(X22753),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_5371,plain,
    ! [X20592,X20593,X20594] :
      ( ~ class_Rings_Ocomm__semiring__1(X20594)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20594),X20593),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)))),X20592)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20594),hAPP(hAPP(c_Power_Opower__class_Opower(X20594),X20593),X20592)),hAPP(hAPP(c_Power_Opower__class_Opower(X20594),X20593),X20592)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J])]) ).

fof(i_0_5372,plain,
    ! [X21069] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21069))
      | 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),X21069),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_5373,plain,
    ! [X20212,X20213] :
      ( ~ class_Groups_Omonoid__mult(X20213)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20213),X20212),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(X20213),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20213),X20212),X20212)),X20212) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power3__eq__cube])]) ).

fof(i_0_5374,plain,
    ! [X20580,X20581] :
      ( ~ class_Rings_Olinordered__idom(X20581)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20581),c_Groups_Ozero__class_Ozero(X20581)),hAPP(hAPP(c_Power_Opower__class_Opower(X20581),X20580),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_5375,plain,
    ! [X21423,X21424] :
      ( ~ class_Rings_Oring__1(X21424)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21424),hAPP(c_Groups_Ouminus__class_Ouminus(X21424),c_Groups_Oone__class_Oone(X21424))),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)))),X21423)) = c_Groups_Oone__class_Oone(X21424) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus1__even])]) ).

fof(i_0_5376,plain,
    ! [X20633,X20634] :
      ( ~ class_Int_Onumber__ring(X20634)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20634),hAPP(c_Int_Onumber__class_Onumber__of(X20634),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)))),X20633)) = c_Groups_Oone__class_Oone(X20634) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__m1__even])]) ).

fof(i_0_5377,plain,
    ! [X93,X119] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X119),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)) = 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),X93),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X119)))),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_5378,plain,
    ! [X31999,X32000,X32001,X32002,X32003] : c_List_OdropWhile(X32003,X32002,hAPP(hAPP(c_List_Omap(X32001,X32003),X32000),X31999)) = hAPP(hAPP(c_List_Omap(X32001,X32003),X32000),c_List_OdropWhile(X32001,hAPP(c_Fun_Ocomp(X32003,tc_HOL_Obool,X32001,X32002),X32000),X31999)),
    inference(variable_rename,[status(thm)],[fact_dropWhile__map]) ).

fof(i_0_5379,plain,
    ! [X19,X137] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X137))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X19)),hAPP(c_Int_Onat,X137)) = hAPP(c_Int_Onat,X19) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X137))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X19)),hAPP(c_Int_Onat,X137)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X137)),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_5380,plain,
    ! [X31967,X31968,X31969] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31969),X31968))
      | ~ hBOOL(hAPP(hAPP(c_member(X31969),X31967),hAPP(c_List_Oset(X31969),X31968)))
      | c_List_OdropWhile(X31969,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31969),c_fNot),hAPP(hAPP(c_COMBC(X31969,X31969,tc_HOL_Obool),c_fequal),X31967)),hAPP(c_List_Orev(X31969),X31968)) = hAPP(hAPP(c_List_Olist_OCons(X31969),X31967),hAPP(c_List_Orev(X31969),c_List_OtakeWhile(X31969,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31969),c_fNot),hAPP(hAPP(c_COMBC(X31969,X31969,tc_HOL_Obool),c_fequal),X31967)),X31968))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev])]) ).

fof(i_0_5381,plain,
    ! [X33491,X33492,X33493,X33496] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33493,X33493)),hAPP(hAPP(c_Product__Type_OPair(X33493,X33493),hAPP(X33492,hAPP(c_Nat_OSuc,esk540_3(X33491,X33492,X33493)))),hAPP(X33492,esk540_3(X33491,X33492,X33493)))),c_Transitive__Closure_Ortrancl(X33493,X33491)))
      | ~ c_Wellfounded_Owf(X33493,c_Transitive__Closure_Otrancl(X33493,X33491))
      | hAPP(X33492,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk541_3(X33491,X33492,X33493)),X33496)) = hAPP(X33492,esk541_3(X33491,X33492,X33493)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__weak__decr__stable])])])]) ).

fof(i_0_5382,plain,
    ! [X13,X11,X12,X14,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X14,X12),X11))
       => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X14),X12))
           => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X13,hAPP(hAPP(c_Set_Oinsert(X10),X14),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))),X11)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph__permute__diff]) ).

fof(i_0_5383,plain,
    ! [X31377,X31378,X31379,X31380] : c_List_Oconcat(X31380,hAPP(hAPP(c_List_Omap(X31379,tc_List_Olist(X31380)),hAPP(hAPP(c_COMBC(X31379,tc_List_Olist(X31380),tc_List_Olist(X31380)),hAPP(hAPP(c_COMBB(X31380,tc_fun(tc_List_Olist(X31380),tc_List_Olist(X31380)),X31379),c_List_Olist_OCons(X31380)),X31378)),c_List_Olist_ONil(X31380))),X31377)) = hAPP(hAPP(c_List_Omap(X31379,X31380),X31378),X31377),
    inference(variable_rename,[status(thm)],[fact_concat__map__singleton]) ).

fof(i_0_5384,plain,
    ! [X29163,X29164,X29165] :
      ( ( ~ c_Nitpick_Oless__eq__frac(X29165,X29164,X29163)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29165),c_Nitpick_Oplus__frac(X29165,X29164,c_Nitpick_Ouminus__frac(X29165,X29163)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29165),c_Nitpick_Oplus__frac(X29165,X29164,c_Nitpick_Ouminus__frac(X29165,X29163)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Oless__eq__frac(X29165,X29164,X29163) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__eq__frac__def])]) ).

fof(i_0_5385,plain,
    ! [X29160,X29161,X29162] :
      ( ( ~ c_Nitpick_Oless__frac(X29162,X29161,X29160)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29162),c_Nitpick_Oplus__frac(X29162,X29161,c_Nitpick_Ouminus__frac(X29162,X29160)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(X29162),c_Nitpick_Oplus__frac(X29162,X29161,c_Nitpick_Ouminus__frac(X29162,X29160)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Oless__frac(X29162,X29161,X29160) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oless__frac__def])]) ).

fof(i_0_5386,plain,
    ! [X20574,X20575,X20576] :
      ( ~ class_Rings_Olinordered__semidom(X20576)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20576),X20575),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(X20576),X20574),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(X20576),c_Groups_Ozero__class_Ozero(X20576)),X20575))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20576),c_Groups_Ozero__class_Ozero(X20576)),X20574))
      | X20575 = X20574 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__imp__eq])]) ).

fof(i_0_5387,plain,
    ! [X20591] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20591),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | X20591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X20591 = 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_5388,plain,
    ! [X20999] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X20999))),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),X20999),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_5389,plain,
    ! [X25982,X25983] :
      ( ~ class_Rings_Olinordered__idom(X25983)
      | hAPP(c_Groups_Oabs__class_Oabs(X25983),hAPP(hAPP(c_Power_Opower__class_Opower(X25983),X25982),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(X25983),X25982),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_5390,plain,
    ! [X29153,X29154,X29155] :
      ( ~ class_Rings_Oinverse(X29155)
      | ~ class_Rings_Oring__1(X29155)
      | c_Nitpick_Oof__frac(X29154,X29155,X29153) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X29155),hAPP(c_Int_Oring__1__class_Oof__int(X29155),hAPP(c_Nitpick_Onum(X29154),X29153))),hAPP(c_Int_Oring__1__class_Oof__int(X29155),hAPP(c_Nitpick_Odenom(X29154),X29153))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Oof__frac__def])]) ).

fof(i_0_5391,plain,
    ! [X110,X198,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),X198),hAPP(c_Relation_Oconverse(X8,X10),X110)))
     => ~ ! [X3,X51] :
            ( X198 = hAPP(hAPP(c_Product__Type_OPair(X10,X8),X51),X3)
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X3),X51)),X110)) ) ),
    inference(fof_simplification,[status(thm)],[fact_converseE]) ).

fof(i_0_5392,plain,
    ! [X2,X30,X31,X10] :
      ( class_Groups_Oab__group__add(X10)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X10)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,X31,X30)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X10),hAPP(X2,X31)),hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X10,X10),hAPP(hAPP(c_COMBB(X10,tc_fun(X10,X10),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X10)),X2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X10,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,X31,X30)) = c_Groups_Ozero__class_Ozero(X10) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__natinterval__difff]) ).

fof(i_0_5393,plain,
    ! [X19,X16,X12,X14,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X14,X12),X16))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X14),X12))
         => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,c_Groups_Otimes__class_Otimes(X10),X19,hAPP(hAPP(c_Set_Oinsert(X10),X14),X12)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X19),X16))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph__insert__swap]) ).

fof(i_0_5394,plain,
    ! [X16,X19,X2,X8,X12,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,X12),X16))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X8,X2,X19,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),hAPP(hAPP(X2,X11),X16))) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__graph_OinsertI]) ).

fof(i_0_5395,plain,
    ! [X29080,X29081,X29082,X29083] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29083,X29083)),hAPP(hAPP(c_Product__Type_OPair(X29083,X29083),X29082),esk354_4(X29080,X29081,X29082,X29083))),X29080))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29083,X29083)),hAPP(hAPP(c_Product__Type_OPair(X29083,X29083),X29082),X29081)),c_Transitive__Closure_Otrancl(X29083,X29080))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29083,X29083)),hAPP(hAPP(c_Product__Type_OPair(X29083,X29083),esk354_4(X29080,X29081,X29082,X29083)),X29081)),c_Transitive__Closure_Ortrancl(X29083,X29080)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29083,X29083)),hAPP(hAPP(c_Product__Type_OPair(X29083,X29083),X29082),X29081)),c_Transitive__Closure_Otrancl(X29083,X29080))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD])])])]) ).

fof(i_0_5396,plain,
    ! [X29085,X29086,X29087,X29088] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29088,X29088)),hAPP(hAPP(c_Product__Type_OPair(X29088,X29088),X29087),esk355_4(X29085,X29086,X29087,X29088))),c_Transitive__Closure_Ortrancl(X29088,X29085)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29088,X29088)),hAPP(hAPP(c_Product__Type_OPair(X29088,X29088),X29087),X29086)),c_Transitive__Closure_Otrancl(X29088,X29085))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29088,X29088)),hAPP(hAPP(c_Product__Type_OPair(X29088,X29088),esk355_4(X29085,X29086,X29087,X29088)),X29086)),X29085))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29088,X29088)),hAPP(hAPP(c_Product__Type_OPair(X29088,X29088),X29087),X29086)),c_Transitive__Closure_Otrancl(X29088,X29085))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tranclD2])])])]) ).

fof(i_0_5397,plain,
    ! [X26060,X26061,X26062,X26063,X26064,X26065] : hAPP(c_Product__Type_Oapfst(X26065,X26064,X26063,X26062),hAPP(hAPP(c_Product__Type_OPair(X26065,X26063),X26061),X26060)) = hAPP(hAPP(c_Product__Type_OPair(X26064,X26063),hAPP(X26062,X26061)),X26060),
    inference(variable_rename,[status(thm)],[fact_apfst__conv]) ).

fof(i_0_5398,plain,
    ! [X25993,X25994,X25995,X25996,X25997,X25998] : hAPP(c_Product__Type_Oapsnd(X25998,X25997,X25996,X25995),hAPP(hAPP(c_Product__Type_OPair(X25996,X25998),X25994),X25993)) = hAPP(hAPP(c_Product__Type_OPair(X25996,X25997),X25994),hAPP(X25995,X25993)),
    inference(variable_rename,[status(thm)],[fact_apsnd__conv]) ).

fof(i_0_5399,plain,
    ! [X200,X11,X42,X10] :
      ( c_List_Olist__ex1(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200))
    <=> ( ( hBOOL(hAPP(X42,X11))
         => c_List_Olist__all(X10,hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X10),c_fNot),X42))),hAPP(c_fequal,X11)),X200) )
        & ( ~ hBOOL(hAPP(X42,X11))
         => c_List_Olist__ex1(X10,X42,X200) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I2_J]) ).

fof(i_0_5400,plain,
    ! [X31531,X31532] : c_List_Ofoldr(tc_List_Olist(X31532),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31532)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31532))),c_List_Otranspose(X31532,X31531),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31532))),hAPP(c_List_Ofilter(tc_List_Olist(X31532),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31532)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31532),tc_List_Olist(X31532),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31532)))),X31531)),
    inference(variable_rename,[status(thm)],[fact_transpose__max__length]) ).

fof(i_0_5401,plain,
    ! [X32017,X32018,X32019,X32020] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32020),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32019)),c_List_OdropWhile(X32019,X32018,X32017))))
      | hAPP(hAPP(c_List_Onth(X32019),c_List_OdropWhile(X32019,X32018,X32017)),X32020) = hAPP(hAPP(c_List_Onth(X32019),X32017),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32020),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32019)),c_List_OtakeWhile(X32019,X32018,X32017)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__nth])]) ).

fof(i_0_5402,plain,
    ! [X21028,X21029] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21029)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X21028))) = 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),X21029),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21028))),
    inference(variable_rename,[status(thm)],[fact_zmod__number__of__Bit0]) ).

fof(i_0_5403,plain,
    ! [X25980,X25981] :
      ( ~ class_Rings_Olinordered__idom(X25981)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X25981),hAPP(c_Groups_Oabs__class_Oabs(X25981),X25980)),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(X25981),X25980),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_5404,plain,
    ! [X21403,X21404] :
      ( ~ class_Rings_Oring__1(X21404)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21404),hAPP(c_Groups_Ouminus__class_Ouminus(X21404),X21403)),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(X21404),X21403),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_5405,plain,
    ! [X21402] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X21402)),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,X21402,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_5406,plain,
    ! [X42,X12,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X9),X12))
       => ( hBOOL(hAPP(X42,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
         => ( ! [X46,X47] :
                ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X47))
               => ( hBOOL(hAPP(hAPP(c_member(X10),X46),X12))
                 => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X46),X47))
                   => ( hBOOL(hAPP(X42,X47))
                     => hBOOL(hAPP(X42,hAPP(hAPP(c_Set_Oinsert(X10),X46),X47))) ) ) ) )
           => hBOOL(hAPP(X42,X9)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__subset__induct]) ).

fof(i_0_5407,plain,
    ! [X20547,X20548] :
      ( ~ class_Int_Onumber__ring(X20548)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20548),hAPP(c_Int_Onumber__class_Onumber__of(X20548),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),X20547) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20548),X20547),X20547) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2])]) ).

fof(i_0_5408,plain,
    ! [X2,X42,X200,X10,X8] :
      ( class_Groups_Omonoid__add(X8)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
           => ( ~ hBOOL(hAPP(X42,X3))
             => hAPP(X2,X3) = c_Groups_Ozero__class_Ozero(X8) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),hAPP(c_List_Ofilter(X10,X42),X200))) = hAPP(c_List_Omonoid__add__class_Olistsum(X8),hAPP(hAPP(c_List_Omap(X10,X8),X2),X200)) ) ),
    inference(fof_simplification,[status(thm)],[fact_listsum__map__filter]) ).

fof(i_0_5409,plain,
    ! [X20569] : 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)))),X20569) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20569),X20569),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2]) ).

fof(i_0_5410,plain,
    ! [X20567] : 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)))),X20567) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,X20567)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc]) ).

fof(i_0_5411,plain,
    ! [X31976,X31977,X31978] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31978)),c_List_OdropWhile(X31978,X31977,X31976))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31978)),X31976))),
    inference(variable_rename,[status(thm)],[fact_length__dropWhile__le]) ).

fof(i_0_5412,plain,
    ! [X11,X12,X9,X1,X19,X2,X8,X10] :
      ( c_Finite__Set_Ofolding__image__simple(X10,X8,X2,X19,X1,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X8),X11),X12))
         => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X8),X11),X12)) = hAPP(hAPP(X2,hAPP(X1,X11)),hAPP(X9,X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__image__simple_Oinsert]) ).

fof(i_0_5413,plain,
    ! [X110,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(c_Relation_ORange(X8,X10),X110)))
     => ~ ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X10)),hAPP(hAPP(c_Product__Type_OPair(X8,X10),X3),X14)),X110)) ),
    inference(fof_simplification,[status(thm)],[fact_RangeE]) ).

fof(i_0_5414,plain,
    ! [X28554,X28555,X28556,X28557,X28558] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28558,X28558)),hAPP(hAPP(c_Product__Type_OPair(X28558,X28558),X28557),X28556)),c_Transitive__Closure_Otrancl(X28558,X28555)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28558,X28558)),hAPP(hAPP(c_Product__Type_OPair(X28558,X28558),X28556),X28554)),c_Transitive__Closure_Otrancl(X28558,X28555)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28558,X28558)),hAPP(hAPP(c_Product__Type_OPair(X28558,X28558),X28557),X28554)),c_Transitive__Closure_Otrancl(X28558,X28555))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__trans])]) ).

fof(i_0_5415,plain,
    ! [X28855,X28856,X28857,X28858] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28858,X28858)),hAPP(hAPP(c_Product__Type_OPair(X28858,X28858),X28857),X28856)),hAPP(c_Relation_Oconverse(X28858,X28858),c_Transitive__Closure_Otrancl(X28858,X28855))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28858,X28858)),hAPP(hAPP(c_Product__Type_OPair(X28858,X28858),X28857),X28856)),c_Transitive__Closure_Otrancl(X28858,hAPP(c_Relation_Oconverse(X28858,X28858),X28855)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseI])]) ).

fof(i_0_5416,plain,
    ! [X28851,X28852,X28853,X28854] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28854,X28854)),hAPP(hAPP(c_Product__Type_OPair(X28854,X28854),X28853),X28852)),c_Transitive__Closure_Otrancl(X28854,hAPP(c_Relation_Oconverse(X28854,X28854),X28851))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28854,X28854)),hAPP(hAPP(c_Product__Type_OPair(X28854,X28854),X28853),X28852)),hAPP(c_Relation_Oconverse(X28854,X28854),c_Transitive__Closure_Otrancl(X28854,X28851)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__converseD])]) ).

fof(i_0_5417,plain,
    ! [X11,X12,X13,X2,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X10,X10,X2,X13,X12),X11))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1Set_Ointros]) ).

fof(i_0_5418,plain,
    ! [X31996,X31997,X31998] :
      ( c_List_OdropWhile(X31998,X31997,X31996) = c_List_Olist_ONil(X31998)
      | ~ hBOOL(hAPP(X31997,hAPP(c_List_Ohd(X31998),c_List_OdropWhile(X31998,X31997,X31996)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5190])]) ).

fof(i_0_5419,plain,
    ! [X21411,X21412] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X21412),X21411),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Oone__class_Oone(X21412)
        | X21411 = c_Groups_Oone__class_Oone(X21412)
        | X21411 = hAPP(c_Groups_Ouminus__class_Ouminus(X21412),c_Groups_Oone__class_Oone(X21412))
        | ~ class_Rings_Oring__1__no__zero__divisors(X21412) )
      & ( X21411 != c_Groups_Oone__class_Oone(X21412)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21412),X21411),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21412)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21412) )
      & ( X21411 != hAPP(c_Groups_Ouminus__class_Ouminus(X21412),c_Groups_Oone__class_Oone(X21412))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X21412),X21411),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X21412)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21412) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__1__iff])])]) ).

fof(i_0_5420,plain,
    ! [X20559,X20560] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X20560),X20559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(X20560)
        | X20559 = c_Groups_Ozero__class_Ozero(X20560)
        | ~ class_Rings_Oring__1__no__zero__divisors(X20560) )
      & ( X20559 != c_Groups_Ozero__class_Ozero(X20560)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20560),X20559),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X20560)
        | ~ class_Rings_Oring__1__no__zero__divisors(X20560) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__eq__power2])])]) ).

fof(i_0_5421,plain,
    ! [X31281,X31282,X31283,X31284] : hAPP(c_List_OremoveAll(X31284,X31283),hAPP(hAPP(c_List_Oappend(X31284),X31282),X31281)) = hAPP(hAPP(c_List_Oappend(X31284),hAPP(c_List_OremoveAll(X31284,X31283),X31282)),hAPP(c_List_OremoveAll(X31284,X31283),X31281)),
    inference(variable_rename,[status(thm)],[fact_removeAll__append]) ).

fof(i_0_5422,plain,
    ! [X31474,X31475] : c_List_OremoveAll(X31475,X31474) = c_List_Ofilter(X31475,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31475),c_fNot),hAPP(c_fequal,X31474))),
    inference(variable_rename,[status(thm)],[fact_removeAll__filter__not__eq]) ).

fof(i_0_5423,plain,
    ! [X31866,X31867,X31868] : hAPP(c_List_Orotate(X31868,X31867),hAPP(c_List_Orev(X31868),X31866)) = hAPP(c_List_Orev(X31868),hAPP(c_List_Orotate(X31868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31868)),X31866)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X31867,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31868)),X31866)))),X31866)),
    inference(variable_rename,[status(thm)],[fact_rotate__rev]) ).

fof(i_0_5424,plain,
    ! [X30415,X30416] : c_List_Orotate(X30416,X30415) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(X30416),tc_List_Olist(X30416)),X30415),c_List_Orotate1(X30416)),
    inference(variable_rename,[status(thm)],[fact_rotate__def]) ).

fof(i_0_5425,plain,
    ! [X28692,X28693,X28694,X28695,X28696] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28696,X28696)),hAPP(hAPP(c_Product__Type_OPair(X28696,X28696),X28695),X28694)),c_Transitive__Closure_Ortrancl(X28696,X28693)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28696,X28696)),hAPP(hAPP(c_Product__Type_OPair(X28696,X28696),X28694),X28692)),c_Transitive__Closure_Otrancl(X28696,X28693)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28696,X28696)),hAPP(hAPP(c_Product__Type_OPair(X28696,X28696),X28695),X28692)),c_Transitive__Closure_Otrancl(X28696,X28693))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trancl__trancl])]) ).

fof(i_0_5426,plain,
    ! [X28697,X28698,X28699,X28700,X28701] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28701,X28701)),hAPP(hAPP(c_Product__Type_OPair(X28701,X28701),X28700),X28699)),c_Transitive__Closure_Otrancl(X28701,X28698)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28701,X28701)),hAPP(hAPP(c_Product__Type_OPair(X28701,X28701),X28699),X28697)),c_Transitive__Closure_Ortrancl(X28701,X28698)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28701,X28701)),hAPP(hAPP(c_Product__Type_OPair(X28701,X28701),X28700),X28697)),c_Transitive__Closure_Otrancl(X28701,X28698))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__rtrancl__trancl])]) ).

fof(i_0_5427,plain,
    ! [X28564,X28565,X28566,X28567,X28568] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28568,X28568)),hAPP(hAPP(c_Product__Type_OPair(X28568,X28568),X28567),X28566)),X28565))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28568,X28568)),hAPP(hAPP(c_Product__Type_OPair(X28568,X28568),X28566),X28564)),c_Transitive__Closure_Otrancl(X28568,X28565)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28568,X28568)),hAPP(hAPP(c_Product__Type_OPair(X28568,X28568),X28567),X28564)),c_Transitive__Closure_Otrancl(X28568,X28565))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__trancl2])]) ).

fof(i_0_5428,plain,
    ! [X28559,X28560,X28561,X28562,X28563] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28563,X28563)),hAPP(hAPP(c_Product__Type_OPair(X28563,X28563),X28562),X28561)),c_Transitive__Closure_Otrancl(X28563,X28560)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28563,X28563)),hAPP(hAPP(c_Product__Type_OPair(X28563,X28563),X28561),X28559)),X28560))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28563,X28563)),hAPP(hAPP(c_Product__Type_OPair(X28563,X28563),X28562),X28559)),c_Transitive__Closure_Otrancl(X28563,X28560))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Transitive__Closure_Otrancl__into__trancl])]) ).

fof(i_0_5429,plain,
    ! [X10,X13,X42] :
      ( ( hBOOL(hAPP(X42,X13))
       => hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X42)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X42,X13))
       => hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(hAPP(c_COMBC(X10,X10,tc_HOL_Obool),c_fequal),X13))),X42)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__conv__if]) ).

fof(i_0_5430,plain,
    ! [X31556,X31557,X31558,X31559,X31560,X31561,X31562] : c_List_Ofoldr(X31562,X31561,X31560,hAPP(hAPP(c_List_Omap(X31559,X31562),X31558),X31557),X31556) = c_List_Ofoldr(X31559,X31561,hAPP(c_Fun_Ocomp(X31562,tc_fun(X31561,X31561),X31559,X31560),X31558),X31557,X31556),
    inference(variable_rename,[status(thm)],[fact_foldr__map]) ).

fof(i_0_5431,plain,
    ! [X16,X2,X8,X12,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Set_Oimage(X10,X8,c_Fun_Ofun__upd(X10,X8,X2,X11,X16)),X12) = hAPP(hAPP(c_Set_Oinsert(X8),X16),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Set_Oimage(X10,X8,c_Fun_Ofun__upd(X10,X8,X2,X11,X16)),X12) = hAPP(c_Set_Oimage(X10,X8,X2),X12) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__upd__image]) ).

fof(i_0_5432,plain,
    ! [X28580,X28581,X28582] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28582,X28582),tc_HOL_Obool)),X28581),hAPP(hAPP(c_Product__Type_OSigma(X28582,X28582),X28580),hAPP(c_COMBK(tc_fun(X28582,tc_HOL_Obool),X28582),X28580))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28582,X28582),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28582,X28581)),hAPP(hAPP(c_Product__Type_OSigma(X28582,X28582),X28580),hAPP(c_COMBK(tc_fun(X28582,tc_HOL_Obool),X28582),X28580)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma])]) ).

fof(i_0_5433,plain,
    ! [X20130,X20131,X20132] :
      ( ( ~ 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),X20131)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20132),hAPP(c_Int_Onumber__class_Onumber__of(X20132),X20130)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X20131))) = hAPP(hAPP(c_HOL_OLet(X20132,X20132),hAPP(hAPP(c_Power_Opower__class_Opower(X20132),hAPP(c_Int_Onumber__class_Onumber__of(X20132),X20130)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20131))),hAPP(hAPP(c_COMBS(X20132,X20132,X20132),hAPP(hAPP(c_COMBB(X20132,tc_fun(X20132,X20132),X20132),c_Groups_Otimes__class_Otimes(X20132)),hAPP(c_Groups_Otimes__class_Otimes(X20132),hAPP(c_Int_Onumber__class_Onumber__of(X20132),X20130)))),c_COMBI(X20132)))
        | ~ class_Int_Onumber__ring(X20132) )
      & ( 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),X20131)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20132),hAPP(c_Int_Onumber__class_Onumber__of(X20132),X20130)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X20131))) = c_Groups_Oone__class_Oone(X20132)
        | ~ class_Int_Onumber__ring(X20132) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5191])])]) ).

fof(i_0_5434,plain,
    ! [X14,X13] :
      ( 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),X13),X14)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => c_Nitpick_Onorm__frac(X13,X14) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => ( ( ( X13 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X14 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X13,X14) = 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)) )
            & ( ~ ( X13 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                  | X14 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
             => c_Nitpick_Onorm__frac(X13,X14) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X13),X14)),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),X13))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_norm__frac_Opsimps]) ).

fof(i_0_5435,plain,
    ! [X31547,X31548,X31549,X31550,X31551,X31552] : c_List_Ofoldr(X31552,X31551,X31550,hAPP(hAPP(c_List_Oappend(X31552),X31549),X31548),X31547) = c_List_Ofoldr(X31552,X31551,X31550,X31549,c_List_Ofoldr(X31552,X31551,X31550,X31548,X31547)),
    inference(variable_rename,[status(thm)],[fact_foldr__append]) ).

fof(i_0_5436,plain,
    ! [X15,X11,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),X15)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),X15)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
         => ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X15)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_psubset__insert__iff]) ).

fof(i_0_5437,plain,
    ! [X16,X110,X10] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X110))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X16),X16)),c_List_Olexord(X10,X110))) ),
    inference(fof_simplification,[status(thm)],[fact_lexord__irreflexive]) ).

fof(i_0_5438,plain,
    ! [X20514,X20515] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X20515)),c_Int_OBit1(X20514)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(X20515)),X20514)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I8_J]) ).

fof(i_0_5439,plain,
    ! [X12,X13,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,hAPP(hAPP(c_Set_Oinsert(X10),X13),X12))
    <=> ( c_Fun_Oinj__on(X10,X8,X2,X12)
        & ~ hBOOL(hAPP(hAPP(c_member(X8),hAPP(X2,X13)),hAPP(c_Set_Oimage(X10,X8,X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_inj__on__insert]) ).

fof(i_0_5440,plain,
    ! [X27811,X27812] : c_Product__Type_Oapfst(X27812,X27812,X27811,c_Fun_Oid(X27812)) = c_Fun_Oid(tc_prod(X27812,X27811)),
    inference(variable_rename,[status(thm)],[fact_apfst__id]) ).

fof(i_0_5441,plain,
    ! [X27802,X27803] : c_Product__Type_Oapsnd(X27803,X27803,X27802,c_Fun_Oid(X27803)) = c_Fun_Oid(tc_prod(X27802,X27803)),
    inference(variable_rename,[status(thm)],[fact_apsnd__id]) ).

fof(i_0_5442,plain,
    ! [X28614,X28615] : c_Transitive__Closure_Otrancl(X28615,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28615,X28615),tc_HOL_Obool)),X28614),c_Relation_OId(X28615))) = c_Transitive__Closure_Ortrancl(X28615,X28614),
    inference(variable_rename,[status(thm)],[fact_trancl__reflcl]) ).

fof(i_0_5443,plain,
    ! [X15,X11,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),X15)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))),X15)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert__iff]) ).

fof(i_0_5444,plain,
    ! [X21430,X21431] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X21431),X21430) != c_Groups_Oone__class_Oone(X21431)
        | c_Int_Oiszero(X21431,hAPP(c_Int_Onumber__class_Onumber__of(X21431),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21430),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | ~ class_Int_Onumber__ring(X21431) )
      & ( ~ c_Int_Oiszero(X21431,hAPP(c_Int_Onumber__class_Onumber__of(X21431),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21430),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X21431),X21430) = c_Groups_Oone__class_Oone(X21431)
        | ~ class_Int_Onumber__ring(X21431) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I4_J])])]) ).

fof(i_0_5445,plain,
    ! [X21428,X21429] :
      ( ( c_Groups_Oone__class_Oone(X21429) != hAPP(c_Int_Onumber__class_Onumber__of(X21429),X21428)
        | c_Int_Oiszero(X21429,hAPP(c_Int_Onumber__class_Onumber__of(X21429),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),X21428))))
        | ~ class_Int_Onumber__ring(X21429) )
      & ( ~ c_Int_Oiszero(X21429,hAPP(c_Int_Onumber__class_Onumber__of(X21429),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),X21428))))
        | c_Groups_Oone__class_Oone(X21429) = hAPP(c_Int_Onumber__class_Onumber__of(X21429),X21428)
        | ~ class_Int_Onumber__ring(X21429) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I2_J])])]) ).

fof(i_0_5446,plain,
    ! [X13,X14] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Nitpick_Onorm__frac(X13,X14) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X14)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => ( ( ( X13 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | X14 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X13,X14) = 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)) )
          & ( ~ ( X13 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                | X14 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
           => c_Nitpick_Onorm__frac(X13,X14) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X13),X14)),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),X13))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_norm__frac_Osimps]) ).

fof(i_0_5447,plain,
    ! [X32031,X32032,X32033] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32033),esk439_3(X32031,X32032,X32033)),hAPP(c_List_Oset(X32033),c_List_OdropWhile(X32033,X32032,X32031))))
        | c_List_OtakeWhile(X32033,X32032,X32031) = hAPP(c_List_Ofilter(X32033,X32032),X32031) )
      & ( hBOOL(hAPP(X32032,esk439_3(X32031,X32032,X32033)))
        | c_List_OtakeWhile(X32033,X32032,X32031) = hAPP(c_List_Ofilter(X32033,X32032),X32031) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5192])])])]) ).

fof(i_0_5448,plain,
    ! [X28711,X28712,X28713,X28714,X28715] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28715,X28715)),hAPP(hAPP(c_Product__Type_OPair(X28715,X28715),X28714),X28713)),X28712))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28715,X28715)),hAPP(hAPP(c_Product__Type_OPair(X28715,X28715),X28713),X28711)),c_Transitive__Closure_Ortrancl(X28715,X28712)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28715,X28715)),hAPP(hAPP(c_Product__Type_OPair(X28715,X28715),X28714),X28711)),c_Transitive__Closure_Otrancl(X28715,X28712))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl2])]) ).

fof(i_0_5449,plain,
    ! [X28702,X28703,X28704,X28705,X28706] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28706,X28706)),hAPP(hAPP(c_Product__Type_OPair(X28706,X28706),X28705),X28704)),c_Transitive__Closure_Ortrancl(X28706,X28703)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28706,X28706)),hAPP(hAPP(c_Product__Type_OPair(X28706,X28706),X28704),X28702)),X28703))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28706,X28706)),hAPP(hAPP(c_Product__Type_OPair(X28706,X28706),X28705),X28702)),c_Transitive__Closure_Otrancl(X28706,X28703))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__into__trancl1])]) ).

fof(i_0_5450,plain,
    ! [X20137,X20138,X20139] :
      ( ( ~ 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),X20138)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20139),X20137),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X20138))) = hAPP(hAPP(c_HOL_OLet(X20139,X20139),hAPP(hAPP(c_Power_Opower__class_Opower(X20139),X20137),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20138))),hAPP(hAPP(c_COMBS(X20139,X20139,X20139),hAPP(hAPP(c_COMBB(X20139,tc_fun(X20139,X20139),X20139),c_Groups_Otimes__class_Otimes(X20139)),hAPP(c_Groups_Otimes__class_Otimes(X20139),X20137))),c_COMBI(X20139)))
        | ~ class_Int_Onumber__ring(X20139) )
      & ( 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),X20138)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20139),X20137),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X20138))) = c_Groups_Oone__class_Oone(X20139)
        | ~ class_Int_Onumber__ring(X20139) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5193])])]) ).

fof(i_0_5451,plain,
    ! [X20589,X20590] :
      ( ~ class_Groups_Omonoid__mult(X20590)
      | ~ class_Int_Onumber(X20590)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20590),hAPP(c_Int_Onumber__class_Onumber__of(X20590),X20589)),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(X20590),hAPP(c_Int_Onumber__class_Onumber__of(X20590),X20589)),hAPP(c_Int_Onumber__class_Onumber__of(X20590),X20589)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of])]) ).

fof(i_0_5452,plain,
    ! [X28569,X28570,X28571,X28572,X28573] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28573,X28573)),hAPP(hAPP(c_Product__Type_OPair(X28573,X28573),X28572),X28571)),X28570))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28573,X28573)),hAPP(hAPP(c_Product__Type_OPair(X28573,X28573),X28571),X28569)),X28570))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28573,X28573)),hAPP(hAPP(c_Product__Type_OPair(X28573,X28573),X28572),X28569)),c_Transitive__Closure_Otrancl(X28573,X28570))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).

fof(i_0_5453,plain,
    ! [X110,X8,X13,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(c_Relation_ODomain(X10,X8),X110)))
     => ~ ! [X51] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X51)),X110)) ),
    inference(fof_simplification,[status(thm)],[fact_DomainE]) ).

fof(i_0_5454,plain,
    ! [X21000] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21000),X21000)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = X21000,
    inference(variable_rename,[status(thm)],[fact_add__self__div__2]) ).

fof(i_0_5455,plain,
    ! [X20,X6,X14,X13] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6,X20)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14))
        | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X6),X13))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X20)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__subset__iff]) ).

fof(i_0_5456,plain,
    ! [X20549,X20550] :
      ( ~ class_Int_Onumber__ring(X20550)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20550),X20549),hAPP(c_Int_Onumber__class_Onumber__of(X20550),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20550),X20549),X20549) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__2__right])]) ).

fof(i_0_5457,plain,
    ! [X20564,X20565] :
      ( ~ class_Groups_Omonoid__mult(X20565)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20565),X20564),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(X20565),X20564),X20564) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power2__eq__square])]) ).

fof(i_0_5458,plain,
    ! [X20562,X20563] :
      ( ~ class_Rings_Ocomm__semiring__1(X20563)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20563),X20562),X20562) = hAPP(hAPP(c_Power_Opower__class_Opower(X20563),X20562),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_5459,plain,
    ! [X13,X6,X14,X15,X12,X18,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_fun(X18,tc_HOL_Obool))),X12),X15),X14),X6))
     => ( ~ hBOOL(hAPP(hAPP(hAPP(X15,X13),X14),X6))
       => ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INF2__E]) ).

fof(i_0_5460,plain,
    ! [X20570] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20570),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),X20570),X20570),
    inference(variable_rename,[status(thm)],[fact_nat__mult__2__right]) ).

fof(i_0_5461,plain,
    ! [X20566] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20566),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,X20566)),
    inference(variable_rename,[status(thm)],[fact_add__2__eq__Suc_H]) ).

fof(i_0_5462,plain,
    ! [X20561] :
      ( ~ class_Rings_Osemiring__1(X20561)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20561),c_Groups_Ozero__class_Ozero(X20561)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(X20561) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__power2])]) ).

fof(i_0_5463,plain,
    ! [X20568] :
      ( ~ class_Rings_Osemiring__1(X20568)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20568),c_Groups_Oone__class_Oone(X20568)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(X20568) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__power2])]) ).

fof(i_0_5464,plain,
    ! [X93,X2,X8,X200,X16,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X16),hAPP(c_List_Oset(X10),X200)))
     => hAPP(hAPP(c_List_Omap(X10,X8),c_Fun_Ofun__upd(X10,X8,X2,X16,X93)),X200) = hAPP(hAPP(c_List_Omap(X10,X8),X2),X200) ),
    inference(fof_simplification,[status(thm)],[fact_map__fun__upd]) ).

fof(i_0_5465,plain,
    ! [X20133,X20134] :
      ( ( ~ 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),X20134)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X20134))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20134))),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),X20133))),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),X20134)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20133),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X20134))) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5194])]) ).

fof(i_0_5466,plain,
    ! [X28574,X28575,X28576,X28577] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28577,X28577)),X28576),c_Transitive__Closure_Otrancl(X28577,X28575)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28577,X28577),tc_HOL_Obool)),X28575),X28574))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28577,X28577)),X28576),c_Transitive__Closure_Otrancl(X28577,X28574))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__mono])]) ).

fof(i_0_5467,plain,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__ring(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X26),X26)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X34),X34))),c_Groups_Ozero__class_Ozero(X27))) ),
    inference(fof_simplification,[status(thm)],[fact_not__sum__squares__lt__zero]) ).

fof(i_0_5468,plain,
    ! [X28539,X28540] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28540,X28540),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28540,X28539)),hAPP(hAPP(c_Product__Type_OSigma(X28540,X28540),hAPP(c_Relation_OField(X28540),X28539)),hAPP(c_COMBK(tc_fun(X28540,tc_HOL_Obool),X28540),hAPP(c_Relation_OField(X28540),X28539))))),
    inference(variable_rename,[status(thm)],[fact_trancl__subset__Field2]) ).

fof(i_0_5469,plain,
    ! [X16,X11,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16))
     => ( ~ hBOOL(hAPP(hAPP(X12,X11),X16))
       => hBOOL(hAPP(hAPP(X15,X11),X16)) ) ),
    inference(fof_simplification,[status(thm)],[fact_sup2E]) ).

fof(i_0_5470,plain,
    ! [X28716,X28717,X28718,X28719] :
      ( ( X28718 != X28717
        | X28718 = X28717
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28719,X28719)),hAPP(hAPP(c_Product__Type_OPair(X28719,X28719),X28718),X28717)),c_Transitive__Closure_Ortrancl(X28719,X28716))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28719,X28719)),hAPP(hAPP(c_Product__Type_OPair(X28719,X28719),X28718),X28717)),c_Transitive__Closure_Otrancl(X28719,X28716)))
        | X28718 = X28717
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28719,X28719)),hAPP(hAPP(c_Product__Type_OPair(X28719,X28719),X28718),X28717)),c_Transitive__Closure_Ortrancl(X28719,X28716))) )
      & ( X28718 != X28717
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28719,X28719)),hAPP(hAPP(c_Product__Type_OPair(X28719,X28719),X28718),X28717)),c_Transitive__Closure_Ortrancl(X28719,X28716))) )
      & ( X28718 = X28717
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28719,X28719)),hAPP(hAPP(c_Product__Type_OPair(X28719,X28719),X28718),X28717)),c_Transitive__Closure_Otrancl(X28719,X28716)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28719,X28719)),hAPP(hAPP(c_Product__Type_OPair(X28719,X28719),X28718),X28717)),c_Transitive__Closure_Ortrancl(X28719,X28716))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__eq__or__trancl])])]) ).

fof(i_0_5471,plain,
    ! [X28604,X28605,X28606,X28607] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28607,X28607)),hAPP(hAPP(c_Product__Type_OPair(X28607,X28607),X28606),X28605)),c_Transitive__Closure_Otrancl(X28607,X28604)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28607,X28607)),hAPP(hAPP(c_Product__Type_OPair(X28607,X28607),X28606),X28605)),c_Transitive__Closure_Ortrancl(X28607,X28604))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__into__rtrancl])]) ).

fof(i_0_5472,plain,
    ! [X16,X11,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16))
     => ~ ( hBOOL(hAPP(hAPP(X12,X11),X16))
         => ~ hBOOL(hAPP(hAPP(X15,X11),X16)) ) ),
    inference(fof_simplification,[status(thm)],[fact_inf2E]) ).

fof(i_0_5473,plain,
    ! [X19970,X19971] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X19971)),c_Int_OBit1(X19970)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19971),X19970)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19971),X19970))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X19971)),c_Int_OBit1(X19970))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I16_J])]) ).

fof(i_0_5474,plain,
    ! [X19968,X19969] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X19969)),c_Int_OBit1(X19968)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),X19968)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19969),X19968))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X19969)),c_Int_OBit1(X19968))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I17_J])]) ).

fof(i_0_5475,plain,
    ! [X19966,X19967] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X19967)),c_Int_OBit1(X19966)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19967),X19966)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19967),X19966))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X19967)),c_Int_OBit1(X19966))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I16_J])]) ).

fof(i_0_5476,plain,
    ! [X19964,X19965] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X19965)),c_Int_OBit1(X19964)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19965),X19964)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19965),X19964))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X19965)),c_Int_OBit1(X19964))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I34_J])]) ).

fof(i_0_5477,plain,
    ! [X31259,X31260,X31261] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31261),X31260))
      | hBOOL(hAPP(c_List_Odistinct(X31261),hAPP(c_List_OremoveAll(X31261,X31259),X31260))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__removeAll])]) ).

fof(i_0_5478,plain,
    ! [X31248,X31249,X31250,X31251,X31252] :
      ( ~ c_Fun_Oinj__on(X31252,X31251,X31250,hAPP(hAPP(c_Set_Oinsert(X31252),X31249),hAPP(c_List_Oset(X31252),X31248)))
      | hAPP(hAPP(c_List_Omap(X31252,X31251),X31250),hAPP(c_List_OremoveAll(X31252,X31249),X31248)) = hAPP(c_List_OremoveAll(X31251,hAPP(X31250,X31249)),hAPP(hAPP(c_List_Omap(X31252,X31251),X31250),X31248)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj__on])]) ).

fof(i_0_5479,plain,
    ! [X28764,X28765,X28766] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28766,X28766),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X28766,X28766),X28765)),c_Transitive__Closure_Ortrancl(X28766,X28765)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28766,X28766),tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28766,X28766)),hAPP(hAPP(c_Product__Type_OPair(X28766,X28766),X28764),X28764)),c_Transitive__Closure_Otrancl(X28766,X28765))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5195])]) ).

fof(i_0_5480,plain,
    ! [X32004,X32005,X32006,X32007,X32008] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32008),X32007),hAPP(c_List_Oset(X32008),X32006)))
      | hBOOL(hAPP(X32005,X32007))
      | c_List_OdropWhile(X32008,X32005,hAPP(hAPP(c_List_Oappend(X32008),X32006),X32004)) = hAPP(hAPP(c_List_Oappend(X32008),c_List_OdropWhile(X32008,X32005,X32006)),X32004) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5196])]) ).

fof(i_0_5481,plain,
    ! [X32149,X32150,X32151,X32152] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32152),esk451_4(X32149,X32150,X32151,X32152)),hAPP(c_List_Oset(X32152),X32151)))
        | c_List_OdropWhile(X32152,X32150,hAPP(hAPP(c_List_Oappend(X32152),X32151),X32149)) = c_List_OdropWhile(X32152,X32150,X32149) )
      & ( ~ hBOOL(hAPP(X32150,esk451_4(X32149,X32150,X32151,X32152)))
        | c_List_OdropWhile(X32152,X32150,hAPP(hAPP(c_List_Oappend(X32152),X32151),X32149)) = c_List_OdropWhile(X32152,X32150,X32149) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dropWhile__append2])])])]) ).

fof(i_0_5482,plain,
    ! [X31303,X31304,X31305,X31306,X31307] :
      ( ~ c_Fun_Oinj__on(X31307,X31306,X31305,c_Orderings_Otop__class_Otop(tc_fun(X31307,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(X31307,X31306),X31305),hAPP(c_List_OremoveAll(X31307,X31304),X31303)) = hAPP(c_List_OremoveAll(X31306,hAPP(X31305,X31304)),hAPP(hAPP(c_List_Omap(X31307,X31306),X31305),X31303)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__removeAll__inj])]) ).

fof(i_0_5483,plain,
    ! [X200,X42,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
     => ~ hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_OtakeWhile(X10,X42,X200))))) ),
    inference(fof_simplification,[status(thm)],[fact_nth__length__takeWhile]) ).

fof(i_0_5484,plain,
    ! [X31568,X31569] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31569))),c_List_Otranspose(X31569,X31568)) = c_List_Ofoldr(tc_List_Olist(X31569),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(X31569)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X31569))),X31568,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__transpose]) ).

fof(i_0_5485,plain,
    ! [X29010,X29011,X29012,X29014,X29015,X29016,X29017] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk339_3(X29010,X29011,X29012)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29012,X29012)),X29011),c_Transitive__Closure_Otrancl(X29012,X29010))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29012,X29012)),X29011),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29012,X29012),tc_HOL_Obool),esk339_3(X29010,X29011,X29012)),X29010)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29012,X29012)),X29011),c_Transitive__Closure_Otrancl(X29012,X29010))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29017))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29016,X29016)),X29015),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29016,X29016),tc_HOL_Obool),X29017),X29014)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29016,X29016)),X29015),c_Transitive__Closure_Otrancl(X29016,X29014))) ) ),
    inference(distribute,[status(thm)],[inference(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_5486,plain,
    ! [X31364,X31365,X31366] : c_List_Oconcat(X31366,hAPP(hAPP(c_List_Oappend(tc_List_Olist(X31366)),X31365),X31364)) = hAPP(hAPP(c_List_Oappend(X31366),c_List_Oconcat(X31366,X31365)),c_List_Oconcat(X31366,X31364)),
    inference(variable_rename,[status(thm)],[fact_concat__append]) ).

fof(i_0_5487,plain,
    ! [X61,X13,X200,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),X200))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(c_List_Oset(X10),X200)),hAPP(hAPP(c_Set_Oinsert(X10),hAPP(hAPP(c_List_Onth(X10),X200),X61)),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olist__update(X10,X200),X61),X13))) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct__list__update]) ).

fof(i_0_5488,plain,
    ! [X12,X2,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_Oimage(X8,X10,X2),X12))),hAPP(c_Finite__Set_Ocard(X8),X12)))
     => ~ c_Fun_Oinj__on(X8,X10,X2,X12) ),
    inference(fof_simplification,[status(thm)],[fact_pigeonhole]) ).

fof(i_0_5489,plain,
    ! [X28707,X28708,X28709,X28710] :
      ( ( X28709 != X28708
        | X28709 = X28708
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28710,X28710)),hAPP(hAPP(c_Product__Type_OPair(X28710,X28710),X28709),X28708)),c_Transitive__Closure_Ortrancl(X28710,X28707))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28710,X28710)),hAPP(hAPP(c_Product__Type_OPair(X28710,X28710),X28709),X28708)),c_Transitive__Closure_Otrancl(X28710,X28707)))
        | X28709 = X28708
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28710,X28710)),hAPP(hAPP(c_Product__Type_OPair(X28710,X28710),X28709),X28708)),c_Transitive__Closure_Ortrancl(X28710,X28707))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtranclD])])]) ).

fof(i_0_5490,plain,
    ! [X42,X200,X10,X30] :
      ( ! [X91] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),X30))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X91),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
           => hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X91))) ) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)))
         => ~ hBOOL(hAPP(X42,hAPP(hAPP(c_List_Onth(X10),X200),X30))) )
       => c_List_OtakeWhile(X10,X42,X200) = hAPP(hAPP(c_List_Otake(X10),X30),X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__eq__take__P__nth]) ).

fof(i_0_5491,plain,
    ! [X28535,X28536,X28537,X28538] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28538,X28538)),hAPP(hAPP(c_Product__Type_OPair(X28538,X28538),X28537),X28536)),X28535))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28538,X28538)),hAPP(hAPP(c_Product__Type_OPair(X28538,X28538),X28537),X28536)),c_Transitive__Closure_Otrancl(X28538,X28535))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl_Or__into__trancl])]) ).

fof(i_0_5492,plain,
    ! [X33813,X33814,X33815,X33816] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33816))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33815),X33813))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33815),X33813))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33816))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33813),X33815))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33816))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33815),X33813))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33814))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33813),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33814))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33813))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33813))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33816))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816),X33814))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33816))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33815),X33813))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33813))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33815),X33813))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33813),X33815))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33816))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33815),X33813))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814),X33813))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33816,X33815)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33814,X33813))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5197])])]) ).

fof(i_0_5493,plain,
    ! [X90,X6,X14,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6)),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of]) ).

fof(i_0_5494,plain,
    ! [X90,X6,X14,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6)),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of]) ).

fof(i_0_5495,plain,
    ! [X6,X14,X90,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6)),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of]) ).

fof(i_0_5496,plain,
    ! [X6,X14,X90,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6)),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),X6))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of]) ).

fof(i_0_5497,plain,
    ! [X11,X16,X12,X2,X8,X10] :
      ( c_Fun_Oinj__on(X10,X8,X2,X12)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X8),X16),hAPP(c_Set_Oimage(X10,X8,X2),X12)))
       => c_Fun_Oinj__on(X10,X8,c_Fun_Ofun__upd(X10,X8,X2,X11,X16),X12) ) ),
    inference(fof_simplification,[status(thm)],[fact_inj__on__fun__updI]) ).

fof(i_0_5498,plain,
    ! [X32089,X32090] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32090)),esk446_2(X32089,X32090)),hAPP(c_List_Oset(tc_List_Olist(X32090)),X32089)))
        | hBOOL(hAPP(c_List_Odistinct(X32090),c_List_Oconcat(X32090,X32089)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32090)),esk445_2(X32089,X32090)),hAPP(c_List_Oset(tc_List_Olist(X32090)),X32089)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32090)),X32089)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32090)),esk447_2(X32089,X32090)),hAPP(c_List_Oset(tc_List_Olist(X32090)),X32089)))
        | hBOOL(hAPP(c_List_Odistinct(X32090),c_List_Oconcat(X32090,X32089)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32090)),esk445_2(X32089,X32090)),hAPP(c_List_Oset(tc_List_Olist(X32090)),X32089)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32090)),X32089)) )
      & ( esk446_2(X32089,X32090) != esk447_2(X32089,X32090)
        | hBOOL(hAPP(c_List_Odistinct(X32090),c_List_Oconcat(X32090,X32089)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32090)),esk445_2(X32089,X32090)),hAPP(c_List_Oset(tc_List_Olist(X32090)),X32089)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32090)),X32089)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32090,tc_HOL_Obool)),hAPP(c_List_Oset(X32090),esk446_2(X32089,X32090))),hAPP(c_List_Oset(X32090),esk447_2(X32089,X32090))) != c_Orderings_Obot__class_Obot(tc_fun(X32090,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X32090),c_List_Oconcat(X32090,X32089)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32090)),esk445_2(X32089,X32090)),hAPP(c_List_Oset(tc_List_Olist(X32090)),X32089)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32090)),X32089)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32090)),esk446_2(X32089,X32090)),hAPP(c_List_Oset(tc_List_Olist(X32090)),X32089)))
        | hBOOL(hAPP(c_List_Odistinct(X32090),c_List_Oconcat(X32090,X32089)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32090),esk445_2(X32089,X32090)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32090)),X32089)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32090)),esk447_2(X32089,X32090)),hAPP(c_List_Oset(tc_List_Olist(X32090)),X32089)))
        | hBOOL(hAPP(c_List_Odistinct(X32090),c_List_Oconcat(X32090,X32089)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32090),esk445_2(X32089,X32090)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32090)),X32089)) )
      & ( esk446_2(X32089,X32090) != esk447_2(X32089,X32090)
        | hBOOL(hAPP(c_List_Odistinct(X32090),c_List_Oconcat(X32090,X32089)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32090),esk445_2(X32089,X32090)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32090)),X32089)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32090,tc_HOL_Obool)),hAPP(c_List_Oset(X32090),esk446_2(X32089,X32090))),hAPP(c_List_Oset(X32090),esk447_2(X32089,X32090))) != c_Orderings_Obot__class_Obot(tc_fun(X32090,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X32090),c_List_Oconcat(X32090,X32089)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X32090),esk445_2(X32089,X32090)))
        | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X32090)),X32089)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__concat])])])]) ).

fof(i_0_5499,plain,
    ! [X10,X13,X42] :
      ( ( hBOOL(hAPP(X42,X13))
       => hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X13))),X42)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X42,X13))
       => hAPP(c_Set_OCollect(X10),hAPP(hAPP(c_COMBS(X10,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X10),c_fconj),hAPP(c_fequal,X13))),X42)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__conv__if2]) ).

fof(i_0_5500,plain,
    ! [X30449,X30450,X30451] : hAPP(c_List_Orotate(X30451,X30450),X30449) = hAPP(hAPP(c_List_Oappend(X30451),hAPP(hAPP(c_List_Odrop(X30451),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30450,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30451)),X30449))),X30449)),hAPP(hAPP(c_List_Otake(X30451),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30450,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30451)),X30449))),X30449)),
    inference(variable_rename,[status(thm)],[fact_rotate__drop__take]) ).

fof(i_0_5501,plain,
    ! [X28529,X28530,X28531,X28532,X28533] :
      ( ( ~ c_Wellfounded_Oacyclic(X28530,X28529)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28530,X28530)),hAPP(hAPP(c_Product__Type_OPair(X28530,X28530),X28531),X28531)),c_Transitive__Closure_Otrancl(X28530,X28529))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28533,X28533)),hAPP(hAPP(c_Product__Type_OPair(X28533,X28533),esk333_2(X28532,X28533)),esk333_2(X28532,X28533))),c_Transitive__Closure_Otrancl(X28533,X28532)))
        | c_Wellfounded_Oacyclic(X28533,X28532) ) ),
    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_5198])])])])]) ).

fof(i_0_5502,plain,
    ! [X199,X200,X16,X11,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X11),X16)),hAPP(c_List_Oset(tc_prod(X10,X8)),hAPP(hAPP(c_List_Ozip(X10,X8),X200),X199))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
         => ~ hBOOL(hAPP(hAPP(c_member(X8),X16),hAPP(c_List_Oset(X8),X199))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__zipE]) ).

fof(i_0_5503,plain,
    ! [X31277,X31278,X31279,X31280] :
      ( ( X31280 != X31279
        | hAPP(c_List_OremoveAll(X31278,X31280),hAPP(hAPP(c_List_Olist_OCons(X31278),X31279),X31277)) = hAPP(c_List_OremoveAll(X31278,X31280),X31277) )
      & ( X31280 = X31279
        | hAPP(c_List_OremoveAll(X31278,X31280),hAPP(hAPP(c_List_Olist_OCons(X31278),X31279),X31277)) = hAPP(hAPP(c_List_Olist_OCons(X31278),X31279),hAPP(c_List_OremoveAll(X31278,X31280),X31277)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_removeAll_Osimps_I2_J])]) ).

fof(i_0_5504,plain,
    ! [X110,X11,X16,X10] :
      ( c_Wellfounded_Oacyclic(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X11)),X110))
    <=> ( c_Wellfounded_Oacyclic(X10,X110)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X110))) ) ),
    inference(fof_simplification,[status(thm)],[fact_acyclic__insert]) ).

fof(i_0_5505,plain,
    ! [X110,X11,X16,X10] :
      ( c_Wellfounded_Owf(X10,hAPP(hAPP(c_Set_Oinsert(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X16),X11)),X110))
    <=> ( c_Wellfounded_Owf(X10,X110)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X110))) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__insert]) ).

fof(i_0_5506,plain,
    ! [X28578,X28579] : c_Transitive__Closure_Otrancl(X28579,X28578) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28579,X28579),tc_HOL_Obool)),X28578),hAPP(hAPP(c_Relation_Orel__comp(X28579,X28579,X28579),c_Transitive__Closure_Otrancl(X28579,X28578)),X28578)),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold]) ).

fof(i_0_5507,plain,
    ! [X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
    <=> ! [X195] :
          ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X10),X3),X195))
         => ? [X3] :
              ( hBOOL(hAPP(hAPP(c_member(X10),X3),X195))
              & ! [X51] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X51),X3)),X110))
                 => ~ hBOOL(hAPP(hAPP(c_member(X10),X51),X195)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__eq__minimal]) ).

fof(i_0_5508,plain,
    ! [X20419,X20420] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20420)),c_Int_OBit0(X20419)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20420),X20419)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20420),X20419))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20420)),c_Int_OBit0(X20419))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I15_J])]) ).

fof(i_0_5509,plain,
    ! [X20417,X20418] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20418)),c_Int_OBit0(X20417)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20418),X20417)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20418),X20417))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20418)),c_Int_OBit0(X20417))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I16_J])]) ).

fof(i_0_5510,plain,
    ! [X20501,X20502] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20502)),c_Int_OBit0(X20501)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20502),X20501)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20502),X20501))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20502)),c_Int_OBit0(X20501))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I15_J])]) ).

fof(i_0_5511,plain,
    ! [X20499,X20500] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20500)),c_Int_OBit0(X20499)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20500),X20499)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20500),X20499))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20500)),c_Int_OBit0(X20499))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I33_J])]) ).

fof(i_0_5512,plain,
    ! [X26032,X26033] : c_Nitpick_Oint__lcm(X26033,X26032) = 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),X26033)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26032)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__lcm__def]) ).

fof(i_0_5513,plain,
    ! [X26030,X26031] : c_Nitpick_Onat__lcm(X26031,X26030) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X26031),X26030)),c_Nitpick_Onat__gcd(X26031,X26030)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Onat__lcm__def]) ).

fof(i_0_5514,plain,
    ! [X31541,X31542,X31543,X31544,X31545,X31546] : c_List_Ofoldr(X31546,X31545,X31544,hAPP(hAPP(c_List_Olist_OCons(X31546),X31543),X31542),X31541) = hAPP(hAPP(X31544,X31543),c_List_Ofoldr(X31546,X31545,X31544,X31542,X31541)),
    inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I2_J]) ).

fof(i_0_5515,plain,
    ! [X11,X13,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X11)),X110))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X13)),X110)) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__not__sym]) ).

fof(i_0_5516,plain,
    ! [X11,X13,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X11)),X110))
       => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X13)),X110)) ) ),
    inference(fof_simplification,[status(thm)],[fact_wf__asym]) ).

fof(i_0_5517,plain,
    ! [X155,X30,X31] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X31,X30),X155))
    <=> ( X31 = 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),X155)),X30)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X155))
        & ( X30 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X155) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( X30 != 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)),X30))
             => ( 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),X155)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X155)),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),X30),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X155)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X155)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__nat__rel__def]) ).

fof(i_0_5518,plain,
    ! [X13,X90,X14,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X13))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq__number__of1]) ).

fof(i_0_5519,plain,
    ! [X13,X90,X14,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X13))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq__number__of1]) ).

fof(i_0_5520,plain,
    ! [X21338] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(X21338)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21338))),
    inference(variable_rename,[status(thm)],[fact_minus__Bit1]) ).

fof(i_0_5521,plain,
    ! [X42,X57,X152] :
      ( 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),X152),X57)))
     => ( ! [X75,X91] :
            ( 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),X75),X91)))
           => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X75),X91))
               => hBOOL(hAPP(hAPP(X42,X75),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X91),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
             => hBOOL(hAPP(hAPP(X42,X75),X91)) ) )
       => hBOOL(hAPP(hAPP(X42,X152),X57)) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opinduct]) ).

fof(i_0_5522,plain,
    ! [X28493,X28494] :
      ( ( ~ 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),X28494),X28493)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28494),X28493)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28494),X28493))
        | 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),X28494),X28493)),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_5523,plain,
    ! [X110,X12,X48,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X48),hAPP(hAPP(c_Equiv__Relations_Oquotient(X10),X12),X110)))
     => ~ ! [X3] :
            ( X48 = hAPP(c_Relation_OImage(X10,X10,X110),hAPP(hAPP(c_Set_Oinsert(X10),X3),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
           => ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_quotientE]) ).

fof(i_0_5524,plain,
    ! [X22244,X22245] :
      ( ( X22245 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Divides_Odivmod__nat(X22244,X22245) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22244) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22244),X22245))
        | c_Divides_Odivmod__nat(X22244,X22245) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22244) )
      & ( X22245 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22244),X22245))
        | c_Divides_Odivmod__nat(X22244,X22245) = 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),X22244),X22245),X22245)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__if])])]) ).

fof(i_0_5525,plain,
    ! [X22277,X22278] : c_Divides_Odivmod__nat(X22278,X22277) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X22278,X22277)),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__def]) ).

fof(i_0_5526,plain,
    ! [X20014] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20014)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20014),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20014),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20014)),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_5527,plain,
    ! [X226,X227,X228,X229,X10] :
      ( hAPP(hAPP(c_List_Oappend(X10),X229),X228) = hAPP(hAPP(c_List_Oappend(X10),X227),X226)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X229)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X227)))
         => ( X229 = hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X229)),X227)
            & X228 = hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X229)),X227)),X226) ) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X229)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X227)))
         => ( hAPP(hAPP(c_List_Otake(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X227)),X229) = X227
            & hAPP(hAPP(c_List_Oappend(X10),hAPP(hAPP(c_List_Odrop(X10),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X227)),X229)),X228) = X226 ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_append__eq__append__conv__if]) ).

fof(i_0_5528,plain,
    ! [X20827] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20827)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20827),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20827),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X20827)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I13_J])]) ).

fof(i_0_5529,plain,
    ! [X19954] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X19954)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19954),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19954),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(X19954)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I12_J])]) ).

fof(i_0_5530,plain,
    ! [X19962] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X19962)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19962),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19962),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X19962)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I29_J])]) ).

fof(i_0_5531,plain,
    ! [X20825] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20825)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20825),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20825),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(X20825)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J])]) ).

fof(i_0_5532,plain,
    ! [X20070] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X20070))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20070))) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20070)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X20070)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit1])]) ).

fof(i_0_5533,plain,
    ! [X31311,X31312] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31312)),c_List_Oremdups(X31312,c_List_Oconcat(X31312,X31311))) = hAPP(c_Finite__Set_Ocard(X31312),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X31312),tc_fun(X31312,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X31312)),X31311)),c_List_Oset(X31312))),
    inference(variable_rename,[status(thm)],[fact_length__remdups__concat]) ).

fof(i_0_5534,plain,
    ! [X19984,X19985] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19985),c_Groups_Oone__class_Oone(X19985)),hAPP(c_Int_Onumber__class_Onumber__of(X19985),X19984)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X19984))
        | ~ class_Int_Onumber__ring(X19985)
        | ~ class_Rings_Olinordered__idom(X19985) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X19984))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19985),c_Groups_Oone__class_Oone(X19985)),hAPP(c_Int_Onumber__class_Onumber__of(X19985),X19984)))
        | ~ class_Int_Onumber__ring(X19985)
        | ~ class_Rings_Olinordered__idom(X19985) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I2_J])])]) ).

fof(i_0_5535,plain,
    ! [X19980,X19981] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19981),c_Groups_Oone__class_Oone(X19981)),hAPP(c_Int_Onumber__class_Onumber__of(X19981),X19980)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X19980))
        | ~ class_Int_Onumber__ring(X19981)
        | ~ class_Rings_Olinordered__idom(X19981) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X19980))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19981),c_Groups_Oone__class_Oone(X19981)),hAPP(c_Int_Onumber__class_Onumber__of(X19981),X19980)))
        | ~ class_Int_Onumber__ring(X19981)
        | ~ class_Rings_Olinordered__idom(X19981) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I2_J])])]) ).

fof(i_0_5536,plain,
    ! [X90,X14,X13,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq__number__of1]) ).

fof(i_0_5537,plain,
    ! [X90,X14,X13,X10] :
      ( ( class_Fields_Olinordered__field__inverse__zero(X10)
        & class_Int_Onumber(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90))),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq__number__of1]) ).

fof(i_0_5538,plain,
    ! [X8,X10,X12,X16,X11,X15] :
      ( ( ~ hBOOL(hAPP(hAPP(X15,X11),X16))
       => hBOOL(hAPP(hAPP(X12,X11),X16)) )
     => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X12),X15),X11),X16)) ),
    inference(fof_simplification,[status(thm)],[fact_sup2CI]) ).

fof(i_0_5539,plain,
    ! [X29,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),c_Wellfounded_Oacc(X10,X29)))
     => ~ ! [X177] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X177),X11)),X29))
           => hBOOL(hAPP(hAPP(c_member(X10),X177),c_Wellfounded_Oacc(X10,X29))) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__acc__down]) ).

fof(i_0_5540,plain,
    ! [X14,X12,X10] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X10,X14,X12) = X14 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))
       => c_Partial__Function_Oflat__lub(X10,X14,X12) = c_HOL_OThe(X10,hAPP(hAPP(c_COMBC(X10,tc_fun(X10,tc_HOL_Obool),tc_HOL_Obool),c_member(X10)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X14),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))))) ) ),
    inference(fof_simplification,[status(thm)],[fact_flat__lub__def]) ).

fof(i_0_5541,plain,
    ! [X20456,X20457] :
      ( ( ~ 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),X20457)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X20456))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X20457))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20456)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20457)) )
      & ( 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),X20457)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X20456))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X20457))) = 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),X20456)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20457)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5199])]) ).

fof(i_0_5542,plain,
    ! [X29045,X29046] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29046,X29046)),hAPP(hAPP(c_Product__Type_OPair(X29046,X29046),esk346_2(X29045,X29046)),esk346_2(X29045,X29046))),c_Transitive__Closure_Otrancl(X29046,X29045)))
      | c_Wellfounded_Oacyclic(X29046,X29045) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5200])])]) ).

fof(i_0_5543,plain,
    ! [X110,X200,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X200)),c_List_Olistrel1(X10,X110))),
    inference(fof_simplification,[status(thm)],[fact_not__Nil__listrel1]) ).

fof(i_0_5544,plain,
    ! [X110,X199,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),c_List_Olist_ONil(X10)),X199)),c_List_Olex(X10,X110))),
    inference(fof_simplification,[status(thm)],[fact_Nil__notin__lex]) ).

fof(i_0_5545,plain,
    ! [X110,X200,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),c_List_Olist_ONil(X10))),c_List_Olistrel1(X10,X110))),
    inference(fof_simplification,[status(thm)],[fact_not__listrel1__Nil]) ).

fof(i_0_5546,plain,
    ! [X110,X11,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X11),c_List_Olist_ONil(X10))),c_List_Olexord(X10,X110))),
    inference(fof_simplification,[status(thm)],[fact_lexord__Nil__right]) ).

fof(i_0_5547,plain,
    ! [X110,X200,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X10),tc_List_Olist(X10))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X200),c_List_Olist_ONil(X10))),c_List_Olex(X10,X110))),
    inference(fof_simplification,[status(thm)],[fact_Nil2__notin__lex]) ).

fof(i_0_5548,plain,
    ! [X31565,X31566,X31567] :
      ( ~ class_Groups_Omonoid__add(X31567)
      | hAPP(c_List_Ofoldl(X31567,X31567,c_Groups_Oplus__class_Oplus(X31567),X31566),X31565) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X31567),X31566),c_List_Ofoldr(X31567,X31567,c_Groups_Oplus__class_Oplus(X31567),X31565,c_Groups_Ozero__class_Ozero(X31567))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1__lemma])]) ).

fof(i_0_5549,plain,
    ! [X28689,X28690,X28691] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28691,X28691)),hAPP(hAPP(c_Product__Type_OPair(X28691,X28691),X28690),X28689)),c_Relation_OId(X28691)))
        | X28690 = X28689 )
      & ( X28690 != X28689
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28691,X28691)),hAPP(hAPP(c_Product__Type_OPair(X28691,X28691),X28690),X28689)),c_Relation_OId(X28691))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__in__Id__conv])]) ).

fof(i_0_5550,plain,
    ! [X42,X9,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
     => ( hBOOL(hAPP(X42,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))
       => ( ! [X3,X47] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X47))
             => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X47))
               => ( hBOOL(hAPP(X42,X47))
                 => hBOOL(hAPP(X42,hAPP(hAPP(c_Set_Oinsert(X10),X3),X47))) ) ) )
         => hBOOL(hAPP(X42,X9)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_finite__induct]) ).

fof(i_0_5551,plain,
    ! [X20551] :
      ( ~ class_Int_Onumber__ring(X20551)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20551),c_Groups_Oone__class_Oone(X20551)),c_Groups_Oone__class_Oone(X20551)) = hAPP(c_Int_Onumber__class_Onumber__of(X20551),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_5552,plain,
    ! [X31308,X31309,X31310] : hAPP(c_List_Oset(X31310),hAPP(c_List_OremoveAll(X31310,X31309),X31308)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31310,tc_HOL_Obool)),hAPP(c_List_Oset(X31310),X31308)),hAPP(hAPP(c_Set_Oinsert(X31310),X31309),c_Orderings_Obot__class_Obot(tc_fun(X31310,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_set__removeAll]) ).

fof(i_0_5553,plain,
    ! [X22201,X22202] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22202))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22202),X22201))
      | c_Divides_Odivmod__nat(X22201,X22202) = 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),X22201),X22202)),X22202))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22201),X22202),X22202)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__step])]) ).

fof(i_0_5554,plain,
    ! [X31835,X31836,X31837,X31838,X31839] : hAPP(c_List_Ofoldl(X31839,X31838,X31837,X31836),X31835) = c_List_Ofoldr(X31838,X31839,hAPP(c_COMBC(X31839,X31838,X31839),X31837),hAPP(c_List_Orev(X31838),X31835),X31836),
    inference(variable_rename,[status(thm)],[fact_foldl__foldr]) ).

fof(i_0_5555,plain,
    ! [X31993,X31994,X31995] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31995),X31994))
      | hBOOL(hAPP(c_List_Odistinct(X31995),c_List_OdropWhile(X31995,X31993,X31994))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile])]) ).

fof(i_0_5556,plain,
    ! [X1,X12,X9,X19,X2,X8,X10] :
      ( c_Big__Operators_Ocomm__monoid__big(X10,X8,X2,X19,X9)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
         => hAPP(hAPP(X9,X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X10,X8,X2),X1),X19),X12) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
         => hAPP(hAPP(X9,X1),X12) = X19 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_OF__eq]) ).

fof(i_0_5557,plain,
    ! [X22297,X22298,X22299,X22300] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22300,X22300)),hAPP(hAPP(c_Product__Type_OPair(X22300,X22300),X22299),X22298)),hAPP(c_Wellfounded_Omeasure(X22300),X22297)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22297,X22299)),hAPP(X22297,X22298))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22297,X22299)),hAPP(X22297,X22298)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22300,X22300)),hAPP(hAPP(c_Product__Type_OPair(X22300,X22300),X22299),X22298)),hAPP(c_Wellfounded_Omeasure(X22300),X22297))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measure])]) ).

fof(i_0_5558,plain,
    ! [X23533] : c_Wellfounded_Omeasure(X23533) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X23533),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[fact_measure__def]) ).

fof(i_0_5559,plain,
    ! [X15,X12,X14,X13,X8,X10] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X8)),hAPP(hAPP(c_Product__Type_OPair(X10,X8),X13),X14)),hAPP(hAPP(c_Product__Type_OSigma(X10,X8),X12),X15)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => ~ hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(X15,X13))) ) ),
    inference(fof_simplification,[status(thm)],[fact_SigmaE2]) ).

fof(i_0_5560,plain,
    ! [X31351,X31352,X31353,X31354] : hAPP(hAPP(c_List_Omap(X31354,X31353),X31352),c_List_Oconcat(X31354,X31351)) = c_List_Oconcat(X31353,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31354),tc_List_Olist(X31353)),hAPP(c_List_Omap(X31354,X31353),X31352)),X31351)),
    inference(variable_rename,[status(thm)],[fact_map__concat]) ).

fof(i_0_5561,plain,
    ! [X20421,X20422] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X20422)),c_Int_OBit0(X20421)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20422),X20421)),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit0]) ).

fof(i_0_5562,plain,
    ! [X20428,X20429] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X20429)),c_Int_OBit0(X20428)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20429),X20428)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I9_J]) ).

fof(i_0_5563,plain,
    ! [X200,X8,X11,X2,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),hAPP(X2,X11)),hAPP(c_Set_Oimage(X8,X10,X2),hAPP(c_List_Oset(X8),X200))))
       => c_List_Olinorder__class_Oinsort__insert__key(X8,X10,X2,X11,X200) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__insert__insort__key]) ).

fof(i_0_5564,plain,
    ! [X28927,X28928,X28929] :
      ( ( ~ c_Relation_Ototal__on(X28929,X28928,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28929,X28929),tc_HOL_Obool)),X28927),c_Relation_OId(X28929)))
        | c_Relation_Ototal__on(X28929,X28928,X28927) )
      & ( ~ c_Relation_Ototal__on(X28929,X28928,X28927)
        | c_Relation_Ototal__on(X28929,X28928,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28929,X28929),tc_HOL_Obool)),X28927),c_Relation_OId(X28929))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__diff__Id])]) ).

fof(i_0_5565,plain,
    ! [X19992,X19993] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),X19993))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19992)),X19993) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19992),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X19993),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_5566,plain,
    ! [X20503,X20504] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(X20504)),X20503) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20504),X20503))),X20503),
    inference(variable_rename,[status(thm)],[fact_mult__Bit1]) ).

fof(i_0_5567,plain,
    ! [X20543] :
      ( ( 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(X20543))))
        | ~ 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),X20543))) )
      & ( 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(X20543))))
        | ~ 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),X20543))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of1])])]) ).

fof(i_0_5568,plain,
    ! [X20530,X20531] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(X20531)),c_Int_OBit1(X20530)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20531),c_Int_Osucc(X20530))),
    inference(variable_rename,[status(thm)],[fact_add__Bit1__Bit1]) ).

fof(i_0_5569,plain,
    ! [X20497,X20498] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20498)),c_Int_OBit1(X20497)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20498),X20497)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20498),X20497))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20498)),c_Int_OBit1(X20497))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I14_J])]) ).

fof(i_0_5570,plain,
    ! [X20495,X20496] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20496)),c_Int_OBit1(X20495)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20496),X20495)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20496),X20495))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20496)),c_Int_OBit1(X20495))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I15_J])]) ).

fof(i_0_5571,plain,
    ! [X20413,X20414] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20414)),c_Int_OBit1(X20413)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20414),X20413)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20414),X20413))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20414)),c_Int_OBit1(X20413))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I14_J])]) ).

fof(i_0_5572,plain,
    ! [X20411,X20412] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20412)),c_Int_OBit1(X20411)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20412),X20411)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20412),X20411))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20412)),c_Int_OBit1(X20411))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I32_J])]) ).

fof(i_0_5573,plain,
    ! [X32990,X32991] :
      ( ( ~ c_Relation_Oantisym(X32991,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32991,X32991),tc_HOL_Obool)),X32990),c_Relation_OId(X32991)))
        | c_Relation_Oantisym(X32991,X32990) )
      & ( ~ c_Relation_Oantisym(X32991,X32990)
        | c_Relation_Oantisym(X32991,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32991,X32991),tc_HOL_Obool)),X32990),c_Relation_OId(X32991))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__reflcl])]) ).

fof(i_0_5574,plain,
    ! [X31987,X31988,X31989,X31990] :
      ( ( ~ hBOOL(hAPP(X31990,X31989))
        | c_List_OdropWhile(X31988,X31990,hAPP(hAPP(c_List_Olist_OCons(X31988),X31989),X31987)) = c_List_OdropWhile(X31988,X31990,X31987) )
      & ( hBOOL(hAPP(X31990,X31989))
        | c_List_OdropWhile(X31988,X31990,hAPP(hAPP(c_List_Olist_OCons(X31988),X31989),X31987)) = hAPP(hAPP(c_List_Olist_OCons(X31988),X31989),X31987) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5201])]) ).

fof(i_0_5575,plain,
    ! [X19928] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19928)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X19928)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19928)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X19928)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19928)),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_5202])]) ).

fof(i_0_5576,plain,
    ! [X28552,X28553] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28553,X28553)),c_Transitive__Closure_Otrancl(X28553,X28552)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28553,X28553)),X28552)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28553,X28553)),X28552))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28553,X28553)),c_Transitive__Closure_Otrancl(X28553,X28552))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__trancl])]) ).

fof(i_0_5577,plain,
    ! [X15,X13,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X15))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Diff__insert]) ).

fof(i_0_5578,plain,
    ! [X31798,X31799] : hAPP(c_List_Orev(X31799),c_List_Oconcat(X31799,X31798)) = c_List_Oconcat(X31799,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31799),tc_List_Olist(X31799)),c_List_Orev(X31799)),hAPP(c_List_Orev(tc_List_Olist(X31799)),X31798))),
    inference(variable_rename,[status(thm)],[fact_rev__concat]) ).

fof(i_0_5579,plain,
    ! [X19,X1,X13,X12,X10,X8] :
      ( class_Groups_Oab__semigroup__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),X19),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X1,X13)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),X19),X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold__image__insert]) ).

fof(i_0_5580,plain,
    ! [X31390,X31391,X31392] : hAPP(c_List_Ofilter(X31392,X31391),c_List_Oconcat(X31392,X31390)) = c_List_Oconcat(X31392,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31392),tc_List_Olist(X31392)),c_List_Ofilter(X31392,X31391)),X31390)),
    inference(variable_rename,[status(thm)],[fact_filter__concat]) ).

fof(i_0_5581,plain,
    ! [X16,X11,X10] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_List_Omeasures(X10,c_List_Olist_ONil(tc_fun(X10,tc_Nat_Onat))))),
    inference(fof_simplification,[status(thm)],[fact_in__measures_I1_J]) ).

fof(i_0_5582,plain,
    ! [X13,X6,X14,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),X13))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__less__eq]) ).

fof(i_0_5583,plain,
    ! [X13,X6,X14,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)),X13))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),c_Groups_Ozero__class_Ozero(X10)),X13)) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divide__le__eq]) ).

fof(i_0_5584,plain,
    ! [X30391,X30392,X30393] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X30393),hAPP(c_List_Orotate(X30393,X30392),X30391)))
        | hBOOL(hAPP(c_List_Odistinct(X30393),X30391)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30393),X30391))
        | hBOOL(hAPP(c_List_Odistinct(X30393),hAPP(c_List_Orotate(X30393,X30392),X30391))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rotate])]) ).

fof(i_0_5585,plain,
    ! [X33574,X33575,X33576] :
      ( ( ~ c_List_Olist__ex(tc_Nat_Onat,X33576,c_List_Oupt(X33575,X33574))
        | ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X33576),X33575,X33574) )
      & ( c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X33576),X33575,X33574)
        | c_List_Olist__ex(tc_Nat_Onat,X33576,c_List_Oupt(X33575,X33574)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5203])]) ).

fof(i_0_5586,plain,
    ! [X16,X29,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_Relation_ODomain(X10,X10),X29)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X11),X16)),c_Transitive__Closure_Ortrancl(X10,X29)))
      <=> X11 = X16 ) ),
    inference(fof_simplification,[status(thm)],[fact_Not__Domain__rtrancl]) ).

fof(i_0_5587,plain,
    ! [X20423,X20424] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X20424)),c_Int_OBit1(X20423)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20424),X20423)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit1]) ).

fof(i_0_5588,plain,
    ! [X1,X12,X9,X19,X2,X8,X10] :
      ( c_Big__Operators_Ocomm__monoid__big(X10,X8,X2,X19,X9)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X12))
       => hAPP(hAPP(X9,X1),X12) = X19 ) ),
    inference(fof_simplification,[status(thm)],[fact_comm__monoid__big_Oinfinite]) ).

fof(i_0_5589,plain,
    ! [X21418,X21419] :
      ( ~ class_Int_Onumber__ring(X21419)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21419),hAPP(c_Int_Onumber__class_Onumber__of(X21419),X21418)),c_Groups_Oone__class_Oone(X21419)) = hAPP(c_Int_Onumber__class_Onumber__of(X21419),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21418),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_5590,plain,
    ! [X200,X11,X2,X10,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X11),X200)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
          & hBOOL(hAPP(c_List_Odistinct(X10),X200)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct__insort]) ).

fof(i_0_5591,plain,
    ! [X21416,X21417] :
      ( ~ class_Int_Onumber__ring(X21417)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21417),c_Groups_Oone__class_Oone(X21417)),hAPP(c_Int_Onumber__class_Onumber__of(X21417),X21416)) = hAPP(c_Int_Onumber__class_Onumber__of(X21417),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),X21416))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__special_I1_J])]) ).

fof(i_0_5592,plain,
    ! [X28544,X28545,X28546] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28546,X28546)),X28545),X28544))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28546,X28546)),X28545),c_Transitive__Closure_Otrancl(X28546,X28544))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__trancl_H])]) ).

fof(i_0_5593,plain,
    ! [X31336,X31337,X31338] : c_List_Oconcat(X31338,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31338)),X31337),X31336)) = hAPP(hAPP(c_List_Oappend(X31338),X31337),c_List_Oconcat(X31338,X31336)),
    inference(variable_rename,[status(thm)],[fact_concat_Osimps_I2_J]) ).

fof(i_0_5594,plain,
    ! [X19988,X19989] :
      ( ~ class_Int_Onumber__ring(X19989)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19989),c_Groups_Oone__class_Oone(X19989)),hAPP(c_Int_Onumber__class_Onumber__of(X19989),X19988)) = hAPP(c_Int_Onumber__class_Onumber__of(X19989),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),X19988)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I2_J])]) ).

fof(i_0_5595,plain,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X6,X20)))
      <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14))
            | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X13))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X20))
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),X13))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),X20)) ) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X20)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__psubset__iff]) ).

fof(i_0_5596,plain,
    ! [X31611,X31612] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31612)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31611)))
        | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31612),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31611)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31612)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31612)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31611))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31612)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31611)))
        | c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31612),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X31611)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5204])]) ).

fof(i_0_5597,plain,
    ! [X9,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X11),X9))
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X11),X9)))
           => ! [X66] :
                ( hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X66),hAPP(hAPP(c_Set_Oinsert(tc_fun(X10,tc_HOL_Obool)),X11),X9)))
               => ( X3 != X66
                 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X3),X66) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) )
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X11),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X9)) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__partition]) ).

fof(i_0_5598,plain,
    ! [X28612,X28613] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28613,X28613),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(X28613,X28612)),c_Relation_OId(X28613)) = c_Transitive__Closure_Ortrancl(X28613,X28612),
    inference(variable_rename,[status(thm)],[fact_reflcl__trancl]) ).

fof(i_0_5599,plain,
    ! [X26,X201,X202,X27,X25] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X25),X26) = hAPP(hAPP(c_List_Oappend(X27),hAPP(hAPP(c_List_Olist__update(X27,X202),X25),X26)),X201) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(hAPP(c_List_Olist__update(X27,hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X25),X26) = hAPP(hAPP(c_List_Oappend(X27),X202),hAPP(hAPP(c_List_Olist__update(X27,X201),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))),X26)) ) ),
    inference(fof_simplification,[status(thm)],[fact_list__update__append]) ).

fof(i_0_5600,plain,
    ! [X6,X14,X13,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__divide__eq]) ).

fof(i_0_5601,plain,
    ! [X6,X14,X13,X10] :
      ( class_Fields_Olinordered__field__inverse__zero(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X10),X14),X6)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6)),X14)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),c_Groups_Ozero__class_Ozero(X10)),X6))
           => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X13),X6))) )
              & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X6),c_Groups_Ozero__class_Ozero(X10)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),c_Groups_Ozero__class_Ozero(X10))) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__divide__eq]) ).

fof(i_0_5602,plain,
    ! [X32684,X32685,X32686,X32687,X32688,X32689] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X32689,X32688,X32687,X32686,c_Lazy__Sequence_Olazy__sequence_OInsert(X32688,X32685,X32684)) = hAPP(hAPP(X32686,X32685),X32684),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I5_J]) ).

fof(i_0_5603,plain,
    ! [X32678,X32679,X32680,X32681,X32682] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X32682,X32681,X32680,X32679,X32678) = c_Option_Ooption_Ooption__case(X32682,tc_prod(X32681,tc_Lazy__Sequence_Olazy__sequence(X32681)),X32680,hAPP(c_Product__Type_Oprod_Oprod__case(X32681,tc_Lazy__Sequence_Olazy__sequence(X32681),X32682),X32679),hAPP(c_Lazy__Sequence_Oyield(X32681),X32678)),
    inference(variable_rename,[status(thm)],[fact_seq__case]) ).

fof(i_0_5604,plain,
    ! [X19956,X19957] :
      ( ~ class_Int_Onumber__ring(X19957)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19957),hAPP(c_Int_Onumber__class_Onumber__of(X19957),c_Int_OBit1(c_Int_OPls))),X19956) = X19956 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1])]) ).

fof(i_0_5605,plain,
    ! [X60,X61,X42] :
      ( c_List_Olist__ex(tc_Int_Oint,X42,c_List_Oupto(X61,X60))
    <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X42),X61,X60) ),
    inference(fof_simplification,[status(thm)],[fact_list__ex__iff__not__all__inverval__int]) ).

fof(i_0_5606,plain,
    ! [X30394,X30395,X30396] : c_List_Orotate(X30396,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30395),X30394)) = hAPP(c_Fun_Ocomp(tc_List_Olist(X30396),tc_List_Olist(X30396),tc_List_Olist(X30396),c_List_Orotate(X30396,X30395)),c_List_Orotate(X30396,X30394)),
    inference(variable_rename,[status(thm)],[fact_rotate__add]) ).

fof(i_0_5607,plain,
    ! [X20,X6,X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)),c_SetInterval_Oord__class_OatLeastAtMost(X10,X6,X20)))
      <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14))
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X6),X13))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X14),X20)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__subset__iff]) ).

fof(i_0_5608,plain,
    ! [X19986,X19987] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19987),hAPP(c_Int_Onumber__class_Onumber__of(X19987),X19986)),c_Groups_Oone__class_Oone(X19987)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19986),c_Int_OBit1(c_Int_OPls)))
        | ~ class_Int_Onumber__ring(X19987)
        | ~ class_Rings_Olinordered__idom(X19987) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19986),c_Int_OBit1(c_Int_OPls)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19987),hAPP(c_Int_Onumber__class_Onumber__of(X19987),X19986)),c_Groups_Oone__class_Oone(X19987)))
        | ~ class_Int_Onumber__ring(X19987)
        | ~ class_Rings_Olinordered__idom(X19987) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I4_J])])]) ).

fof(i_0_5609,plain,
    ! [X19982,X19983] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19983),hAPP(c_Int_Onumber__class_Onumber__of(X19983),X19982)),c_Groups_Oone__class_Oone(X19983)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19982),c_Int_OBit1(c_Int_OPls)))
        | ~ class_Int_Onumber__ring(X19983)
        | ~ class_Rings_Olinordered__idom(X19983) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19982),c_Int_OBit1(c_Int_OPls)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19983),hAPP(c_Int_Onumber__class_Onumber__of(X19983),X19982)),c_Groups_Oone__class_Oone(X19983)))
        | ~ class_Int_Onumber__ring(X19983)
        | ~ class_Rings_Olinordered__idom(X19983) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I4_J])])]) ).

fof(i_0_5610,plain,
    ! [X29090,X29091] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29091,X29091)),X29090),c_Relation_OId(X29091)))
      | X29090 = hAPP(hAPP(c_Product__Type_OPair(X29091,X29091),esk356_2(X29090,X29091)),esk356_2(X29090,X29091)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IdE])])]) ).

fof(i_0_5611,plain,
    ! [X20914] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X20914)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X20914)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I4_J]) ).

fof(i_0_5612,plain,
    ! [X28602,X28603] : hBOOL(hAPP(hAPP(c_member(tc_prod(X28603,X28603)),hAPP(hAPP(c_Product__Type_OPair(X28603,X28603),X28602),X28602)),c_Relation_OId(X28603))),
    inference(variable_rename,[status(thm)],[fact_IdI]) ).

fof(i_0_5613,plain,
    ! [X31320,X31321,X31322] : hAPP(c_List_Ofoldl(tc_List_Olist(X31322),tc_List_Olist(X31322),c_List_Oappend(X31322),X31321),X31320) = hAPP(hAPP(c_List_Oappend(X31322),X31321),c_List_Oconcat(X31322,X31320)),
    inference(variable_rename,[status(thm)],[fact_foldl__conv__concat]) ).

fof(i_0_5614,plain,
    ! [X20426,X20427] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(X20427)),c_Int_OBit1(X20426)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20427),X20426)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I10_J]) ).

fof(i_0_5615,plain,
    ! [X200,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Olinorder__class_Oinsort__insert__key(X10,X10,c_COMBI(X10),X11,X200) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X10,c_COMBI(X10)),X11),X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__insert__insort]) ).

fof(i_0_5616,plain,
    ! [X110,X10] :
      ( c_Relation_Oirrefl(X10,X110)
    <=> ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X3),X3)),X110)) ),
    inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).

fof(i_0_5617,plain,
    ! [X13,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X13)),X110)) ),
    inference(fof_simplification,[status(thm)],[fact_wf__not__refl]) ).

fof(i_0_5618,plain,
    ! [X13,X110,X10] :
      ( c_Wellfounded_Owf(X10,X110)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X10,X10)),hAPP(hAPP(c_Product__Type_OPair(X10,X10),X13),X13)),X110)) ),
    inference(fof_simplification,[status(thm)],[fact_wf__irrefl]) ).

fof(i_0_5619,plain,
    ! [X28628,X28629] : c_Transitive__Closure_Ortrancl(X28629,X28628) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28629,X28629),tc_HOL_Obool)),c_Relation_OId(X28629)),hAPP(hAPP(c_Relation_Orel__comp(X28629,X28629,X28629),c_Transitive__Closure_Ortrancl(X28629,X28628)),X28628)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__unfold]) ).

fof(i_0_5620,plain,
    ! [X13,X15,X12,X8,X14,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X8,tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X14),hAPP(X15,X13)))
       => ~ hBOOL(hAPP(hAPP(c_member(X8),X13),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INT__E]) ).

fof(i_0_5621,plain,
    ! [X20828] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20828)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X20828)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X20828))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20828))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I9_J])]) ).

fof(i_0_5622,plain,
    ! [X20826] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X20826)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),X20826))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20826))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J])]) ).

fof(i_0_5623,plain,
    ! [X19963] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X19963)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X19963)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X19963))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X19963))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I5_J])]) ).

fof(i_0_5624,plain,
    ! [X19955] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X19955)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X19955)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X19955))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X19955))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I22_J])]) ).

fof(i_0_5625,plain,
    ! [X20544,X20545,X20546] :
      ( ~ class_Int_Onumber__ring(X20546)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20546),hAPP(c_Int_Onumber__class_Onumber__of(X20546),X20545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X20544))) = hAPP(hAPP(c_HOL_OLet(X20546,X20546),hAPP(hAPP(c_Power_Opower__class_Opower(X20546),hAPP(c_Int_Onumber__class_Onumber__of(X20546),X20545)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20544))),hAPP(hAPP(c_COMBS(X20546,X20546,X20546),c_Groups_Otimes__class_Otimes(X20546)),c_COMBI(X20546))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even__number__of])]) ).

fof(i_0_5626,plain,
    ! [X11,X16,X6] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X16))
       => 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)),X6)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11),X16)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X11),X6)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X16),X6)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X16))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X11),X16))
           => 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)),X6)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11),X16)) = 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),X11),X16))
           => 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)),X6)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X11),X16)) = 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_5627,plain,
    ! [X31563,X31564] :
      ( ~ class_Groups_Omonoid__add(X31564)
      | hAPP(c_List_Ofoldl(X31564,X31564,c_Groups_Oplus__class_Oplus(X31564),c_Groups_Ozero__class_Ozero(X31564)),X31563) = c_List_Ofoldr(X31564,X31564,c_Groups_Oplus__class_Oplus(X31564),X31563,c_Groups_Ozero__class_Ozero(X31564)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__foldr1])]) ).

fof(i_0_5628,plain,
    ! [X31642,X31643,X31644,X31645,X31646] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31646),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31645),X31644)))
      | hAPP(hAPP(c_List_Onth(X31643),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31643),X31642),c_List_Oupt(X31644,X31645))),X31646) = hAPP(X31642,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31644),X31646)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map__upt])]) ).

fof(i_0_5629,plain,
    ! [X30397,X30398,X30399,X30400] : hAPP(c_List_Orotate(X30400,X30399),hAPP(c_List_Orotate(X30400,X30398),X30397)) = hAPP(c_List_Orotate(X30400,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30399),X30398)),X30397),
    inference(variable_rename,[status(thm)],[fact_rotate__rotate]) ).

fof(i_0_5630,plain,
    ! [X31553,X31554,X31555] :
      ( ~ class_Groups_Oab__semigroup__add(X31555)
      | c_List_Ofoldr(X31555,X31555,c_Groups_Oplus__class_Oplus(X31555),X31554,X31553) = hAPP(c_List_Ofoldl(X31555,X31555,c_Groups_Oplus__class_Oplus(X31555),X31553),X31554) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__conv__foldl])]) ).

fof(i_0_5631,plain,
    ! [X32768,X32769,X32770,X32771] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X32771,X32770,X32769,X32768,c_Lazy__Sequence_Olazy__sequence_OEmpty(X32770)) = X32769,
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I4_J]) ).

fof(i_0_5632,plain,
    ! [X30423,X30424,X30425] : hAPP(c_List_Orotate(X30425,X30424),X30423) = hAPP(c_List_Orotate(X30425,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30424,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30425)),X30423))),X30423),
    inference(variable_rename,[status(thm)],[fact_rotate__conv__mod]) ).

fof(i_0_5633,plain,
    ! [X21463,X21464] :
      ( ~ class_Int_Onumber__ring(X21464)
      | ~ class_Int_Oring__char__0(X21464)
      | ~ c_Int_Oiszero(X21464,hAPP(c_Int_Onumber__class_Onumber__of(X21464),c_Int_OBit1(X21463))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5205])]) ).

fof(i_0_5634,plain,
    ! [X20450] : c_Int_Opred(c_Int_OBit0(X20450)) = c_Int_OBit1(c_Int_Opred(X20450)),
    inference(variable_rename,[status(thm)],[fact_pred__Bit0]) ).

fof(i_0_5635,plain,
    ! [X13,X2,X12,X10,X8] :
      ( class_Fields_Ofield(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( hAPP(X2,X13) != c_Groups_Ozero__class_Ozero(X8)
         => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12)),hAPP(X2,X13)) )
            & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
             => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__diff1]) ).

fof(i_0_5636,plain,
    ! [X28743,X28744] : c_Relation_Orefl__on(X28744,c_Orderings_Otop__class_Otop(tc_fun(X28744,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28744,X28744),tc_HOL_Obool)),X28743),c_Relation_OId(X28744))),
    inference(variable_rename,[status(thm)],[fact_refl__reflcl]) ).

fof(i_0_5637,plain,
    ! [X31970,X31971,X31972] : hAPP(hAPP(c_List_Oappend(X31972),c_List_OtakeWhile(X31972,X31971,X31970)),c_List_OdropWhile(X31972,X31971,X31970)) = X31970,
    inference(variable_rename,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(i_0_5638,plain,
    ! [X2,X13,X12,X10,X8] :
      ( class_Groups_Oab__group__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12)),hAPP(X2,X13)) )
          & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__diff1]) ).

fof(i_0_5639,plain,
    ! [X31357,X31358] : hAPP(c_List_Oset(X31358),c_List_Oconcat(X31358,X31357)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(X31358),tc_fun(X31358,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(X31358)),X31357)),c_List_Oset(X31358)),
    inference(variable_rename,[status(thm)],[fact_set__concat]) ).

fof(i_0_5640,plain,
    ! [X31355,X31356] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31356)),c_List_Oconcat(X31356,X31355)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31356),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31356))),X31355)),
    inference(variable_rename,[status(thm)],[fact_length__concat]) ).

fof(i_0_5641,plain,
    ! [X13,X14,X15,X12,X8,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X10,tc_fun(X8,tc_HOL_Obool)),X12),X15),X14))
     => ( ~ hBOOL(hAPP(hAPP(X15,X13),X14))
       => ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_INF1__E]) ).

fof(i_0_5642,plain,
    ! [X32967,X32968] :
      ( ~ c_Relation_Otrans(X32968,X32967)
      | ~ c_Relation_Oantisym(X32968,X32967)
      | c_Relation_Otrans(X32968,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X32968,X32968),tc_HOL_Obool)),X32967),c_Relation_OId(X32968))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__diff__Id])]) ).

fof(i_0_5643,plain,
    ! [X31880,X31881,X31882] :
      ( ( X31881 != c_List_Olist_ONil(X31882)
        | c_List_Ofoldr(X31882,X31882,c_Orderings_Oord__class_Omax(X31882),X31881,X31880) = X31880
        | ~ c_List_Olinorder__class_Osorted(X31882,hAPP(c_List_Orev(X31882),X31881))
        | ~ class_Orderings_Olinorder(X31882) )
      & ( X31881 = c_List_Olist_ONil(X31882)
        | c_List_Ofoldr(X31882,X31882,c_Orderings_Oord__class_Omax(X31882),X31881,X31880) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X31882),hAPP(hAPP(c_List_Onth(X31882),X31881),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X31880)
        | ~ c_List_Olinorder__class_Osorted(X31882,hAPP(c_List_Orev(X31882),X31881))
        | ~ class_Orderings_Olinorder(X31882) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldr__max__sorted])])]) ).

fof(i_0_5644,plain,
    ! [X32847,X32848] :
      ( ~ c_Relation_Otrans(X32848,X32847)
      | c_Relation_Otrans(X32848,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X32848,X32848),tc_HOL_Obool)),X32847),c_Relation_OId(X32848))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__reflclI])]) ).

fof(i_0_5645,plain,
    ! [X42,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ( ~ hBOOL(hAPP(X42,X11))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),hAPP(c_List_Ofilter(X10,X42),X200))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200))) ) ),
    inference(fof_simplification,[status(thm)],[fact_length__filter__less]) ).

fof(i_0_5646,plain,
    ! [X28630,X28631] : c_Transitive__Closure_Ortrancl(X28631,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28631,X28631),tc_HOL_Obool)),X28630),c_Relation_OId(X28631))) = c_Transitive__Closure_Ortrancl(X28631,X28630),
    inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl]) ).

fof(i_0_5647,plain,
    ! [X28675,X28676] : c_Transitive__Closure_Ortrancl(X28676,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28676,X28676),tc_HOL_Obool)),X28675),c_Relation_OId(X28676))) = c_Transitive__Closure_Ortrancl(X28676,X28675),
    inference(variable_rename,[status(thm)],[fact_rtrancl__r__diff__Id]) ).

fof(i_0_5648,plain,
    ! [X32009,X32010,X32011,X32012,X32013] :
      ( ( X32011 = hAPP(hAPP(c_List_Oappend(X32013),c_List_OtakeWhile(X32013,X32012,X32011)),hAPP(hAPP(c_List_Olist_OCons(X32013),X32010),X32009))
        | c_List_OdropWhile(X32013,X32012,X32011) != hAPP(hAPP(c_List_Olist_OCons(X32013),X32010),X32009) )
      & ( ~ hBOOL(hAPP(X32012,X32010))
        | c_List_OdropWhile(X32013,X32012,X32011) != hAPP(hAPP(c_List_Olist_OCons(X32013),X32010),X32009) )
      & ( X32011 != hAPP(hAPP(c_List_Oappend(X32013),c_List_OtakeWhile(X32013,X32012,X32011)),hAPP(hAPP(c_List_Olist_OCons(X32013),X32010),X32009))
        | hBOOL(hAPP(X32012,X32010))
        | c_List_OdropWhile(X32013,X32012,X32011) = hAPP(hAPP(c_List_Olist_OCons(X32013),X32010),X32009) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5206])])]) ).

fof(i_0_5649,plain,
    ! [X28746,X28747] : c_Relation_Oirrefl(X28747,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28747,X28747),tc_HOL_Obool)),X28746),c_Relation_OId(X28747))),
    inference(variable_rename,[status(thm)],[fact_irrefl__diff__Id]) ).

fof(i_0_5650,plain,
    ! [X21468] :
      ( ~ class_Int_Onumber__ring(X21468)
      | ~ c_Int_Oiszero(X21468,hAPP(c_Int_Onumber__class_Onumber__of(X21468),c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5207])]) ).

fof(i_0_5651,plain,
    ! [X80,X114,X36,X37] :
      ( X37 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X36),X114)),X80)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X80))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X80),X36)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X80))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X80),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(X37,X36),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X114),X80))) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__relI]) ).

fof(i_0_5652,plain,
    ! [X20919] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X20919)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X20919)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I5_J]) ).

fof(i_0_5653,plain,
    ! [X2,X12,X13,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12)),hAPP(X2,X13)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,tc_Nat_Onat),X2),X12) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__diff1__nat]) ).

fof(i_0_5654,plain,
    ! [X28829,X28830] :
      ( ~ c_Wellfounded_Owf(X28830,hAPP(c_Relation_Oconverse(X28830,X28830),X28829))
      | c_Wellfounded_Owf(X28830,hAPP(c_Relation_Oconverse(X28830,X28830),c_Transitive__Closure_Otrancl(X28830,X28829))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__converse__trancl])]) ).

fof(i_0_5655,plain,
    ! [X31339,X31340,X31341,X31342,X31343] :
      ( ( c_List_Oconcat(X31340,X31339) != c_List_Olist_ONil(X31340)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31340)),X31341),hAPP(c_List_Oset(tc_List_Olist(X31340)),X31339)))
        | X31341 = c_List_Olist_ONil(X31340) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31343)),esk420_2(X31342,X31343)),hAPP(c_List_Oset(tc_List_Olist(X31343)),X31342)))
        | c_List_Oconcat(X31343,X31342) = c_List_Olist_ONil(X31343) )
      & ( esk420_2(X31342,X31343) != c_List_Olist_ONil(X31343)
        | c_List_Oconcat(X31343,X31342) = c_List_Olist_ONil(X31343) ) ),
    inference(distribute,[status(thm)],[inference(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_5656,plain,
    ! [X31345,X31346,X31347,X31348,X31349] :
      ( ( c_List_Olist_ONil(X31346) != c_List_Oconcat(X31346,X31345)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31346)),X31347),hAPP(c_List_Oset(tc_List_Olist(X31346)),X31345)))
        | X31347 = c_List_Olist_ONil(X31346) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31349)),esk421_2(X31348,X31349)),hAPP(c_List_Oset(tc_List_Olist(X31349)),X31348)))
        | c_List_Olist_ONil(X31349) = c_List_Oconcat(X31349,X31348) )
      & ( esk421_2(X31348,X31349) != c_List_Olist_ONil(X31349)
        | c_List_Olist_ONil(X31349) = c_List_Oconcat(X31349,X31348) ) ),
    inference(distribute,[status(thm)],[inference(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_5657,plain,
    ! [X31585,X31586,X31587] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31587),X31586))
      | c_List_Oupt(X31587,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31586),X31585)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31587,X31586)),c_List_Oupt(X31586,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31586),X31585))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__add__eq__append])]) ).

fof(i_0_5658,plain,
    ! [X2,X31,X30,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,hAPP(c_Nat_OSuc,X30))) = c_Groups_Ozero__class_Ozero(X10) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,hAPP(c_Nat_OSuc,X30))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31,X30))),hAPP(X2,hAPP(c_Nat_OSuc,X30))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__cl__ivl__Suc]) ).

fof(i_0_5659,plain,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_UnE]) ).

fof(i_0_5660,plain,
    ! [X31979,X31980,X31981,X31982,X31983,X31984,X31985] :
      ( ( c_List_OdropWhile(X31981,X31980,X31979) != c_List_Olist_ONil(X31981)
        | ~ hBOOL(hAPP(hAPP(c_member(X31981),X31982),hAPP(c_List_Oset(X31981),X31979)))
        | hBOOL(hAPP(X31980,X31982)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31985),esk435_3(X31983,X31984,X31985)),hAPP(c_List_Oset(X31985),X31983)))
        | c_List_OdropWhile(X31985,X31984,X31983) = c_List_Olist_ONil(X31985) )
      & ( ~ hBOOL(hAPP(X31984,esk435_3(X31983,X31984,X31985)))
        | c_List_OdropWhile(X31985,X31984,X31983) = c_List_Olist_ONil(X31985) ) ),
    inference(distribute,[status(thm)],[inference(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_5661,plain,
    ! [X31292,X31293,X31294] :
      ( hBOOL(hAPP(hAPP(c_member(X31294),X31293),hAPP(c_List_Oset(X31294),X31292)))
      | hAPP(c_List_OremoveAll(X31294,X31293),X31292) = X31292 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5208])]) ).

fof(i_0_5662,plain,
    ! [X11,X12,X9,X2,X8,X10] :
      ( c_Finite__Set_Ofolding(X10,X8,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Fun_Ocomp(X8,X8,X8,hAPP(X9,X12)),hAPP(X2,X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding_Oinsert]) ).

fof(i_0_5663,plain,
    ! [X31973,X31974,X31975] :
      ( ~ class_Orderings_Olinorder(X31975)
      | ~ c_List_Olinorder__class_Osorted(X31975,X31974)
      | c_List_Olinorder__class_Osorted(X31975,c_List_OdropWhile(X31975,X31973,X31974)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__dropWhile])]) ).

fof(i_0_5664,plain,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
    <=> ? [X207,X240] :
          ( X200 = hAPP(hAPP(c_List_Oappend(X10),X207),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X240))
          & ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X240))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__last]) ).

fof(i_0_5665,plain,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
    <=> ? [X207] :
          ( ? [X240] : X200 = hAPP(hAPP(c_List_Oappend(X10),X207),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X240))
          & ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X207))) ) ),
    inference(fof_simplification,[status(thm)],[fact_in__set__conv__decomp__first]) ).

fof(i_0_5666,plain,
    ! [X20453] : c_Int_Osucc(c_Int_OBit1(X20453)) = c_Int_OBit0(c_Int_Osucc(X20453)),
    inference(variable_rename,[status(thm)],[fact_succ__Bit1]) ).

fof(i_0_5667,plain,
    ! [X20532,X20533,X20534] :
      ( ~ class_Int_Onumber__ring(X20534)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20534),X20533),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X20532))) = hAPP(hAPP(c_HOL_OLet(X20534,X20534),hAPP(hAPP(c_Power_Opower__class_Opower(X20534),X20533),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20532))),hAPP(hAPP(c_COMBS(X20534,X20534,X20534),c_Groups_Otimes__class_Otimes(X20534)),c_COMBI(X20534))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__number__of__even])]) ).

fof(i_0_5668,plain,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
    <=> ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
        & ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_Diff__iff]) ).

fof(i_0_5669,plain,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ),
    inference(fof_simplification,[status(thm)],[fact_DiffD2]) ).

fof(i_0_5670,plain,
    ! [X31479,X31480,X31481,X31482] :
      ( hBOOL(hAPP(X31482,X31481))
      | hAPP(c_List_OremoveAll(X31480,X31481),hAPP(c_List_Ofilter(X31480,X31482),X31479)) = hAPP(c_List_Ofilter(X31480,X31482),X31479) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5209])]) ).

fof(i_0_5671,plain,
    ! [X31961,X31962] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),X31962),X31961) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(X31962)),c_List_Oembed__list(X31961))),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J]) ).

fof(i_0_5672,plain,
    ! [X31940] : c_List_Oreturn__list(X31940) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X31940),
    inference(variable_rename,[status(thm)],[fact_return__list__def]) ).

fof(i_0_5673,plain,
    ! [X31963] : c_List_Oembed__list(X31963) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X31963),
    inference(variable_rename,[status(thm)],[fact_embed__list__def]) ).

fof(i_0_5674,plain,
    ! [X32,X12,X10] :
      ( hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(c_Nat_OSuc,X32)
    <=> ? [X81,X82] :
          ( X12 = hAPP(hAPP(c_Set_Oinsert(X10),X81),X82)
          & ~ hBOOL(hAPP(hAPP(c_member(X10),X81),X82))
          & hAPP(c_Finite__Set_Ocard(X10),X82) = X32
          & ( X32 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
           => X82 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Suc__eq]) ).

fof(i_0_5675,plain,
    ! [X31295,X31296,X31297] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31297),X31296))
      | c_List_Oremove1(X31297,X31295,X31296) = hAPP(c_List_OremoveAll(X31297,X31295),X31296) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1__removeAll])]) ).

fof(i_0_5676,plain,
    ! [X31597,X31598,X31599] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31599),X31598)),X31597))
      | hAPP(hAPP(c_List_Otake(tc_Nat_Onat),X31598),c_List_Oupt(X31599,X31597)) = c_List_Oupt(X31599,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31599),X31598)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__upt])]) ).

fof(i_0_5677,plain,
    ! [X30675,X30676,X30677,X30678,X30679] : hAPP(c_List_Orotate(X30679,X30678),hAPP(hAPP(c_List_Omap(X30677,X30679),X30676),X30675)) = hAPP(hAPP(c_List_Omap(X30677,X30679),X30676),hAPP(c_List_Orotate(X30677,X30678),X30675)),
    inference(variable_rename,[status(thm)],[fact_rotate__map]) ).

fof(i_0_5678,plain,
    ! [X28774,X28775] : c_Transitive__Closure_Otrancl(X28775,hAPP(c_Relation_Oconverse(X28775,X28775),X28774)) = hAPP(c_Relation_Oconverse(X28775,X28775),c_Transitive__Closure_Otrancl(X28775,X28774)),
    inference(variable_rename,[status(thm)],[fact_trancl__converse]) ).

fof(i_0_5679,plain,
    ! [X199,X8,X16,X11,X2,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X11)),hAPP(X2,X16)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),hAPP(hAPP(c_List_Olist_OCons(X8),X16),X199)) = hAPP(hAPP(c_List_Olist_OCons(X8),X11),hAPP(hAPP(c_List_Olist_OCons(X8),X16),X199)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(X2,X11)),hAPP(X2,X16)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),hAPP(hAPP(c_List_Olist_OCons(X8),X16),X199)) = hAPP(hAPP(c_List_Olist_OCons(X8),X16),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X10,X2),X11),X199)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insort__key_Osimps_I2_J]) ).

fof(i_0_5680,plain,
    ! [X25,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X24),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X25)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto__rec__number__of]) ).

fof(i_0_5681,plain,
    ! [X15,X12,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),X15)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_subset__insert]) ).

fof(i_0_5682,plain,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)))
     => ~ ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
         => ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_IntE]) ).

fof(i_0_5683,plain,
    ! [X60,X61] :
      ( 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),X61),X60)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),X60))
         => c_List_Oupto(X61,X60) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X61),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)),X60)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X61),X60))
         => c_List_Oupto(X61,X60) = c_List_Olist_ONil(tc_Int_Oint) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto_Opsimps]) ).

fof(i_0_5684,plain,
    ! [X19,X11,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(X2,X11),hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert]) ).

fof(i_0_5685,plain,
    ! [X61,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),X61)))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X61))
         => c_Lazy__Sequence_Osmall__lazy_H(X20,X61) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20),X61))
         => c_Lazy__Sequence_Osmall__lazy_H(X20,X61) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X61),c_Lazy__Sequence_Osmall__lazy_H(X20,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Opsimps]) ).

fof(i_0_5686,plain,
    ! [X16,X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Oremove1(X10,X16,X200)))) ),
    inference(fof_simplification,[status(thm)],[fact_notin__set__remove1]) ).

fof(i_0_5687,plain,
    ! [X161,X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),c_List_Osublist(X10,X200,X161)))) ),
    inference(fof_simplification,[status(thm)],[fact_notin__set__sublistI]) ).

fof(i_0_5688,plain,
    ! [X31624,X31625,X31626] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31626),X31625)),X31624))
      | hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(X31626,X31624)),X31625) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31626),X31625) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__upt])]) ).

fof(i_0_5689,plain,
    ! [X20535,X20536] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20536),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X20535))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20536),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20535))),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_5690,plain,
    ! [X1,X2,X10,X8] :
      ( class_Orderings_Oord(X8)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,X8)),X2),X1))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X2),X1))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,X8)),X1),X2)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__fun__def]) ).

fof(i_0_5691,plain,
    ! [X202,X26,X27,X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X44),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X27),X26)))
       => hAPP(c_Random_Opick(X27,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X27)),X26),X202)),X44) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X27),X26) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X44),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X27),X26)))
       => hAPP(c_Random_Opick(X27,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X27)),X26),X202)),X44) = hAPP(c_Random_Opick(X27,X202),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X44),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X27),X26))) ) ),
    inference(fof_simplification,[status(thm)],[fact_pick_Osimps]) ).

fof(i_0_5692,plain,
    ! [X17,X12,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X12),c_Complete__Lattice_OSup__class_OSup(tc_fun(X10,tc_HOL_Obool),X17)))
     => ~ ! [X184] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X12),X184))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X10,tc_HOL_Obool)),X184),X17)) ) ),
    inference(fof_simplification,[status(thm)],[fact_UnionE]) ).

fof(i_0_5693,plain,
    ! [X20378,X20379] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20379)),c_Int_OBit0(X20378)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20379),X20378)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20379),X20378))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20379)),c_Int_OBit0(X20378))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I14_J])]) ).

fof(i_0_5694,plain,
    ! [X20376,X20377] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20377)),c_Int_OBit0(X20376)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20377),X20376)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20377),X20376))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20377)),c_Int_OBit0(X20376))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__int__code_I13_J])]) ).

fof(i_0_5695,plain,
    ! [X20374,X20375] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20375)),c_Int_OBit0(X20374)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20375),X20374)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20375),X20374))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20375)),c_Int_OBit0(X20374))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I31_J])]) ).

fof(i_0_5696,plain,
    ! [X20372,X20373] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20373)),c_Int_OBit0(X20372)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20373),X20372)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20373),X20372))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20373)),c_Int_OBit0(X20372))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__int__code_I13_J])]) ).

fof(i_0_5697,plain,
    ! [X31272,X31273] : hAPP(c_List_OremoveAll(X31273,X31272),c_List_Olist_ONil(X31273)) = c_List_Olist_ONil(X31273),
    inference(variable_rename,[status(thm)],[fact_removeAll_Osimps_I1_J]) ).

fof(i_0_5698,plain,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X10),X12)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X10),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__Diff__singleton__if]) ).

fof(i_0_5699,plain,
    ! [X19990,X19991] :
      ( ~ class_Int_Onumber__ring(X19991)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19991),hAPP(c_Int_Onumber__class_Onumber__of(X19991),X19990)),c_Groups_Oone__class_Oone(X19991)) = hAPP(c_Int_Onumber__class_Onumber__of(X19991),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19990),c_Int_OBit1(c_Int_OPls))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__special_I3_J])]) ).

fof(i_0_5700,plain,
    ! [X90,X93,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Orderings_Olinorder(X10) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X90)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X93))) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__number__of__eq__not__less]) ).

fof(i_0_5701,plain,
    ! [X16,X11,X8,X10] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X10,tc_fun(X8,tc_HOL_Obool))),X11),X16)),
    inference(fof_simplification,[status(thm)],[fact_bot2E]) ).

fof(i_0_5702,plain,
    ! [X34,X142,X131,X132] :
      ( X132 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X131),X142)),X34)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34),X131)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X34))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X131 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => c_Divides_Odiv__class_Omod(tc_Int_Oint,X132,X131) = X34 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__mod__eq]) ).

fof(i_0_5703,plain,
    ! [X31537,X31538,X31539,X31540] : c_List_Ofoldr(X31540,X31539,X31538,c_List_Olist_ONil(X31540),X31537) = X31537,
    inference(variable_rename,[status(thm)],[fact_foldr_Osimps_I1_J]) ).

fof(i_0_5704,plain,
    ! [X32077,X32078,X32079,X32080] : c_List_Oconcat(X32080,hAPP(hAPP(c_List_Omap(X32079,tc_List_Olist(X32080)),X32078),X32077)) = c_List_Omaps(X32079,X32080,X32078,X32077),
    inference(variable_rename,[status(thm)],[fact_concat__map__maps]) ).

fof(i_0_5705,plain,
    ! [X32073,X32074,X32075,X32076] : c_List_Omaps(X32076,X32075,X32074,X32073) = c_List_Oconcat(X32075,hAPP(hAPP(c_List_Omap(X32076,tc_List_Olist(X32075)),X32074),X32073)),
    inference(variable_rename,[status(thm)],[fact_maps__def]) ).

fof(i_0_5706,plain,
    ! [X130,X34,X131,X132] :
      ( X132 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X131),X34)),X130)
     => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X130))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X130),X131)) ) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X131))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X131),X130))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X130),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
       => ( X131 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X132),X131) = X34 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__rel__div__eq]) ).

fof(i_0_5707,plain,
    ! [X30429,X30430,X30431] : hAPP(c_List_Orotate(X30431,hAPP(c_Nat_OSuc,X30430)),X30429) = hAPP(c_List_Orotate1(X30431),hAPP(c_List_Orotate(X30431,X30430),X30429)),
    inference(variable_rename,[status(thm)],[fact_rotate__Suc]) ).

fof(i_0_5708,plain,
    ! [X19,X11,X12,X2,X8,X10] :
      ( c_Finite__Set_Ofun__left__comm(X10,X8,X2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),X19),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X8,X2),hAPP(hAPP(X2,X11),X19)),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fun__left__comm_Ofold__insert2]) ).

fof(i_0_5709,plain,
    ! [X31613,X31614,X31615,X31616] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31616),X31615))
        | c_List_Oupt(X31616,X31615) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31614),X31613) )
      & ( X31616 = X31614
        | c_List_Oupt(X31616,X31615) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31614),X31613) )
      & ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31616),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X31615) = X31613
        | c_List_Oupt(X31616,X31615) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31614),X31613) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31616),X31615))
        | X31616 != X31614
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31616),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X31615) != X31613
        | c_List_Oupt(X31616,X31615) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31614),X31613) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__eq__Cons__conv])])]) ).

fof(i_0_5710,plain,
    ! [X2,X31,X30,X10] :
      ( class_Groups_Ocomm__monoid__add(X10)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),hAPP(c_Nat_OSuc,X30))) = c_Groups_Ozero__class_Ozero(X10) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),hAPP(c_Nat_OSuc,X30))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X10),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X10),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30))),hAPP(X2,X30)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__op__ivl__Suc]) ).

fof(i_0_5711,plain,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11))
     => ( ~ hBOOL(hAPP(X12,X11))
       => hBOOL(hAPP(X15,X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_sup1E]) ).

fof(i_0_5712,plain,
    ! [X20449] : c_Int_Opred(c_Int_OBit1(X20449)) = c_Int_OBit0(X20449),
    inference(variable_rename,[status(thm)],[fact_pred__Bit1]) ).

fof(i_0_5713,plain,
    ! [X33,X120,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X33) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = 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),X68),X120))),X33) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__add__left]) ).

fof(i_0_5714,plain,
    ! [X28547] : c_Transitive__Closure_Otrancl(X28547,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28547,X28547),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28547,X28547),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_trancl__empty]) ).

fof(i_0_5715,plain,
    ! [X31634,X31635,X31636,X31637] :
      ( ~ class_Groups_Ocomm__monoid__add(X31637)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X31637),X31636),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31635,X31634))) = hAPP(c_List_Omonoid__add__class_Olistsum(X31637),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31637),X31636),c_List_Oupt(X31635,X31634))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upt__conv__listsum__nat])]) ).

fof(i_0_5716,plain,
    ! [X31638,X31639,X31640,X31641] :
      ( ~ class_Groups_Ocomm__monoid__add(X31641)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31641),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31641),X31640),c_List_Oupt(X31639,X31638))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X31641),X31640),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31639,X31638))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__nat])]) ).

fof(i_0_5717,plain,
    ! [X11,X15,X12,X10] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11))
     => ~ ( hBOOL(hAPP(X12,X11))
         => ~ hBOOL(hAPP(X15,X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_inf1E]) ).

fof(i_0_5718,plain,
    ! [X30412,X30413,X30414] : hAPP(c_List_Orotate1(X30414),hAPP(c_List_Orotate(X30414,X30413),X30412)) = hAPP(c_List_Orotate(X30414,X30413),hAPP(c_List_Orotate1(X30414),X30412)),
    inference(variable_rename,[status(thm)],[fact_rotate1__rotate__swap]) ).

fof(i_0_5719,plain,
    ! [X20082,X20083] :
      ( ~ class_Int_Onumber__ring(X20083)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20083),c_Int_OBit1(X20082)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20083),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20083),c_Groups_Oone__class_Oone(X20083)),hAPP(c_Int_Onumber__class_Onumber__of(X20083),X20082))),hAPP(c_Int_Onumber__class_Onumber__of(X20083),X20082)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit1])]) ).

fof(i_0_5720,plain,
    ! [X15,X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ) ),
    inference(fof_simplification,[status(thm)],[fact_DiffI]) ).

fof(i_0_5721,plain,
    ! [X32786,X32787,X32788,X32789] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X32789,X32788,X32787,c_Code__Numeral_OSuc__code__numeral(X32786)) = hAPP(hAPP(X32787,X32786),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X32789,X32788,X32787,X32786)),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I2_J]) ).

fof(i_0_5722,plain,
    ! [X30989] : c_Code__Numeral_OSuc__code__numeral(X30989) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X30989))),
    inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__def]) ).

fof(i_0_5723,plain,
    ! [X12,X10] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(c_Finite__Set_Ocard(X10),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X10,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X10),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(c_Finite__Set_Ocard(X10),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__def]) ).

fof(i_0_5724,plain,
    ! [X28686,X28687,X28688] : hAPP(hAPP(c_Relation_Orel__comp(X28688,X28688,X28687),c_Relation_OId(X28688)),X28686) = X28686,
    inference(variable_rename,[status(thm)],[fact_Id__O__R]) ).

fof(i_0_5725,plain,
    ! [X22695,X22696] :
      ( ~ class_Fields_Ofield(X22696)
      | ~ class_Int_Onumber__ring(X22696)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22696),X22695),hAPP(c_Int_Onumber__class_Onumber__of(X22696),c_Int_OBit1(c_Int_OPls))) = X22695 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral1])]) ).

fof(i_0_5726,plain,
    ! [X22693,X22694] :
      ( ~ class_Fields_Ofield(X22694)
      | ~ class_Int_Onumber__ring(X22694)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22694),X22693),hAPP(c_Int_Onumber__class_Onumber__of(X22694),c_Int_OBit1(c_Int_OPls))) = X22693 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__numeral__1])]) ).

fof(i_0_5727,plain,
    ! [X26,X36,X37,X27] :
      ( class_Lattices_Osemilattice__sup(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27),X37),X36)),X26))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X26))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__supE]) ).

fof(i_0_5728,plain,
    ! [X26,X36,X37,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),hAPP(hAPP(c_Orderings_Oord__class_Omax(X27),X37),X36)),X26))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X37),X26))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X36),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_Ole__supE]) ).

fof(i_0_5729,plain,
    ! [X19958,X19959] :
      ( ~ class_Int_Onumber__ring(X19959)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19959),X19958),hAPP(c_Int_Onumber__class_Onumber__of(X19959),c_Int_OBit1(c_Int_OPls))) = X19958 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right])]) ).

fof(i_0_5730,plain,
    ! [X32699,X32700,X32701,X32702] :
      ( ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X32702),hAPP(hAPP(c_List_Olist_OCons(X32702),X32701),X32700)),X32699))
        | X32701 = X32699
        | hBOOL(hAPP(hAPP(c_List_Omember(X32702),X32700),X32699)) )
      & ( X32701 != X32699
        | hBOOL(hAPP(hAPP(c_List_Omember(X32702),hAPP(hAPP(c_List_Olist_OCons(X32702),X32701),X32700)),X32699)) )
      & ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X32702),X32700),X32699))
        | hBOOL(hAPP(hAPP(c_List_Omember(X32702),hAPP(hAPP(c_List_Olist_OCons(X32702),X32701),X32700)),X32699)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_member__rec_I1_J])])]) ).

fof(i_0_5731,plain,
    ! [X32703] : c_List_Omember(X32703) = c_List_Oset(X32703),
    inference(variable_rename,[status(thm)],[fact_member__set]) ).

fof(i_0_5732,plain,
    ! [X30377,X30378,X30379] :
      ( X30379 = c_List_Olist_ONil(X30378)
      | hAPP(c_List_Ohd(X30378),hAPP(c_List_Orotate(X30378,X30377),X30379)) = hAPP(hAPP(c_List_Onth(X30378),X30379),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30377,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30378)),X30379))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rotate__conv__nth])]) ).

fof(i_0_5733,plain,
    ! [X33,X120,X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)),X33)) = 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),X68),X120))),X33) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__number__of__mult__left]) ).

fof(i_0_5734,plain,
    ! [X30438,X30439,X30440] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30440)),X30439)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | hAPP(c_List_Orotate(X30440,X30438),X30439) = X30439 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__length01])]) ).

fof(i_0_5735,plain,
    ! [X15,X17,X13,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X17))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)),X17) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X17))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__left]) ).

fof(i_0_5736,plain,
    ! [X12,X15,X6,X10] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X15))
       => hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) )
     => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15))) ),
    inference(fof_simplification,[status(thm)],[fact_UnCI]) ).

fof(i_0_5737,plain,
    ! [X37,X27] :
      ( class_Rings_Olinordered__ring(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27),X37),X37)),c_Groups_Ozero__class_Ozero(X27))) ),
    inference(fof_simplification,[status(thm)],[fact_not__square__less__zero]) ).

fof(i_0_5738,plain,
    ! [X20408] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20408)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20408),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20408),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20408)),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_5739,plain,
    ! [X20369,X20370] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X20370))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X20369))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20370)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20369)),
    inference(variable_rename,[status(thm)],[fact_zdiv__number__of__Bit0]) ).

fof(i_0_5740,plain,
    ! [X25,X33,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X33)),X25))
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33),X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__leE]) ).

fof(i_0_5741,plain,
    ! [X20416] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20416)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20416),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20416),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20416)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I10_J])]) ).

fof(i_0_5742,plain,
    ! [X20901] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20901)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20901),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20901),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X20901)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I11_J])]) ).

fof(i_0_5743,plain,
    ! [X20829] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20829)),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20829),c_Int_OMin)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20829),c_Int_OMin))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20829)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J])]) ).

fof(i_0_5744,plain,
    ! [X20410] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20410)),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20410),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20410),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X20410)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I27_J])]) ).

fof(i_0_5745,plain,
    ! [X20430] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X20430))))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20430))) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20430)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X20430)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__Bit0])]) ).

fof(i_0_5746,plain,
    ! [X28681,X28682] : hAPP(c_Relation_OImage(X28682,X28682,c_Relation_OId(X28682)),X28681) = X28681,
    inference(variable_rename,[status(thm)],[fact_Image__Id]) ).

fof(i_0_5747,plain,
    ! [X12,X15,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),X15) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),X15) = hAPP(hAPP(c_Set_Oinsert(X10),X11),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),X12),X15)) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__Diff__if]) ).

fof(i_0_5748,plain,
    ! [X20078,X20079] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20079),X20078))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X20079)),X20078)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X20079)),X20078))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20079),X20078)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__pred__less])]) ).

fof(i_0_5749,plain,
    ! [X20920] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X20920)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),X20920)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I6_J]) ).

fof(i_0_5750,plain,
    ! [X19865,X19866] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19866)))
        | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19866)),X19865)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X19865) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19866)))
        | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19866)),X19865)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X19866))),X19865) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5210])]) ).

fof(i_0_5751,plain,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X25)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__if]) ).

fof(i_0_5752,plain,
    ! [X24,X25] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X25) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)),X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__geq]) ).

fof(i_0_5753,plain,
    ! [X25] : ~ 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,X25))))),
    inference(fof_simplification,[status(thm)],[fact_not__zle__0__negative]) ).

fof(i_0_5754,plain,
    ! [X28635,X28636] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28636,X28636),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28636,X28635)),c_Relation_OId(X28636)) = c_Transitive__Closure_Ortrancl(X28636,X28635),
    inference(variable_rename,[status(thm)],[fact_rtrancl__reflcl__absorb]) ).

fof(i_0_5755,plain,
    ! [X31583,X31584] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31584),X31583))
        | c_List_Oupt(X31584,hAPP(c_Nat_OSuc,X31583)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31584,X31583)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31583),c_List_Olist_ONil(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31584),X31583))
        | c_List_Oupt(X31584,hAPP(c_Nat_OSuc,X31583)) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5211])]) ).

fof(i_0_5756,plain,
    ! [X31581,X31582] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31582),X31581))
      | c_List_Oupt(X31582,hAPP(c_Nat_OSuc,X31581)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X31582,X31581)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31581),c_List_Olist_ONil(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__Suc__append])]) ).

fof(i_0_5757,plain,
    ! [X15,X12,X13,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Set_Oinsert(X10),X13),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) ) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right]) ).

fof(i_0_5758,plain,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Oplus__class_Oplus(X8)),X1),c_Groups_Ozero__class_Ozero(X8)),X12) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12) = c_Groups_Ozero__class_Ozero(X8) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_OF__eq]) ).

fof(i_0_5759,plain,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X8,X10,c_Groups_Otimes__class_Otimes(X8)),X1),c_Groups_Oone__class_Oone(X8)),X12) )
        & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12) = c_Groups_Oone__class_Oone(X8) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_OF__eq]) ).

fof(i_0_5760,plain,
    ! [X201,X202,X27,X25] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X25) = hAPP(hAPP(c_List_Onth(X27),X202),X25) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202)))
       => hAPP(hAPP(c_List_Onth(X27),hAPP(hAPP(c_List_Oappend(X27),X202),X201)),X25) = hAPP(hAPP(c_List_Onth(X27),X201),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X25),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X27)),X202))) ) ),
    inference(fof_simplification,[status(thm)],[fact_nth__append]) ).

fof(i_0_5761,plain,
    ! [X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)))
    <=> ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_Compl__iff]) ).

fof(i_0_5762,plain,
    ! [X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_ComplD]) ).

fof(i_0_5763,plain,
    ! [X12,X6,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12)))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_ComplE]) ).

fof(i_0_5764,plain,
    ! [X20455] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X20455)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20455)),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_5765,plain,
    ! [X68,X69,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Orderings_Oord(X10) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X68) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X69) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_max__number__of]) ).

fof(i_0_5766,plain,
    ! [X68,X69,X10] :
      ( ( class_Int_Onumber(X10)
        & class_Orderings_Oord(X10) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X69) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),hAPP(c_Int_Onumber__class_Onumber__of(X10),X69)),hAPP(c_Int_Onumber__class_Onumber__of(X10),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X10),X68) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__number__of]) ).

fof(i_0_5767,plain,
    ! [X43,X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X43)),X44)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less1]) ).

fof(i_0_5768,plain,
    ! [X44,X43] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X43),X44)),X44)),
    inference(fof_simplification,[status(thm)],[fact_not__add__less2]) ).

fof(i_0_5769,plain,
    ! [X199,X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oremove1(X10,X11,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),c_List_Oremove1(X10,X11,X200)),X199) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oremove1(X10,X11,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = hAPP(hAPP(c_List_Oappend(X10),X200),c_List_Oremove1(X10,X11,X199)) ) ),
    inference(fof_simplification,[status(thm)],[fact_remove1__append]) ).

fof(i_0_5770,plain,
    ! [X19943] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(X19943))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19943) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19943) != 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(X19943)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__number__of__pred__iff__0])]) ).

fof(i_0_5771,plain,
    ! [X11,X2,X10] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X10,X2,c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))),X11)),
    inference(fof_simplification,[status(thm)],[fact_empty__fold1SetE]) ).

fof(i_0_5772,plain,
    ! [X19947,X19948] :
      ( ( c_Int_OBit1(X19948) != c_Int_OBit1(X19947)
        | X19948 = X19947 )
      & ( X19948 != X19947
        | c_Int_OBit1(X19948) = c_Int_OBit1(X19947) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I51_J])]) ).

fof(i_0_5773,plain,
    ! [X32592,X32593] : c_List_Oconcat(X32593,c_List_Oreplicate(tc_List_Olist(X32593),X32592,c_List_Olist_ONil(X32593))) = c_List_Olist_ONil(X32593),
    inference(variable_rename,[status(thm)],[fact_concat__replicate__trivial]) ).

fof(i_0_5774,plain,
    ! [X14,X13,X42] :
      ( hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X13),X14)))
    <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X13),X14))
            & ~ hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
          | ? [X75] :
              ( X13 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X14),X75)
              & ~ hBOOL(hAPP(X42,X75)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__diff__split__asm]) ).

fof(i_0_5775,plain,
    ! [X200,X11,X10] :
      ( hBOOL(hAPP(c_List_Odistinct(X10),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
        & hBOOL(hAPP(c_List_Odistinct(X10),X200)) ) ),
    inference(fof_simplification,[status(thm)],[fact_distinct_Osimps_I2_J]) ).

fof(i_0_5776,plain,
    ! [X30402,X30403,X30404] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30404)),hAPP(c_List_Orotate(X30404,X30403),X30402)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30404)),X30402),
    inference(variable_rename,[status(thm)],[fact_length__rotate]) ).

fof(i_0_5777,plain,
    ! [X31991,X31992] : c_List_OdropWhile(X31992,X31991,c_List_Olist_ONil(X31992)) = c_List_Olist_ONil(X31992),
    inference(variable_rename,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).

fof(i_0_5778,plain,
    ! [X12,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)),hAPP(hAPP(c_Set_Oinsert(X10),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))) = X12 ),
    inference(fof_simplification,[status(thm)],[fact_Diff__insert__absorb]) ).

fof(i_0_5779,plain,
    ! [X1,X11,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(X1,X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_Oinsert]) ).

fof(i_0_5780,plain,
    ! [X2,X13,X9,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X9))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X9))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),hAPP(hAPP(c_Set_Oinsert(X10),X13),X9)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),hAPP(X2,X13)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X9)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__insert]) ).

fof(i_0_5781,plain,
    ! [X1,X11,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X1,X11)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_Oinsert]) ).

fof(i_0_5782,plain,
    ! [X2,X13,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),hAPP(X2,X13)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__insert]) ).

fof(i_0_5783,plain,
    ! [X31604,X31605,X31606] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),X31606),c_List_Oupt(X31605,X31604)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X31605),X31606),X31604),
    inference(variable_rename,[status(thm)],[fact_drop__upt]) ).

fof(i_0_5784,plain,
    ! [X200,X42,X10] :
      ( hAPP(c_List_Ofilter(X10,X42),X200) = c_List_Olist_ONil(X10)
    <=> ! [X3] :
          ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X200)))
         => ~ hBOOL(hAPP(X42,X3)) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__empty__conv]) ).

fof(i_0_5785,plain,
    ! [X24,X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)))),
    inference(fof_simplification,[status(thm)],[fact_not__int__zless__negative]) ).

fof(i_0_5786,plain,
    ! [X30405,X30406,X30407] : hAPP(c_List_Oset(X30407),hAPP(c_List_Orotate(X30407,X30406),X30405)) = hAPP(c_List_Oset(X30407),X30405),
    inference(variable_rename,[status(thm)],[fact_set__rotate]) ).

fof(i_0_5787,plain,
    ! [X10,X12,X11,X15] :
      ( ( ~ hBOOL(hAPP(X15,X11))
       => hBOOL(hAPP(X12,X11)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X10,tc_HOL_Obool)),X12),X15),X11)) ),
    inference(fof_simplification,[status(thm)],[fact_sup1CI]) ).

fof(i_0_5788,plain,
    ! [X233,X234,X200,X42,X10] :
      ( c_List_Opartition(X10,X42,X200) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X10),tc_List_Olist(X10)),X234),X233)
     => ( ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X234)))
           => hBOOL(hAPP(X42,X3)) )
        & ! [X3] :
            ( hBOOL(hAPP(hAPP(c_member(X10),X3),hAPP(c_List_Oset(X10),X233)))
           => ~ hBOOL(hAPP(X42,X3)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_partition__P]) ).

fof(i_0_5789,plain,
    ! [X28548,X28549] : hAPP(c_Relation_ODomain(X28549,X28549),c_Transitive__Closure_Otrancl(X28549,X28548)) = hAPP(c_Relation_ODomain(X28549,X28549),X28548),
    inference(variable_rename,[status(thm)],[fact_trancl__domain]) ).

fof(i_0_5790,plain,
    ! [X28550,X28551] : hAPP(c_Relation_ORange(X28551,X28551),c_Transitive__Closure_Otrancl(X28551,X28550)) = hAPP(c_Relation_ORange(X28551,X28551),X28550),
    inference(variable_rename,[status(thm)],[fact_trancl__range]) ).

fof(i_0_5791,plain,
    ! [X119,X93] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)))
    <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X93),X119))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X93),c_Int_OPls)) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__nat__number__of]) ).

fof(i_0_5792,plain,
    ! [X38,X34,X26] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X26)) )
     => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X34)) )
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Oless__trans]) ).

fof(i_0_5793,plain,
    ! [X20387,X20388] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X20388)),c_Int_OBit0(X20387)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20388),X20387)),
    inference(variable_rename,[status(thm)],[fact_add__Bit0__Bit0]) ).

fof(i_0_5794,plain,
    ! [X20391,X20392] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X20392)),c_Int_OBit0(X20391)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20392),X20391)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I7_J]) ).

fof(i_0_5795,plain,
    ! [X11,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,X2),X11),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__one_Oeq__fold_H]) ).

fof(i_0_5796,plain,
    ! [X11] :
      ~ ! [X51] :
          ( X11 = hAPP(c_Int_OAbs__Integ,X51)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X51),c_Int_OInteg)) ),
    inference(fof_simplification,[status(thm)],[fact_Abs__Integ__cases]) ).

fof(i_0_5797,plain,
    ! [X31590,X31591] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31591),X31590))
      | c_List_Oupt(X31591,X31590) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31591),c_List_Oupt(hAPP(c_Nat_OSuc,X31591),X31590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Cons])]) ).

fof(i_0_5798,plain,
    ! [X31588,X31589] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31589),X31588))
        | c_List_Oupt(X31589,X31588) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X31589),c_List_Oupt(hAPP(c_Nat_OSuc,X31589),X31588)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31589),X31588))
        | c_List_Oupt(X31589,X31588) = c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5212])]) ).

fof(i_0_5799,plain,
    ! [X200,X2,X10,X11,X42,X8] :
      ( class_Orderings_Olinorder(X8)
     => ( ~ hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X10,X8,X2),X11),X200)) = hAPP(c_List_Ofilter(X10,X42),X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__insort__triv]) ).

fof(i_0_5800,plain,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X11),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold_H]) ).

fof(i_0_5801,plain,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X11),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold_H]) ).

fof(i_0_5802,plain,
    ! [X12,X10] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X10,tc_HOL_Obool)),X12),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_not__psubset__empty]) ).

fof(i_0_5803,plain,
    ! [X13,X12,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
         => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Groups_Otimes__class_Otimes(X10)),X13),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1__eq__fold]) ).

fof(i_0_5804,plain,
    ! [X20458,X20459] :
      ( ~ class_Int_Onumber__ring(X20459)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20459),c_Int_OBit0(X20458)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20459),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20459),c_Groups_Ozero__class_Ozero(X20459)),hAPP(c_Int_Onumber__class_Onumber__of(X20459),X20458))),hAPP(c_Int_Onumber__class_Onumber__of(X20459),X20458)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Bit0])]) ).

fof(i_0_5805,plain,
    ! [X31632,X31633] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X31633),hAPP(c_List_Onth(X31633),X31632)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31633)),X31632))) = X31632,
    inference(variable_rename,[status(thm)],[fact_map__nth]) ).

fof(i_0_5806,plain,
    ! [X36,X37,X26,X27] :
      ( class_Lattices_Osemilattice__inf(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27),X37),X36)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X36)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__infE]) ).

fof(i_0_5807,plain,
    ! [X36,X37,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),hAPP(hAPP(c_Orderings_Oord__class_Omin(X27),X37),X36)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X37))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X36)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_Ole__infE]) ).

fof(i_0_5808,plain,
    ! [X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremove1(X10,X11,X200)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),c_List_Oremove1(X10,X11,X200)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X10)),X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_length__remove1]) ).

fof(i_0_5809,plain,
    ! [X15,X17,X13,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X17))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)),X17) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X15),X17) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__left__if0]) ).

fof(i_0_5810,plain,
    ! [X20353,X20354] :
      ( ( X20354 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | c_Code__Numeral_Onat__of__aux(X20354,X20353) = X20353 )
      & ( X20354 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | c_Code__Numeral_Onat__of__aux(X20354,X20353) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X20354),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X20353)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__aux__code])]) ).

fof(i_0_5811,plain,
    ! [X30987,X30988] : c_Code__Numeral_Onat__of__aux(X30988,X30987) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30988)),X30987),
    inference(variable_rename,[status(thm)],[fact_nat__of__aux__def]) ).

fof(i_0_5812,plain,
    ! [X33033,X33034] :
      ( ~ c_Relation_Osym(X33034,X33033)
      | c_Relation_Osym(X33034,c_Transitive__Closure_Otrancl(X33034,X33033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__trancl])]) ).

fof(i_0_5813,plain,
    ! [X28520,X28521] :
      ( ~ c_Wellfounded_Owf(X28521,X28520)
      | c_Wellfounded_Owf(X28521,c_Transitive__Closure_Otrancl(X28521,X28520)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__trancl])]) ).

fof(i_0_5814,plain,
    ! [X28683,X28684,X28685] : hAPP(hAPP(c_Relation_Orel__comp(X28685,X28684,X28684),X28683),c_Relation_OId(X28684)) = X28683,
    inference(variable_rename,[status(thm)],[fact_R__O__Id]) ).

fof(i_0_5815,plain,
    ! [X28618,X28619] : c_Transitive__Closure_Otrancl(X28619,X28618) = hAPP(hAPP(c_Relation_Orel__comp(X28619,X28619,X28619),c_Transitive__Closure_Ortrancl(X28619,X28618)),X28618),
    inference(variable_rename,[status(thm)],[fact_trancl__unfold__right]) ).

fof(i_0_5816,plain,
    ! [X28610,X28611] : c_Transitive__Closure_Ortrancl(X28611,c_Transitive__Closure_Otrancl(X28611,X28610)) = c_Transitive__Closure_Ortrancl(X28611,X28610),
    inference(variable_rename,[status(thm)],[fact_trancl__rtrancl__absorb]) ).

fof(i_0_5817,plain,
    ! [X31335] : c_List_Oconcat(X31335,c_List_Olist_ONil(tc_List_Olist(X31335))) = c_List_Olist_ONil(X31335),
    inference(variable_rename,[status(thm)],[fact_concat_Osimps_I1_J]) ).

fof(i_0_5818,plain,
    ! [X14,X13] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14)) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff]) ).

fof(i_0_5819,plain,
    ! [X14,X13] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14)
    <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14)) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty__iff2]) ).

fof(i_0_5820,plain,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__inf__class_Oinf(X10)),X11),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oeq__fold_H]) ).

fof(i_0_5821,plain,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Lattices_Osemilattice__sup__class_Osup(X10)),X11),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oeq__fold_H]) ).

fof(i_0_5822,plain,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omax(X10)),X11),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Max_Oeq__fold_H]) ).

fof(i_0_5823,plain,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Finite__Set_Ofold(X10,X10,c_Orderings_Oord__class_Omin(X10)),X11),X12) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Min_Oeq__fold_H]) ).

fof(i_0_5824,plain,
    ! [X32884,X32885] : c_Relation_Otrans(X32885,c_Transitive__Closure_Otrancl(X32885,X32884)),
    inference(variable_rename,[status(thm)],[fact_trans__trancl]) ).

fof(i_0_5825,plain,
    ! [X119,X93] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X93) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X119)
    <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X119)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93)))
         => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X119)))
             => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X93) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X119)))
             => X93 = X119 ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_eq__nat__number__of]) ).

fof(i_0_5826,plain,
    ! [X26,X27] :
      ( ( class_Int_Onumber__ring(X27)
        & class_Rings_Olinordered__idom(X27) )
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)),c_Groups_Ozero__class_Ozero(X27)))
         => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)),c_Groups_Ozero__class_Ozero(X27)))
         => hAPP(c_Groups_Oabs__class_Oabs(X27),hAPP(c_Int_Onumber__class_Onumber__of(X27),X26)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),X26) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__number__of]) ).

fof(i_0_5827,plain,
    ! [X28769] : hAPP(c_Relation_Oconverse(X28769,X28769),c_Relation_OId(X28769)) = c_Relation_OId(X28769),
    inference(variable_rename,[status(thm)],[fact_converse__Id]) ).

fof(i_0_5828,plain,
    ! [X120,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) )
          & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
           => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_mod__nat__number__of]) ).

fof(i_0_5829,plain,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olattice_OSup__fin(X10,c_Orderings_Oord__class_Omax(X10),X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OSup__fin_Oinsert]) ).

fof(i_0_5830,plain,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olattice_OInf__fin(X10,c_Orderings_Oord__class_Omin(X10),X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_min__max_OInf__fin_Oinsert]) ).

fof(i_0_5831,plain,
    ! [X20389,X20390] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X20390)),X20389) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20390),X20389)),
    inference(variable_rename,[status(thm)],[fact_mult__Bit0]) ).

fof(i_0_5832,plain,
    ! [X38,X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
     => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X34)) )
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less__trans]) ).

fof(i_0_5833,plain,
    ! [X38,X34,X26] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X26)) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X38))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X38))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X38),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le__trans]) ).

fof(i_0_5834,plain,
    ! [X199,X42,X200,X11,X10] :
      ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => ( ~ hBOOL(hAPP(X42,X11))
       => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),X199)) = c_List_OtakeWhile(X10,X42,X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__append1]) ).

fof(i_0_5835,plain,
    ! [X120,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120))) ) ),
    inference(fof_simplification,[status(thm)],[fact_div__nat__number__of]) ).

fof(i_0_5836,plain,
    ! [X92,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)) = 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),X92)) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X92))) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__nat__number__of__number__of]) ).

fof(i_0_5837,plain,
    ! [X11,X12,X10] :
      ( class_Groups_Oab__semigroup__mult(X10)
     => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
         => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
           => hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X10),X11),hAPP(c_Finite__Set_Ofold1(X10,c_Groups_Otimes__class_Otimes(X10)),X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_fold1__insert]) ).

fof(i_0_5838,plain,
    ! [X13,X14] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X14),X13))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X14)) )
     => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_OatLeastatMost__empty]) ).

fof(i_0_5839,plain,
    ! [X20071,X20072] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20072))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X20071)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20072)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20071),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X20072))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__number__of])]) ).

fof(i_0_5840,plain,
    ! [X30,X42] :
      ( ~ hBOOL(hAPP(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(X42,X30))
       => ? [X59] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X59),X30))
            & ! [X91] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X91),X59))
               => ~ hBOOL(hAPP(X42,X91)) )
            & hBOOL(hAPP(X42,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X59),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_ex__least__nat__less]) ).

fof(i_0_5841,plain,
    ! [X31627,X31628] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X31628,X31627) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X31628),hAPP(c_Nat_OSuc,X31627))),
    inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upt]) ).

fof(i_0_5842,plain,
    ! [X20830] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X20830)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X20830)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X20830))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X20830))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I8_J])]) ).

fof(i_0_5843,plain,
    ! [X20902] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X20902)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X20902)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),X20902))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X20902))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I25_J])]) ).

fof(i_0_5844,plain,
    ! [X20415] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X20415)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20415)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20415))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X20415))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I4_J])]) ).

fof(i_0_5845,plain,
    ! [X20409] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X20409)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20409)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20409))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X20409))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I21_J])]) ).

fof(i_0_5846,plain,
    ! [X15,X12,X13,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12))
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),hAPP(hAPP(c_Set_Oinsert(X10),X13),X15)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X10,tc_HOL_Obool)),X12),X15) ),
    inference(fof_simplification,[status(thm)],[fact_Int__insert__right__if0]) ).

fof(i_0_5847,plain,
    ! [X30435,X30436,X30437] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X30437,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30436)),X30435)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Orotate(X30436,X30437),X30435) = X30435 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__id])]) ).

fof(i_0_5848,plain,
    ! [X30409,X30410,X30411] :
      ( ( hAPP(c_List_Orotate(X30411,X30410),X30409) != c_List_Olist_ONil(X30411)
        | X30409 = c_List_Olist_ONil(X30411) )
      & ( X30409 != c_List_Olist_ONil(X30411)
        | hAPP(c_List_Orotate(X30411,X30410),X30409) = c_List_Olist_ONil(X30411) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate__is__Nil__conv])]) ).

fof(i_0_5849,plain,
    ! [X61,X60] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X61,X60) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X60),X61))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X61,X60) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X61),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)),X60)) ) ),
    inference(fof_simplification,[status(thm)],[fact_simp__from__to]) ).

fof(i_0_5850,plain,
    ! [X20541,X20542] :
      ( ~ class_Int_Onumber__ring(X20542)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20542),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20542),c_Groups_Oone__class_Oone(X20542)),c_Groups_Oone__class_Oone(X20542))),hAPP(c_Int_Onumber__class_Onumber__of(X20542),X20541)) = hAPP(c_Int_Onumber__class_Onumber__of(X20542),c_Int_OBit0(X20541)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0])]) ).

fof(i_0_5851,plain,
    ! [X14,X15,X13,X10] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X15))
       => X13 = X14 )
     => hBOOL(hAPP(hAPP(c_member(X10),X13),hAPP(hAPP(c_Set_Oinsert(X10),X14),X15))) ),
    inference(fof_simplification,[status(thm)],[fact_insertCI]) ).

fof(i_0_5852,plain,
    ! [X20040] : c_Int_OBit1(X20040) = 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)),X20040)),X20040),
    inference(variable_rename,[status(thm)],[fact_Bit1__def]) ).

fof(i_0_5853,plain,
    ! [X29176,X29177,X29178,X29179,X29180,X29181] : hAPP(hAPP(c_Product__Type_Ointernal__split(X29181,X29180,X29179),X29178),hAPP(hAPP(c_Product__Type_OPair(X29181,X29180),X29177),X29176)) = hAPP(hAPP(X29178,X29177),X29176),
    inference(variable_rename,[status(thm)],[fact_internal__split__conv]) ).

fof(i_0_5854,plain,
    ! [X29168,X29169,X29170] : c_Product__Type_Ointernal__split(X29170,X29169,X29168) = c_Product__Type_Oprod_Oprod__case(X29170,X29169,X29168),
    inference(variable_rename,[status(thm)],[fact_internal__split__def]) ).

fof(i_0_5855,plain,
    ! [X32614,X32615,X32616] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X32616),hAPP(c_COMBK(X32616,tc_Nat_Onat),X32615)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32614)) = c_List_Oreplicate(X32616,X32614,X32615),
    inference(variable_rename,[status(thm)],[fact_map__replicate__trivial]) ).

fof(i_0_5856,plain,
    ! [X12,X6,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
     => hBOOL(hAPP(hAPP(c_member(X10),X6),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X10,tc_HOL_Obool)),X12))) ),
    inference(fof_simplification,[status(thm)],[fact_ComplI]) ).

fof(i_0_5857,plain,
    ! [X8,X12,X6,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => hAPP(c_Set_Ovimage(X8,X10,hAPP(c_COMBK(X10,X8),X6)),X12) = c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X6),X12))
       => hAPP(c_Set_Ovimage(X8,X10,hAPP(c_COMBK(X10,X8),X6)),X12) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_vimage__const]) ).

fof(i_0_5858,plain,
    ! [X11,X12,X9,X2,X10] :
      ( c_Finite__Set_Ofolding__one(X10,X2,X9)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => hAPP(X9,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(X2,X11),hAPP(X9,X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_folding__one_Oinsert]) ).

fof(i_0_5859,plain,
    ! [X25,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),X24),X25))
       => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X25),X24)) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__dvd__not__less]) ).

fof(i_0_5860,plain,
    ! [X31619,X31620] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(X31620,X31619)) = c_List_Oupt(hAPP(c_Nat_OSuc,X31620),hAPP(c_Nat_OSuc,X31619)),
    inference(variable_rename,[status(thm)],[fact_map__Suc__upt]) ).

fof(i_0_5861,plain,
    ! [X36,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)),X36))
           => c_Divides_Odivmod__int(X37,X36) = c_Divides_OposDivAlg(X37,X36) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => ( ( X37 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X37,X36) = 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)) )
              & ( X37 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
               => c_Divides_Odivmod__int(X37,X36) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36))) ) ) ) ) )
      & ( ~ 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(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => c_Divides_Odivmod__int(X37,X36) = c_Divides_OnegDivAlg(X37,X36) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36))
           => c_Divides_Odivmod__int(X37,X36) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X37),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X36))) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_divmod__int__def]) ).

fof(i_0_5862,plain,
    ! [X83,X200,X10,X11,X42] :
      ( ~ hBOOL(hAPP(X42,X11))
     => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Oappend(X10),X200),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X83))) = c_List_OtakeWhile(X10,X42,X200) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile__tail]) ).

fof(i_0_5863,plain,
    ! [X28722] : c_Relation_Orefl__on(X28722,c_Orderings_Otop__class_Otop(tc_fun(X28722,tc_HOL_Obool)),c_Relation_OId(X28722)),
    inference(variable_rename,[status(thm)],[fact_refl__Id]) ).

fof(i_0_5864,plain,
    ! [X19960] :
      ( ~ class_Int_Onumber__ring(X19960)
      | hAPP(c_Int_Onumber__class_Onumber__of(X19960),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(X19960) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_numeral__1__eq__1])]) ).

fof(i_0_5865,plain,
    ! [X19961] :
      ( ~ class_Int_Onumber__ring(X19961)
      | c_Groups_Oone__class_Oone(X19961) = hAPP(c_Int_Onumber__class_Onumber__of(X19961),c_Int_OBit1(c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I110_J])]) ).

fof(i_0_5866,plain,
    ! [X30,X31] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X30)),X31)) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq__eq]) ).

fof(i_0_5867,plain,
    ! [X37,X27] :
      ( class_Groups_Oordered__ab__group__add__abs(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Groups_Oabs__class_Oabs(X27),X37)),c_Groups_Ozero__class_Ozero(X27))) ),
    inference(fof_simplification,[status(thm)],[fact_abs__not__less__zero]) ).

fof(i_0_5868,plain,
    ! [X24,X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),X24)),c_Groups_Ozero__class_Ozero(X27))) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__less__0__iff]) ).

fof(i_0_5869,plain,
    ! [X21465,X21466] :
      ( ( ~ c_Int_Oiszero(X21466,hAPP(c_Int_Onumber__class_Onumber__of(X21466),c_Int_OBit0(X21465)))
        | c_Int_Oiszero(X21466,hAPP(c_Int_Onumber__class_Onumber__of(X21466),X21465))
        | ~ class_Int_Onumber__ring(X21466)
        | ~ class_Int_Oring__char__0(X21466) )
      & ( ~ c_Int_Oiszero(X21466,hAPP(c_Int_Onumber__class_Onumber__of(X21466),X21465))
        | c_Int_Oiszero(X21466,hAPP(c_Int_Onumber__class_Onumber__of(X21466),c_Int_OBit0(X21465)))
        | ~ class_Int_Onumber__ring(X21466)
        | ~ class_Int_Oring__char__0(X21466) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__number__of__Bit0])])]) ).

fof(i_0_5870,plain,
    ! [X120,X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X120),c_Int_OPls))
           => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X68),X120)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_add__nat__number__of]) ).

fof(i_0_5871,plain,
    ! [X25,X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X25) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X25) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),X25) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)),X25)) ) ),
    inference(fof_simplification,[status(thm)],[fact_power__nat__number__of]) ).

fof(i_0_5872,plain,
    ! [X20425] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X20425)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X20425)),
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I3_J]) ).

fof(i_0_5873,plain,
    ! [X80,X45,X33] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33),X45))
       => c_Random_Ominus__shift(X80,X33,X45) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X80),X33)),X45) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33),X45))
       => c_Random_Ominus__shift(X80,X33,X45) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X33),X45) ) ),
    inference(fof_simplification,[status(thm)],[fact_minus__shift__def]) ).

fof(i_0_5874,axiom,
    ! [X32,X30,X42] :
      ( hBOOL(hAPP(X42,c_Divides_Odiv__class_Omod(tc_Int_Oint,X30,X32)))
    <=> epred2_3(X42,X32,X30) ),
    inference(apply_def,[status(thm)],[fact_split__zmod,c_0_5213]) ).

fof(i_0_5875,plain,
    ! [X43,X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X44),X43))
       => c_List_Oupto(X44,X43) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X44),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X44),c_Groups_Oone__class_Oone(tc_Int_Oint)),X43)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X44),X43))
       => c_List_Oupto(X44,X43) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_upto_Osimps]) ).

fof(i_0_5876,plain,
    ! [X20382,X20383] : c_Int_OBit0(X20383) != c_Int_OBit1(X20382),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I49_J]) ).

fof(i_0_5877,plain,
    ! [X20384,X20385] : c_Int_OBit1(X20385) != c_Int_OBit0(X20384),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I50_J]) ).

fof(i_0_5878,plain,
    ! [X22239,X22240] : c_Divides_Odivmod__nat(X22240,X22239) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22240),X22239)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22240,X22239)),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__div__mod]) ).

fof(i_0_5879,plain,
    ! [X25825,X25826,X25827,X25828] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X25828,X25827,X25826,c_Code__Numeral_OSuc__code__numeral(X25825)) = hAPP(X25826,X25825),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I5_J]) ).

fof(i_0_5880,plain,
    ! [X31629,X31630] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X31630,X31629) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X31630),X31629)),
    inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upt]) ).

fof(i_0_5881,plain,
    ! [X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oremdups(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = c_List_Oremdups(X10,X200) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oremdups(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Oremdups(X10,X200)) ) ),
    inference(fof_simplification,[status(thm)],[fact_remdups_Osimps_I2_J]) ).

fof(i_0_5882,plain,
    ! [X33,X27] :
      ( class_Rings_Oring__1(X27)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X27),X33) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33)))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
         => hAPP(c_Int_Oring__1__class_Oof__int(X27),X33) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onat,X33)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__int__of__nat]) ).

fof(i_0_5883,plain,
    ! [X44,X58] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X58),X44))
       => c_Lazy__Sequence_Osmall__lazy_H(X58,X44) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X58),X44))
       => c_Lazy__Sequence_Osmall__lazy_H(X58,X44) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X44),c_Lazy__Sequence_Osmall__lazy_H(X58,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X44),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(fof_simplification,[status(thm)],[fact_small__lazy_H_Osimps]) ).

fof(i_0_5884,plain,
    ! [X28720] : hAPP(c_Relation_ODomain(X28720,X28720),c_Relation_OId(X28720)) = c_Orderings_Otop__class_Otop(tc_fun(X28720,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__Id]) ).

fof(i_0_5885,plain,
    ! [X28721] : hAPP(c_Relation_ORange(X28721,X28721),c_Relation_OId(X28721)) = c_Orderings_Otop__class_Otop(tc_fun(X28721,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__Id]) ).

fof(i_0_5886,plain,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OInf__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X10),X11),c_Big__Operators_Olattice__class_OInf__fin(X10,X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Inf__fin_Oinsert]) ).

fof(i_0_5887,plain,
    ! [X11,X12,X10] :
      ( class_Lattices_Olattice(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olattice__class_OSup__fin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X10),X11),c_Big__Operators_Olattice__class_OSup__fin(X10,X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Sup__fin_Oinsert]) ).

fof(i_0_5888,plain,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMax(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X10),X11),c_Big__Operators_Olinorder__class_OMax(X10,X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Max_Oinsert]) ).

fof(i_0_5889,plain,
    ! [X11,X12,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => ( X12 != c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
           => c_Big__Operators_Olinorder__class_OMin(X10,hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X10),X11),c_Big__Operators_Olinorder__class_OMin(X10,X12)) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_Min_Oinsert]) ).

fof(i_0_5890,plain,
    ! [X33562,X33563,X33564] :
      ( ( ~ c_List_Olist__all(tc_Nat_Onat,X33564,c_List_Oupt(X33563,X33562))
        | c_List_Oall__interval__nat(X33564,X33563,X33562) )
      & ( ~ c_List_Oall__interval__nat(X33564,X33563,X33562)
        | c_List_Olist__all(tc_Nat_Onat,X33564,c_List_Oupt(X33563,X33562)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__nat])]) ).

fof(i_0_5891,plain,
    ! [X28608,X28609] : c_Transitive__Closure_Otrancl(X28609,c_Transitive__Closure_Ortrancl(X28609,X28608)) = c_Transitive__Closure_Ortrancl(X28609,X28608),
    inference(variable_rename,[status(thm)],[fact_rtrancl__trancl__absorb]) ).

fof(i_0_5892,plain,
    ! [X11,X10,X12] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12))
       => c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)),X12) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12))
       => c_List_Osublist(X10,hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_Olist_ONil(X10)),X12) = c_List_Olist_ONil(X10) ) ),
    inference(fof_simplification,[status(thm)],[fact_sublist__singleton]) ).

fof(i_0_5893,plain,
    ! [X32706,X32707,X32708] :
      ( ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X32708),X32707),X32706))
        | hBOOL(hAPP(hAPP(c_member(X32708),X32706),hAPP(c_List_Oset(X32708),X32707))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32708),X32706),hAPP(c_List_Oset(X32708),X32707)))
        | hBOOL(hAPP(hAPP(c_List_Omember(X32708),X32707),X32706)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_List_Omember__def])]) ).

fof(i_0_5894,plain,
    ! [X32696,X32697,X32698] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32698),X32697),hAPP(c_List_Oset(X32698),X32696)))
        | hBOOL(hAPP(hAPP(c_List_Omember(X32698),X32696),X32697)) )
      & ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X32698),X32696),X32697))
        | hBOOL(hAPP(hAPP(c_member(X32698),X32697),hAPP(c_List_Oset(X32698),X32696))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__member])]) ).

fof(i_0_5895,plain,
    ! [X120] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X120)))
       => 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),X120)) = 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),X120)))
       => 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),X120)) = 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),X120))) ) ),
    inference(fof_simplification,[status(thm)],[fact_one__mod__nat__number__of]) ).

fof(i_0_5896,plain,
    ! [X28892] : c_Relation_Osingle__valued(X28892,X28892,c_Relation_OId(X28892)),
    inference(variable_rename,[status(thm)],[fact_single__valued__Id]) ).

fof(i_0_5897,plain,
    ! [X16,X11,X10] :
      ( class_Orderings_Opreorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_less__le__not__le]) ).

fof(i_0_5898,plain,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X10),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card_Oinsert]) ).

fof(i_0_5899,axiom,
    ! [X32,X30,X42] :
      ( hBOOL(hAPP(X42,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30),X32)))
    <=> epred1_3(X42,X32,X30) ),
    inference(apply_def,[status(thm)],[fact_split__zdiv,c_0_5214]) ).

fof(i_0_5900,plain,
    ! [X15,X12,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X15))
       => ( hAPP(hAPP(c_Set_Oinsert(X10),X11),X12) = hAPP(hAPP(c_Set_Oinsert(X10),X11),X15)
        <=> X12 = X15 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_insert__ident]) ).

fof(i_0_5901,plain,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Finite__Set_Ocard(X10),X12) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
         => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),X12)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__if]) ).

fof(i_0_5902,plain,
    ! [X31617,X31618] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31618),X31617))
      | c_List_Olast(tc_Nat_Onat,c_List_Oupt(X31618,X31617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31617),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__upt])]) ).

fof(i_0_5903,plain,
    ! [X20977] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X20977)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X20977,
    inference(variable_rename,[status(thm)],[fact_Suc__code__numeral__minus__one]) ).

fof(i_0_5904,plain,
    ! [X30,X31] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31),X30))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_OSuc,X31))) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__eq]) ).

fof(i_0_5905,plain,
    ! [X31607,X31608] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X31608,X31607))),
    inference(variable_rename,[status(thm)],[fact_distinct__upt]) ).

fof(i_0_5906,plain,
    ! [X28975,X28976] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28976,X28976),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28975) = c_Relation_OId(X28976),
    inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I1_J]) ).

fof(i_0_5907,plain,
    ! [X200,X10,X11,X42] :
      ( ( hBOOL(hAPP(X42,X11))
       => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),c_List_OtakeWhile(X10,X42,X200)) )
      & ( ~ hBOOL(hAPP(X42,X11))
       => c_List_OtakeWhile(X10,X42,hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = c_List_Olist_ONil(X10) ) ),
    inference(fof_simplification,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(i_0_5908,plain,
    ! [X33] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X33)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(fof_simplification,[status(thm)],[fact_int__less__0__conv]) ).

fof(i_0_5909,plain,
    ! [X20745] :
      ( ( c_Int_OMin != c_Int_OBit1(X20745)
        | c_Int_OMin = X20745 )
      & ( c_Int_OMin != X20745
        | c_Int_OMin = c_Int_OBit1(X20745) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J])]) ).

fof(i_0_5910,plain,
    ! [X20744] :
      ( ( c_Int_OBit1(X20744) != c_Int_OMin
        | X20744 = c_Int_OMin )
      & ( X20744 != c_Int_OMin
        | c_Int_OBit1(X20744) = c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J])]) ).

fof(i_0_5911,plain,
    ! [X19949] : c_Int_OBit1(X19949) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(i_0_5912,plain,
    ! [X19950] : c_Int_OPls != c_Int_OBit1(X19950),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(i_0_5913,plain,
    ! [X33029] : c_Relation_Osym(X33029,c_Relation_OId(X33029)),
    inference(variable_rename,[status(thm)],[fact_sym__Id]) ).

fof(i_0_5914,plain,
    ! [X32974] : c_Relation_Oantisym(X32974,c_Relation_OId(X32974)),
    inference(variable_rename,[status(thm)],[fact_antisym__Id]) ).

fof(i_0_5915,plain,
    ! [X32883] : c_Relation_Otrans(X32883,c_Relation_OId(X32883)),
    inference(variable_rename,[status(thm)],[fact_trans__Id]) ).

fof(i_0_5916,plain,
    ! [X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => ( ( 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),X68)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),X68) )
        & ( ~ 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),X68)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = c_Groups_Ozero__class_Ozero(X27) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__lemma]) ).

fof(i_0_5917,plain,
    ! [X11,X12,X10] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),X12))
       => hAPP(c_Finite__Set_Ocard(X10),hAPP(hAPP(c_Set_Oinsert(X10),X11),X12)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X10),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__insert__disjoint]) ).

fof(i_0_5918,plain,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
        <=> X11 = X16 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv2]) ).

fof(i_0_5919,plain,
    ! [X10] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X10)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X10),tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_infinite__UNIV__listI]) ).

fof(i_0_5920,plain,
    ! [X200,X11,X10] :
      ( ( hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oinsert(X10,X11,X200) = X200 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
       => c_List_Oinsert(X10,X11,X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_List_Oinsert__def]) ).

fof(i_0_5921,plain,
    ! [X37,X36,X27] :
      ( class_Orderings_Oorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36)) ) ),
    inference(fof_simplification,[status(thm)],[fact_xt1_I9_J]) ).

fof(i_0_5922,plain,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X11))
          | X11 = X16 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).

fof(i_0_5923,plain,
    ! [X26,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leD]) ).

fof(i_0_5924,plain,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X16),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__less]) ).

fof(i_0_5925,plain,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X11)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__not__le]) ).

fof(i_0_5926,plain,
    ! [X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym]) ).

fof(i_0_5927,plain,
    ! [X36,X37,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),X36))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X36),X37)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__asym_H]) ).

fof(i_0_5928,plain,
    ! [X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__imp__not__less]) ).

fof(i_0_5929,plain,
    ! [X34,X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__not__sym]) ).

fof(i_0_5930,plain,
    ! [X120,X68] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X68),c_Int_OPls))
       => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X120)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X68),X120)) ) ),
    inference(fof_simplification,[status(thm)],[fact_mult__nat__number__of]) ).

fof(i_0_5931,plain,
    ! [X31602,X31603] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31603),X31602))
      | hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(X31603,X31602)) = X31603 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__upt])]) ).

fof(i_0_5932,plain,
    ! [X6,X10] : ~ hBOOL(hAPP(hAPP(c_member(X10),X6),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_empty__iff]) ).

fof(i_0_5933,plain,
    ! [X13,X10] : ~ hBOOL(hAPP(hAPP(c_member(X10),X13),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))),
    inference(fof_simplification,[status(thm)],[fact_emptyE]) ).

fof(i_0_5934,plain,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X25))
       => X24 = hAPP(c_Nat_OSuc,X25) ) ),
    inference(fof_simplification,[status(thm)],[fact_le__SucE]) ).

fof(i_0_5935,plain,
    ! [X31621,X31622] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X31622,X31621) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31622,hAPP(c_Nat_OSuc,X31621))),
    inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upt]) ).

fof(i_0_5936,plain,
    ! [X30,X31] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),hAPP(c_Nat_OSuc,X30)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X30),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),X30)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31),X30))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31),hAPP(c_Nat_OSuc,X30)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThanSuc]) ).

fof(i_0_5937,plain,
    ! [X200,X10,X11,X42] :
      ( ( hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),hAPP(c_List_Ofilter(X10,X42),X200)) )
      & ( ~ hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200)) = hAPP(c_List_Ofilter(X10,X42),X200) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(i_0_5938,plain,
    ! [X25,X24] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,X25)))
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => X24 = X25 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__SucE]) ).

fof(i_0_5939,plain,
    ! [X24,X25] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X24))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),hAPP(c_Nat_OSuc,X24)))
       => X24 = X25 ) ),
    inference(fof_simplification,[status(thm)],[fact_less__antisym]) ).

fof(i_0_5940,plain,
    ! [X31,X30] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),X31))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30),hAPP(c_Nat_OSuc,X31)))
      <=> X30 = X31 ) ),
    inference(fof_simplification,[status(thm)],[fact_not__less__less__Suc__eq]) ).

fof(i_0_5941,plain,
    ! [X22272,X22273] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22273,X22272),c_Divides_Odivmod__nat(X22273,X22272))),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__rel__divmod__nat]) ).

fof(i_0_5942,plain,
    ! [X21078] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X21078)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),X21078)),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_5943,plain,
    ! [X31631] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X31631) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X31631))),
    inference(variable_rename,[status(thm)],[fact_atMost__upto]) ).

fof(i_0_5944,plain,
    ! [X19931] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19931),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19931)),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),X19931),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19931)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X19931)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5215])]) ).

fof(i_0_5945,plain,
    ! [X20081] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20081),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20081)),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),X20081),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20081)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(X20081)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5216])]) ).

fof(i_0_5946,plain,
    ! [X21392,X21393] :
      ( ~ class_Int_Onumber__ring(X21393)
      | hAPP(c_Int_Onumber__class_Onumber__of(X21393),c_Int_Opred(X21392)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21393),hAPP(c_Groups_Ouminus__class_Ouminus(X21393),c_Groups_Oone__class_Oone(X21393))),hAPP(c_Int_Onumber__class_Onumber__of(X21393),X21392)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__pred])]) ).

fof(i_0_5947,plain,
    ! [X32886,X32887] :
      ( ~ c_Relation_Otrans(X32887,X32886)
      | c_Transitive__Closure_Otrancl(X32887,X32886) = X32886 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).

fof(i_0_5948,plain,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff2]) ).

fof(i_0_5949,plain,
    ! [X83,X32,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X32,X83)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X83)) ) ),
    inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff2]) ).

fof(i_0_5950,plain,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_SetInterval_Oord__class_OatLeastAtMost(X10,X13,X14) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X13),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastatMost__empty__iff]) ).

fof(i_0_5951,plain,
    ! [X83,X32,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(X10,X32,X83) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X32),X83)) ) ),
    inference(fof_simplification,[status(thm)],[fact_greaterThanAtMost__empty__iff]) ).

fof(i_0_5952,plain,
    ! [X36,X37] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X37),X36))
     => ( X37 != X36
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X37),X36))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X36),X37)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Ole__neq__trans]) ).

fof(i_0_5953,plain,
    ! [X34,X26] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
     => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X26),X34))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X34),X26)) )
        | X26 = X34 ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).

fof(i_0_5954,plain,
    ! [X36,X37] :
      ( X37 != X36
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X37),X36))
       => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X37),X36))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X36),X37)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Oneq__le__trans]) ).

fof(i_0_5955,plain,
    ! [X16,X11] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X11)) )
    <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
        & X11 != X16 ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Oless__le]) ).

fof(i_0_5956,plain,
    ! [X16,X11] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
    <=> ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X11),X16))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X16),X11)) )
        | X11 = X16 ) ),
    inference(fof_simplification,[status(thm)],[fact_dvd_Ole__less]) ).

fof(i_0_5957,plain,
    ! [X22235,X22236] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22236),X22235))
      | c_Divides_Odivmod__nat(X22236,X22235) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22236) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__base])]) ).

fof(i_0_5958,plain,
    ! [X10,X15,X12] :
      ( X12 = X15
     => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X12),X15))
         => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X10,tc_HOL_Obool)),X15),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_equalityE]) ).

fof(i_0_5959,plain,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25)),X25)),
    inference(fof_simplification,[status(thm)],[fact_Suc__n__not__le__n]) ).

fof(i_0_5960,plain,
    ! [X33,X45] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_SMT_Oz3div(X33,X45) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),X45) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_SMT_Oz3div(X33,X45) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X45))) ) ),
    inference(fof_simplification,[status(thm)],[fact_z3div__def]) ).

fof(i_0_5961,plain,
    ! [X25,X24] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),X25) ),
    inference(fof_simplification,[status(thm)],[fact_mod__geq]) ).

fof(i_0_5962,plain,
    ! [X25,X24] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = X24 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X25) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25),X25) ) ),
    inference(fof_simplification,[status(thm)],[fact_mod__if]) ).

fof(i_0_5963,plain,
    ! [X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => c_List_Oinsert(X10,X11,X200) = hAPP(hAPP(c_List_Olist_OCons(X10),X11),X200) ),
    inference(fof_simplification,[status(thm)],[fact_not__in__set__insert]) ).

fof(i_0_5964,plain,
    ! [X16,X11,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X10),X11),X16))
        <=> X11 = X16 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv1]) ).

fof(i_0_5965,plain,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff]) ).

fof(i_0_5966,plain,
    ! [X14,X13,X10] :
      ( class_Orderings_Oorder(X10)
     => ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X10,X13),X14)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X13),X14)) ) ),
    inference(fof_simplification,[status(thm)],[fact_atLeastLessThan__empty__iff2]) ).

fof(i_0_5967,plain,
    ! [X19932] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19932),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),X19932)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19932),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),X19932)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X19932)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5217])]) ).

fof(i_0_5968,plain,
    ! [X29,X10] :
      ( c_Equiv__Relations_Opart__equivp(X10,X29)
     => ~ ( ? [X3] : hBOOL(hAPP(hAPP(X29,X3),X3))
         => ( c_Predicate_Osymp(X10,X29)
           => ~ c_Predicate_Otransp(X10,X29) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_part__equivpE]) ).

fof(i_0_5969,plain,
    ! [X20635,X20636] :
      ( ( c_Code__Numeral_OSuc__code__numeral(X20636) != c_Code__Numeral_OSuc__code__numeral(X20635)
        | X20636 = X20635 )
      & ( X20636 != X20635
        | c_Code__Numeral_OSuc__code__numeral(X20636) = c_Code__Numeral_OSuc__code__numeral(X20635) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oinject])]) ).

fof(i_0_5970,plain,
    ! [X20630] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X20630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X20630)),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_5971,plain,
    ! [X21220] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X21220)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21220)),
    inference(variable_rename,[status(thm)],[fact_minus__Bit0]) ).

fof(i_0_5972,plain,
    ! [X30,X10,X11,X42] :
      ( ( hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),c_List_Oreplicate(X10,X30,X11)) = c_List_Oreplicate(X10,X30,X11) )
      & ( ~ hBOOL(hAPP(X42,X11))
       => hAPP(c_List_Ofilter(X10,X42),c_List_Oreplicate(X10,X30,X11)) = c_List_Olist_ONil(X10) ) ),
    inference(fof_simplification,[status(thm)],[fact_filter__replicate]) ).

fof(i_0_5973,plain,
    ! [X31960] :
      ( ~ c_List_Onat__list(X31960)
      | c_List_Oembed__list(c_List_Oreturn__list(X31960)) = X31960 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed])]) ).

fof(i_0_5974,plain,
    ! [X19927] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19927)))
        | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19927)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19927)))
        | hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19927)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X19927)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5218])]) ).

fof(i_0_5975,plain,
    ! [X12,X10] :
      ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X10),X3),X12))
    <=> X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) ),
    inference(fof_simplification,[status(thm)],[fact_all__not__in__conv]) ).

fof(i_0_5976,plain,
    ! [X200,X11,X10] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X10),X11),hAPP(c_List_Oset(X10),X200)))
     => c_List_Oremove1(X10,X11,X200) = X200 ),
    inference(fof_simplification,[status(thm)],[fact_remove1__idem]) ).

fof(i_0_5977,plain,
    ! [X31609,X31610] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(X31610,X31609)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X31609),X31610),
    inference(variable_rename,[status(thm)],[fact_length__upt]) ).

fof(i_0_5978,plain,
    ! [X26,X27] :
      ( class_Groups_Osgn__if(X27)
     => ( ( X26 = c_Groups_Ozero__class_Ozero(X27)
         => c_Groups_Osgn__class_Osgn(X27,X26) = c_Groups_Ozero__class_Ozero(X27) )
        & ( X26 != c_Groups_Ozero__class_Ozero(X27)
         => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
             => c_Groups_Osgn__class_Osgn(X27,X26) = c_Groups_Oone__class_Oone(X27) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Ozero__class_Ozero(X27)),X26))
             => c_Groups_Osgn__class_Osgn(X27,X26) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),c_Groups_Oone__class_Oone(X27)) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_sgn__if]) ).

fof(i_0_5979,plain,
    ! [X31594,X31595] :
      ( ( c_List_Oupt(X31595,X31594) != c_List_Olist_ONil(tc_Nat_Onat)
        | X31594 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31594),X31595)) )
      & ( X31594 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(X31595,X31594) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31594),X31595))
        | c_List_Oupt(X31595,X31594) = 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_5980,plain,
    ! [X31592,X31593] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31593),X31592))
      | c_List_Oupt(X31592,X31593) = c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upt__conv__Nil])]) ).

fof(i_0_5981,plain,
    ! [X33,X45] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_SMT_Oz3mod(X33,X45) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,X45) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X45))
       => c_SMT_Oz3mod(X33,X45) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X45)) ) ),
    inference(fof_simplification,[status(thm)],[fact_z3mod__def]) ).

fof(i_0_5982,plain,
    ! [X37,X27] :
      ( class_Groups_Oabs__if(X27)
     => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
         => hAPP(c_Groups_Oabs__class_Oabs(X27),X37) = hAPP(c_Groups_Ouminus__class_Ouminus(X27),X37) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X37),c_Groups_Ozero__class_Ozero(X27)))
         => hAPP(c_Groups_Oabs__class_Oabs(X27),X37) = X37 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_abs__if]) ).

fof(i_0_5983,plain,
    ! [X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Ozero__class_Ozero(X27))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__less__zero]) ).

fof(i_0_5984,plain,
    ! [X27] :
      ( class_Rings_Olinordered__semidom(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),c_Groups_Oone__class_Oone(X27)),c_Groups_Ozero__class_Ozero(X27))) ),
    inference(fof_simplification,[status(thm)],[fact_not__one__le__zero]) ).

fof(i_0_5985,plain,
    ! [X25,X24] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X25))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X25)) = X24 ),
    inference(fof_simplification,[status(thm)],[fact_add__diff__inverse]) ).

fof(i_0_5986,plain,
    ! [X31623] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X31623) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31623)),
    inference(variable_rename,[status(thm)],[fact_atLeast__upt]) ).

fof(i_0_5987,plain,
    ! [X34,X26,X27] :
      ( class_Rings_Olinordered__idom(X27)
     => ( X26 != X34
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__linordered__idom]) ).

fof(i_0_5988,plain,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => ( X26 != X34
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__cases]) ).

fof(i_0_5989,plain,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( X26 != X34
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X34),X26)) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE]) ).

fof(i_0_5990,plain,
    ! [X11,X16,X10] :
      ( class_Orderings_Olinorder(X10)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X16),X11))
       => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X10),X11),X16))
        <=> X11 = X16 ) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__antisym__conv3]) ).

fof(i_0_5991,plain,
    ! [X26,X34,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34)) ) ),
    inference(fof_simplification,[status(thm)],[fact_not__leE]) ).

fof(i_0_5992,plain,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26)) ) ),
    inference(fof_simplification,[status(thm)],[fact_leI]) ).

fof(i_0_5993,plain,
    ! [X34,X26,X27] :
      ( class_Orderings_Olinorder(X27)
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X26),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27),X34),X26)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__le__cases]) ).

fof(i_0_5994,plain,
    ! [X31577,X31578] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31578,X31577)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31578),X31577),
    inference(variable_rename,[status(thm)],[fact_set__upt]) ).

fof(i_0_5995,plain,
    ! [X31579,X31580] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X31580),X31579) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X31580,X31579)),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upt]) ).

fof(i_0_5996,plain,
    ! [X19979] : c_Int_Osucc(c_Int_Opred(X19979)) = X19979,
    inference(variable_rename,[status(thm)],[fact_succ__pred]) ).

fof(i_0_5997,plain,
    ! [X19411,X19412] :
      ( ~ class_Int_Onumber__ring(X19412)
      | hAPP(c_Int_Onumber__class_Onumber__of(X19412),c_Int_Osucc(X19411)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19412),c_Groups_Oone__class_Oone(X19412)),hAPP(c_Int_Onumber__class_Onumber__of(X19412),X19411)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__succ])]) ).

fof(i_0_5998,plain,
    ! [X13,X10,X12] :
      ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
     => ~ hBOOL(hAPP(hAPP(c_member(X10),X13),X12)) ),
    inference(fof_simplification,[status(thm)],[fact_equals0D]) ).

fof(i_0_5999,plain,
    ! [X11] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X11))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X11)) ),
    inference(fof_simplification,[status(thm)],[fact_not__neg__eq__ge__0]) ).

fof(i_0_6000,plain,
    ! [X11] :
      ~ ! [X51] :
          ( X11 = hAPP(c_Code__Numeral_Oof__nat,X51)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X51),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__cases]) ).

fof(i_0_6001,plain,
    ! [X31,X90] :
      ( hAPP(c_Int_Onat,X90) = X31
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => X90 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__eq__iff]) ).

fof(i_0_6002,plain,
    ! [X90,X31] :
      ( X31 = hAPP(c_Int_Onat,X90)
    <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => X90 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X90))
         => X31 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_nat__eq__iff2]) ).

fof(i_0_6003,plain,
    ! [X38] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X38)) = X38 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X38))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X38)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_int__nat__eq]) ).

fof(i_0_6004,plain,
    ! [X26,X34] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34),X26))
       => c_Nat__Transfer_Otsub(X26,X34) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X26),X34) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34),X26))
       => c_Nat__Transfer_Otsub(X26,X34) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(fof_simplification,[status(thm)],[fact_tsub__def]) ).

fof(i_0_6005,plain,
    ! [X68,X27] :
      ( class_Int_Onumber__ring(X27)
     => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = c_Groups_Ozero__class_Ozero(X27) )
        & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
         => hAPP(c_Nat_Osemiring__1__class_Oof__nat(X27),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(X27),X68) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_of__nat__number__of__eq]) ).

fof(i_0_6006,plain,
    ! [X32704,X32705] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X32705),c_List_Olist_ONil(X32705)),X32704)),
    inference(variable_rename,[status(thm)],[i_0_5219]) ).

fof(i_0_6007,plain,
    ! [X22426,X22427] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22427,X22426) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X22427,X22426)),
    inference(variable_rename,[status(thm)],[fact_mod__nat__def]) ).

fof(i_0_6008,plain,
    ! [X200,X10,X11,X42] :
      ( ~ hBOOL(hAPP(X42,X11))
     => c_List_Oremove1(X10,X11,hAPP(c_List_Ofilter(X10,X42),X200)) = hAPP(c_List_Ofilter(X10,X42),X200) ),
    inference(fof_simplification,[status(thm)],[fact_remove1__filter__not]) ).

fof(i_0_6009,plain,
    ! [X22424,X22425] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22425),X22424) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(X22425,X22424)),
    inference(variable_rename,[status(thm)],[fact_div__nat__def]) ).

fof(i_0_6010,plain,
    ! [X68] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68)))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X68)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X68) ) ),
    inference(fof_simplification,[status(thm)],[fact_int__nat__number__of]) ).

fof(i_0_6011,plain,
    ! [X44] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X44) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X44) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X44),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X44) = X44 ) ),
    inference(fof_simplification,[status(thm)],[fact_zabs__def]) ).

fof(i_0_6012,plain,
    ! [X34,X26] :
      ( X26 != X34
     => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X26),X34))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X34),X26)) ) ),
    inference(fof_simplification,[status(thm)],[fact_linorder__neqE__nat]) ).

fof(i_0_6013,plain,
    ! [X22274,X22275,X22276] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22276,X22275),X22274))
      | c_Divides_Odivmod__nat(X22276,X22275) = X22274 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__eq])]) ).

fof(i_0_6014,plain,
    ! [X44] :
      ( ( X44 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X44) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X44 != 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)),X44))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X44) = 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)),X44))
           => c_Groups_Osgn__class_Osgn(tc_Int_Oint,X44) = 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_6015,plain,
    ! [X31659,X31660] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X31660,X31659)),
    inference(variable_rename,[status(thm)],[fact_sorted__upt]) ).

fof(i_0_6016,plain,
    ! [X28068,X28069] : c_Wellfounded_Owf(X28069,hAPP(c_Wellfounded_Omeasure(X28069),X28068)),
    inference(variable_rename,[status(thm)],[fact_wf__measure]) ).

fof(i_0_6017,plain,
    ! [X26,X27] :
      ( class_Orderings_Opreorder(X27)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27),X26),X26)) ),
    inference(fof_simplification,[status(thm)],[fact_order__less__irrefl]) ).

fof(i_0_6018,plain,
    ! [X45,X33] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33),X45))
       => c_Quickcheck_Obeyond(X33,X45) = X45 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33),X45))
       => c_Quickcheck_Obeyond(X33,X45) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(fof_simplification,[status(thm)],[fact_beyond__def]) ).

fof(i_0_6019,plain,
    ! [X30401] : c_List_Orotate(X30401,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(X30401)),
    inference(variable_rename,[status(thm)],[fact_rotate0]) ).

fof(i_0_6020,plain,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__nat__zero__code]) ).

fof(i_0_6021,plain,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_not__less0]) ).

fof(i_0_6022,plain,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(fof_simplification,[status(thm)],[fact_less__zeroE]) ).

fof(i_0_6023,plain,
    ! [X22231] : c_Divides_Odivmod__nat(X22231,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)),X22231),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__zero]) ).

fof(i_0_6024,plain,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X25)),
    inference(fof_simplification,[status(thm)],[fact_less__irrefl__nat]) ).

fof(i_0_6025,plain,
    ! [X25] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X25),X25)),
    inference(fof_simplification,[status(thm)],[fact_less__not__refl]) ).

fof(i_0_6026,plain,
    ! [X20367,X20368] :
      ( ( c_Int_OBit0(X20368) != c_Int_OBit0(X20367)
        | X20368 = X20367 )
      & ( X20368 != X20367
        | c_Int_OBit0(X20368) = c_Int_OBit0(X20367) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I48_J])]) ).

fof(i_0_6027,plain,
    ! [X2,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X2),X12) = c_Groups_Ozero__class_Ozero(X8) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum__infinite]) ).

fof(i_0_6028,plain,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__add(X8)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X10,X8),X1),X12) = c_Groups_Ozero__class_Ozero(X8) ) ),
    inference(fof_simplification,[status(thm)],[fact_setsum_Oinfinite]) ).

fof(i_0_6029,plain,
    ! [X1,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X1),X12) = c_Groups_Oone__class_Oone(X8) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod_Oinfinite]) ).

fof(i_0_6030,plain,
    ! [X2,X12,X10,X8] :
      ( class_Groups_Ocomm__monoid__mult(X8)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X10,X8),X2),X12) = c_Groups_Oone__class_Oone(X8) ) ),
    inference(fof_simplification,[status(thm)],[fact_setprod__infinite]) ).

fof(i_0_6031,plain,
    ! [X25] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25))),
    inference(fof_simplification,[status(thm)],[fact_not__neg__int]) ).

fof(i_0_6032,plain,
    ! [X110,X12,X10] :
      ( c_Equiv__Relations_Oequiv(X10,X12,X110)
     => ~ ( c_Relation_Orefl__on(X10,X12,X110)
         => ( c_Relation_Osym(X10,X110)
           => ~ c_Relation_Otrans(X10,X110) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_equivE]) ).

fof(i_0_6033,plain,
    ! [X20838] : c_Code__Numeral_OSuc__code__numeral(X20838) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I3_J]) ).

fof(i_0_6034,plain,
    ! [X20837] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X20837),
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I2_J]) ).

fof(i_0_6035,plain,
    ! [X41,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X42),X41))
      | ~ hBOOL(X42)
      | hBOOL(X41) ),
    inference(fof_simplification,[status(thm)],[help_c__fimplies__3]) ).

fof(i_0_6036,plain,
    ! [X12,X10] :
      ( hAPP(c_Finite__Set_Ocard(X10),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ( X12 = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12)) ) ),
    inference(fof_simplification,[status(thm)],[fact_card__eq__0__iff]) ).

fof(i_0_6037,plain,
    ! [X41,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X42),X41))
      | hBOOL(X42)
      | hBOOL(X41) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__3]) ).

fof(i_0_6038,plain,
    ! [X41,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X42),X41))
      | hBOOL(X42) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__2]) ).

fof(i_0_6039,plain,
    ! [X41,X42] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X42),X41))
      | hBOOL(X41) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__3]) ).

fof(i_0_6040,plain,
    ! [X42,X10] :
      ( c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X10),X42)
    <=> ! [X3] : ~ hBOOL(hAPP(X42,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_empty__Collect__eq]) ).

fof(i_0_6041,plain,
    ! [X42,X10] :
      ( hAPP(c_Set_OCollect(X10),X42) = c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool))
    <=> ! [X3] : ~ hBOOL(hAPP(X42,X3)) ),
    inference(fof_simplification,[status(thm)],[fact_Collect__empty__eq]) ).

fof(i_0_6042,plain,
    ! [X16,X11] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X11),X16))
      | X11 = X16 ),
    inference(fof_simplification,[status(thm)],[help_c__fequal__1]) ).

fof(i_0_6043,plain,
    ! [X30986] : hAPP(c_Code__Numeral_Onat__of,X30986) = c_Code__Numeral_Onat__of__aux(X30986,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_nat__of__code]) ).

fof(i_0_6044,plain,
    ! [X42,X10] : ~ c_List_Olist__ex1(X10,X42,c_List_Olist_ONil(X10)),
    inference(fof_simplification,[status(thm)],[fact_list__ex1__simps_I1_J]) ).

fof(i_0_6045,plain,
    ! [X42,X10] : ~ c_List_Olist__ex(X10,X42,c_List_Olist_ONil(X10)),
    inference(fof_simplification,[status(thm)],[fact_list__ex__simps_I2_J]) ).

fof(i_0_6046,plain,
    ! [X20080] : c_Int_Opred(X20080) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20080),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_pred__def]) ).

fof(i_0_6047,plain,
    ! [X19486] : c_Int_Osucc(X19486) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19486),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[fact_succ__def]) ).

fof(i_0_6048,plain,
    ! [X31596] : c_List_Oupt(X31596,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_6049,plain,
    ! [X41,X42] :
      ( ~ hBOOL(X42)
      | ~ hBOOL(X41)
      | hBOOL(hAPP(hAPP(c_fconj,X42),X41)) ),
    inference(fof_simplification,[status(thm)],[help_c__fconj__1]) ).

fof(i_0_6050,plain,
    ! [X20839] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X20839) = c_Int_Opred(X20839),
    inference(variable_rename,[status(thm)],[fact_add__Min]) ).

fof(i_0_6051,plain,
    ! [X27] :
      ( class_Int_Onumber__ring(X27)
     => ~ c_Int_Oiszero(X27,hAPP(c_Int_Onumber__class_Onumber__of(X27),c_Int_OMin)) ),
    inference(fof_simplification,[status(thm)],[fact_nonzero__number__of__Min]) ).

fof(i_0_6052,plain,
    ! [X41,X42] :
      ( ~ hBOOL(X42)
      | hBOOL(hAPP(hAPP(c_fdisj,X42),X41)) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__1]) ).

fof(i_0_6053,plain,
    ! [X42,X41] :
      ( ~ hBOOL(X41)
      | hBOOL(hAPP(hAPP(c_fdisj,X42),X41)) ),
    inference(fof_simplification,[status(thm)],[help_c__fdisj__2]) ).

fof(i_0_6054,plain,
    ! [X42,X41] :
      ( ~ hBOOL(X41)
      | hBOOL(hAPP(hAPP(c_fimplies,X42),X41)) ),
    inference(fof_simplification,[status(thm)],[help_c__fimplies__2]) ).

fof(i_0_6055,plain,
    ! [X20380] :
      ( ( c_Int_OPls != c_Int_OBit0(X20380)
        | c_Int_OPls = X20380 )
      & ( c_Int_OPls != X20380
        | c_Int_OPls = c_Int_OBit0(X20380) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I38_J])]) ).

fof(i_0_6056,plain,
    ! [X20381] :
      ( ( c_Int_OBit0(X20381) != c_Int_OPls
        | X20381 = c_Int_OPls )
      & ( X20381 != c_Int_OPls
        | c_Int_OBit0(X20381) = c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__simps_I44_J])]) ).

fof(i_0_6057,plain,
    ! [X20746] : c_Int_OBit0(X20746) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(i_0_6058,plain,
    ! [X20747] : c_Int_OMin != c_Int_OBit0(X20747),
    inference(variable_rename,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(i_0_6059,plain,
    ! [X38] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X38))
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X38)) = X38 ),
    inference(fof_simplification,[status(thm)],[fact_not__neg__nat]) ).

fof(i_0_6060,plain,
    ! [X12,X10] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X10),X12))
     => hAPP(c_Finite__Set_Ocard(X10),X12) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_simplification,[status(thm)],[fact_card__infinite]) ).

fof(i_0_6061,plain,
    ! [X42] :
      ( ~ hBOOL(hAPP(c_fNot,X42))
      | ~ hBOOL(X42) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__1]) ).

fof(i_0_6062,plain,
    ! [X27] :
      ( class_Rings_Osemiring__1(X27)
     => ~ c_Int_Oiszero(X27,c_Groups_Oone__class_Oone(X27)) ),
    inference(fof_simplification,[status(thm)],[fact_not__iszero__1]) ).

fof(i_0_6063,plain,
    ! [X29,X10] :
      ( c_Equiv__Relations_Oequivp(X10,X29)
     => ~ ( c_Predicate_Oreflp(X10,X29)
         => ( c_Predicate_Osymp(X10,X29)
           => ~ c_Predicate_Otransp(X10,X29) ) ) ),
    inference(fof_simplification,[status(thm)],[fact_equivpE]) ).

fof(i_0_6064,plain,
    ! [X42] :
      ( hBOOL(X42)
      | hBOOL(hAPP(c_fNot,X42)) ),
    inference(fof_simplification,[status(thm)],[help_c__fNot__2]) ).

fof(i_0_6065,plain,
    ! [X24816,X24817,X24818,X24819,X24820,X24821,X24822,X24823,X24824,X24825,X24826] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24826),esk192_11(X24816,X24817,X24818,X24819,X24820,X24821,X24822,X24823,X24824,X24825,X24826)),X24825))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X24820,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24826,tc_fun(X24820,tc_HOL_Obool)),X24818),hAPP(hAPP(c_COMBB(tc_fun(X24823,tc_fun(X24820,tc_HOL_Obool)),tc_fun(X24820,tc_HOL_Obool),X24826),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24823,tc_fun(X24820,tc_HOL_Obool)),X24817)),X24819))),X24816))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24823,tc_HOL_Obool)),X24817),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24823),X24822),X24821)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24826,tc_HOL_Obool)),X24818),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24826),X24825),X24824)))
        | ~ c_Equiv__Relations_Ocongruent2(X24826,X24823,tc_fun(X24820,tc_HOL_Obool),X24824,X24821,X24819)
        | ~ c_Equiv__Relations_Oequiv(X24823,X24822,X24821)
        | ~ c_Equiv__Relations_Oequiv(X24826,X24825,X24824) )
      & ( hBOOL(hAPP(hAPP(c_member(X24823),esk193_11(X24816,X24817,X24818,X24819,X24820,X24821,X24822,X24823,X24824,X24825,X24826)),X24822))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X24820,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24826,tc_fun(X24820,tc_HOL_Obool)),X24818),hAPP(hAPP(c_COMBB(tc_fun(X24823,tc_fun(X24820,tc_HOL_Obool)),tc_fun(X24820,tc_HOL_Obool),X24826),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24823,tc_fun(X24820,tc_HOL_Obool)),X24817)),X24819))),X24816))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24823,tc_HOL_Obool)),X24817),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24823),X24822),X24821)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24826,tc_HOL_Obool)),X24818),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24826),X24825),X24824)))
        | ~ c_Equiv__Relations_Ocongruent2(X24826,X24823,tc_fun(X24820,tc_HOL_Obool),X24824,X24821,X24819)
        | ~ c_Equiv__Relations_Oequiv(X24823,X24822,X24821)
        | ~ c_Equiv__Relations_Oequiv(X24826,X24825,X24824) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24820,tc_HOL_Obool)),hAPP(hAPP(X24819,esk192_11(X24816,X24817,X24818,X24819,X24820,X24821,X24822,X24823,X24824,X24825,X24826)),esk193_11(X24816,X24817,X24818,X24819,X24820,X24821,X24822,X24823,X24824,X24825,X24826))),X24816))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X24820,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24826,tc_fun(X24820,tc_HOL_Obool)),X24818),hAPP(hAPP(c_COMBB(tc_fun(X24823,tc_fun(X24820,tc_HOL_Obool)),tc_fun(X24820,tc_HOL_Obool),X24826),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24823,tc_fun(X24820,tc_HOL_Obool)),X24817)),X24819))),X24816))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24823,tc_HOL_Obool)),X24817),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24823),X24822),X24821)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24826,tc_HOL_Obool)),X24818),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24826),X24825),X24824)))
        | ~ c_Equiv__Relations_Ocongruent2(X24826,X24823,tc_fun(X24820,tc_HOL_Obool),X24824,X24821,X24819)
        | ~ c_Equiv__Relations_Oequiv(X24823,X24822,X24821)
        | ~ c_Equiv__Relations_Oequiv(X24826,X24825,X24824) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class__type2])])])]) ).

fof(i_0_6066,plain,
    ! [X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33526,X33525),tc_prod(X33526,X33525))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33526,X33525),tc_prod(X33526,X33525)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33524),X33523)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),esk546_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)),esk547_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)))),c_Transitive__Closure_Ortrancl(tc_prod(X33526,X33525),X33520)))
        | hBOOL(hAPP(hAPP(X33519,X33522),X33521))
        | ~ hBOOL(hAPP(hAPP(X33519,X33524),X33523))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33526,X33525),tc_prod(X33526,X33525))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33526,X33525),tc_prod(X33526,X33525)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33524),X33523)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33522),X33521))),c_Transitive__Closure_Ortrancl(tc_prod(X33526,X33525),X33520))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33526,X33525),tc_prod(X33526,X33525))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33526,X33525),tc_prod(X33526,X33525)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),esk546_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)),esk547_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526))),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),esk548_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)),esk549_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)))),X33520))
        | hBOOL(hAPP(hAPP(X33519,X33522),X33521))
        | ~ hBOOL(hAPP(hAPP(X33519,X33524),X33523))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33526,X33525),tc_prod(X33526,X33525))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33526,X33525),tc_prod(X33526,X33525)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33524),X33523)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33522),X33521))),c_Transitive__Closure_Ortrancl(tc_prod(X33526,X33525),X33520))) )
      & ( hBOOL(hAPP(hAPP(X33519,esk546_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)),esk547_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)))
        | hBOOL(hAPP(hAPP(X33519,X33522),X33521))
        | ~ hBOOL(hAPP(hAPP(X33519,X33524),X33523))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33526,X33525),tc_prod(X33526,X33525))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33526,X33525),tc_prod(X33526,X33525)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33524),X33523)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33522),X33521))),c_Transitive__Closure_Ortrancl(tc_prod(X33526,X33525),X33520))) )
      & ( ~ hBOOL(hAPP(hAPP(X33519,esk548_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)),esk549_8(X33519,X33520,X33521,X33522,X33523,X33524,X33525,X33526)))
        | hBOOL(hAPP(hAPP(X33519,X33522),X33521))
        | ~ hBOOL(hAPP(hAPP(X33519,X33524),X33523))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33526,X33525),tc_prod(X33526,X33525))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33526,X33525),tc_prod(X33526,X33525)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33524),X33523)),hAPP(hAPP(c_Product__Type_OPair(X33526,X33525),X33522),X33521))),c_Transitive__Closure_Ortrancl(tc_prod(X33526,X33525),X33520))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__induct2])])])]) ).

fof(i_0_6067,plain,
    ! [X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33538,X33537),tc_prod(X33538,X33537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33538,X33537),tc_prod(X33538,X33537)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),esk550_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538)),esk551_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538))),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),esk552_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538)),esk553_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538)))),X33532))
        | hBOOL(hAPP(hAPP(X33531,X33536),X33535))
        | ~ hBOOL(hAPP(hAPP(X33531,X33534),X33533))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33538,X33537),tc_prod(X33538,X33537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33538,X33537),tc_prod(X33538,X33537)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33536),X33535)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33534),X33533))),c_Transitive__Closure_Ortrancl(tc_prod(X33538,X33537),X33532))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33538,X33537),tc_prod(X33538,X33537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33538,X33537),tc_prod(X33538,X33537)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),esk552_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538)),esk553_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538))),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33534),X33533))),c_Transitive__Closure_Ortrancl(tc_prod(X33538,X33537),X33532)))
        | hBOOL(hAPP(hAPP(X33531,X33536),X33535))
        | ~ hBOOL(hAPP(hAPP(X33531,X33534),X33533))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33538,X33537),tc_prod(X33538,X33537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33538,X33537),tc_prod(X33538,X33537)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33536),X33535)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33534),X33533))),c_Transitive__Closure_Ortrancl(tc_prod(X33538,X33537),X33532))) )
      & ( hBOOL(hAPP(hAPP(X33531,esk552_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538)),esk553_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538)))
        | hBOOL(hAPP(hAPP(X33531,X33536),X33535))
        | ~ hBOOL(hAPP(hAPP(X33531,X33534),X33533))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33538,X33537),tc_prod(X33538,X33537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33538,X33537),tc_prod(X33538,X33537)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33536),X33535)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33534),X33533))),c_Transitive__Closure_Ortrancl(tc_prod(X33538,X33537),X33532))) )
      & ( ~ hBOOL(hAPP(hAPP(X33531,esk550_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538)),esk551_8(X33531,X33532,X33533,X33534,X33535,X33536,X33537,X33538)))
        | hBOOL(hAPP(hAPP(X33531,X33536),X33535))
        | ~ hBOOL(hAPP(hAPP(X33531,X33534),X33533))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33538,X33537),tc_prod(X33538,X33537))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33538,X33537),tc_prod(X33538,X33537)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33536),X33535)),hAPP(hAPP(c_Product__Type_OPair(X33538,X33537),X33534),X33533))),c_Transitive__Closure_Ortrancl(tc_prod(X33538,X33537),X33532))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__induct2])])])]) ).

cnf(i_0_6068,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_5220]) ).

cnf(i_0_6069,plain,
    c_Int_Osucc(c_Int_OBit0(X1)) = c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_5221]) ).

cnf(i_0_6070,plain,
    c_Int_OBit0(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(split_conjunct,[status(thm)],[i_0_5222]) ).

cnf(i_0_6071,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_5223]) ).

fof(i_0_6072,plain,
    ! [X27780,X27781,X27782,X27783,X27784,X27785,X27786] :
      ( ~ class_Rings_Osemiring__0(X27786)
      | ~ c_Fun_Oinj__on(tc_prod(X27785,X27784),X27786,hAPP(c_Product__Type_Oprod_Oprod__case(X27785,X27784,X27786),hAPP(hAPP(c_COMBC(X27785,tc_fun(X27784,X27786),tc_fun(X27784,X27786)),hAPP(hAPP(c_COMBB(tc_fun(X27786,X27786),tc_fun(tc_fun(X27784,X27786),tc_fun(X27784,X27786)),X27785),c_COMBB(X27786,X27786,X27784)),hAPP(hAPP(c_COMBB(X27786,tc_fun(X27786,X27786),X27785),c_Groups_Otimes__class_Otimes(X27786)),X27783))),X27782)),hAPP(hAPP(c_Product__Type_OSigma(X27785,X27784),X27781),hAPP(c_COMBK(tc_fun(X27784,tc_HOL_Obool),X27785),X27780)))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X27786),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27785,X27786),X27783),X27781)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27784,X27786),X27782),X27780)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27786,X27786),c_Fun_Oid(X27786)),hAPP(c_Set_OCollect(X27786),hAPP(hAPP(c_COMBB(tc_fun(X27785,tc_HOL_Obool),tc_HOL_Obool,X27786),c_HOL_OEx(X27785)),hAPP(hAPP(c_COMBB(tc_fun(X27785,tc_fun(X27784,tc_HOL_Obool)),tc_fun(X27785,tc_HOL_Obool),X27786),hAPP(c_COMBB(tc_fun(X27784,tc_HOL_Obool),tc_HOL_Obool,X27785),c_HOL_OEx(X27784))),hAPP(hAPP(c_COMBC(X27786,tc_fun(X27785,tc_fun(X27784,tc_HOL_Obool)),tc_fun(X27785,tc_fun(X27784,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27785,tc_fun(tc_fun(X27784,tc_HOL_Obool),tc_fun(X27784,tc_HOL_Obool))),tc_fun(tc_fun(X27785,tc_fun(X27784,tc_HOL_Obool)),tc_fun(X27785,tc_fun(X27784,tc_HOL_Obool))),X27786),c_COMBS(X27785,tc_fun(X27784,tc_HOL_Obool),tc_fun(X27784,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27785,tc_fun(X27784,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27785,tc_fun(tc_fun(X27784,tc_HOL_Obool),tc_fun(X27784,tc_HOL_Obool))),X27786),hAPP(c_COMBB(tc_fun(X27784,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27784,tc_HOL_Obool),tc_fun(X27784,tc_HOL_Obool)),X27785),c_COMBS(X27784,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27785,tc_fun(X27784,tc_HOL_Obool)),tc_fun(X27785,tc_fun(X27784,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27786),hAPP(c_COMBB(tc_fun(X27784,tc_HOL_Obool),tc_fun(X27784,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27785),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27784),c_fconj))),hAPP(hAPP(c_COMBC(X27786,tc_fun(X27785,tc_fun(X27784,X27786)),tc_fun(X27785,tc_fun(X27784,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27784,X27786),tc_fun(X27784,tc_HOL_Obool)),tc_fun(tc_fun(X27785,tc_fun(X27784,X27786)),tc_fun(X27785,tc_fun(X27784,tc_HOL_Obool))),X27786),c_COMBB(tc_fun(X27784,X27786),tc_fun(X27784,tc_HOL_Obool),X27785)),hAPP(hAPP(c_COMBB(tc_fun(X27786,tc_HOL_Obool),tc_fun(tc_fun(X27784,X27786),tc_fun(X27784,tc_HOL_Obool)),X27786),c_COMBB(X27786,tc_HOL_Obool,X27784)),c_fequal))),hAPP(hAPP(c_COMBC(X27785,tc_fun(X27784,X27786),tc_fun(X27784,X27786)),hAPP(hAPP(c_COMBB(tc_fun(X27786,X27786),tc_fun(tc_fun(X27784,X27786),tc_fun(X27784,X27786)),X27785),c_COMBB(X27786,X27786,X27784)),hAPP(hAPP(c_COMBB(X27786,tc_fun(X27786,X27786),X27785),c_Groups_Otimes__class_Otimes(X27786)),X27783))),X27782)))))),hAPP(hAPP(c_COMBC(X27785,tc_fun(X27784,tc_HOL_Obool),tc_fun(X27784,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27784,tc_HOL_Obool),tc_fun(X27784,tc_HOL_Obool)),X27785),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27784)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27785),c_fconj),hAPP(hAPP(c_COMBC(X27785,tc_fun(X27785,tc_HOL_Obool),tc_HOL_Obool),c_member(X27785)),X27781)))),hAPP(hAPP(c_COMBC(X27784,tc_fun(X27784,tc_HOL_Obool),tc_HOL_Obool),c_member(X27784)),X27780))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mult__setsum__if__inj])]) ).

fof(i_0_6073,plain,
    ! [X27859,X27860,X27861,X27862,X27863] : hAPP(hAPP(c_Relation_Orel__comp(X27863,X27862,X27861),X27860),X27859) = hAPP(c_Set_OCollect(tc_prod(X27863,X27861)),hAPP(c_Product__Type_Oprod_Oprod__case(X27863,X27861,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X27861,tc_fun(X27862,tc_HOL_Obool)),tc_fun(X27861,tc_HOL_Obool),X27863),hAPP(c_COMBB(tc_fun(X27862,tc_HOL_Obool),tc_HOL_Obool,X27861),c_HOL_OEx(X27862))),hAPP(hAPP(c_COMBC(X27863,tc_fun(X27861,tc_fun(X27862,tc_HOL_Obool)),tc_fun(X27861,tc_fun(X27862,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27862,tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool)),tc_fun(tc_fun(X27861,tc_fun(X27862,tc_HOL_Obool)),tc_fun(X27861,tc_fun(X27862,tc_HOL_Obool))),X27863),c_COMBB(tc_fun(X27862,tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool),X27861)),hAPP(hAPP(c_COMBB(tc_fun(X27862,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27862,tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool)),X27863),c_COMBS(X27862,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27862,tc_HOL_Obool),tc_fun(X27862,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27863),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27862),c_fconj)),hAPP(hAPP(c_COMBC(X27863,tc_fun(tc_prod(X27863,X27862),tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27862,tc_fun(tc_fun(tc_prod(X27863,X27862),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27863,X27862),tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool)),X27863),c_COMBC(X27862,tc_fun(tc_prod(X27863,X27862),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27862,tc_prod(X27863,X27862)),tc_fun(X27862,tc_fun(tc_fun(tc_prod(X27863,X27862),tc_HOL_Obool),tc_HOL_Obool)),X27863),hAPP(c_COMBB(tc_prod(X27863,X27862),tc_fun(tc_fun(tc_prod(X27863,X27862),tc_HOL_Obool),tc_HOL_Obool),X27862),c_member(tc_prod(X27863,X27862)))),c_Product__Type_OPair(X27863,X27862)))),X27860))))),hAPP(hAPP(c_COMBC(X27861,tc_fun(tc_prod(X27862,X27861),tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27862,tc_fun(tc_fun(tc_prod(X27862,X27861),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27862,X27861),tc_HOL_Obool),tc_fun(X27862,tc_HOL_Obool)),X27861),c_COMBC(X27862,tc_fun(tc_prod(X27862,X27861),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27862,tc_prod(X27862,X27861)),tc_fun(X27862,tc_fun(tc_fun(tc_prod(X27862,X27861),tc_HOL_Obool),tc_HOL_Obool)),X27861),hAPP(c_COMBB(tc_prod(X27862,X27861),tc_fun(tc_fun(tc_prod(X27862,X27861),tc_HOL_Obool),tc_HOL_Obool),X27862),c_member(tc_prod(X27862,X27861)))),hAPP(c_COMBC(X27862,X27861,tc_prod(X27862,X27861)),c_Product__Type_OPair(X27862,X27861))))),X27859))))),
    inference(variable_rename,[status(thm)],[fact_rel__comp__def]) ).

fof(i_0_6074,plain,
    ! [X27716,X27717,X27718] :
      ( ~ class_Orderings_Olinorder(X27718)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),X27717))
      | X27717 = c_Orderings_Obot__class_Obot(tc_fun(X27718,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27718),X27716))
      | X27716 = c_Orderings_Obot__class_Obot(tc_fun(X27718,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X27718),c_Big__Operators_Olattice_OInf__fin(X27718,c_Orderings_Oord__class_Omin(X27718),X27717)),c_Big__Operators_Olattice_OInf__fin(X27718,c_Orderings_Oord__class_Omin(X27718),X27716)) = c_Big__Operators_Olattice_OInf__fin(X27718,c_Orderings_Oord__class_Omin(X27718),hAPP(c_Set_OCollect(X27718),hAPP(hAPP(c_COMBB(tc_fun(X27718,tc_HOL_Obool),tc_HOL_Obool,X27718),c_HOL_OEx(X27718)),hAPP(hAPP(c_COMBB(tc_fun(X27718,tc_fun(X27718,tc_HOL_Obool)),tc_fun(X27718,tc_HOL_Obool),X27718),hAPP(c_COMBB(tc_fun(X27718,tc_HOL_Obool),tc_HOL_Obool,X27718),c_HOL_OEx(X27718))),hAPP(hAPP(c_COMBC(X27718,tc_fun(X27718,tc_fun(X27718,tc_HOL_Obool)),tc_fun(X27718,tc_fun(X27718,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27718,tc_fun(tc_fun(X27718,tc_HOL_Obool),tc_fun(X27718,tc_HOL_Obool))),tc_fun(tc_fun(X27718,tc_fun(X27718,tc_HOL_Obool)),tc_fun(X27718,tc_fun(X27718,tc_HOL_Obool))),X27718),c_COMBS(X27718,tc_fun(X27718,tc_HOL_Obool),tc_fun(X27718,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27718,tc_fun(X27718,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27718,tc_fun(tc_fun(X27718,tc_HOL_Obool),tc_fun(X27718,tc_HOL_Obool))),X27718),hAPP(c_COMBB(tc_fun(X27718,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27718,tc_HOL_Obool),tc_fun(X27718,tc_HOL_Obool)),X27718),c_COMBS(X27718,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27718,tc_fun(X27718,tc_HOL_Obool)),tc_fun(X27718,tc_fun(X27718,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27718),hAPP(c_COMBB(tc_fun(X27718,tc_HOL_Obool),tc_fun(X27718,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27718),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27718),c_fconj))),hAPP(hAPP(c_COMBC(X27718,tc_fun(X27718,tc_fun(X27718,X27718)),tc_fun(X27718,tc_fun(X27718,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27718,X27718),tc_fun(X27718,tc_HOL_Obool)),tc_fun(tc_fun(X27718,tc_fun(X27718,X27718)),tc_fun(X27718,tc_fun(X27718,tc_HOL_Obool))),X27718),c_COMBB(tc_fun(X27718,X27718),tc_fun(X27718,tc_HOL_Obool),X27718)),hAPP(hAPP(c_COMBB(tc_fun(X27718,tc_HOL_Obool),tc_fun(tc_fun(X27718,X27718),tc_fun(X27718,tc_HOL_Obool)),X27718),c_COMBB(X27718,tc_HOL_Obool,X27718)),c_fequal))),c_Orderings_Oord__class_Omax(X27718)))))),hAPP(hAPP(c_COMBC(X27718,tc_fun(X27718,tc_HOL_Obool),tc_fun(X27718,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27718,tc_HOL_Obool),tc_fun(X27718,tc_HOL_Obool)),X27718),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27718)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27718),c_fconj),hAPP(hAPP(c_COMBC(X27718,tc_fun(X27718,tc_HOL_Obool),tc_HOL_Obool),c_member(X27718)),X27717)))),hAPP(hAPP(c_COMBC(X27718,tc_fun(X27718,tc_HOL_Obool),tc_HOL_Obool),c_member(X27718)),X27716))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf2__distrib])]) ).

fof(i_0_6075,plain,
    ! [X27769,X27770,X27771] :
      ( ~ class_Orderings_Olinorder(X27771)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27771),X27770))
      | X27770 = c_Orderings_Obot__class_Obot(tc_fun(X27771,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27771),X27769))
      | X27769 = c_Orderings_Obot__class_Obot(tc_fun(X27771,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X27771),c_Big__Operators_Olattice_OSup__fin(X27771,c_Orderings_Oord__class_Omax(X27771),X27770)),c_Big__Operators_Olattice_OSup__fin(X27771,c_Orderings_Oord__class_Omax(X27771),X27769)) = c_Big__Operators_Olattice_OSup__fin(X27771,c_Orderings_Oord__class_Omax(X27771),hAPP(c_Set_OCollect(X27771),hAPP(hAPP(c_COMBB(tc_fun(X27771,tc_HOL_Obool),tc_HOL_Obool,X27771),c_HOL_OEx(X27771)),hAPP(hAPP(c_COMBB(tc_fun(X27771,tc_fun(X27771,tc_HOL_Obool)),tc_fun(X27771,tc_HOL_Obool),X27771),hAPP(c_COMBB(tc_fun(X27771,tc_HOL_Obool),tc_HOL_Obool,X27771),c_HOL_OEx(X27771))),hAPP(hAPP(c_COMBC(X27771,tc_fun(X27771,tc_fun(X27771,tc_HOL_Obool)),tc_fun(X27771,tc_fun(X27771,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27771,tc_fun(tc_fun(X27771,tc_HOL_Obool),tc_fun(X27771,tc_HOL_Obool))),tc_fun(tc_fun(X27771,tc_fun(X27771,tc_HOL_Obool)),tc_fun(X27771,tc_fun(X27771,tc_HOL_Obool))),X27771),c_COMBS(X27771,tc_fun(X27771,tc_HOL_Obool),tc_fun(X27771,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27771,tc_fun(X27771,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27771,tc_fun(tc_fun(X27771,tc_HOL_Obool),tc_fun(X27771,tc_HOL_Obool))),X27771),hAPP(c_COMBB(tc_fun(X27771,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27771,tc_HOL_Obool),tc_fun(X27771,tc_HOL_Obool)),X27771),c_COMBS(X27771,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27771,tc_fun(X27771,tc_HOL_Obool)),tc_fun(X27771,tc_fun(X27771,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27771),hAPP(c_COMBB(tc_fun(X27771,tc_HOL_Obool),tc_fun(X27771,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27771),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27771),c_fconj))),hAPP(hAPP(c_COMBC(X27771,tc_fun(X27771,tc_fun(X27771,X27771)),tc_fun(X27771,tc_fun(X27771,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27771,X27771),tc_fun(X27771,tc_HOL_Obool)),tc_fun(tc_fun(X27771,tc_fun(X27771,X27771)),tc_fun(X27771,tc_fun(X27771,tc_HOL_Obool))),X27771),c_COMBB(tc_fun(X27771,X27771),tc_fun(X27771,tc_HOL_Obool),X27771)),hAPP(hAPP(c_COMBB(tc_fun(X27771,tc_HOL_Obool),tc_fun(tc_fun(X27771,X27771),tc_fun(X27771,tc_HOL_Obool)),X27771),c_COMBB(X27771,tc_HOL_Obool,X27771)),c_fequal))),c_Orderings_Oord__class_Omin(X27771)))))),hAPP(hAPP(c_COMBC(X27771,tc_fun(X27771,tc_HOL_Obool),tc_fun(X27771,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27771,tc_HOL_Obool),tc_fun(X27771,tc_HOL_Obool)),X27771),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27771)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27771),c_fconj),hAPP(hAPP(c_COMBC(X27771,tc_fun(X27771,tc_HOL_Obool),tc_HOL_Obool),c_member(X27771)),X27770)))),hAPP(hAPP(c_COMBC(X27771,tc_fun(X27771,tc_HOL_Obool),tc_HOL_Obool),c_member(X27771)),X27769))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup2__distrib])]) ).

fof(i_0_6076,plain,
    ! [X27763,X27764,X27765] :
      ( ~ class_Lattices_Odistrib__lattice(X27765)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27765),X27764))
      | X27764 = c_Orderings_Obot__class_Obot(tc_fun(X27765,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27765),X27763))
      | X27763 = c_Orderings_Obot__class_Obot(tc_fun(X27765,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27765),c_Big__Operators_Olattice__class_OSup__fin(X27765,X27764)),c_Big__Operators_Olattice__class_OSup__fin(X27765,X27763)) = c_Big__Operators_Olattice__class_OSup__fin(X27765,hAPP(c_Set_OCollect(X27765),hAPP(hAPP(c_COMBB(tc_fun(X27765,tc_HOL_Obool),tc_HOL_Obool,X27765),c_HOL_OEx(X27765)),hAPP(hAPP(c_COMBB(tc_fun(X27765,tc_fun(X27765,tc_HOL_Obool)),tc_fun(X27765,tc_HOL_Obool),X27765),hAPP(c_COMBB(tc_fun(X27765,tc_HOL_Obool),tc_HOL_Obool,X27765),c_HOL_OEx(X27765))),hAPP(hAPP(c_COMBC(X27765,tc_fun(X27765,tc_fun(X27765,tc_HOL_Obool)),tc_fun(X27765,tc_fun(X27765,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27765,tc_fun(tc_fun(X27765,tc_HOL_Obool),tc_fun(X27765,tc_HOL_Obool))),tc_fun(tc_fun(X27765,tc_fun(X27765,tc_HOL_Obool)),tc_fun(X27765,tc_fun(X27765,tc_HOL_Obool))),X27765),c_COMBS(X27765,tc_fun(X27765,tc_HOL_Obool),tc_fun(X27765,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27765,tc_fun(X27765,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27765,tc_fun(tc_fun(X27765,tc_HOL_Obool),tc_fun(X27765,tc_HOL_Obool))),X27765),hAPP(c_COMBB(tc_fun(X27765,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27765,tc_HOL_Obool),tc_fun(X27765,tc_HOL_Obool)),X27765),c_COMBS(X27765,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27765,tc_fun(X27765,tc_HOL_Obool)),tc_fun(X27765,tc_fun(X27765,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27765),hAPP(c_COMBB(tc_fun(X27765,tc_HOL_Obool),tc_fun(X27765,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27765),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27765),c_fconj))),hAPP(hAPP(c_COMBC(X27765,tc_fun(X27765,tc_fun(X27765,X27765)),tc_fun(X27765,tc_fun(X27765,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27765,X27765),tc_fun(X27765,tc_HOL_Obool)),tc_fun(tc_fun(X27765,tc_fun(X27765,X27765)),tc_fun(X27765,tc_fun(X27765,tc_HOL_Obool))),X27765),c_COMBB(tc_fun(X27765,X27765),tc_fun(X27765,tc_HOL_Obool),X27765)),hAPP(hAPP(c_COMBB(tc_fun(X27765,tc_HOL_Obool),tc_fun(tc_fun(X27765,X27765),tc_fun(X27765,tc_HOL_Obool)),X27765),c_COMBB(X27765,tc_HOL_Obool,X27765)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(X27765)))))),hAPP(hAPP(c_COMBC(X27765,tc_fun(X27765,tc_HOL_Obool),tc_fun(X27765,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27765,tc_HOL_Obool),tc_fun(X27765,tc_HOL_Obool)),X27765),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27765)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27765),c_fconj),hAPP(hAPP(c_COMBC(X27765,tc_fun(X27765,tc_HOL_Obool),tc_HOL_Obool),c_member(X27765)),X27764)))),hAPP(hAPP(c_COMBC(X27765,tc_fun(X27765,tc_HOL_Obool),tc_HOL_Obool),c_member(X27765)),X27763))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup2__distrib])]) ).

fof(i_0_6077,plain,
    ! [X27757,X27758,X27759] :
      ( ~ class_Lattices_Odistrib__lattice(X27759)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27759),X27758))
      | X27758 = c_Orderings_Obot__class_Obot(tc_fun(X27759,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27759),X27757))
      | X27757 = c_Orderings_Obot__class_Obot(tc_fun(X27759,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27759),c_Big__Operators_Olattice__class_OInf__fin(X27759,X27758)),c_Big__Operators_Olattice__class_OInf__fin(X27759,X27757)) = c_Big__Operators_Olattice__class_OInf__fin(X27759,hAPP(c_Set_OCollect(X27759),hAPP(hAPP(c_COMBB(tc_fun(X27759,tc_HOL_Obool),tc_HOL_Obool,X27759),c_HOL_OEx(X27759)),hAPP(hAPP(c_COMBB(tc_fun(X27759,tc_fun(X27759,tc_HOL_Obool)),tc_fun(X27759,tc_HOL_Obool),X27759),hAPP(c_COMBB(tc_fun(X27759,tc_HOL_Obool),tc_HOL_Obool,X27759),c_HOL_OEx(X27759))),hAPP(hAPP(c_COMBC(X27759,tc_fun(X27759,tc_fun(X27759,tc_HOL_Obool)),tc_fun(X27759,tc_fun(X27759,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27759,tc_fun(tc_fun(X27759,tc_HOL_Obool),tc_fun(X27759,tc_HOL_Obool))),tc_fun(tc_fun(X27759,tc_fun(X27759,tc_HOL_Obool)),tc_fun(X27759,tc_fun(X27759,tc_HOL_Obool))),X27759),c_COMBS(X27759,tc_fun(X27759,tc_HOL_Obool),tc_fun(X27759,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27759,tc_fun(X27759,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X27759,tc_fun(tc_fun(X27759,tc_HOL_Obool),tc_fun(X27759,tc_HOL_Obool))),X27759),hAPP(c_COMBB(tc_fun(X27759,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27759,tc_HOL_Obool),tc_fun(X27759,tc_HOL_Obool)),X27759),c_COMBS(X27759,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27759,tc_fun(X27759,tc_HOL_Obool)),tc_fun(X27759,tc_fun(X27759,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),X27759),hAPP(c_COMBB(tc_fun(X27759,tc_HOL_Obool),tc_fun(X27759,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27759),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27759),c_fconj))),hAPP(hAPP(c_COMBC(X27759,tc_fun(X27759,tc_fun(X27759,X27759)),tc_fun(X27759,tc_fun(X27759,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27759,X27759),tc_fun(X27759,tc_HOL_Obool)),tc_fun(tc_fun(X27759,tc_fun(X27759,X27759)),tc_fun(X27759,tc_fun(X27759,tc_HOL_Obool))),X27759),c_COMBB(tc_fun(X27759,X27759),tc_fun(X27759,tc_HOL_Obool),X27759)),hAPP(hAPP(c_COMBB(tc_fun(X27759,tc_HOL_Obool),tc_fun(tc_fun(X27759,X27759),tc_fun(X27759,tc_HOL_Obool)),X27759),c_COMBB(X27759,tc_HOL_Obool,X27759)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(X27759)))))),hAPP(hAPP(c_COMBC(X27759,tc_fun(X27759,tc_HOL_Obool),tc_fun(X27759,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27759,tc_HOL_Obool),tc_fun(X27759,tc_HOL_Obool)),X27759),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27759)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27759),c_fconj),hAPP(hAPP(c_COMBC(X27759,tc_fun(X27759,tc_HOL_Obool),tc_HOL_Obool),c_member(X27759)),X27758)))),hAPP(hAPP(c_COMBC(X27759,tc_fun(X27759,tc_HOL_Obool),tc_HOL_Obool),c_member(X27759)),X27757))))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf2__distrib])]) ).

fof(i_0_6078,plain,
    ! [X29227,X29228,X29229] : c_List_Oset__Cons(X29229,X29228,X29227) = hAPP(c_Set_OCollect(tc_List_Olist(X29229)),hAPP(hAPP(c_COMBB(tc_fun(X29229,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(X29229)),c_HOL_OEx(X29229)),hAPP(hAPP(c_COMBB(tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),tc_fun(X29229,tc_HOL_Obool),tc_List_Olist(X29229)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_HOL_Obool,X29229),c_HOL_OEx(tc_List_Olist(X29229)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29229),tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29229,tc_fun(tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool))),tc_fun(tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool))),tc_List_Olist(X29229)),c_COMBS(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(X29229,tc_fun(tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool))),tc_List_Olist(X29229)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X29229),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),X29229),c_COMBS(tc_List_Olist(X29229),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(X29229)),hAPP(c_COMBB(tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_fun(tc_List_Olist(X29229),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X29229),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29229)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29229),tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_List_Olist(X29229))),tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(X29229),tc_List_Olist(X29229)),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),tc_fun(tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_List_Olist(X29229))),tc_fun(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool))),tc_List_Olist(X29229)),c_COMBB(tc_fun(tc_List_Olist(X29229),tc_List_Olist(X29229)),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),X29229)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29229),tc_List_Olist(X29229)),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),tc_List_Olist(X29229)),c_COMBB(tc_List_Olist(X29229),tc_HOL_Obool,tc_List_Olist(X29229))),c_fequal))),c_List_Olist_OCons(X29229)))))),hAPP(hAPP(c_COMBC(X29229,tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool)),X29229),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X29229))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X29229),c_fconj),hAPP(hAPP(c_COMBC(X29229,tc_fun(X29229,tc_HOL_Obool),tc_HOL_Obool),c_member(X29229)),X29228)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29229),tc_fun(tc_List_Olist(X29229),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X29229))),X29227)))))),
    inference(variable_rename,[status(thm)],[fact_set__Cons__def]) ).

fof(i_0_6079,plain,
    ! [X27475,X27476,X27477,X27478,X27479,X27480,X27481,X27482] :
      ( ( X27480 = hAPP(hAPP(c_Product__Type_OPair(X27482,X27481),hAPP(X27477,esk265_8(X27475,X27476,X27477,X27478,X27479,X27480,X27481,X27482))),hAPP(X27476,esk266_8(X27475,X27476,X27477,X27478,X27479,X27480,X27481,X27482)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27482,X27481)),X27480),hAPP(c_Set_Oimage(tc_prod(X27479,X27478),tc_prod(X27482,X27481),c_Product__Type_Omap__pair(X27479,X27482,X27478,X27481,X27477,X27476)),X27475))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X27479,X27478)),hAPP(hAPP(c_Product__Type_OPair(X27479,X27478),esk265_8(X27475,X27476,X27477,X27478,X27479,X27480,X27481,X27482)),esk266_8(X27475,X27476,X27477,X27478,X27479,X27480,X27481,X27482))),X27475))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27482,X27481)),X27480),hAPP(c_Set_Oimage(tc_prod(X27479,X27478),tc_prod(X27482,X27481),c_Product__Type_Omap__pair(X27479,X27482,X27478,X27481,X27477,X27476)),X27475))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5224])])])]) ).

fof(i_0_6080,plain,
    ! [X33510,X33511,X33512,X33513,X33514,X33515,X33516] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33516,X33515),tc_prod(X33516,X33515))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33516,X33515),tc_prod(X33516,X33515)),hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33514),X33513)),hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),esk544_7(X33510,X33511,X33512,X33513,X33514,X33515,X33516)),esk545_7(X33510,X33511,X33512,X33513,X33514,X33515,X33516)))),X33510))
        | hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33514),X33513) = hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33512),X33511)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33516,X33515),tc_prod(X33516,X33515))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33516,X33515),tc_prod(X33516,X33515)),hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33514),X33513)),hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33512),X33511))),c_Transitive__Closure_Ortrancl(tc_prod(X33516,X33515),X33510))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33516,X33515),tc_prod(X33516,X33515))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33516,X33515),tc_prod(X33516,X33515)),hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),esk544_7(X33510,X33511,X33512,X33513,X33514,X33515,X33516)),esk545_7(X33510,X33511,X33512,X33513,X33514,X33515,X33516))),hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33512),X33511))),c_Transitive__Closure_Ortrancl(tc_prod(X33516,X33515),X33510)))
        | hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33514),X33513) = hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33512),X33511)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X33516,X33515),tc_prod(X33516,X33515))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X33516,X33515),tc_prod(X33516,X33515)),hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33514),X33513)),hAPP(hAPP(c_Product__Type_OPair(X33516,X33515),X33512),X33511))),c_Transitive__Closure_Ortrancl(tc_prod(X33516,X33515),X33510))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5225])])])]) ).

cnf(i_0_6081,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_5226]) ).

cnf(i_0_6082,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_5227]) ).

cnf(i_0_6083,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_5228]) ).

fof(i_0_6084,plain,
    ! [X26665,X26666,X26667,X26668,X26669,X26670,X26671,X26672] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26668),esk238_8(X26665,X26666,X26667,X26668,X26669,X26670,X26671,X26672)),X26667))
        | ~ hBOOL(hAPP(hAPP(c_member(X26668),X26665),X26667))
        | hAPP(c_Set_Oimage(X26672,X26671,X26670),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26668,tc_fun(X26672,tc_HOL_Obool)),X26667),X26666)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26668,tc_fun(X26671,tc_HOL_Obool)),X26667),hAPP(hAPP(c_COMBB(tc_fun(X26672,tc_HOL_Obool),tc_fun(X26671,tc_HOL_Obool),X26668),c_Set_Oimage(X26672,X26671,X26670)),X26666))
        | ~ c_Fun_Oinj__on(X26672,X26671,X26670,X26669) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26672,tc_HOL_Obool)),hAPP(X26666,esk238_8(X26665,X26666,X26667,X26668,X26669,X26670,X26671,X26672))),X26669))
        | ~ hBOOL(hAPP(hAPP(c_member(X26668),X26665),X26667))
        | hAPP(c_Set_Oimage(X26672,X26671,X26670),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26668,tc_fun(X26672,tc_HOL_Obool)),X26667),X26666)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26668,tc_fun(X26671,tc_HOL_Obool)),X26667),hAPP(hAPP(c_COMBB(tc_fun(X26672,tc_HOL_Obool),tc_fun(X26671,tc_HOL_Obool),X26668),c_Set_Oimage(X26672,X26671,X26670)),X26666))
        | ~ c_Fun_Oinj__on(X26672,X26671,X26670,X26669) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__INT])])])]) ).

fof(i_0_6085,plain,
    ! [X25585,X25586,X25587,X25588,X25589,X25590] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25590,tc_fun(X25589,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X25590,tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_fun(X25589,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25589,tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_fun(X25589,tc_HOL_Obool)),X25590),c_COMBC(X25589,tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25589,tc_prod(X25590,X25589)),tc_fun(X25589,tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),X25590),hAPP(c_COMBB(tc_prod(X25590,X25589),tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool),X25589),c_member(tc_prod(X25590,X25589)))),c_Product__Type_OPair(X25590,X25589)))),X25588)),hAPP(hAPP(c_COMBC(X25590,tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_fun(X25589,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25589,tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_fun(X25589,tc_HOL_Obool)),X25590),c_COMBC(X25589,tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25589,tc_prod(X25590,X25589)),tc_fun(X25589,tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),X25590),hAPP(c_COMBB(tc_prod(X25590,X25589),tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool),X25589),c_member(tc_prod(X25590,X25589)))),c_Product__Type_OPair(X25590,X25589)))),X25587)),X25586),X25585))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X25590,X25589)),hAPP(hAPP(c_Product__Type_OPair(X25590,X25589),X25586),X25585)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool)),X25588),X25587))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X25590,X25589)),hAPP(hAPP(c_Product__Type_OPair(X25590,X25589),X25586),X25585)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool)),X25588),X25587)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25590,tc_fun(X25589,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X25590,tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_fun(X25589,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25589,tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_fun(X25589,tc_HOL_Obool)),X25590),c_COMBC(X25589,tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25589,tc_prod(X25590,X25589)),tc_fun(X25589,tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),X25590),hAPP(c_COMBB(tc_prod(X25590,X25589),tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool),X25589),c_member(tc_prod(X25590,X25589)))),c_Product__Type_OPair(X25590,X25589)))),X25588)),hAPP(hAPP(c_COMBC(X25590,tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_fun(X25589,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25589,tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_fun(X25589,tc_HOL_Obool)),X25590),c_COMBC(X25589,tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25589,tc_prod(X25590,X25589)),tc_fun(X25589,tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool)),X25590),hAPP(c_COMBB(tc_prod(X25590,X25589),tc_fun(tc_fun(tc_prod(X25590,X25589),tc_HOL_Obool),tc_HOL_Obool),X25589),c_member(tc_prod(X25590,X25589)))),c_Product__Type_OPair(X25590,X25589)))),X25587)),X25586),X25585)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq2])]) ).

fof(i_0_6086,plain,
    ! [X23504,X23505,X23506,X23507,X23508,X23509] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23509,tc_fun(X23508,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23509,tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_fun(X23508,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23508,tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_fun(X23508,tc_HOL_Obool)),X23509),c_COMBC(X23508,tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23508,tc_prod(X23509,X23508)),tc_fun(X23508,tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),X23509),hAPP(c_COMBB(tc_prod(X23509,X23508),tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool),X23508),c_member(tc_prod(X23509,X23508)))),c_Product__Type_OPair(X23509,X23508)))),X23507)),hAPP(hAPP(c_COMBC(X23509,tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_fun(X23508,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23508,tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_fun(X23508,tc_HOL_Obool)),X23509),c_COMBC(X23508,tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23508,tc_prod(X23509,X23508)),tc_fun(X23508,tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),X23509),hAPP(c_COMBB(tc_prod(X23509,X23508),tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool),X23508),c_member(tc_prod(X23509,X23508)))),c_Product__Type_OPair(X23509,X23508)))),X23506)),X23505),X23504))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23509,X23508)),hAPP(hAPP(c_Product__Type_OPair(X23509,X23508),X23505),X23504)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool)),X23507),X23506))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23509,X23508)),hAPP(hAPP(c_Product__Type_OPair(X23509,X23508),X23505),X23504)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool)),X23507),X23506)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23509,tc_fun(X23508,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23509,tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_fun(X23508,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23508,tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_fun(X23508,tc_HOL_Obool)),X23509),c_COMBC(X23508,tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23508,tc_prod(X23509,X23508)),tc_fun(X23508,tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),X23509),hAPP(c_COMBB(tc_prod(X23509,X23508),tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool),X23508),c_member(tc_prod(X23509,X23508)))),c_Product__Type_OPair(X23509,X23508)))),X23507)),hAPP(hAPP(c_COMBC(X23509,tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_fun(X23508,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23508,tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_fun(X23508,tc_HOL_Obool)),X23509),c_COMBC(X23508,tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23508,tc_prod(X23509,X23508)),tc_fun(X23508,tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool)),X23509),hAPP(c_COMBB(tc_prod(X23509,X23508),tc_fun(tc_fun(tc_prod(X23509,X23508),tc_HOL_Obool),tc_HOL_Obool),X23508),c_member(tc_prod(X23509,X23508)))),c_Product__Type_OPair(X23509,X23508)))),X23506)),X23505),X23504)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq2])]) ).

fof(i_0_6087,plain,
    ! [X29195,X29196] : c_List_Olenlex(X29196,X29195) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X29196),tc_List_Olist(X29196),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(X29196),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29196),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X29196),tc_HOL_Obool),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),tc_List_Olist(X29196)),c_COMBS(tc_List_Olist(X29196),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29196),tc_HOL_Obool),tc_fun(tc_List_Olist(X29196),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X29196)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29196)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X29196),tc_fun(tc_List_Olist(X29196),tc_Nat_Onat),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29196),tc_Nat_Onat),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),tc_List_Olist(X29196)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X29196))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29196)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X29196))))),c_Nat_Osize__class_Osize(tc_List_Olist(X29196)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(X29196),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29196),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(X29196),tc_HOL_Obool),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),tc_List_Olist(X29196)),c_COMBS(tc_List_Olist(X29196),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29196),tc_HOL_Obool),tc_fun(tc_List_Olist(X29196),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(X29196)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29196)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(X29196),tc_fun(tc_List_Olist(X29196),tc_Nat_Onat),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29196),tc_Nat_Onat),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),tc_List_Olist(X29196)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X29196))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29196)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X29196))))),c_Nat_Osize__class_Osize(tc_List_Olist(X29196)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29196),tc_fun(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196)),tc_HOL_Obool),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29196),tc_fun(tc_fun(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196)),tc_HOL_Obool),tc_fun(tc_List_Olist(X29196),tc_HOL_Obool)),tc_List_Olist(X29196)),c_COMBC(tc_List_Olist(X29196),tc_fun(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29196),tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196))),tc_fun(tc_List_Olist(X29196),tc_fun(tc_fun(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(X29196)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196)),tc_fun(tc_fun(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29196)),c_member(tc_prod(tc_List_Olist(X29196),tc_List_Olist(X29196))))),c_Product__Type_OPair(tc_List_Olist(X29196),tc_List_Olist(X29196))))),c_List_Olex(X29196,X29195)))))),
    inference(variable_rename,[status(thm)],[fact_lenlex__conv]) ).

fof(i_0_6088,plain,
    ! [X32116,X32117,X32118,X32119,X32120,X32121,X32122,X32123] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32123),esk448_8(X32116,X32117,X32118,X32119,X32120,X32121,X32122,X32123)),hAPP(c_List_Oset(X32123),X32122)))
        | hAPP(c_List_Ofoldl(X32121,X32123,hAPP(c_COMBC(X32123,X32121,X32121),X32119),hAPP(X32118,X32116)),X32122) = hAPP(X32118,hAPP(c_List_Ofoldl(X32120,X32123,hAPP(c_COMBC(X32123,X32120,X32120),X32117),X32116),X32122)) )
      & ( hAPP(c_Fun_Ocomp(X32121,X32121,X32120,hAPP(X32119,esk448_8(X32116,X32117,X32118,X32119,X32120,X32121,X32122,X32123))),X32118) != hAPP(c_Fun_Ocomp(X32120,X32121,X32120,X32118),hAPP(X32117,esk448_8(X32116,X32117,X32118,X32119,X32120,X32121,X32122,X32123)))
        | hAPP(c_List_Ofoldl(X32121,X32123,hAPP(c_COMBC(X32123,X32121,X32121),X32119),hAPP(X32118,X32116)),X32122) = hAPP(X32118,hAPP(c_List_Ofoldl(X32120,X32123,hAPP(c_COMBC(X32123,X32120,X32120),X32117),X32116),X32122)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__apply])])])]) ).

cnf(i_0_6089,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_5229]) ).

cnf(i_0_6090,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_5230]) ).

cnf(i_0_6091,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_5231]) ).

fof(i_0_6092,plain,
    ! [X26373,X26374,X26375,X26376,X26377,X26378] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26378,tc_fun(X26377,tc_fun(X26376,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26378,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_fun(X26377,tc_fun(X26376,tc_HOL_Obool)),X26378),hAPP(c_COMBC(X26377,tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_fun(X26376,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26376,tc_fun(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_fun(X26376,tc_HOL_Obool)),X26377),c_COMBC(X26376,tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26376,tc_prod(X26377,X26376)),tc_fun(X26376,tc_fun(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_HOL_Obool)),X26377),hAPP(c_COMBB(tc_prod(X26377,X26376),tc_fun(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_HOL_Obool),X26376),c_member(tc_prod(X26377,X26376)))),c_Product__Type_OPair(X26377,X26376))))),X26375)),X26374),X26373))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26377,X26376)),hAPP(hAPP(c_Product__Type_OPair(X26377,X26376),X26374),X26373)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26378,tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26378,tc_HOL_Obool))),X26375))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26377,X26376)),hAPP(hAPP(c_Product__Type_OPair(X26377,X26376),X26374),X26373)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26378,tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26378,tc_HOL_Obool))),X26375)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26378,tc_fun(X26377,tc_fun(X26376,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26378,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_fun(X26377,tc_fun(X26376,tc_HOL_Obool)),X26378),hAPP(c_COMBC(X26377,tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_fun(X26376,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26376,tc_fun(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_fun(X26376,tc_HOL_Obool)),X26377),c_COMBC(X26376,tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26376,tc_prod(X26377,X26376)),tc_fun(X26376,tc_fun(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_HOL_Obool)),X26377),hAPP(c_COMBB(tc_prod(X26377,X26376),tc_fun(tc_fun(tc_prod(X26377,X26376),tc_HOL_Obool),tc_HOL_Obool),X26376),c_member(tc_prod(X26377,X26376)))),c_Product__Type_OPair(X26377,X26376))))),X26375)),X26374),X26373)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq2])]) ).

fof(i_0_6093,plain,
    ! [X26279,X26280,X26281,X26282,X26283,X26284] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26284,tc_fun(X26283,tc_fun(X26282,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26284,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_fun(X26283,tc_fun(X26282,tc_HOL_Obool)),X26284),hAPP(c_COMBC(X26283,tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_fun(X26282,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26282,tc_fun(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_fun(X26282,tc_HOL_Obool)),X26283),c_COMBC(X26282,tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26282,tc_prod(X26283,X26282)),tc_fun(X26282,tc_fun(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_HOL_Obool)),X26283),hAPP(c_COMBB(tc_prod(X26283,X26282),tc_fun(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_HOL_Obool),X26282),c_member(tc_prod(X26283,X26282)))),c_Product__Type_OPair(X26283,X26282))))),X26281)),X26280),X26279))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X26283,X26282)),hAPP(hAPP(c_Product__Type_OPair(X26283,X26282),X26280),X26279)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26284,tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26284,tc_HOL_Obool))),X26281))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26283,X26282)),hAPP(hAPP(c_Product__Type_OPair(X26283,X26282),X26280),X26279)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26284,tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26284,tc_HOL_Obool))),X26281)))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26284,tc_fun(X26283,tc_fun(X26282,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26284,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_fun(X26283,tc_fun(X26282,tc_HOL_Obool)),X26284),hAPP(c_COMBC(X26283,tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_fun(X26282,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26282,tc_fun(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_fun(X26282,tc_HOL_Obool)),X26283),c_COMBC(X26282,tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26282,tc_prod(X26283,X26282)),tc_fun(X26282,tc_fun(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_HOL_Obool)),X26283),hAPP(c_COMBB(tc_prod(X26283,X26282),tc_fun(tc_fun(tc_prod(X26283,X26282),tc_HOL_Obool),tc_HOL_Obool),X26282),c_member(tc_prod(X26283,X26282)))),c_Product__Type_OPair(X26283,X26282))))),X26281)),X26280),X26279)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq2])]) ).

fof(i_0_6094,plain,
    ! [X28002,X28003,X28004,X28005,X28006,X28007,X28008] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28008,X28007,X28006,hAPP(hAPP(c_COMBC(X28008,tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_fun(X28007,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28007,tc_fun(tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_fun(X28007,tc_HOL_Obool)),X28008),c_COMBC(X28007,tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28007,tc_prod(X28008,X28007)),tc_fun(X28007,tc_fun(tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_HOL_Obool)),X28008),hAPP(c_COMBB(tc_prod(X28008,X28007),tc_fun(tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_HOL_Obool),X28007),c_member(tc_prod(X28008,X28007)))),c_Product__Type_OPair(X28008,X28007)))),X28005),hAPP(hAPP(c_COMBC(X28007,tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_fun(X28006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28006,tc_fun(tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_fun(X28006,tc_HOL_Obool)),X28007),c_COMBC(X28006,tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28006,tc_prod(X28007,X28006)),tc_fun(X28006,tc_fun(tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_HOL_Obool)),X28007),hAPP(c_COMBB(tc_prod(X28007,X28006),tc_fun(tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_HOL_Obool),X28006),c_member(tc_prod(X28007,X28006)))),c_Product__Type_OPair(X28007,X28006)))),X28004)),X28003),X28002))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28008,X28006)),hAPP(hAPP(c_Product__Type_OPair(X28008,X28006),X28003),X28002)),hAPP(hAPP(c_Relation_Orel__comp(X28008,X28007,X28006),X28005),X28004))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28008,X28006)),hAPP(hAPP(c_Product__Type_OPair(X28008,X28006),X28003),X28002)),hAPP(hAPP(c_Relation_Orel__comp(X28008,X28007,X28006),X28005),X28004)))
        | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28008,X28007,X28006,hAPP(hAPP(c_COMBC(X28008,tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_fun(X28007,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28007,tc_fun(tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_fun(X28007,tc_HOL_Obool)),X28008),c_COMBC(X28007,tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28007,tc_prod(X28008,X28007)),tc_fun(X28007,tc_fun(tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_HOL_Obool)),X28008),hAPP(c_COMBB(tc_prod(X28008,X28007),tc_fun(tc_fun(tc_prod(X28008,X28007),tc_HOL_Obool),tc_HOL_Obool),X28007),c_member(tc_prod(X28008,X28007)))),c_Product__Type_OPair(X28008,X28007)))),X28005),hAPP(hAPP(c_COMBC(X28007,tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_fun(X28006,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28006,tc_fun(tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_fun(X28006,tc_HOL_Obool)),X28007),c_COMBC(X28006,tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28006,tc_prod(X28007,X28006)),tc_fun(X28006,tc_fun(tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_HOL_Obool)),X28007),hAPP(c_COMBB(tc_prod(X28007,X28006),tc_fun(tc_fun(tc_prod(X28007,X28006),tc_HOL_Obool),tc_HOL_Obool),X28006),c_member(tc_prod(X28007,X28006)))),c_Product__Type_OPair(X28007,X28006)))),X28004)),X28003),X28002)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp__rel__comp__eq])]) ).

cnf(i_0_6095,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_5232]) ).

cnf(i_0_6096,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_5233]) ).

fof(i_0_6097,plain,
    ! [X24807,X24808,X24809,X24810,X24811,X24812,X24813] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24813),esk190_7(X24807,X24808,X24809,X24810,X24811,X24812,X24813)),X24812))
        | X24808 = X24807
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24813,tc_HOL_Obool)),X24807),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24813),X24812),X24811)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24813,tc_HOL_Obool)),X24808),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24813),X24812),X24811)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24813,tc_fun(X24810,tc_HOL_Obool)),X24808),X24809) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24813,tc_fun(X24810,tc_HOL_Obool)),X24807),X24809)
        | ~ c_Equiv__Relations_Ocongruent(X24813,tc_fun(X24810,tc_HOL_Obool),X24811,X24809)
        | ~ c_Equiv__Relations_Oequiv(X24813,X24812,X24811) )
      & ( hBOOL(hAPP(hAPP(c_member(X24813),esk191_7(X24807,X24808,X24809,X24810,X24811,X24812,X24813)),X24812))
        | X24808 = X24807
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24813,tc_HOL_Obool)),X24807),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24813),X24812),X24811)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24813,tc_HOL_Obool)),X24808),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24813),X24812),X24811)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24813,tc_fun(X24810,tc_HOL_Obool)),X24808),X24809) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24813,tc_fun(X24810,tc_HOL_Obool)),X24807),X24809)
        | ~ c_Equiv__Relations_Ocongruent(X24813,tc_fun(X24810,tc_HOL_Obool),X24811,X24809)
        | ~ c_Equiv__Relations_Oequiv(X24813,X24812,X24811) )
      & ( hAPP(X24809,esk190_7(X24807,X24808,X24809,X24810,X24811,X24812,X24813)) = hAPP(X24809,esk191_7(X24807,X24808,X24809,X24810,X24811,X24812,X24813))
        | X24808 = X24807
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24813,tc_HOL_Obool)),X24807),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24813),X24812),X24811)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24813,tc_HOL_Obool)),X24808),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24813),X24812),X24811)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24813,tc_fun(X24810,tc_HOL_Obool)),X24808),X24809) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24813,tc_fun(X24810,tc_HOL_Obool)),X24807),X24809)
        | ~ c_Equiv__Relations_Ocongruent(X24813,tc_fun(X24810,tc_HOL_Obool),X24811,X24809)
        | ~ c_Equiv__Relations_Oequiv(X24813,X24812,X24811) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24813,X24813)),hAPP(hAPP(c_Product__Type_OPair(X24813,X24813),esk190_7(X24807,X24808,X24809,X24810,X24811,X24812,X24813)),esk191_7(X24807,X24808,X24809,X24810,X24811,X24812,X24813))),X24811))
        | X24808 = X24807
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24813,tc_HOL_Obool)),X24807),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24813),X24812),X24811)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24813,tc_HOL_Obool)),X24808),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24813),X24812),X24811)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24813,tc_fun(X24810,tc_HOL_Obool)),X24808),X24809) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24813,tc_fun(X24810,tc_HOL_Obool)),X24807),X24809)
        | ~ c_Equiv__Relations_Ocongruent(X24813,tc_fun(X24810,tc_HOL_Obool),X24811,X24809)
        | ~ c_Equiv__Relations_Oequiv(X24813,X24812,X24811) ) ),
    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_6098,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_5232]) ).

cnf(i_0_6099,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_5234]) ).

fof(i_0_6100,plain,
    ! [X27728,X27729,X27730,X27731] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27731),hAPP(c_Set_OCollect(X27731),X27730)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27729),hAPP(c_Set_OCollect(X27729),hAPP(hAPP(c_COMBB(tc_fun(X27731,tc_HOL_Obool),tc_HOL_Obool,X27729),c_HOL_OEx(X27731)),hAPP(hAPP(c_COMBC(X27729,tc_fun(X27731,tc_HOL_Obool),tc_fun(X27731,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27731,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27731,tc_HOL_Obool),tc_fun(X27731,tc_HOL_Obool)),X27729),c_COMBS(X27731,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27731,tc_HOL_Obool),tc_fun(X27731,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27729),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27731),c_fconj)),hAPP(hAPP(c_COMBC(X27729,tc_fun(X27731,X27729),tc_fun(X27731,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27729,tc_HOL_Obool),tc_fun(tc_fun(X27731,X27729),tc_fun(X27731,tc_HOL_Obool)),X27729),c_COMBB(X27729,tc_HOL_Obool,X27731)),c_fequal)),X27728)))),X27730))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__image__set])]) ).

fof(i_0_6101,plain,
    ! [X28468,X28469,X28470,X28471,X28472,X28473,X28474,X28475] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28474),esk331_8(X28468,X28469,X28470,X28471,X28472,X28473,X28474,X28475)),X28471))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28473,X28475),X28468),X28470) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28474,X28475),X28469),X28471)
        | X28470 != hAPP(c_Set_Oimage(X28474,X28473,X28472),X28471)
        | ~ c_Fun_Oinj__on(X28474,X28473,X28472,X28471)
        | ~ class_Groups_Ocomm__monoid__add(X28475) )
      & ( hAPP(X28469,esk331_8(X28468,X28469,X28470,X28471,X28472,X28473,X28474,X28475)) != hAPP(X28468,hAPP(X28472,esk331_8(X28468,X28469,X28470,X28471,X28472,X28473,X28474,X28475)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28473,X28475),X28468),X28470) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28474,X28475),X28469),X28471)
        | X28470 != hAPP(c_Set_Oimage(X28474,X28473,X28472),X28471)
        | ~ c_Fun_Oinj__on(X28474,X28473,X28472,X28471)
        | ~ class_Groups_Ocomm__monoid__add(X28475) ) ),
    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_6102,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_5235]) ).

cnf(i_0_6103,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_5236]) ).

cnf(i_0_6104,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_5237]) ).

fof(i_0_6105,plain,
    ! [X32499,X32500,X32501,X32502,X32503] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32503,X32502,hAPP(hAPP(c_COMBC(X32503,tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_fun(X32502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32502,tc_fun(tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_fun(X32502,tc_HOL_Obool)),X32503),c_COMBC(X32502,tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32502,tc_prod(X32503,X32502)),tc_fun(X32502,tc_fun(tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_HOL_Obool)),X32503),hAPP(c_COMBB(tc_prod(X32503,X32502),tc_fun(tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_HOL_Obool),X32502),c_member(tc_prod(X32503,X32502)))),c_Product__Type_OPair(X32503,X32502)))),X32501)),X32500),X32499))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32502,X32503)),hAPP(hAPP(c_Product__Type_OPair(X32502,X32503),X32500),X32499)),hAPP(c_Relation_Oconverse(X32503,X32502),X32501))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32502,X32503)),hAPP(hAPP(c_Product__Type_OPair(X32502,X32503),X32500),X32499)),hAPP(c_Relation_Oconverse(X32503,X32502),X32501)))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32503,X32502,hAPP(hAPP(c_COMBC(X32503,tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_fun(X32502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32502,tc_fun(tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_fun(X32502,tc_HOL_Obool)),X32503),c_COMBC(X32502,tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32502,tc_prod(X32503,X32502)),tc_fun(X32502,tc_fun(tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_HOL_Obool)),X32503),hAPP(c_COMBB(tc_prod(X32503,X32502),tc_fun(tc_fun(tc_prod(X32503,X32502),tc_HOL_Obool),tc_HOL_Obool),X32502),c_member(tc_prod(X32503,X32502)))),c_Product__Type_OPair(X32503,X32502)))),X32501)),X32500),X32499)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq])]) ).

fof(i_0_6106,plain,
    ! [X23626,X23627,X23628,X23629,X23630,X23631,X23632,X23633] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23632),esk125_8(X23626,X23627,X23628,X23629,X23630,X23631,X23632,X23633)),X23629))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23631,X23633),X23626),X23628) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23632,X23633),X23627),X23629)
        | X23628 != hAPP(c_Set_Oimage(X23632,X23631,X23630),X23629)
        | ~ c_Fun_Oinj__on(X23632,X23631,X23630,X23629)
        | ~ class_Groups_Ocomm__monoid__mult(X23633) )
      & ( hAPP(X23627,esk125_8(X23626,X23627,X23628,X23629,X23630,X23631,X23632,X23633)) != hAPP(hAPP(c_Fun_Ocomp(X23631,X23633,X23632,X23626),X23630),esk125_8(X23626,X23627,X23628,X23629,X23630,X23631,X23632,X23633))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23631,X23633),X23626),X23628) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23632,X23633),X23627),X23629)
        | X23628 != hAPP(c_Set_Oimage(X23632,X23631,X23630),X23629)
        | ~ c_Fun_Oinj__on(X23632,X23631,X23630,X23629)
        | ~ class_Groups_Ocomm__monoid__mult(X23633) ) ),
    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_6107,plain,
    ! [X28484,X28485,X28486,X28487,X28488,X28489,X28490,X28491] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28490),X28488),esk332_8(X28484,X28485,X28486,X28487,X28488,X28489,X28490,X28491)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28490,X28491),X28485),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28490,X28489),X28487)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28490,X28491),X28484),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28490,X28488),X28486))
        | X28487 != X28486
        | X28489 != X28488
        | ~ class_Groups_Ocomm__monoid__add(X28491)
        | ~ class_Orderings_Oord(X28490) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X28490),esk332_8(X28484,X28485,X28486,X28487,X28488,X28489,X28490,X28491)),X28486))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28490,X28491),X28485),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28490,X28489),X28487)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28490,X28491),X28484),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28490,X28488),X28486))
        | X28487 != X28486
        | X28489 != X28488
        | ~ class_Groups_Ocomm__monoid__add(X28491)
        | ~ class_Orderings_Oord(X28490) )
      & ( hAPP(X28485,esk332_8(X28484,X28485,X28486,X28487,X28488,X28489,X28490,X28491)) != hAPP(X28484,esk332_8(X28484,X28485,X28486,X28487,X28488,X28489,X28490,X28491))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28490,X28491),X28485),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28490,X28489),X28487)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28490,X28491),X28484),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X28490,X28488),X28486))
        | X28487 != X28486
        | X28489 != X28488
        | ~ class_Groups_Ocomm__monoid__add(X28491)
        | ~ class_Orderings_Oord(X28490) ) ),
    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_6108,plain,
    ! [X24233] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X24233) = 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,X24233)),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_6109,plain,
    ! [X32808,X32809,X32810,X32811,X32812,X32813,X32814] :
      ( ( hBOOL(hAPP(hAPP(X32814,esk499_7(X32808,X32809,X32810,X32811,X32812,X32813,X32814)),esk498_7(X32808,X32809,X32810,X32811,X32812,X32813,X32814)))
        | hBOOL(hAPP(X32810,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32813,X32812,X32808),X32809),X32811)))
        | ~ hBOOL(hAPP(hAPP(X32814,hAPP(c_Product__Type_Osnd(X32813,X32812),X32811)),hAPP(c_Product__Type_Ofst(X32813,X32812),X32811))) )
      & ( ~ hBOOL(hAPP(X32810,hAPP(hAPP(X32809,esk498_7(X32808,X32809,X32810,X32811,X32812,X32813,X32814)),esk499_7(X32808,X32809,X32810,X32811,X32812,X32813,X32814))))
        | hBOOL(hAPP(X32810,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X32813,X32812,X32808),X32809),X32811)))
        | ~ hBOOL(hAPP(hAPP(X32814,hAPP(c_Product__Type_Osnd(X32813,X32812),X32811)),hAPP(c_Product__Type_Ofst(X32813,X32812),X32811))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__realizer])])])]) ).

fof(i_0_6110,plain,
    ! [X23409,X23410] : c_FunDef_Orp__inv__image(X23410,X23409) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool),tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool),tc_fun(tc_fun(X23409,X23410),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool),tc_fun(tc_fun(X23409,X23410),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool),tc_fun(tc_fun(X23409,X23410),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(X23409,X23410),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)),tc_fun(tc_fun(X23409,X23410),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool),tc_fun(tc_fun(X23409,X23410),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool),tc_fun(tc_fun(X23409,X23410),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool))))),tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(X23409,X23410),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)),tc_fun(tc_fun(X23409,X23410),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool))),tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X23409,X23410),tc_fun(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(X23409,X23410),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)),tc_fun(tc_fun(X23409,X23410),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)))),tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool)),c_COMBS(tc_fun(X23409,X23410),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X23409,X23410),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)),tc_fun(tc_fun(X23409,X23410),tc_fun(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)))),tc_fun(tc_prod(X23410,X23410),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool))),tc_fun(X23409,X23410)),c_Product__Type_OPair(tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool),tc_fun(tc_prod(X23409,X23409),tc_HOL_Obool)))),c_Relation_Oinv__image(X23410,X23409))))),c_Relation_Oinv__image(X23410,X23409))),
    inference(variable_rename,[status(thm)],[fact_rp__inv__image__def]) ).

fof(i_0_6111,plain,
    ! [X27742,X27743,X27744,X27745] : hAPP(hAPP(c_Relation_Oinv__image(X27745,X27744),X27743),X27742) = hAPP(c_Set_OCollect(tc_prod(X27744,X27744)),hAPP(c_Product__Type_Oprod_Oprod__case(X27744,X27744,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27744,tc_fun(tc_prod(X27745,X27745),tc_HOL_Obool),tc_fun(X27744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27744,tc_fun(tc_fun(tc_prod(X27745,X27745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27745,X27745),tc_HOL_Obool),tc_fun(X27744,tc_HOL_Obool)),X27744),c_COMBC(X27744,tc_fun(tc_prod(X27745,X27745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27744,tc_prod(X27745,X27745)),tc_fun(X27744,tc_fun(tc_fun(tc_prod(X27745,X27745),tc_HOL_Obool),tc_HOL_Obool)),X27744),hAPP(c_COMBB(tc_prod(X27745,X27745),tc_fun(tc_fun(tc_prod(X27745,X27745),tc_HOL_Obool),tc_HOL_Obool),X27744),c_member(tc_prod(X27745,X27745)))),hAPP(hAPP(c_COMBC(X27744,tc_fun(X27744,X27745),tc_fun(X27744,tc_prod(X27745,X27745))),hAPP(hAPP(c_COMBB(tc_fun(X27745,tc_prod(X27745,X27745)),tc_fun(tc_fun(X27744,X27745),tc_fun(X27744,tc_prod(X27745,X27745))),X27744),c_COMBB(X27745,tc_prod(X27745,X27745),X27744)),hAPP(hAPP(c_COMBB(X27745,tc_fun(X27745,tc_prod(X27745,X27745)),X27744),c_Product__Type_OPair(X27745,X27745)),X27742))),X27742)))),X27743))),
    inference(variable_rename,[status(thm)],[fact_inv__image__def]) ).

fof(i_0_6112,plain,
    ! [X29574,X29575,X29576,X29577] : hAPP(c_List_Oset(tc_prod(X29577,X29576)),hAPP(hAPP(c_List_Ozip(X29577,X29576),X29575),X29574)) = hAPP(c_Set_OCollect(tc_prod(X29577,X29576)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(X29577,X29576)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(X29577,X29576),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(X29577,X29576)),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(X29577,X29576)),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(X29577,X29576),tc_fun(tc_Nat_Onat,tc_prod(X29577,X29576)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X29577,X29576),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(X29577,X29576)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(X29577,X29576)),c_COMBB(tc_prod(X29577,X29576),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X29576,tc_prod(X29577,X29576)),hAPP(hAPP(c_COMBB(X29577,tc_fun(X29576,tc_prod(X29577,X29576)),tc_Nat_Onat),c_Product__Type_OPair(X29577,X29576)),hAPP(c_List_Onth(X29577),X29575))),hAPP(c_List_Onth(X29576),X29574)))))),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(X29577)),X29575)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29576)),X29574)))))),
    inference(variable_rename,[status(thm)],[fact_set__zip]) ).

fof(i_0_6113,plain,
    ! [X21863,X21864,X21865,X21866] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21866,tc_fun(X21865,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X21866,tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_fun(X21865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21865,tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_fun(X21865,tc_HOL_Obool)),X21866),c_COMBC(X21865,tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21865,tc_prod(X21866,X21865)),tc_fun(X21865,tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),X21866),hAPP(c_COMBB(tc_prod(X21866,X21865),tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool),X21865),c_member(tc_prod(X21866,X21865)))),c_Product__Type_OPair(X21866,X21865)))),X21864)),hAPP(hAPP(c_COMBC(X21866,tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_fun(X21865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21865,tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_fun(X21865,tc_HOL_Obool)),X21866),c_COMBC(X21865,tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21865,tc_prod(X21866,X21865)),tc_fun(X21865,tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),X21866),hAPP(c_COMBB(tc_prod(X21866,X21865),tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool),X21865),c_member(tc_prod(X21866,X21865)))),c_Product__Type_OPair(X21866,X21865)))),X21863)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool)),X21864),X21863)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool)),X21864),X21863))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21866,tc_fun(X21865,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X21866,tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_fun(X21865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21865,tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_fun(X21865,tc_HOL_Obool)),X21866),c_COMBC(X21865,tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21865,tc_prod(X21866,X21865)),tc_fun(X21865,tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),X21866),hAPP(c_COMBB(tc_prod(X21866,X21865),tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool),X21865),c_member(tc_prod(X21866,X21865)))),c_Product__Type_OPair(X21866,X21865)))),X21864)),hAPP(hAPP(c_COMBC(X21866,tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_fun(X21865,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21865,tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_fun(X21865,tc_HOL_Obool)),X21866),c_COMBC(X21865,tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21865,tc_prod(X21866,X21865)),tc_fun(X21865,tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool)),X21866),hAPP(c_COMBB(tc_prod(X21866,X21865),tc_fun(tc_fun(tc_prod(X21866,X21865),tc_HOL_Obool),tc_HOL_Obool),X21865),c_member(tc_prod(X21866,X21865)))),c_Product__Type_OPair(X21866,X21865)))),X21863))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq2])]) ).

fof(i_0_6114,plain,
    ! [X27724,X27725] : hAPP(c_Set_OPow(X27725),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27725,tc_HOL_Obool)),X27724)) = hAPP(c_Set_OCollect(tc_fun(X27725,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X27725,tc_HOL_Obool)),c_HOL_OEx(tc_fun(X27725,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(X27725,tc_HOL_Obool),tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X27725,tc_HOL_Obool)),c_COMBS(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X27725,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X27725,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(X27725,tc_HOL_Obool),tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_fun(X27725,tc_HOL_Obool)),tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_fun(X27725,tc_HOL_Obool)),tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X27725,tc_HOL_Obool)),c_COMBB(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X27725,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(X27725,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27725,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(X27725,tc_HOL_Obool)),hAPP(c_member(tc_fun(X27725,tc_HOL_Obool)),X27724)),c_Set_OPow(X27725))))),
    inference(variable_rename,[status(thm)],[fact_Pow__Compl]) ).

fof(i_0_6115,plain,
    ! [X24829,X24830,X24831,X24832,X24833,X24834,X24835] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24835),esk194_7(X24829,X24830,X24831,X24832,X24833,X24834,X24835)),X24834))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X24832,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24835,tc_fun(X24832,tc_HOL_Obool)),X24830),X24831)),X24829))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24835,tc_HOL_Obool)),X24830),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24835),X24834),X24833)))
        | ~ c_Equiv__Relations_Ocongruent(X24835,tc_fun(X24832,tc_HOL_Obool),X24833,X24831)
        | ~ c_Equiv__Relations_Oequiv(X24835,X24834,X24833) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24832,tc_HOL_Obool)),hAPP(X24831,esk194_7(X24829,X24830,X24831,X24832,X24833,X24834,X24835))),X24829))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X24832,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24835,tc_fun(X24832,tc_HOL_Obool)),X24830),X24831)),X24829))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24835,tc_HOL_Obool)),X24830),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24835),X24834),X24833)))
        | ~ c_Equiv__Relations_Ocongruent(X24835,tc_fun(X24832,tc_HOL_Obool),X24833,X24831)
        | ~ c_Equiv__Relations_Oequiv(X24835,X24834,X24833) ) ),
    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_6116,plain,
    ! [X32745,X32746,X32747,X32748,X32749,X32750,X32751] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32751),esk495_7(X32745,X32746,X32747,X32748,X32749,X32750,X32751)),X32750))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32751,tc_fun(X32746,tc_fun(X32745,tc_HOL_Obool))),X32750),X32749),X32748),X32747)) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X32749,esk495_7(X32745,X32746,X32747,X32748,X32749,X32750,X32751)),X32748),X32747))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32751,tc_fun(X32746,tc_fun(X32745,tc_HOL_Obool))),X32750),X32749),X32748),X32747)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__I])])])]) ).

fof(i_0_6117,plain,
    ! [X26635,X26636,X26637,X26638,X26639,X26640,X26641,X26642,X26643,X26644,X26645,X26646,X26647,X26648,X26649] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26641,tc_fun(X26640,tc_fun(X26639,tc_HOL_Obool))),X26638),X26637),X26636),X26635))
        | ~ hBOOL(hAPP(hAPP(c_member(X26641),X26642),X26638))
        | hBOOL(hAPP(hAPP(hAPP(X26637,X26642),X26636),X26635)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26649),esk237_7(X26643,X26644,X26645,X26646,X26647,X26648,X26649)),X26646))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26649,tc_fun(X26648,tc_fun(X26647,tc_HOL_Obool))),X26646),X26645),X26644),X26643)) )
      & ( ~ hBOOL(hAPP(hAPP(hAPP(X26645,esk237_7(X26643,X26644,X26645,X26646,X26647,X26648,X26649)),X26644),X26643))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26649,tc_fun(X26648,tc_fun(X26647,tc_HOL_Obool))),X26646),X26645),X26644),X26643)) ) ),
    inference(distribute,[status(thm)],[inference(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_6118,plain,
    ! [X27719,X27720,X27721] :
      ( ~ class_Orderings_Olinorder(X27721)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27721),X27720))
      | X27720 = c_Orderings_Obot__class_Obot(tc_fun(X27721,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X27721),X27719),c_Big__Operators_Olattice_OInf__fin(X27721,c_Orderings_Oord__class_Omin(X27721),X27720)) = c_Big__Operators_Olattice_OInf__fin(X27721,c_Orderings_Oord__class_Omin(X27721),hAPP(c_Set_OCollect(X27721),hAPP(hAPP(c_COMBB(tc_fun(X27721,tc_HOL_Obool),tc_HOL_Obool,X27721),c_HOL_OEx(X27721)),hAPP(hAPP(c_COMBC(X27721,tc_fun(X27721,tc_HOL_Obool),tc_fun(X27721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27721,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27721,tc_HOL_Obool),tc_fun(X27721,tc_HOL_Obool)),X27721),c_COMBS(X27721,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27721,tc_HOL_Obool),tc_fun(X27721,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27721),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27721),c_fconj)),hAPP(hAPP(c_COMBC(X27721,tc_fun(X27721,X27721),tc_fun(X27721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27721,tc_HOL_Obool),tc_fun(tc_fun(X27721,X27721),tc_fun(X27721,tc_HOL_Obool)),X27721),c_COMBB(X27721,tc_HOL_Obool,X27721)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(X27721),X27719))))),hAPP(hAPP(c_COMBC(X27721,tc_fun(X27721,tc_HOL_Obool),tc_HOL_Obool),c_member(X27721)),X27720))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf1__distrib])]) ).

fof(i_0_6119,plain,
    ! [X27766,X27767,X27768] :
      ( ~ class_Orderings_Olinorder(X27768)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27768),X27767))
      | X27767 = c_Orderings_Obot__class_Obot(tc_fun(X27768,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X27768),X27766),c_Big__Operators_Olattice_OSup__fin(X27768,c_Orderings_Oord__class_Omax(X27768),X27767)) = c_Big__Operators_Olattice_OSup__fin(X27768,c_Orderings_Oord__class_Omax(X27768),hAPP(c_Set_OCollect(X27768),hAPP(hAPP(c_COMBB(tc_fun(X27768,tc_HOL_Obool),tc_HOL_Obool,X27768),c_HOL_OEx(X27768)),hAPP(hAPP(c_COMBC(X27768,tc_fun(X27768,tc_HOL_Obool),tc_fun(X27768,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27768,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27768,tc_HOL_Obool),tc_fun(X27768,tc_HOL_Obool)),X27768),c_COMBS(X27768,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27768,tc_HOL_Obool),tc_fun(X27768,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27768),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27768),c_fconj)),hAPP(hAPP(c_COMBC(X27768,tc_fun(X27768,X27768),tc_fun(X27768,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27768,tc_HOL_Obool),tc_fun(tc_fun(X27768,X27768),tc_fun(X27768,tc_HOL_Obool)),X27768),c_COMBB(X27768,tc_HOL_Obool,X27768)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(X27768),X27766))))),hAPP(hAPP(c_COMBC(X27768,tc_fun(X27768,tc_HOL_Obool),tc_HOL_Obool),c_member(X27768)),X27767))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup1__distrib])]) ).

fof(i_0_6120,plain,
    ! [X27760,X27761,X27762] :
      ( ~ class_Lattices_Odistrib__lattice(X27762)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27762),X27761))
      | X27761 = c_Orderings_Obot__class_Obot(tc_fun(X27762,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27762),X27760),c_Big__Operators_Olattice__class_OSup__fin(X27762,X27761)) = c_Big__Operators_Olattice__class_OSup__fin(X27762,hAPP(c_Set_OCollect(X27762),hAPP(hAPP(c_COMBB(tc_fun(X27762,tc_HOL_Obool),tc_HOL_Obool,X27762),c_HOL_OEx(X27762)),hAPP(hAPP(c_COMBC(X27762,tc_fun(X27762,tc_HOL_Obool),tc_fun(X27762,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27762,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27762,tc_HOL_Obool),tc_fun(X27762,tc_HOL_Obool)),X27762),c_COMBS(X27762,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27762,tc_HOL_Obool),tc_fun(X27762,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27762),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27762),c_fconj)),hAPP(hAPP(c_COMBC(X27762,tc_fun(X27762,X27762),tc_fun(X27762,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27762,tc_HOL_Obool),tc_fun(tc_fun(X27762,X27762),tc_fun(X27762,tc_HOL_Obool)),X27762),c_COMBB(X27762,tc_HOL_Obool,X27762)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X27762),X27760))))),hAPP(hAPP(c_COMBC(X27762,tc_fun(X27762,tc_HOL_Obool),tc_HOL_Obool),c_member(X27762)),X27761))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup1__distrib])]) ).

fof(i_0_6121,plain,
    ! [X27754,X27755,X27756] :
      ( ~ class_Lattices_Odistrib__lattice(X27756)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27756),X27755))
      | X27755 = c_Orderings_Obot__class_Obot(tc_fun(X27756,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27756),X27754),c_Big__Operators_Olattice__class_OInf__fin(X27756,X27755)) = c_Big__Operators_Olattice__class_OInf__fin(X27756,hAPP(c_Set_OCollect(X27756),hAPP(hAPP(c_COMBB(tc_fun(X27756,tc_HOL_Obool),tc_HOL_Obool,X27756),c_HOL_OEx(X27756)),hAPP(hAPP(c_COMBC(X27756,tc_fun(X27756,tc_HOL_Obool),tc_fun(X27756,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27756,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27756,tc_HOL_Obool),tc_fun(X27756,tc_HOL_Obool)),X27756),c_COMBS(X27756,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27756,tc_HOL_Obool),tc_fun(X27756,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27756),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27756),c_fconj)),hAPP(hAPP(c_COMBC(X27756,tc_fun(X27756,X27756),tc_fun(X27756,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27756,tc_HOL_Obool),tc_fun(tc_fun(X27756,X27756),tc_fun(X27756,tc_HOL_Obool)),X27756),c_COMBB(X27756,tc_HOL_Obool,X27756)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27756),X27754))))),hAPP(hAPP(c_COMBC(X27756,tc_fun(X27756,tc_HOL_Obool),tc_HOL_Obool),c_member(X27756)),X27755))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf1__distrib])]) ).

fof(i_0_6122,plain,
    ! [X27748,X27749,X27750] :
      ( ~ class_Groups_Olinordered__ab__semigroup__add(X27750)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27750),X27749))
      | X27749 = c_Orderings_Obot__class_Obot(tc_fun(X27750,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27750),X27748),c_Big__Operators_Olinorder__class_OMax(X27750,X27749)) = c_Big__Operators_Olinorder__class_OMax(X27750,hAPP(c_Set_OCollect(X27750),hAPP(hAPP(c_COMBB(tc_fun(X27750,tc_HOL_Obool),tc_HOL_Obool,X27750),c_HOL_OEx(X27750)),hAPP(hAPP(c_COMBC(X27750,tc_fun(X27750,tc_HOL_Obool),tc_fun(X27750,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27750,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27750,tc_HOL_Obool),tc_fun(X27750,tc_HOL_Obool)),X27750),c_COMBS(X27750,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27750,tc_HOL_Obool),tc_fun(X27750,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27750),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27750),c_fconj)),hAPP(hAPP(c_COMBC(X27750,tc_fun(X27750,X27750),tc_fun(X27750,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27750,tc_HOL_Obool),tc_fun(tc_fun(X27750,X27750),tc_fun(X27750,tc_HOL_Obool)),X27750),c_COMBB(X27750,tc_HOL_Obool,X27750)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X27750),X27748))))),hAPP(hAPP(c_COMBC(X27750,tc_fun(X27750,tc_HOL_Obool),tc_HOL_Obool),c_member(X27750)),X27749))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Max__commute])]) ).

fof(i_0_6123,plain,
    ! [X27751,X27752,X27753] :
      ( ~ class_Groups_Olinordered__ab__semigroup__add(X27753)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27753),X27752))
      | X27752 = c_Orderings_Obot__class_Obot(tc_fun(X27753,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27753),X27751),c_Big__Operators_Olinorder__class_OMin(X27753,X27752)) = c_Big__Operators_Olinorder__class_OMin(X27753,hAPP(c_Set_OCollect(X27753),hAPP(hAPP(c_COMBB(tc_fun(X27753,tc_HOL_Obool),tc_HOL_Obool,X27753),c_HOL_OEx(X27753)),hAPP(hAPP(c_COMBC(X27753,tc_fun(X27753,tc_HOL_Obool),tc_fun(X27753,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27753,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(X27753,tc_HOL_Obool),tc_fun(X27753,tc_HOL_Obool)),X27753),c_COMBS(X27753,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27753,tc_HOL_Obool),tc_fun(X27753,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X27753),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27753),c_fconj)),hAPP(hAPP(c_COMBC(X27753,tc_fun(X27753,X27753),tc_fun(X27753,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27753,tc_HOL_Obool),tc_fun(tc_fun(X27753,X27753),tc_fun(X27753,tc_HOL_Obool)),X27753),c_COMBB(X27753,tc_HOL_Obool,X27753)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(X27753),X27751))))),hAPP(hAPP(c_COMBC(X27753,tc_fun(X27753,tc_HOL_Obool),tc_HOL_Obool),c_member(X27753)),X27752))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__Min__commute])]) ).

fof(i_0_6124,plain,
    ! [X29564,X29565,X29566,X29567,X29568,X29569,X29570,X29571,X29572] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29567)),X29566) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29567)),X29565)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29567),tc_List_Olist(X29567))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29567),tc_List_Olist(X29567)),X29566),X29565)),c_List_Olistrel(X29567,X29564))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29567,X29567)),X29568),hAPP(c_List_Oset(tc_prod(X29567,X29567)),hAPP(hAPP(c_List_Ozip(X29567,X29567),X29566),X29565))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29567,X29567,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29567,tc_fun(tc_prod(X29567,X29567),tc_HOL_Obool),tc_fun(X29567,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29567,tc_fun(tc_fun(tc_prod(X29567,X29567),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29567,X29567),tc_HOL_Obool),tc_fun(X29567,tc_HOL_Obool)),X29567),c_COMBC(X29567,tc_fun(tc_prod(X29567,X29567),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29567,tc_prod(X29567,X29567)),tc_fun(X29567,tc_fun(tc_fun(tc_prod(X29567,X29567),tc_HOL_Obool),tc_HOL_Obool)),X29567),hAPP(c_COMBB(tc_prod(X29567,X29567),tc_fun(tc_fun(tc_prod(X29567,X29567),tc_HOL_Obool),tc_HOL_Obool),X29567),c_member(tc_prod(X29567,X29567)))),c_Product__Type_OPair(X29567,X29567)))),X29564)),X29568))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29567),tc_List_Olist(X29567))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29567),tc_List_Olist(X29567)),X29566),X29565)),c_List_Olistrel(X29567,X29564))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29572,X29572)),esk388_4(X29569,X29570,X29571,X29572)),hAPP(c_List_Oset(tc_prod(X29572,X29572)),hAPP(hAPP(c_List_Ozip(X29572,X29572),X29571),X29570))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29572)),X29571) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29572)),X29570)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29572),tc_List_Olist(X29572))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29572),tc_List_Olist(X29572)),X29571),X29570)),c_List_Olistrel(X29572,X29569))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29572,X29572,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X29572,tc_fun(tc_prod(X29572,X29572),tc_HOL_Obool),tc_fun(X29572,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29572,tc_fun(tc_fun(tc_prod(X29572,X29572),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29572,X29572),tc_HOL_Obool),tc_fun(X29572,tc_HOL_Obool)),X29572),c_COMBC(X29572,tc_fun(tc_prod(X29572,X29572),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29572,tc_prod(X29572,X29572)),tc_fun(X29572,tc_fun(tc_fun(tc_prod(X29572,X29572),tc_HOL_Obool),tc_HOL_Obool)),X29572),hAPP(c_COMBB(tc_prod(X29572,X29572),tc_fun(tc_fun(tc_prod(X29572,X29572),tc_HOL_Obool),tc_HOL_Obool),X29572),c_member(tc_prod(X29572,X29572)))),c_Product__Type_OPair(X29572,X29572)))),X29569)),esk388_4(X29569,X29570,X29571,X29572)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29572)),X29571) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29572)),X29570)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29572),tc_List_Olist(X29572))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29572),tc_List_Olist(X29572)),X29571),X29570)),c_List_Olistrel(X29572,X29569))) ) ),
    inference(distribute,[status(thm)],[inference(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_6125,plain,
    ! [X28201,X28202,X28203,X28204] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X28204,X28203,hAPP(hAPP(c_COMBC(X28204,tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_fun(X28203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28203,tc_fun(tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_fun(X28203,tc_HOL_Obool)),X28204),c_COMBC(X28203,tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28203,tc_prod(X28204,X28203)),tc_fun(X28203,tc_fun(tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_HOL_Obool)),X28204),hAPP(c_COMBB(tc_prod(X28204,X28203),tc_fun(tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_HOL_Obool),X28203),c_member(tc_prod(X28204,X28203)))),c_Product__Type_OPair(X28204,X28203)))),X28202)),X28201))
        | hBOOL(hAPP(hAPP(c_member(X28204),X28201),hAPP(c_Relation_ODomain(X28204,X28203),X28202))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28204),X28201),hAPP(c_Relation_ODomain(X28204,X28203),X28202)))
        | hBOOL(hAPP(c_Predicate_ODomainP(X28204,X28203,hAPP(hAPP(c_COMBC(X28204,tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_fun(X28203,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28203,tc_fun(tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_fun(X28203,tc_HOL_Obool)),X28204),c_COMBC(X28203,tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28203,tc_prod(X28204,X28203)),tc_fun(X28203,tc_fun(tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_HOL_Obool)),X28204),hAPP(c_COMBB(tc_prod(X28204,X28203),tc_fun(tc_fun(tc_prod(X28204,X28203),tc_HOL_Obool),tc_HOL_Obool),X28203),c_member(tc_prod(X28204,X28203)))),c_Product__Type_OPair(X28204,X28203)))),X28202)),X28201)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP__Domain__eq])]) ).

fof(i_0_6126,plain,
    ! [X27993,X27994,X27995,X27996] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X27996,X27995,hAPP(hAPP(c_COMBC(X27996,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(X27995,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27995,tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(X27995,tc_HOL_Obool)),X27996),c_COMBC(X27995,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27995,tc_prod(X27996,X27995)),tc_fun(X27995,tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_HOL_Obool)),X27996),hAPP(c_COMBB(tc_prod(X27996,X27995),tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_HOL_Obool),X27995),c_member(tc_prod(X27996,X27995)))),c_Product__Type_OPair(X27996,X27995)))),X27994)),X27993))
        | hBOOL(hAPP(hAPP(c_member(X27995),X27993),hAPP(c_Relation_ORange(X27996,X27995),X27994))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27995),X27993),hAPP(c_Relation_ORange(X27996,X27995),X27994)))
        | hBOOL(hAPP(c_Predicate_ORangeP(X27996,X27995,hAPP(hAPP(c_COMBC(X27996,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(X27995,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27995,tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_fun(X27995,tc_HOL_Obool)),X27996),c_COMBC(X27995,tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27995,tc_prod(X27996,X27995)),tc_fun(X27995,tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_HOL_Obool)),X27996),hAPP(c_COMBB(tc_prod(X27996,X27995),tc_fun(tc_fun(tc_prod(X27996,X27995),tc_HOL_Obool),tc_HOL_Obool),X27995),c_member(tc_prod(X27996,X27995)))),c_Product__Type_OPair(X27996,X27995)))),X27994)),X27993)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP__Range__eq])]) ).

fof(i_0_6127,plain,
    ! [X26098,X26099,X26100] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X26100,hAPP(hAPP(c_COMBC(X26100,tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_fun(X26100,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26100,tc_fun(tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_fun(X26100,tc_HOL_Obool)),X26100),c_COMBC(X26100,tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26100,tc_prod(X26100,X26100)),tc_fun(X26100,tc_fun(tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_HOL_Obool)),X26100),hAPP(c_COMBB(tc_prod(X26100,X26100),tc_fun(tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_HOL_Obool),X26100),c_member(tc_prod(X26100,X26100)))),c_Product__Type_OPair(X26100,X26100)))),X26099)),X26098))
        | hBOOL(hAPP(hAPP(c_member(X26100),X26098),c_Wellfounded_Oacc(X26100,X26099))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26100),X26098),c_Wellfounded_Oacc(X26100,X26099)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X26100,hAPP(hAPP(c_COMBC(X26100,tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_fun(X26100,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26100,tc_fun(tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_fun(X26100,tc_HOL_Obool)),X26100),c_COMBC(X26100,tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26100,tc_prod(X26100,X26100)),tc_fun(X26100,tc_fun(tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_HOL_Obool)),X26100),hAPP(c_COMBB(tc_prod(X26100,X26100),tc_fun(tc_fun(tc_prod(X26100,X26100),tc_HOL_Obool),tc_HOL_Obool),X26100),c_member(tc_prod(X26100,X26100)))),c_Product__Type_OPair(X26100,X26100)))),X26099)),X26098)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__acc__eq])]) ).

fof(i_0_6128,plain,
    ! [X32675,X32676,X32677] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X32677,X32676),X32675) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X32677,tc_Lazy__Sequence_Olazy__sequence(X32677)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X32677,tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X32677,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat)),X32677),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X32677),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X32677)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X32677,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32677),tc_Nat_Onat)),X32677),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X32677))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X32677),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X32676))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X32677,X32676))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X32677),X32675)),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence__size__code]) ).

fof(i_0_6129,plain,
    ! [X18160,X18161,X18162,X18163,X18164,X18165,X18166,X18169,X18170,X18171,X18172,X18173,X18174,X18175,X18176,X18177] :
      ( ( hAPP(hAPP(X18164,X18161),X18160) = hAPP(hAPP(X18164,esk20_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166)),esk21_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166))
        | X18162 = c_Orderings_Obot__class_Obot(tc_fun(X18166,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X18166,X18165,X18164,X18163,X18162,hAPP(hAPP(X18164,X18161),X18160)) )
      & ( hBOOL(hAPP(hAPP(c_member(X18166),esk20_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166)),X18162))
        | X18162 = c_Orderings_Obot__class_Obot(tc_fun(X18166,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X18166,X18165,X18164,X18163,X18162,hAPP(hAPP(X18164,X18161),X18160)) )
      & ( c_Nitpick_Ofold__graph_H(X18166,X18165,X18164,X18163,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18166,tc_HOL_Obool)),X18162),hAPP(hAPP(c_Set_Oinsert(X18166),esk20_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166)),c_Orderings_Obot__class_Obot(tc_fun(X18166,tc_HOL_Obool)))),esk21_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166))
        | X18162 = c_Orderings_Obot__class_Obot(tc_fun(X18166,tc_HOL_Obool))
        | ~ c_Nitpick_Ofold__graph_H(X18166,X18165,X18164,X18163,X18162,hAPP(hAPP(X18164,X18161),X18160)) )
      & ( hAPP(hAPP(X18164,X18161),X18160) = hAPP(hAPP(X18164,esk20_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166)),esk21_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166))
        | hAPP(hAPP(X18164,X18161),X18160) = X18163
        | ~ c_Nitpick_Ofold__graph_H(X18166,X18165,X18164,X18163,X18162,hAPP(hAPP(X18164,X18161),X18160)) )
      & ( hBOOL(hAPP(hAPP(c_member(X18166),esk20_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166)),X18162))
        | hAPP(hAPP(X18164,X18161),X18160) = X18163
        | ~ c_Nitpick_Ofold__graph_H(X18166,X18165,X18164,X18163,X18162,hAPP(hAPP(X18164,X18161),X18160)) )
      & ( c_Nitpick_Ofold__graph_H(X18166,X18165,X18164,X18163,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18166,tc_HOL_Obool)),X18162),hAPP(hAPP(c_Set_Oinsert(X18166),esk20_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166)),c_Orderings_Obot__class_Obot(tc_fun(X18166,tc_HOL_Obool)))),esk21_7(X18160,X18161,X18162,X18163,X18164,X18165,X18166))
        | hAPP(hAPP(X18164,X18161),X18160) = X18163
        | ~ c_Nitpick_Ofold__graph_H(X18166,X18165,X18164,X18163,X18162,hAPP(hAPP(X18164,X18161),X18160)) )
      & ( X18171 != c_Orderings_Obot__class_Obot(tc_fun(X18175,tc_HOL_Obool))
        | hAPP(hAPP(X18173,X18170),X18169) != X18172
        | c_Nitpick_Ofold__graph_H(X18175,X18174,X18173,X18172,X18171,hAPP(hAPP(X18173,X18170),X18169)) )
      & ( hAPP(hAPP(X18173,X18170),X18169) != hAPP(hAPP(X18173,X18176),X18177)
        | ~ hBOOL(hAPP(hAPP(c_member(X18175),X18176),X18171))
        | ~ c_Nitpick_Ofold__graph_H(X18175,X18174,X18173,X18172,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18175,tc_HOL_Obool)),X18171),hAPP(hAPP(c_Set_Oinsert(X18175),X18176),c_Orderings_Obot__class_Obot(tc_fun(X18175,tc_HOL_Obool)))),X18177)
        | c_Nitpick_Ofold__graph_H(X18175,X18174,X18173,X18172,X18171,hAPP(hAPP(X18173,X18170),X18169)) ) ),
    inference(distribute,[status(thm)],[inference(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_6130,plain,
    ! [X32737,X32738,X32739,X32740,X32741,X32742,X32743] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32743),esk494_7(X32737,X32738,X32739,X32740,X32741,X32742,X32743)),X32740))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32743,tc_fun(X32742,tc_fun(X32741,tc_HOL_Obool))),X32740),X32739),X32738),X32737)) )
      & ( hBOOL(hAPP(hAPP(hAPP(X32739,esk494_7(X32737,X32738,X32739,X32740,X32741,X32742,X32743)),X32738),X32737))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32743,tc_fun(X32742,tc_fun(X32741,tc_HOL_Obool))),X32740),X32739),X32738),X32737)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5238])])])]) ).

fof(i_0_6131,plain,
    ! [X23722,X23723,X23724,X23725,X23726,X23727,X23728,X23730,X23731,X23732,X23733,X23734,X23735,X23736,X23737] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23728),esk129_7(X23722,X23723,X23724,X23725,X23726,X23727,X23728)),X23725))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23728,tc_fun(X23727,tc_fun(X23726,tc_HOL_Obool))),X23725),X23724),X23723),X23722)) )
      & ( hBOOL(hAPP(hAPP(hAPP(X23724,esk129_7(X23722,X23723,X23724,X23725,X23726,X23727,X23728)),X23723),X23722))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23728,tc_fun(X23727,tc_fun(X23726,tc_HOL_Obool))),X23725),X23724),X23723),X23722)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23736),X23737),X23733))
        | ~ hBOOL(hAPP(hAPP(hAPP(X23732,X23737),X23731),X23730))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23736,tc_fun(X23735,tc_fun(X23734,tc_HOL_Obool))),X23733),X23732),X23731),X23730)) ) ),
    inference(distribute,[status(thm)],[inference(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_6132,plain,
    ! [X31064,X31065,X31066,X31067] : c_List_Opartition(X31067,X31066,hAPP(hAPP(c_List_Olist_OCons(X31067),X31065),X31064)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X31067),tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067))),hAPP(hAPP(c_COMBS(tc_List_Olist(X31067),tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067))),tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X31067),tc_fun(tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)))),tc_fun(tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067))),tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)))),tc_List_Olist(X31067)),c_COMBS(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067))),tc_fun(tc_List_Olist(X31067),tc_fun(tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)))),tc_List_Olist(X31067)),hAPP(c_COMBB(tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)),tc_fun(tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067))),tc_List_Olist(X31067)),hAPP(c_If(tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067))),hAPP(X31066,X31065)))),hAPP(hAPP(c_COMBB(tc_List_Olist(X31067),tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067))),tc_List_Olist(X31067)),c_Product__Type_OPair(tc_List_Olist(X31067),tc_List_Olist(X31067))),hAPP(c_List_Olist_OCons(X31067),X31065))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31067),tc_fun(tc_List_Olist(X31067),tc_List_Olist(X31067)),tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067))),tc_fun(tc_fun(tc_List_Olist(X31067),tc_List_Olist(X31067)),tc_fun(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)))),tc_List_Olist(X31067)),c_COMBB(tc_List_Olist(X31067),tc_prod(tc_List_Olist(X31067),tc_List_Olist(X31067)),tc_List_Olist(X31067))),c_Product__Type_OPair(tc_List_Olist(X31067),tc_List_Olist(X31067)))),hAPP(c_List_Olist_OCons(X31067),X31065)))),c_List_Opartition(X31067,X31066,X31064)),
    inference(variable_rename,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(i_0_6133,plain,
    ! [X29200,X29201,X29202] : hAPP(c_List_Olexn(X29202,X29201),hAPP(c_Nat_OSuc,X29200)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(X29202),tc_List_Olist(X29202)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(X29202,tc_List_Olist(X29202)),tc_prod(X29202,tc_List_Olist(X29202))),tc_prod(tc_List_Olist(X29202),tc_List_Olist(X29202)),c_Product__Type_Omap__pair(tc_prod(X29202,tc_List_Olist(X29202)),tc_List_Olist(X29202),tc_prod(X29202,tc_List_Olist(X29202)),tc_List_Olist(X29202),hAPP(c_Product__Type_Oprod_Oprod__case(X29202,tc_List_Olist(X29202),tc_List_Olist(X29202)),c_List_Olist_OCons(X29202)),hAPP(c_Product__Type_Oprod_Oprod__case(X29202,tc_List_Olist(X29202),tc_List_Olist(X29202)),c_List_Olist_OCons(X29202)))),c_Wellfounded_Olex__prod(X29202,tc_List_Olist(X29202),X29201,hAPP(c_List_Olexn(X29202,X29201),X29200)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(X29202),tc_List_Olist(X29202))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X29202),tc_List_Olist(X29202),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(X29202),tc_fun(tc_List_Olist(X29202),tc_HOL_Obool),tc_fun(tc_List_Olist(X29202),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(X29202),tc_HOL_Obool),tc_fun(tc_List_Olist(X29202),tc_HOL_Obool)),tc_List_Olist(X29202)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X29202))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29202)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X29202),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29202)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X29202)))),hAPP(c_Nat_OSuc,X29200))))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29202),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29202)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X29202)))),hAPP(c_Nat_OSuc,X29200)))))),
    inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I2_J]) ).

cnf(i_0_6134,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_5239]) ).

cnf(i_0_6135,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_5239]) ).

cnf(i_0_6136,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_5240]) ).

fof(i_0_6137,plain,
    ! [X29452,X29453,X29454] : hAPP(c_List_Oset(X29454),c_List_Osublist(X29454,X29453,X29452)) = hAPP(c_Set_OCollect(X29454),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X29454),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X29454,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)),X29454),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)),X29454),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X29454,tc_fun(tc_Nat_Onat,X29454),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29454,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X29454),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X29454),c_COMBB(X29454,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X29454),X29453))))),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(X29454)),X29453)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X29452))))),
    inference(variable_rename,[status(thm)],[fact_set__sublist]) ).

cnf(i_0_6138,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_5241]) ).

cnf(i_0_6139,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_5242]) ).

cnf(i_0_6140,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_5243]) ).

fof(i_0_6141,plain,
    ! [X27787,X27788,X27789,X27790,X27791,X27792] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27790),esk282_6(X27787,X27788,X27789,X27790,X27791,X27792)),X27789))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27792,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27790,tc_HOL_Obool),tc_Nat_Onat,X27792),c_Finite__Set_Ocard(X27790)),hAPP(hAPP(c_COMBB(tc_fun(X27790,tc_HOL_Obool),tc_fun(X27790,tc_HOL_Obool),X27792),c_Set_OCollect(X27790)),hAPP(hAPP(c_COMBB(tc_fun(X27790,tc_HOL_Obool),tc_fun(X27790,tc_HOL_Obool),X27792),hAPP(c_COMBS(X27790,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27790),c_fconj),hAPP(hAPP(c_COMBC(X27790,tc_fun(X27790,tc_HOL_Obool),tc_HOL_Obool),c_member(X27790)),X27789)))),X27788)))),X27791) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27790,tc_Nat_Onat),X27787),X27789)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27790),X27789))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27792),X27791)) )
      & ( hAPP(c_Finite__Set_Ocard(X27792),hAPP(c_Set_OCollect(X27792),hAPP(hAPP(c_COMBS(X27792,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27792),c_fconj),hAPP(hAPP(c_COMBC(X27792,tc_fun(X27792,tc_HOL_Obool),tc_HOL_Obool),c_member(X27792)),X27791))),hAPP(hAPP(c_COMBC(X27792,X27790,tc_HOL_Obool),X27788),esk282_6(X27787,X27788,X27789,X27790,X27791,X27792))))) != hAPP(X27787,esk282_6(X27787,X27788,X27789,X27790,X27791,X27792))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27792,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27790,tc_HOL_Obool),tc_Nat_Onat,X27792),c_Finite__Set_Ocard(X27790)),hAPP(hAPP(c_COMBB(tc_fun(X27790,tc_HOL_Obool),tc_fun(X27790,tc_HOL_Obool),X27792),c_Set_OCollect(X27790)),hAPP(hAPP(c_COMBB(tc_fun(X27790,tc_HOL_Obool),tc_fun(X27790,tc_HOL_Obool),X27792),hAPP(c_COMBS(X27790,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27790),c_fconj),hAPP(hAPP(c_COMBC(X27790,tc_fun(X27790,tc_HOL_Obool),tc_HOL_Obool),c_member(X27790)),X27789)))),X27788)))),X27791) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27790,tc_Nat_Onat),X27787),X27789)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27790),X27789))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27792),X27791)) ) ),
    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_6142,plain,
    ! [X29556,X29557] : hAPP(c_List_Oset(X29557),X29556) = hAPP(c_Set_OCollect(X29557),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,X29557),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(X29557,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)),X29557),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)),X29557),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(X29557,tc_fun(tc_Nat_Onat,X29557),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29557,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,X29557),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X29557),c_COMBB(X29557,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(X29557),X29556))))),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(X29557)),X29556))))),
    inference(variable_rename,[status(thm)],[fact_set__conv__nth]) ).

fof(i_0_6143,plain,
    ! [X27318,X27319,X27320,X27321] : hAPP(hAPP(c_Product__Type_OSigma(X27321,X27320),X27319),X27318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27321,tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool)),X27319),hAPP(hAPP(c_COMBS(X27321,tc_fun(X27320,tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool)),tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27320,tc_HOL_Obool),tc_fun(tc_fun(X27320,tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool)),tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool)),X27321),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27320,tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool))),X27318)),hAPP(hAPP(c_COMBC(X27321,tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool),tc_fun(X27320,tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27320,tc_fun(tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool),tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool),tc_fun(X27320,tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool))),X27321),c_COMBC(X27320,tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool),tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27320,tc_prod(X27321,X27320)),tc_fun(X27320,tc_fun(tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool),tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool))),X27321),hAPP(c_COMBB(tc_prod(X27321,X27320),tc_fun(tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool),tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool)),X27320),c_Set_Oinsert(tc_prod(X27321,X27320)))),c_Product__Type_OPair(X27321,X27320)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27321,X27320),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Sigma__def]) ).

cnf(i_0_6144,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_5244]) ).

fof(i_0_6145,plain,
    ! [X27709,X27710,X27711,X27712,X27713,X27714] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27712),esk280_6(X27709,X27710,X27711,X27712,X27713,X27714)),X27711))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27714,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27712,tc_HOL_Obool),tc_Nat_Onat,X27714),c_Finite__Set_Ocard(X27712)),hAPP(hAPP(c_COMBB(tc_fun(X27712,tc_HOL_Obool),tc_fun(X27712,tc_HOL_Obool),X27714),c_Set_OCollect(X27712)),hAPP(hAPP(c_COMBB(tc_fun(X27712,tc_HOL_Obool),tc_fun(X27712,tc_HOL_Obool),X27714),hAPP(c_COMBS(X27712,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27712),c_fconj),hAPP(hAPP(c_COMBC(X27712,tc_fun(X27712,tc_HOL_Obool),tc_HOL_Obool),c_member(X27712)),X27711)))),X27710)))),X27713) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27709),hAPP(c_Finite__Set_Ocard(X27712),X27711))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27712),X27711))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27714),X27713)) )
      & ( hAPP(c_Finite__Set_Ocard(X27714),hAPP(c_Set_OCollect(X27714),hAPP(hAPP(c_COMBS(X27714,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27714),c_fconj),hAPP(hAPP(c_COMBC(X27714,tc_fun(X27714,tc_HOL_Obool),tc_HOL_Obool),c_member(X27714)),X27713))),hAPP(hAPP(c_COMBC(X27714,X27712,tc_HOL_Obool),X27710),esk280_6(X27709,X27710,X27711,X27712,X27713,X27714))))) != X27709
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27714,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27712,tc_HOL_Obool),tc_Nat_Onat,X27714),c_Finite__Set_Ocard(X27712)),hAPP(hAPP(c_COMBB(tc_fun(X27712,tc_HOL_Obool),tc_fun(X27712,tc_HOL_Obool),X27714),c_Set_OCollect(X27712)),hAPP(hAPP(c_COMBB(tc_fun(X27712,tc_HOL_Obool),tc_fun(X27712,tc_HOL_Obool),X27714),hAPP(c_COMBS(X27712,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27712),c_fconj),hAPP(hAPP(c_COMBC(X27712,tc_fun(X27712,tc_HOL_Obool),tc_HOL_Obool),c_member(X27712)),X27711)))),X27710)))),X27713) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27709),hAPP(c_Finite__Set_Ocard(X27712),X27711))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27712),X27711))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27714),X27713)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__multicount])])])]) ).

fof(i_0_6146,plain,
    ! [X27669,X27670,X27671,X27672,X27673,X27674,X27675] :
      ( ~ class_Groups_Ocomm__monoid__add(X27675)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27674),X27673))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27672),X27671))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27674,X27675),hAPP(hAPP(c_COMBS(X27674,tc_fun(X27672,tc_HOL_Obool),X27675),hAPP(hAPP(c_COMBB(tc_fun(X27672,X27675),tc_fun(tc_fun(X27672,tc_HOL_Obool),X27675),X27674),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27672,X27675)),X27670)),hAPP(hAPP(c_COMBB(tc_fun(X27672,tc_HOL_Obool),tc_fun(X27672,tc_HOL_Obool),X27674),c_Set_OCollect(X27672)),hAPP(hAPP(c_COMBB(tc_fun(X27672,tc_HOL_Obool),tc_fun(X27672,tc_HOL_Obool),X27674),hAPP(c_COMBS(X27672,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27672),c_fconj),hAPP(hAPP(c_COMBC(X27672,tc_fun(X27672,tc_HOL_Obool),tc_HOL_Obool),c_member(X27672)),X27671)))),X27669)))),X27673) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27672,X27675),hAPP(hAPP(c_COMBS(X27672,tc_fun(X27674,tc_HOL_Obool),X27675),hAPP(hAPP(c_COMBB(tc_fun(X27674,X27675),tc_fun(tc_fun(X27674,tc_HOL_Obool),X27675),X27672),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27674,X27675)),hAPP(c_COMBC(X27674,X27672,X27675),X27670))),hAPP(hAPP(c_COMBB(tc_fun(X27674,tc_HOL_Obool),tc_fun(X27674,tc_HOL_Obool),X27672),c_Set_OCollect(X27674)),hAPP(hAPP(c_COMBB(tc_fun(X27674,tc_HOL_Obool),tc_fun(X27674,tc_HOL_Obool),X27672),hAPP(c_COMBS(X27674,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27674),c_fconj),hAPP(hAPP(c_COMBC(X27674,tc_fun(X27674,tc_HOL_Obool),tc_HOL_Obool),c_member(X27674)),X27673)))),hAPP(c_COMBC(X27674,X27672,tc_HOL_Obool),X27669))))),X27671) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__setsum__restrict])]) ).

fof(i_0_6147,plain,
    ! [X29997,X29998,X29999,X30000,X30001] :
      ( ( X30001 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X30000,X29999,X29998),X30001),X29997) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29999),X30000),c_List_Olist_ONil(X29999)),X29997) )
      & ( X30001 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X30000,X29999,X29998),X30001),X29997) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X29999),X30000),tc_prod(X29999,X30000),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29999),X30000),c_List_Olist_ONil(X29999)),X29997),hAPP(c_Product__Type_Oprod_Oprod__case(X29999,X30000,tc_prod(tc_List_Olist(X29999),X30000)),hAPP(hAPP(c_COMBC(X29999,tc_fun(X30000,tc_prod(tc_List_Olist(X29999),X30000)),tc_fun(X30000,tc_prod(tc_List_Olist(X29999),X30000))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X29999),X30000),tc_prod(tc_List_Olist(X29999),X30000)),tc_fun(tc_fun(X30000,tc_prod(tc_List_Olist(X29999),X30000)),tc_fun(X30000,tc_prod(tc_List_Olist(X29999),X30000))),X29999),c_COMBB(tc_prod(tc_List_Olist(X29999),X30000),tc_prod(tc_List_Olist(X29999),X30000),X30000)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29999),tc_fun(X30000,tc_prod(tc_List_Olist(X29999),X30000))),tc_fun(tc_prod(tc_List_Olist(X29999),X30000),tc_prod(tc_List_Olist(X29999),X30000)),X29999),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X29999),X30000,tc_prod(tc_List_Olist(X29999),X30000))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X29999),tc_List_Olist(X29999)),tc_fun(tc_List_Olist(X29999),tc_fun(X30000,tc_prod(tc_List_Olist(X29999),X30000))),X29999),hAPP(c_COMBB(tc_List_Olist(X29999),tc_fun(X30000,tc_prod(tc_List_Olist(X29999),X30000)),tc_List_Olist(X29999)),c_Product__Type_OPair(tc_List_Olist(X29999),X30000))),c_List_Olist_OCons(X29999))))),hAPP(c_Lazy__Sequence_Oanamorph(X30000,X29999,X29998),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30001),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X29998,X29997)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_anamorph_Osimps])]) ).

fof(i_0_6148,plain,
    ! [X28881,X28882,X28883,X28884,X28885] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28885,X28885)),hAPP(hAPP(c_Product__Type_OPair(X28885,X28885),hAPP(X28884,hAPP(c_Nat_OSuc,esk334_5(X28881,X28882,X28883,X28884,X28885)))),hAPP(X28884,esk334_5(X28881,X28882,X28883,X28884,X28885)))),c_Transitive__Closure_Ortrancl(X28885,X28883)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28885,X28885)),hAPP(hAPP(c_Product__Type_OPair(X28885,X28885),hAPP(X28884,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28882),X28881))),hAPP(X28884,X28882))),c_Transitive__Closure_Ortrancl(X28885,X28883))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sequence__trans])])]) ).

fof(i_0_6149,plain,
    ! [X32994,X32995,X32996,X32997,X32998,X32999] : c_Partial__Function_Ofun__lub(X32999,X32998,X32997,X32996,X32995,X32994) = hAPP(X32996,hAPP(c_Set_OCollect(X32999),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32997,X32999),tc_HOL_Obool),tc_HOL_Obool,X32999),c_HOL_OEx(tc_fun(X32997,X32999))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32997,X32999),tc_HOL_Obool),tc_fun(tc_fun(X32997,X32999),tc_HOL_Obool),X32999),hAPP(c_COMBS(tc_fun(X32997,X32999),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X32997,X32999)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X32997,X32999),tc_fun(tc_fun(X32997,X32999),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X32997,X32999))),X32995)))),hAPP(hAPP(c_COMBC(X32999,tc_fun(tc_fun(X32997,X32999),X32999),tc_fun(tc_fun(X32997,X32999),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32999,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X32997,X32999),X32999),tc_fun(tc_fun(X32997,X32999),tc_HOL_Obool)),X32999),c_COMBB(X32999,tc_HOL_Obool,tc_fun(X32997,X32999))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X32997,X32999),X32997,X32999),c_COMBI(tc_fun(X32997,X32999))),X32994)))))),
    inference(variable_rename,[status(thm)],[fact_fun__lub__def]) ).

fof(i_0_6150,plain,
    ! [X32920,X32921,X32922,X32923] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32923)
      | hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X32922,X32923),X32921),X32920) = c_Complete__Lattice_OSup__class_OSup(X32923,hAPP(c_Set_OCollect(X32923),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32922,X32923),tc_HOL_Obool),tc_HOL_Obool,X32923),c_HOL_OEx(tc_fun(X32922,X32923))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32922,X32923),tc_HOL_Obool),tc_fun(tc_fun(X32922,X32923),tc_HOL_Obool),X32923),hAPP(c_COMBS(tc_fun(X32922,X32923),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X32922,X32923)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X32922,X32923),tc_fun(tc_fun(X32922,X32923),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X32922,X32923))),X32921)))),hAPP(hAPP(c_COMBC(X32923,tc_fun(tc_fun(X32922,X32923),X32923),tc_fun(tc_fun(X32922,X32923),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32923,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X32922,X32923),X32923),tc_fun(tc_fun(X32922,X32923),tc_HOL_Obool)),X32923),c_COMBB(X32923,tc_HOL_Obool,tc_fun(X32922,X32923))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X32922,X32923),X32922,X32923),c_COMBI(tc_fun(X32922,X32923))),X32920)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__apply])]) ).

fof(i_0_6151,plain,
    ! [X32916,X32917,X32918,X32919] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32919)
      | hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X32918,X32919),X32917),X32916) = c_Complete__Lattice_OSup__class_OSup(X32919,hAPP(c_Set_OCollect(X32919),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32918,X32919),tc_HOL_Obool),tc_HOL_Obool,X32919),c_HOL_OEx(tc_fun(X32918,X32919))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32918,X32919),tc_HOL_Obool),tc_fun(tc_fun(X32918,X32919),tc_HOL_Obool),X32919),hAPP(c_COMBS(tc_fun(X32918,X32919),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X32918,X32919)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X32918,X32919),tc_fun(tc_fun(X32918,X32919),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X32918,X32919))),X32917)))),hAPP(hAPP(c_COMBC(X32919,tc_fun(tc_fun(X32918,X32919),X32919),tc_fun(tc_fun(X32918,X32919),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32919,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X32918,X32919),X32919),tc_fun(tc_fun(X32918,X32919),tc_HOL_Obool)),X32919),c_COMBB(X32919,tc_HOL_Obool,tc_fun(X32918,X32919))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X32918,X32919),X32918,X32919),c_COMBI(tc_fun(X32918,X32919))),X32916)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fun__def])]) ).

fof(i_0_6152,plain,
    ! [X32928,X32929,X32930,X32931] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32931)
      | hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X32930,X32931),X32929),X32928) = c_Complete__Lattice_OInf__class_OInf(X32931,hAPP(c_Set_OCollect(X32931),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32930,X32931),tc_HOL_Obool),tc_HOL_Obool,X32931),c_HOL_OEx(tc_fun(X32930,X32931))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32930,X32931),tc_HOL_Obool),tc_fun(tc_fun(X32930,X32931),tc_HOL_Obool),X32931),hAPP(c_COMBS(tc_fun(X32930,X32931),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X32930,X32931)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X32930,X32931),tc_fun(tc_fun(X32930,X32931),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X32930,X32931))),X32929)))),hAPP(hAPP(c_COMBC(X32931,tc_fun(tc_fun(X32930,X32931),X32931),tc_fun(tc_fun(X32930,X32931),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32931,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X32930,X32931),X32931),tc_fun(tc_fun(X32930,X32931),tc_HOL_Obool)),X32931),c_COMBB(X32931,tc_HOL_Obool,tc_fun(X32930,X32931))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X32930,X32931),X32930,X32931),c_COMBI(tc_fun(X32930,X32931))),X32928)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__apply])]) ).

fof(i_0_6153,plain,
    ! [X32924,X32925,X32926,X32927] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X32927)
      | hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X32926,X32927),X32925),X32924) = c_Complete__Lattice_OInf__class_OInf(X32927,hAPP(c_Set_OCollect(X32927),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32926,X32927),tc_HOL_Obool),tc_HOL_Obool,X32927),c_HOL_OEx(tc_fun(X32926,X32927))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32926,X32927),tc_HOL_Obool),tc_fun(tc_fun(X32926,X32927),tc_HOL_Obool),X32927),hAPP(c_COMBS(tc_fun(X32926,X32927),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X32926,X32927)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X32926,X32927),tc_fun(tc_fun(X32926,X32927),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X32926,X32927))),X32925)))),hAPP(hAPP(c_COMBC(X32927,tc_fun(tc_fun(X32926,X32927),X32927),tc_fun(tc_fun(X32926,X32927),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32927,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X32926,X32927),X32927),tc_fun(tc_fun(X32926,X32927),tc_HOL_Obool)),X32927),c_COMBB(X32927,tc_HOL_Obool,tc_fun(X32926,X32927))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X32926,X32927),X32926,X32927),c_COMBI(tc_fun(X32926,X32927))),X32924)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fun__def])]) ).

fof(i_0_6154,plain,
    ! [X33549,X33550,X33551,X33552,X33553,X33554] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33554,X33554)),hAPP(hAPP(c_Product__Type_OPair(X33554,X33554),esk556_6(X33549,X33550,X33551,X33552,X33553,X33554)),esk557_6(X33549,X33550,X33551,X33552,X33553,X33554))),X33553))
        | c_Equiv__Relations_Ocongruent2(X33554,X33552,X33549,X33553,X33551,X33550) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33552,X33552)),hAPP(hAPP(c_Product__Type_OPair(X33552,X33552),esk558_6(X33549,X33550,X33551,X33552,X33553,X33554)),esk559_6(X33549,X33550,X33551,X33552,X33553,X33554))),X33551))
        | c_Equiv__Relations_Ocongruent2(X33554,X33552,X33549,X33553,X33551,X33550) )
      & ( hAPP(hAPP(X33550,esk556_6(X33549,X33550,X33551,X33552,X33553,X33554)),esk558_6(X33549,X33550,X33551,X33552,X33553,X33554)) != hAPP(hAPP(X33550,esk557_6(X33549,X33550,X33551,X33552,X33553,X33554)),esk559_6(X33549,X33550,X33551,X33552,X33553,X33554))
        | c_Equiv__Relations_Ocongruent2(X33554,X33552,X33549,X33553,X33551,X33550) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2I_H])])])]) ).

fof(i_0_6155,plain,
    ! [X29127,X29128,X29129,X29130,X29131,X29132] :
      ( ( X29130 = hAPP(hAPP(c_Product__Type_OPair(X29132,X29131),esk366_6(X29127,X29128,X29129,X29130,X29131,X29132)),esk368_6(X29127,X29128,X29129,X29130,X29131,X29132))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29132,X29131)),X29130),hAPP(hAPP(c_Relation_Orel__comp(X29132,X29129,X29131),X29128),X29127))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29132,X29129)),hAPP(hAPP(c_Product__Type_OPair(X29132,X29129),esk366_6(X29127,X29128,X29129,X29130,X29131,X29132)),esk367_6(X29127,X29128,X29129,X29130,X29131,X29132))),X29128))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29132,X29131)),X29130),hAPP(hAPP(c_Relation_Orel__comp(X29132,X29129,X29131),X29128),X29127))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29129,X29131)),hAPP(hAPP(c_Product__Type_OPair(X29129,X29131),esk367_6(X29127,X29128,X29129,X29130,X29131,X29132)),esk368_6(X29127,X29128,X29129,X29130,X29131,X29132))),X29127))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29132,X29131)),X29130),hAPP(hAPP(c_Relation_Orel__comp(X29132,X29129,X29131),X29128),X29127))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5245])])])]) ).

fof(i_0_6156,plain,
    ! [X21742,X21743] : c_Divides_Odivmod__int__rel(X21743,X21742) = 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,X21743))),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),X21742)))))),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)),X21742))),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)),X21742))))),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)),X21742)))),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),X21742))),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_6157,plain,
    ! [X24442,X24443,X24444,X24445,X24446,X24447,X24448] :
      ( ~ class_Rings_Osemiring__0(X24448)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24448),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24447,X24448),X24446),X24445)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24444,X24448),X24443),X24442)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24447,X24448),hAPP(hAPP(c_COMBC(X24447,tc_fun(X24444,tc_HOL_Obool),X24448),hAPP(hAPP(c_COMBB(tc_fun(X24444,X24448),tc_fun(tc_fun(X24444,tc_HOL_Obool),X24448),X24447),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24444,X24448)),hAPP(hAPP(c_COMBC(X24447,tc_fun(X24444,X24448),tc_fun(X24444,X24448)),hAPP(hAPP(c_COMBB(tc_fun(X24448,X24448),tc_fun(tc_fun(X24444,X24448),tc_fun(X24444,X24448)),X24447),c_COMBB(X24448,X24448,X24444)),hAPP(hAPP(c_COMBB(X24448,tc_fun(X24448,X24448),X24447),c_Groups_Otimes__class_Otimes(X24448)),X24446))),X24443))),X24442)),X24445) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__product])]) ).

fof(i_0_6158,plain,
    ! [X27330,X27331,X27332,X27333,X27334,X27335] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27334),esk258_6(X27330,X27331,X27332,X27333,X27334,X27335)),X27333))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27335,X27334,c_Groups_Otimes__class_Otimes(X27335)),hAPP(hAPP(c_COMBS(X27334,tc_fun(X27332,tc_HOL_Obool),X27335),hAPP(hAPP(c_COMBC(X27334,X27335,tc_fun(tc_fun(X27332,tc_HOL_Obool),X27335)),hAPP(hAPP(c_COMBB(tc_fun(X27332,X27335),tc_fun(X27335,tc_fun(tc_fun(X27332,tc_HOL_Obool),X27335)),X27334),c_Finite__Set_Ofold__image(X27335,X27332,c_Groups_Otimes__class_Otimes(X27335))),X27330)),c_Groups_Oone__class_Oone(X27335))),X27331)),c_Groups_Oone__class_Oone(X27335)),X27333) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27335,tc_prod(X27334,X27332),c_Groups_Otimes__class_Otimes(X27335)),hAPP(c_Product__Type_Oprod_Oprod__case(X27334,X27332,X27335),X27330)),c_Groups_Oone__class_Oone(X27335)),hAPP(hAPP(c_Product__Type_OSigma(X27334,X27332),X27333),X27331))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27334),X27333))
        | ~ class_Groups_Ocomm__monoid__mult(X27335) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27332),hAPP(X27331,esk258_6(X27330,X27331,X27332,X27333,X27334,X27335))))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27335,X27334,c_Groups_Otimes__class_Otimes(X27335)),hAPP(hAPP(c_COMBS(X27334,tc_fun(X27332,tc_HOL_Obool),X27335),hAPP(hAPP(c_COMBC(X27334,X27335,tc_fun(tc_fun(X27332,tc_HOL_Obool),X27335)),hAPP(hAPP(c_COMBB(tc_fun(X27332,X27335),tc_fun(X27335,tc_fun(tc_fun(X27332,tc_HOL_Obool),X27335)),X27334),c_Finite__Set_Ofold__image(X27335,X27332,c_Groups_Otimes__class_Otimes(X27335))),X27330)),c_Groups_Oone__class_Oone(X27335))),X27331)),c_Groups_Oone__class_Oone(X27335)),X27333) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X27335,tc_prod(X27334,X27332),c_Groups_Otimes__class_Otimes(X27335)),hAPP(c_Product__Type_Oprod_Oprod__case(X27334,X27332,X27335),X27330)),c_Groups_Oone__class_Oone(X27335)),hAPP(hAPP(c_Product__Type_OSigma(X27334,X27332),X27333),X27331))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27334),X27333))
        | ~ class_Groups_Ocomm__monoid__mult(X27335) ) ),
    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_6159,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_5246]) ).

fof(i_0_6160,plain,
    ! [X29561,X29562,X29563] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29563),X29562))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X29563)),hAPP(c_Set_OCollect(tc_List_Olist(X29563)),hAPP(hAPP(c_COMBS(tc_List_Olist(X29563),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29563)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X29563),tc_fun(X29563,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29563,tc_HOL_Obool),tc_fun(tc_fun(X29563,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29563)),c_Orderings_Oord__class_Oless__eq(tc_fun(X29563,tc_HOL_Obool))),c_List_Oset(X29563))),X29562))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29563),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29563)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(X29563)))),X29561))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__le])]) ).

fof(i_0_6161,plain,
    ! [X29558,X29559,X29560] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29560),X29559))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X29560)),hAPP(c_Set_OCollect(tc_List_Olist(X29560)),hAPP(hAPP(c_COMBS(tc_List_Olist(X29560),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29560)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X29560),tc_fun(X29560,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29560,tc_HOL_Obool),tc_fun(tc_fun(X29560,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29560)),c_Orderings_Oord__class_Oless__eq(tc_fun(X29560,tc_HOL_Obool))),c_List_Oset(X29560))),X29559))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29560),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X29560)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X29560)))),X29558))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__lists__length__eq])]) ).

cnf(i_0_6162,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_5239]) ).

fof(i_0_6163,plain,
    ! [X27543,X27544,X27545,X27546,X27547,X27548,X27549,X27550] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27549),esk276_7(X27543,X27544,X27545,X27546,X27547,X27548,X27549)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27549,tc_HOL_Obool)),X27544),X27543)))
        | hAPP(X27545,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27549,tc_HOL_Obool)),X27544),X27543)) = hAPP(hAPP(X27548,hAPP(X27545,X27544)),hAPP(X27545,X27543))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27549),X27543))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27549),X27544))
        | ~ c_Finite__Set_Ofolding__image__simple(X27550,X27549,X27548,X27547,X27546,X27545) )
      & ( hAPP(X27546,esk276_7(X27543,X27544,X27545,X27546,X27547,X27548,X27549)) != X27547
        | hAPP(X27545,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27549,tc_HOL_Obool)),X27544),X27543)) = hAPP(hAPP(X27548,hAPP(X27545,X27544)),hAPP(X27545,X27543))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27549),X27543))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27549),X27544))
        | ~ c_Finite__Set_Ofolding__image__simple(X27550,X27549,X27548,X27547,X27546,X27545) ) ),
    inference(distribute,[status(thm)],[inference(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_6164,plain,
    ! [X23926] : hAPP(c_Int_Onat,X23926) = 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,X23926)),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_6165,plain,
    ! [X33581,X33582,X33583,X33584,X33585,X33586,X33587,X33588] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33587),esk561_7(X33581,X33582,X33583,X33584,X33585,X33586,X33587)),X33583))
        | hAPP(hAPP(X33584,X33582),X33583) = hAPP(hAPP(X33584,X33581),X33583)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33587),X33583))
        | ~ c_Finite__Set_Ofolding__image(X33588,X33587,X33586,X33585,X33584) )
      & ( hAPP(X33582,esk561_7(X33581,X33582,X33583,X33584,X33585,X33586,X33587)) != hAPP(X33581,esk561_7(X33581,X33582,X33583,X33584,X33585,X33586,X33587))
        | hAPP(hAPP(X33584,X33582),X33583) = hAPP(hAPP(X33584,X33581),X33583)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33587),X33583))
        | ~ c_Finite__Set_Ofolding__image(X33588,X33587,X33586,X33585,X33584) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Ocong])])])])])]) ).

fof(i_0_6166,plain,
    ! [X32175,X32176,X32177,X32178,X32179,X32182,X32183,X32184,X32185,X32186,X32187,X32188,X32189] :
      ( ( X32175 = hAPP(hAPP(c_List_Oappend(X32179),esk456_5(X32175,X32176,X32177,X32178,X32179)),hAPP(hAPP(c_List_Olist_OCons(X32179),X32178),esk457_5(X32175,X32176,X32177,X32178,X32179)))
        | hAPP(hAPP(c_List_Olist_OCons(X32179),X32178),X32177) != hAPP(c_List_Ofilter(X32179,X32176),X32175) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32179),X32182),hAPP(c_List_Oset(X32179),esk456_5(X32175,X32176,X32177,X32178,X32179))))
        | ~ hBOOL(hAPP(X32176,X32182))
        | hAPP(hAPP(c_List_Olist_OCons(X32179),X32178),X32177) != hAPP(c_List_Ofilter(X32179,X32176),X32175) )
      & ( hBOOL(hAPP(X32176,X32178))
        | hAPP(hAPP(c_List_Olist_OCons(X32179),X32178),X32177) != hAPP(c_List_Ofilter(X32179,X32176),X32175) )
      & ( X32177 = hAPP(c_List_Ofilter(X32179,X32176),esk457_5(X32175,X32176,X32177,X32178,X32179))
        | hAPP(hAPP(c_List_Olist_OCons(X32179),X32178),X32177) != hAPP(c_List_Ofilter(X32179,X32176),X32175) )
      & ( hBOOL(hAPP(hAPP(c_member(X32187),esk458_7(X32183,X32184,X32185,X32186,X32187,X32188,X32189)),hAPP(c_List_Oset(X32187),X32188)))
        | X32183 != hAPP(hAPP(c_List_Oappend(X32187),X32188),hAPP(hAPP(c_List_Olist_OCons(X32187),X32186),X32189))
        | ~ hBOOL(hAPP(X32184,X32186))
        | X32185 != hAPP(c_List_Ofilter(X32187,X32184),X32189)
        | hAPP(hAPP(c_List_Olist_OCons(X32187),X32186),X32185) = hAPP(c_List_Ofilter(X32187,X32184),X32183) )
      & ( hBOOL(hAPP(X32184,esk458_7(X32183,X32184,X32185,X32186,X32187,X32188,X32189)))
        | X32183 != hAPP(hAPP(c_List_Oappend(X32187),X32188),hAPP(hAPP(c_List_Olist_OCons(X32187),X32186),X32189))
        | ~ hBOOL(hAPP(X32184,X32186))
        | X32185 != hAPP(c_List_Ofilter(X32187,X32184),X32189)
        | hAPP(hAPP(c_List_Olist_OCons(X32187),X32186),X32185) = hAPP(c_List_Ofilter(X32187,X32184),X32183) ) ),
    inference(distribute,[status(thm)],[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_5247])])])])])]) ).

fof(i_0_6167,plain,
    ! [X32191,X32192,X32193,X32194,X32195,X32198,X32199,X32200,X32201,X32202,X32203,X32204,X32205] :
      ( ( X32193 = hAPP(hAPP(c_List_Oappend(X32195),esk459_5(X32191,X32192,X32193,X32194,X32195)),hAPP(hAPP(c_List_Olist_OCons(X32195),X32192),esk460_5(X32191,X32192,X32193,X32194,X32195)))
        | hAPP(c_List_Ofilter(X32195,X32194),X32193) != hAPP(hAPP(c_List_Olist_OCons(X32195),X32192),X32191) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32195),X32198),hAPP(c_List_Oset(X32195),esk459_5(X32191,X32192,X32193,X32194,X32195))))
        | ~ hBOOL(hAPP(X32194,X32198))
        | hAPP(c_List_Ofilter(X32195,X32194),X32193) != hAPP(hAPP(c_List_Olist_OCons(X32195),X32192),X32191) )
      & ( hBOOL(hAPP(X32194,X32192))
        | hAPP(c_List_Ofilter(X32195,X32194),X32193) != hAPP(hAPP(c_List_Olist_OCons(X32195),X32192),X32191) )
      & ( X32191 = hAPP(c_List_Ofilter(X32195,X32194),esk460_5(X32191,X32192,X32193,X32194,X32195))
        | hAPP(c_List_Ofilter(X32195,X32194),X32193) != hAPP(hAPP(c_List_Olist_OCons(X32195),X32192),X32191) )
      & ( hBOOL(hAPP(hAPP(c_member(X32203),esk461_7(X32199,X32200,X32201,X32202,X32203,X32204,X32205)),hAPP(c_List_Oset(X32203),X32204)))
        | X32201 != hAPP(hAPP(c_List_Oappend(X32203),X32204),hAPP(hAPP(c_List_Olist_OCons(X32203),X32200),X32205))
        | ~ hBOOL(hAPP(X32202,X32200))
        | X32199 != hAPP(c_List_Ofilter(X32203,X32202),X32205)
        | hAPP(c_List_Ofilter(X32203,X32202),X32201) = hAPP(hAPP(c_List_Olist_OCons(X32203),X32200),X32199) )
      & ( hBOOL(hAPP(X32202,esk461_7(X32199,X32200,X32201,X32202,X32203,X32204,X32205)))
        | X32201 != hAPP(hAPP(c_List_Oappend(X32203),X32204),hAPP(hAPP(c_List_Olist_OCons(X32203),X32200),X32205))
        | ~ hBOOL(hAPP(X32202,X32200))
        | X32199 != hAPP(c_List_Ofilter(X32203,X32202),X32205)
        | hAPP(c_List_Ofilter(X32203,X32202),X32201) = hAPP(hAPP(c_List_Olist_OCons(X32203),X32200),X32199) ) ),
    inference(distribute,[status(thm)],[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_5248])])])])])]) ).

fof(i_0_6168,plain,
    ! [X29093,X29094,X29095,X29096] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29096),esk358_4(X29093,X29094,X29095,X29096)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29096),esk357_4(X29093,X29094,X29095,X29096))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk358_4(X29093,X29094,X29095,X29096)),X29095))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29096),esk357_4(X29093,X29094,X29095,X29096))) )
      & ( hAPP(X29094,esk358_4(X29093,X29094,X29095,X29096)) = X29093
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29096),esk357_4(X29093,X29094,X29095,X29096))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29096),esk358_4(X29093,X29094,X29095,X29096)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk357_4(X29093,X29094,X29095,X29096)),X29095)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk358_4(X29093,X29094,X29095,X29096)),X29095))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk357_4(X29093,X29094,X29095,X29096)),X29095)) )
      & ( hAPP(X29094,esk358_4(X29093,X29094,X29095,X29096)) = X29093
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk357_4(X29093,X29094,X29095,X29096)),X29095)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29096),esk358_4(X29093,X29094,X29095,X29096)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | ~ 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(X29094,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk357_4(X29093,X29094,X29095,X29096)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29094,esk357_4(X29093,X29094,X29095,X29096))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk358_4(X29093,X29094,X29095,X29096)),X29095))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | ~ 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(X29094,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk357_4(X29093,X29094,X29095,X29096)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29094,esk357_4(X29093,X29094,X29095,X29096))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X29094,esk358_4(X29093,X29094,X29095,X29096)) = X29093
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29093),hAPP(X29094,X29095)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X29094,X29096)),X29093))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29096),X29095))
        | ~ 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(X29094,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk357_4(X29093,X29094,X29095,X29096)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X29094,esk357_4(X29093,X29094,X29095,X29096))))),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_6169,plain,
    ! [X32867,X32868,X32869,X32870,X32871] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32868),hAPP(c_Set_OCollect(X32868),hAPP(hAPP(c_COMBB(tc_fun(X32870,tc_HOL_Obool),tc_HOL_Obool,X32868),c_HOL_OEx(X32870)),hAPP(hAPP(c_COMBB(tc_fun(X32870,tc_HOL_Obool),tc_fun(X32870,tc_HOL_Obool),X32868),hAPP(c_COMBS(X32870,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32870),c_fconj),hAPP(hAPP(c_COMBC(X32870,tc_fun(X32870,tc_HOL_Obool),tc_HOL_Obool),c_member(X32870)),X32869)))),X32867)))))
        | ~ hBOOL(hAPP(hAPP(c_member(X32870),X32871),X32869))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X32868),hAPP(c_Set_OCollect(X32868),hAPP(hAPP(c_COMBC(X32868,X32870,tc_HOL_Obool),X32867),X32871))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32870),X32869)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32870),esk505_4(X32867,X32868,X32869,X32870)),X32869))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X32868),hAPP(c_Set_OCollect(X32868),hAPP(hAPP(c_COMBB(tc_fun(X32870,tc_HOL_Obool),tc_HOL_Obool,X32868),c_HOL_OEx(X32870)),hAPP(hAPP(c_COMBB(tc_fun(X32870,tc_HOL_Obool),tc_fun(X32870,tc_HOL_Obool),X32868),hAPP(c_COMBS(X32870,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32870),c_fconj),hAPP(hAPP(c_COMBC(X32870,tc_fun(X32870,tc_HOL_Obool),tc_HOL_Obool),c_member(X32870)),X32869)))),X32867)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32870),X32869)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32868),hAPP(c_Set_OCollect(X32868),hAPP(hAPP(c_COMBC(X32868,X32870,tc_HOL_Obool),X32867),esk505_4(X32867,X32868,X32869,X32870)))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X32868),hAPP(c_Set_OCollect(X32868),hAPP(hAPP(c_COMBB(tc_fun(X32870,tc_HOL_Obool),tc_HOL_Obool,X32868),c_HOL_OEx(X32870)),hAPP(hAPP(c_COMBB(tc_fun(X32870,tc_HOL_Obool),tc_fun(X32870,tc_HOL_Obool),X32868),hAPP(c_COMBS(X32870,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32870),c_fconj),hAPP(hAPP(c_COMBC(X32870,tc_fun(X32870,tc_HOL_Obool),tc_HOL_Obool),c_member(X32870)),X32869)))),X32867)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32870),X32869)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__bex])])])])]) ).

fof(i_0_6170,plain,
    ! [X33497,X33498,X33499,X33500,X33501,X33502] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33502),esk542_6(X33497,X33498,X33499,X33500,X33501,X33502)),X33500))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33499,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33502,tc_fun(X33499,tc_HOL_Obool)),X33500),X33498)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33502,tc_fun(X33499,tc_HOL_Obool)),X33500),X33497)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33502,tc_HOL_Obool)),X33501),X33500)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33499,tc_HOL_Obool)),hAPP(X33498,esk542_6(X33497,X33498,X33499,X33500,X33501,X33502))),hAPP(X33497,esk542_6(X33497,X33498,X33499,X33500,X33501,X33502))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33499,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33502,tc_fun(X33499,tc_HOL_Obool)),X33500),X33498)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33502,tc_fun(X33499,tc_HOL_Obool)),X33500),X33497)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33502,tc_HOL_Obool)),X33501),X33500)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__anti__mono])])])]) ).

fof(i_0_6171,plain,
    ! [X28401,X28402,X28403,X28404,X28405,X28406] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28406),esk317_6(X28401,X28402,X28403,X28404,X28405,X28406)),X28405))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28406,X28403),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28406,X28403),X28405),X28402)),hAPP(hAPP(c_Product__Type_OSigma(X28406,X28403),X28404),X28401)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28406,tc_HOL_Obool)),X28405),X28404)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28403,tc_HOL_Obool)),hAPP(X28402,esk317_6(X28401,X28402,X28403,X28404,X28405,X28406))),hAPP(X28401,esk317_6(X28401,X28402,X28403,X28404,X28405,X28406))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28406,X28403),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X28406,X28403),X28405),X28402)),hAPP(hAPP(c_Product__Type_OSigma(X28406,X28403),X28404),X28401)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28406,tc_HOL_Obool)),X28405),X28404)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sigma__mono])])])]) ).

fof(i_0_6172,plain,
    ! [X28348,X28349,X28350,X28351,X28352,X28353] :
      ( ( X28353 = hAPP(hAPP(c_Product__Type_OPair(X28352,X28351),esk311_6(X28348,X28349,X28350,X28351,X28352,X28353)),esk312_6(X28348,X28349,X28350,X28351,X28352,X28353))
        | hBOOL(hAPP(hAPP(c_member(X28350),X28349),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28352,X28351,tc_fun(X28350,tc_HOL_Obool)),X28348),X28353))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28350),X28349),hAPP(hAPP(X28348,esk311_6(X28348,X28349,X28350,X28351,X28352,X28353)),esk312_6(X28348,X28349,X28350,X28351,X28352,X28353))))
        | hBOOL(hAPP(hAPP(c_member(X28350),X28349),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28352,X28351,tc_fun(X28350,tc_HOL_Obool)),X28348),X28353))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI2])])])]) ).

cnf(i_0_6173,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_5249]) ).

cnf(i_0_6174,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_5250]) ).

fof(i_0_6175,plain,
    ! [X33665,X33666] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33665),X33666))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33666),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33665))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33666),X33665))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33666),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33665))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33665),X33666))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33666),X33665))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33666),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33665))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5251])])]) ).

fof(i_0_6176,plain,
    ! [X33663,X33664] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33664),X33663))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33664),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33663))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33663),X33664))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33664),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33663))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33664),X33663))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33663),X33664))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33664),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33663))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5252])])]) ).

fof(i_0_6177,plain,
    ! [X28872,X28873,X28874] : hAPP(c_Relation_Oconverse(X28874,X28873),X28872) = hAPP(c_Set_OCollect(tc_prod(X28873,X28874)),hAPP(c_Product__Type_Oprod_Oprod__case(X28873,X28874,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28873,tc_fun(tc_prod(X28874,X28873),tc_HOL_Obool),tc_fun(X28874,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28874,tc_fun(tc_fun(tc_prod(X28874,X28873),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28874,X28873),tc_HOL_Obool),tc_fun(X28874,tc_HOL_Obool)),X28873),c_COMBC(X28874,tc_fun(tc_prod(X28874,X28873),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28874,tc_prod(X28874,X28873)),tc_fun(X28874,tc_fun(tc_fun(tc_prod(X28874,X28873),tc_HOL_Obool),tc_HOL_Obool)),X28873),hAPP(c_COMBB(tc_prod(X28874,X28873),tc_fun(tc_fun(tc_prod(X28874,X28873),tc_HOL_Obool),tc_HOL_Obool),X28874),c_member(tc_prod(X28874,X28873)))),hAPP(c_COMBC(X28874,X28873,tc_prod(X28874,X28873)),c_Product__Type_OPair(X28874,X28873))))),X28872))),
    inference(variable_rename,[status(thm)],[fact_converse__def]) ).

fof(i_0_6178,plain,
    ! [X30912,X30913,X30914,X30915] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30914),X30913))
        | c_Nitpick_Osetsum_H(X30914,X30915,X30912,X30913) = hAPP(c_List_Omonoid__add__class_Olistsum(X30915),hAPP(hAPP(c_List_Omap(X30914,X30915),X30912),c_Hilbert__Choice_OEps(tc_List_Olist(X30914),hAPP(hAPP(c_COMBS(tc_List_Olist(X30914),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X30914)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X30914),tc_fun(X30914,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X30914,tc_HOL_Obool),tc_fun(tc_fun(X30914,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X30914)),c_fequal),c_List_Oset(X30914))),X30913))),c_List_Odistinct(X30914)))))
        | ~ class_Groups_Ocomm__monoid__add(X30915) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X30914),X30913))
        | c_Nitpick_Osetsum_H(X30914,X30915,X30912,X30913) = c_Groups_Ozero__class_Ozero(X30915)
        | ~ class_Groups_Ocomm__monoid__add(X30915) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5253])])]) ).

fof(i_0_6179,plain,
    ! [X33209,X33210,X33211,X33212,X33213,X33214] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33213),esk524_6(X33209,X33210,X33211,X33212,X33213,X33214)),X33212))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33213,tc_fun(X33211,tc_HOL_Obool)),X33212),X33210)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33213,c_Groups_Otimes__class_Otimes(X33214)),hAPP(hAPP(c_COMBB(tc_fun(X33211,tc_HOL_Obool),X33214,X33213),hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214))),X33210)),c_Groups_Oone__class_Oone(X33214)),X33212)
        | hBOOL(hAPP(hAPP(c_member(X33213),esk523_6(X33209,X33210,X33211,X33212,X33213,X33214)),X33212))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33213),X33212))
        | ~ class_Groups_Ocomm__monoid__mult(X33214) )
      & ( hBOOL(hAPP(hAPP(c_member(X33213),esk525_6(X33209,X33210,X33211,X33212,X33213,X33214)),X33212))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33213,tc_fun(X33211,tc_HOL_Obool)),X33212),X33210)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33213,c_Groups_Otimes__class_Otimes(X33214)),hAPP(hAPP(c_COMBB(tc_fun(X33211,tc_HOL_Obool),X33214,X33213),hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214))),X33210)),c_Groups_Oone__class_Oone(X33214)),X33212)
        | hBOOL(hAPP(hAPP(c_member(X33213),esk523_6(X33209,X33210,X33211,X33212,X33213,X33214)),X33212))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33213),X33212))
        | ~ class_Groups_Ocomm__monoid__mult(X33214) )
      & ( esk524_6(X33209,X33210,X33211,X33212,X33213,X33214) != esk525_6(X33209,X33210,X33211,X33212,X33213,X33214)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33213,tc_fun(X33211,tc_HOL_Obool)),X33212),X33210)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33213,c_Groups_Otimes__class_Otimes(X33214)),hAPP(hAPP(c_COMBB(tc_fun(X33211,tc_HOL_Obool),X33214,X33213),hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214))),X33210)),c_Groups_Oone__class_Oone(X33214)),X33212)
        | hBOOL(hAPP(hAPP(c_member(X33213),esk523_6(X33209,X33210,X33211,X33212,X33213,X33214)),X33212))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33213),X33212))
        | ~ class_Groups_Ocomm__monoid__mult(X33214) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33211,tc_HOL_Obool)),hAPP(X33210,esk524_6(X33209,X33210,X33211,X33212,X33213,X33214))),hAPP(X33210,esk525_6(X33209,X33210,X33211,X33212,X33213,X33214))) != c_Orderings_Obot__class_Obot(tc_fun(X33211,tc_HOL_Obool))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33213,tc_fun(X33211,tc_HOL_Obool)),X33212),X33210)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33213,c_Groups_Otimes__class_Otimes(X33214)),hAPP(hAPP(c_COMBB(tc_fun(X33211,tc_HOL_Obool),X33214,X33213),hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214))),X33210)),c_Groups_Oone__class_Oone(X33214)),X33212)
        | hBOOL(hAPP(hAPP(c_member(X33213),esk523_6(X33209,X33210,X33211,X33212,X33213,X33214)),X33212))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33213),X33212))
        | ~ class_Groups_Ocomm__monoid__mult(X33214) )
      & ( hBOOL(hAPP(hAPP(c_member(X33213),esk524_6(X33209,X33210,X33211,X33212,X33213,X33214)),X33212))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33213,tc_fun(X33211,tc_HOL_Obool)),X33212),X33210)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33213,c_Groups_Otimes__class_Otimes(X33214)),hAPP(hAPP(c_COMBB(tc_fun(X33211,tc_HOL_Obool),X33214,X33213),hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214))),X33210)),c_Groups_Oone__class_Oone(X33214)),X33212)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33211),hAPP(X33210,esk523_6(X33209,X33210,X33211,X33212,X33213,X33214))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33213),X33212))
        | ~ class_Groups_Ocomm__monoid__mult(X33214) )
      & ( hBOOL(hAPP(hAPP(c_member(X33213),esk525_6(X33209,X33210,X33211,X33212,X33213,X33214)),X33212))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33213,tc_fun(X33211,tc_HOL_Obool)),X33212),X33210)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33213,c_Groups_Otimes__class_Otimes(X33214)),hAPP(hAPP(c_COMBB(tc_fun(X33211,tc_HOL_Obool),X33214,X33213),hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214))),X33210)),c_Groups_Oone__class_Oone(X33214)),X33212)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33211),hAPP(X33210,esk523_6(X33209,X33210,X33211,X33212,X33213,X33214))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33213),X33212))
        | ~ class_Groups_Ocomm__monoid__mult(X33214) )
      & ( esk524_6(X33209,X33210,X33211,X33212,X33213,X33214) != esk525_6(X33209,X33210,X33211,X33212,X33213,X33214)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33213,tc_fun(X33211,tc_HOL_Obool)),X33212),X33210)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33213,c_Groups_Otimes__class_Otimes(X33214)),hAPP(hAPP(c_COMBB(tc_fun(X33211,tc_HOL_Obool),X33214,X33213),hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214))),X33210)),c_Groups_Oone__class_Oone(X33214)),X33212)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33211),hAPP(X33210,esk523_6(X33209,X33210,X33211,X33212,X33213,X33214))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33213),X33212))
        | ~ class_Groups_Ocomm__monoid__mult(X33214) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33211,tc_HOL_Obool)),hAPP(X33210,esk524_6(X33209,X33210,X33211,X33212,X33213,X33214))),hAPP(X33210,esk525_6(X33209,X33210,X33211,X33212,X33213,X33214))) != c_Orderings_Obot__class_Obot(tc_fun(X33211,tc_HOL_Obool))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33213,tc_fun(X33211,tc_HOL_Obool)),X33212),X33210)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33213,c_Groups_Otimes__class_Otimes(X33214)),hAPP(hAPP(c_COMBB(tc_fun(X33211,tc_HOL_Obool),X33214,X33213),hAPP(hAPP(c_Finite__Set_Ofold__image(X33214,X33211,c_Groups_Otimes__class_Otimes(X33214)),X33209),c_Groups_Oone__class_Oone(X33214))),X33210)),c_Groups_Oone__class_Oone(X33214)),X33212)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33211),hAPP(X33210,esk523_6(X33209,X33210,X33211,X33212,X33213,X33214))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33213),X33212))
        | ~ class_Groups_Ocomm__monoid__mult(X33214) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__UN__disjoint])])])]) ).

fof(i_0_6180,plain,
    ! [X32912,X32913,X32914,X32915] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32915,tc_fun(X32914,tc_HOL_Obool)),X32913),X32912) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X32914,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X32914,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32915,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X32914,tc_HOL_Obool)),c_HOL_OEx(X32915)),hAPP(hAPP(c_COMBB(tc_fun(X32915,tc_HOL_Obool),tc_fun(X32915,tc_HOL_Obool),tc_fun(X32914,tc_HOL_Obool)),hAPP(c_COMBS(X32915,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32915),c_fconj),hAPP(hAPP(c_COMBC(X32915,tc_fun(X32915,tc_HOL_Obool),tc_HOL_Obool),c_member(X32915)),X32913)))),hAPP(hAPP(c_COMBC(tc_fun(X32914,tc_HOL_Obool),tc_fun(X32915,tc_fun(X32914,tc_HOL_Obool)),tc_fun(X32915,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32914,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X32915,tc_fun(X32914,tc_HOL_Obool)),tc_fun(X32915,tc_HOL_Obool)),tc_fun(X32914,tc_HOL_Obool)),c_COMBB(tc_fun(X32914,tc_HOL_Obool),tc_HOL_Obool,X32915)),c_fequal)),X32912))))),
    inference(variable_rename,[status(thm)],[fact_INT__eq]) ).

fof(i_0_6181,plain,
    ! [X32908,X32909,X32910,X32911] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X32911,tc_fun(X32910,tc_HOL_Obool)),X32909),X32908) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X32910,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X32910,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X32911,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X32910,tc_HOL_Obool)),c_HOL_OEx(X32911)),hAPP(hAPP(c_COMBB(tc_fun(X32911,tc_HOL_Obool),tc_fun(X32911,tc_HOL_Obool),tc_fun(X32910,tc_HOL_Obool)),hAPP(c_COMBS(X32911,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32911),c_fconj),hAPP(hAPP(c_COMBC(X32911,tc_fun(X32911,tc_HOL_Obool),tc_HOL_Obool),c_member(X32911)),X32909)))),hAPP(hAPP(c_COMBC(tc_fun(X32910,tc_HOL_Obool),tc_fun(X32911,tc_fun(X32910,tc_HOL_Obool)),tc_fun(X32911,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32910,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X32911,tc_fun(X32910,tc_HOL_Obool)),tc_fun(X32911,tc_HOL_Obool)),tc_fun(X32910,tc_HOL_Obool)),c_COMBB(tc_fun(X32910,tc_HOL_Obool),tc_HOL_Obool,X32911)),c_fequal)),X32908))))),
    inference(variable_rename,[status(thm)],[fact_UN__eq]) ).

cnf(i_0_6182,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_5254]) ).

cnf(i_0_6183,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_5255]) ).

cnf(i_0_6184,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_5256]) ).

fof(i_0_6185,plain,
    ! [X33087,X33088] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33088,X33087)
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X33088,tc_HOL_Obool)),esk520_2(X33087,X33088)),hAPP(hAPP(c_COMBB(tc_fun(X33088,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X33088,tc_HOL_Obool)),c_HOL_OEx(X33088)),hAPP(hAPP(c_COMBB(tc_fun(X33088,tc_HOL_Obool),tc_fun(X33088,tc_HOL_Obool),tc_fun(X33088,tc_HOL_Obool)),hAPP(c_COMBS(X33088,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33088),c_fconj),hAPP(hAPP(c_COMBS(X33088,X33088,tc_HOL_Obool),X33087),c_COMBI(X33088))))),hAPP(hAPP(c_COMBC(tc_fun(X33088,tc_HOL_Obool),tc_fun(X33088,tc_fun(X33088,tc_HOL_Obool)),tc_fun(X33088,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X33088,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X33088,tc_fun(X33088,tc_HOL_Obool)),tc_fun(X33088,tc_HOL_Obool)),tc_fun(X33088,tc_HOL_Obool)),c_COMBB(tc_fun(X33088,tc_HOL_Obool),tc_HOL_Obool,X33088)),c_fequal)),X33087))))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__typedef])])]) ).

cnf(i_0_6186,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_5257]) ).

cnf(i_0_6187,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_5258]) ).

fof(i_0_6188,plain,
    ! [X27559,X27560] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27560))
      | 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)),X27560))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X27559))))) = 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)),X27560))),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,X27559))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less__Suc])]) ).

fof(i_0_6189,plain,
    ! [X27691,X27692,X27693,X27694,X27695,X27696] :
      ( ~ class_Groups_Ocomm__monoid__add(X27696)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27695),X27694))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27695,X27696),X27693),X27694) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27692,X27696),hAPP(hAPP(c_COMBB(tc_fun(X27695,tc_HOL_Obool),X27696,X27692),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27695,X27696),X27693)),hAPP(hAPP(c_COMBB(tc_fun(X27695,tc_HOL_Obool),tc_fun(X27695,tc_HOL_Obool),X27692),c_Set_OCollect(X27695)),hAPP(hAPP(c_COMBB(tc_fun(X27695,tc_HOL_Obool),tc_fun(X27695,tc_HOL_Obool),X27692),hAPP(c_COMBS(X27695,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27695),c_fconj),hAPP(hAPP(c_COMBC(X27695,tc_fun(X27695,tc_HOL_Obool),tc_HOL_Obool),c_member(X27695)),X27694)))),hAPP(c_COMBC(X27695,X27692,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27692,tc_fun(X27692,tc_HOL_Obool),X27695),c_fequal),X27691)))))),hAPP(c_Set_Oimage(X27695,X27692,X27691),X27694)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__image__gen])]) ).

fof(i_0_6190,plain,
    ! [X28267,X28268,X28269,X28270,X28271,X28272,X28273,X28274] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28269,X28269)),X28270),X28267))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28269,X28269,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28269,tc_fun(X28269,tc_HOL_Obool),tc_fun(X28269,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28269,tc_HOL_Obool),tc_fun(X28269,tc_HOL_Obool)),X28269),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28269)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28269),c_fconj),hAPP(hAPP(c_COMBC(X28269,tc_fun(X28269,tc_HOL_Obool),tc_HOL_Obool),c_member(X28269)),X28268)))),hAPP(hAPP(c_COMBC(X28269,tc_fun(X28269,tc_HOL_Obool),tc_HOL_Obool),c_member(X28269)),X28268))),X28270))
        | ~ c_Relation_Orefl__on(X28269,X28268,X28267) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28269),X28271),X28268))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28269,X28269)),hAPP(hAPP(c_Product__Type_OPair(X28269,X28269),X28271),X28271)),X28267))
        | ~ c_Relation_Orefl__on(X28269,X28268,X28267) )
      & ( hBOOL(hAPP(hAPP(c_member(X28274),esk300_3(X28272,X28273,X28274)),X28273))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28274,X28274)),esk299_3(X28272,X28273,X28274)),X28272))
        | c_Relation_Orefl__on(X28274,X28273,X28272) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28274,X28274)),hAPP(hAPP(c_Product__Type_OPair(X28274,X28274),esk300_3(X28272,X28273,X28274)),esk300_3(X28272,X28273,X28274))),X28272))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28274,X28274)),esk299_3(X28272,X28273,X28274)),X28272))
        | c_Relation_Orefl__on(X28274,X28273,X28272) )
      & ( hBOOL(hAPP(hAPP(c_member(X28274),esk300_3(X28272,X28273,X28274)),X28273))
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28274,X28274,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28274,tc_fun(X28274,tc_HOL_Obool),tc_fun(X28274,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28274,tc_HOL_Obool),tc_fun(X28274,tc_HOL_Obool)),X28274),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28274)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28274),c_fconj),hAPP(hAPP(c_COMBC(X28274,tc_fun(X28274,tc_HOL_Obool),tc_HOL_Obool),c_member(X28274)),X28273)))),hAPP(hAPP(c_COMBC(X28274,tc_fun(X28274,tc_HOL_Obool),tc_HOL_Obool),c_member(X28274)),X28273))),esk299_3(X28272,X28273,X28274)))
        | c_Relation_Orefl__on(X28274,X28273,X28272) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28274,X28274)),hAPP(hAPP(c_Product__Type_OPair(X28274,X28274),esk300_3(X28272,X28273,X28274)),esk300_3(X28272,X28273,X28274))),X28272))
        | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28274,X28274,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28274,tc_fun(X28274,tc_HOL_Obool),tc_fun(X28274,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28274,tc_HOL_Obool),tc_fun(X28274,tc_HOL_Obool)),X28274),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28274)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28274),c_fconj),hAPP(hAPP(c_COMBC(X28274,tc_fun(X28274,tc_HOL_Obool),tc_HOL_Obool),c_member(X28274)),X28273)))),hAPP(hAPP(c_COMBC(X28274,tc_fun(X28274,tc_HOL_Obool),tc_HOL_Obool),c_member(X28274)),X28273))),esk299_3(X28272,X28273,X28274)))
        | c_Relation_Orefl__on(X28274,X28273,X28272) ) ),
    inference(distribute,[status(thm)],[inference(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_6191,plain,
    ! [X32790,X32791,X32792,X32793] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X32793),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
        | c_Random__Sequence_ORandom(X32792,X32791,X32793,X32790) = 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(X32792)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X32792)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X32793),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
        | c_Random__Sequence_ORandom(X32792,X32791,X32793,X32790) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X32792,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(X32792)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(X32791,X32790)),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(X32792)))),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(X32792)))),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(X32792)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(X32792,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(X32792)))),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(X32792)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(X32792,X32791,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32793),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X32790))),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(X32792)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X32792))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X32792)))),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(X32792)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(X32792,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(X32792)))),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(X32792)))),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(X32792))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X32792)))),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(X32792)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X32792)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X32792))))),tc_prod(X32792,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(X32792)),hAPP(hAPP(c_COMBB(X32792,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(X32792)))),tc_prod(X32792,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(X32792)),c_Product__Type_Ofst(X32792,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5259])]) ).

cnf(i_0_6192,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_5260]) ).

cnf(i_0_6193,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_5261]) ).

cnf(i_0_6194,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_5262]) ).

fof(i_0_6195,plain,
    ! [X29983,X29984,X29985,X29986,X29987] : hAPP(hAPP(c_List_Ozip(X29987,X29986),X29985),hAPP(hAPP(c_List_Olist_OCons(X29986),X29984),X29983)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X29987,X29986)),X29987,c_List_Olist_ONil(tc_prod(X29987,X29986)),hAPP(hAPP(c_COMBC(X29987,tc_fun(tc_List_Olist(X29987),tc_List_Olist(tc_prod(X29987,X29986))),tc_fun(tc_List_Olist(X29987),tc_List_Olist(tc_prod(X29987,X29986)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X29987,X29986)),tc_List_Olist(tc_prod(X29987,X29986))),tc_fun(tc_fun(tc_List_Olist(X29987),tc_List_Olist(tc_prod(X29987,X29986))),tc_fun(tc_List_Olist(X29987),tc_List_Olist(tc_prod(X29987,X29986)))),X29987),c_COMBB(tc_List_Olist(tc_prod(X29987,X29986)),tc_List_Olist(tc_prod(X29987,X29986)),tc_List_Olist(X29987))),hAPP(hAPP(c_COMBB(tc_prod(X29987,X29986),tc_fun(tc_List_Olist(tc_prod(X29987,X29986)),tc_List_Olist(tc_prod(X29987,X29986))),X29987),c_List_Olist_OCons(tc_prod(X29987,X29986))),hAPP(hAPP(c_COMBC(X29987,X29986,tc_prod(X29987,X29986)),c_Product__Type_OPair(X29987,X29986)),X29984)))),hAPP(hAPP(c_COMBC(tc_List_Olist(X29987),tc_List_Olist(X29986),tc_List_Olist(tc_prod(X29987,X29986))),c_List_Ozip(X29987,X29986)),X29983))),X29985),
    inference(variable_rename,[status(thm)],[fact_zip__Cons]) ).

fof(i_0_6196,plain,
    ! [X23549,X23550,X23551,X23552] :
      ( ( ~ c_Wellfounded_Omax__extp(X23552,hAPP(hAPP(c_COMBC(X23552,tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_fun(X23552,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23552,tc_fun(tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_fun(X23552,tc_HOL_Obool)),X23552),c_COMBC(X23552,tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23552,tc_prod(X23552,X23552)),tc_fun(X23552,tc_fun(tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_HOL_Obool)),X23552),hAPP(c_COMBB(tc_prod(X23552,X23552),tc_fun(tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_HOL_Obool),X23552),c_member(tc_prod(X23552,X23552)))),c_Product__Type_OPair(X23552,X23552)))),X23551),X23550,X23549)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23552,tc_HOL_Obool),tc_fun(X23552,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23552,tc_HOL_Obool),tc_fun(X23552,tc_HOL_Obool)),X23550),X23549)),c_Wellfounded_Omax__ext(X23552,X23551))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23552,tc_HOL_Obool),tc_fun(X23552,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23552,tc_HOL_Obool),tc_fun(X23552,tc_HOL_Obool)),X23550),X23549)),c_Wellfounded_Omax__ext(X23552,X23551)))
        | c_Wellfounded_Omax__extp(X23552,hAPP(hAPP(c_COMBC(X23552,tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_fun(X23552,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23552,tc_fun(tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_fun(X23552,tc_HOL_Obool)),X23552),c_COMBC(X23552,tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23552,tc_prod(X23552,X23552)),tc_fun(X23552,tc_fun(tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_HOL_Obool)),X23552),hAPP(c_COMBB(tc_prod(X23552,X23552),tc_fun(tc_fun(tc_prod(X23552,X23552),tc_HOL_Obool),tc_HOL_Obool),X23552),c_member(tc_prod(X23552,X23552)))),c_Product__Type_OPair(X23552,X23552)))),X23551),X23550,X23549) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp__max__ext__eq])]) ).

fof(i_0_6197,plain,
    ! [X29347,X29348,X29349,X29350] :
      ( ( ~ c_List_Olistrelp(X29350,hAPP(hAPP(c_COMBC(X29350,tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_fun(X29350,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29350,tc_fun(tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_fun(X29350,tc_HOL_Obool)),X29350),c_COMBC(X29350,tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29350,tc_prod(X29350,X29350)),tc_fun(X29350,tc_fun(tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_HOL_Obool)),X29350),hAPP(c_COMBB(tc_prod(X29350,X29350),tc_fun(tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_HOL_Obool),X29350),c_member(tc_prod(X29350,X29350)))),c_Product__Type_OPair(X29350,X29350)))),X29349),X29348,X29347)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29350),tc_List_Olist(X29350))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29350),tc_List_Olist(X29350)),X29348),X29347)),c_List_Olistrel(X29350,X29349))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29350),tc_List_Olist(X29350))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29350),tc_List_Olist(X29350)),X29348),X29347)),c_List_Olistrel(X29350,X29349)))
        | c_List_Olistrelp(X29350,hAPP(hAPP(c_COMBC(X29350,tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_fun(X29350,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29350,tc_fun(tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_fun(X29350,tc_HOL_Obool)),X29350),c_COMBC(X29350,tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X29350,tc_prod(X29350,X29350)),tc_fun(X29350,tc_fun(tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_HOL_Obool)),X29350),hAPP(c_COMBB(tc_prod(X29350,X29350),tc_fun(tc_fun(tc_prod(X29350,X29350),tc_HOL_Obool),tc_HOL_Obool),X29350),c_member(tc_prod(X29350,X29350)))),c_Product__Type_OPair(X29350,X29350)))),X29349),X29348,X29347) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp__listrel__eq])]) ).

fof(i_0_6198,plain,
    ! [X27310,X27311,X27312,X27313,X27314,X27315,X27316,X27317] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(X27317,X27316),tc_fun(tc_prod(X27315,X27314),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27317,X27316),X27313),hAPP(c_COMBK(tc_fun(X27316,tc_HOL_Obool),X27317),X27312))),hAPP(c_Product__Type_Oprod_Oprod__case(X27317,X27316,tc_fun(tc_prod(X27315,X27314),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X27317,tc_fun(X27316,tc_fun(X27315,tc_fun(X27314,tc_HOL_Obool))),tc_fun(X27316,tc_fun(tc_prod(X27315,X27314),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27315,tc_fun(X27314,tc_HOL_Obool)),tc_fun(tc_prod(X27315,X27314),tc_HOL_Obool)),tc_fun(tc_fun(X27316,tc_fun(X27315,tc_fun(X27314,tc_HOL_Obool))),tc_fun(X27316,tc_fun(tc_prod(X27315,X27314),tc_HOL_Obool))),X27317),c_COMBB(tc_fun(X27315,tc_fun(X27314,tc_HOL_Obool)),tc_fun(tc_prod(X27315,X27314),tc_HOL_Obool),X27316)),hAPP(hAPP(c_COMBB(tc_fun(X27315,tc_HOL_Obool),tc_fun(tc_fun(X27315,tc_fun(X27314,tc_HOL_Obool)),tc_fun(tc_prod(X27315,X27314),tc_HOL_Obool)),X27317),c_Product__Type_OSigma(X27315,X27314)),X27311))),hAPP(hAPP(c_COMBB(tc_fun(X27314,tc_HOL_Obool),tc_fun(X27315,tc_fun(X27314,tc_HOL_Obool)),X27316),c_COMBK(tc_fun(X27314,tc_HOL_Obool),X27315)),X27310)))) = hAPP(hAPP(c_Product__Type_OSigma(X27315,X27314),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27317,tc_fun(X27315,tc_HOL_Obool)),X27313),X27311)),hAPP(c_COMBK(tc_fun(X27314,tc_HOL_Obool),X27315),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27316,tc_fun(X27314,tc_HOL_Obool)),X27312),X27310))),
    inference(variable_rename,[status(thm)],[fact_UN__Times__distrib]) ).

fof(i_0_6199,plain,
    ! [X26674,X26675] :
      ( ( ~ c_Equiv__Relations_Oequiv(X26675,c_Orderings_Otop__class_Otop(tc_fun(X26675,tc_HOL_Obool)),X26674)
        | c_Equiv__Relations_Oequivp(X26675,hAPP(hAPP(c_COMBC(X26675,tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_fun(X26675,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26675,tc_fun(tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_fun(X26675,tc_HOL_Obool)),X26675),c_COMBC(X26675,tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26675,tc_prod(X26675,X26675)),tc_fun(X26675,tc_fun(tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_HOL_Obool)),X26675),hAPP(c_COMBB(tc_prod(X26675,X26675),tc_fun(tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_HOL_Obool),X26675),c_member(tc_prod(X26675,X26675)))),c_Product__Type_OPair(X26675,X26675)))),X26674)) )
      & ( ~ c_Equiv__Relations_Oequivp(X26675,hAPP(hAPP(c_COMBC(X26675,tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_fun(X26675,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26675,tc_fun(tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_fun(X26675,tc_HOL_Obool)),X26675),c_COMBC(X26675,tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26675,tc_prod(X26675,X26675)),tc_fun(X26675,tc_fun(tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_HOL_Obool)),X26675),hAPP(c_COMBB(tc_prod(X26675,X26675),tc_fun(tc_fun(tc_prod(X26675,X26675),tc_HOL_Obool),tc_HOL_Obool),X26675),c_member(tc_prod(X26675,X26675)))),c_Product__Type_OPair(X26675,X26675)))),X26674))
        | c_Equiv__Relations_Oequiv(X26675,c_Orderings_Otop__class_Otop(tc_fun(X26675,tc_HOL_Obool)),X26674) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__equiv])]) ).

fof(i_0_6200,plain,
    ! [X28263,X28264] :
      ( ( ~ c_Wellfounded_OwfP(X28264,hAPP(hAPP(c_COMBC(X28264,tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_fun(X28264,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28264,tc_fun(tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_fun(X28264,tc_HOL_Obool)),X28264),c_COMBC(X28264,tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28264,tc_prod(X28264,X28264)),tc_fun(X28264,tc_fun(tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_HOL_Obool)),X28264),hAPP(c_COMBB(tc_prod(X28264,X28264),tc_fun(tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_HOL_Obool),X28264),c_member(tc_prod(X28264,X28264)))),c_Product__Type_OPair(X28264,X28264)))),X28263))
        | c_Wellfounded_Owf(X28264,X28263) )
      & ( ~ c_Wellfounded_Owf(X28264,X28263)
        | c_Wellfounded_OwfP(X28264,hAPP(hAPP(c_COMBC(X28264,tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_fun(X28264,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28264,tc_fun(tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_fun(X28264,tc_HOL_Obool)),X28264),c_COMBC(X28264,tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28264,tc_prod(X28264,X28264)),tc_fun(X28264,tc_fun(tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_HOL_Obool)),X28264),hAPP(c_COMBB(tc_prod(X28264,X28264),tc_fun(tc_fun(tc_prod(X28264,X28264),tc_HOL_Obool),tc_HOL_Obool),X28264),c_member(tc_prod(X28264,X28264)))),c_Product__Type_OPair(X28264,X28264)))),X28263)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__wf__eq])]) ).

fof(i_0_6201,plain,
    ! [X21859,X21860,X21861,X21862] :
      ( ( hAPP(hAPP(c_COMBC(X21862,tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool)),X21862),c_COMBC(X21861,tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_prod(X21862,X21861)),tc_fun(X21861,tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),X21862),hAPP(c_COMBB(tc_prod(X21862,X21861),tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool),X21861),c_member(tc_prod(X21862,X21861)))),c_Product__Type_OPair(X21862,X21861)))),X21860) != hAPP(hAPP(c_COMBC(X21862,tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool)),X21862),c_COMBC(X21861,tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_prod(X21862,X21861)),tc_fun(X21861,tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),X21862),hAPP(c_COMBB(tc_prod(X21862,X21861),tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool),X21861),c_member(tc_prod(X21862,X21861)))),c_Product__Type_OPair(X21862,X21861)))),X21859)
        | X21860 = X21859 )
      & ( X21860 != X21859
        | hAPP(hAPP(c_COMBC(X21862,tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool)),X21862),c_COMBC(X21861,tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_prod(X21862,X21861)),tc_fun(X21861,tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),X21862),hAPP(c_COMBB(tc_prod(X21862,X21861),tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool),X21861),c_member(tc_prod(X21862,X21861)))),c_Product__Type_OPair(X21862,X21861)))),X21860) = hAPP(hAPP(c_COMBC(X21862,tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_fun(X21861,tc_HOL_Obool)),X21862),c_COMBC(X21861,tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X21861,tc_prod(X21862,X21861)),tc_fun(X21861,tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool)),X21862),hAPP(c_COMBB(tc_prod(X21862,X21861),tc_fun(tc_fun(tc_prod(X21862,X21861),tc_HOL_Obool),tc_HOL_Obool),X21861),c_member(tc_prod(X21862,X21861)))),c_Product__Type_OPair(X21862,X21861)))),X21859) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq2])]) ).

fof(i_0_6202,plain,
    ! [X28340,X28341,X28342,X28343,X28344,X28345] :
      ( ( X28340 = hAPP(hAPP(c_Product__Type_OPair(X28343,X28342),esk309_6(X28340,X28341,X28342,X28343,X28344,X28345)),esk310_6(X28340,X28341,X28342,X28343,X28344,X28345))
        | ~ hBOOL(hAPP(hAPP(c_member(X28345),X28344),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28343,X28342,tc_fun(X28345,tc_HOL_Obool)),X28341),X28340))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28345),X28344),hAPP(hAPP(X28341,esk309_6(X28340,X28341,X28342,X28343,X28344,X28345)),esk310_6(X28340,X28341,X28342,X28343,X28344,X28345))))
        | ~ hBOOL(hAPP(hAPP(c_member(X28345),X28344),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28343,X28342,tc_fun(X28345,tc_HOL_Obool)),X28341),X28340))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5263])])])]) ).

fof(i_0_6203,plain,
    ! [X30708,X30709,X30710,X30711,X30712,X30713,X30714,X30715] : hAPP(hAPP(c_List_Omap(tc_prod(X30715,X30714),X30713),X30712),hAPP(hAPP(c_List_Ozip(X30715,X30714),X30711),hAPP(hAPP(c_List_Omap(X30710,X30714),X30709),X30708))) = hAPP(hAPP(c_List_Omap(tc_prod(X30715,X30710),X30713),hAPP(c_Product__Type_Oprod_Oprod__case(X30715,X30710,X30713),hAPP(hAPP(c_COMBB(tc_fun(X30710,tc_prod(X30715,X30714)),tc_fun(X30710,X30713),X30715),hAPP(c_COMBB(tc_prod(X30715,X30714),X30713,X30710),X30712)),hAPP(hAPP(c_COMBC(X30715,tc_fun(X30710,X30714),tc_fun(X30710,tc_prod(X30715,X30714))),hAPP(hAPP(c_COMBB(tc_fun(X30714,tc_prod(X30715,X30714)),tc_fun(tc_fun(X30710,X30714),tc_fun(X30710,tc_prod(X30715,X30714))),X30715),c_COMBB(X30714,tc_prod(X30715,X30714),X30710)),c_Product__Type_OPair(X30715,X30714))),X30709)))),hAPP(hAPP(c_List_Ozip(X30715,X30710),X30711),X30708)),
    inference(variable_rename,[status(thm)],[fact_map__zip__map2]) ).

fof(i_0_6204,plain,
    ! [X19848,X19849,X19850,X19851,X19852,X19853,X19854] :
      ( ( X19849 = hAPP(hAPP(X19852,X19848),esk50_7(X19848,X19849,X19850,X19851,X19852,X19853,X19854))
        | ~ hBOOL(hAPP(hAPP(c_member(X19854),X19848),X19850))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19854,X19853,X19852,X19851,X19850),X19849))
        | ~ c_Finite__Set_Ofun__left__comm(X19854,X19853,X19852) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19854,X19853,X19852,X19851,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19854,tc_HOL_Obool)),X19850),hAPP(hAPP(c_Set_Oinsert(X19854),X19848),c_Orderings_Obot__class_Obot(tc_fun(X19854,tc_HOL_Obool))))),esk50_7(X19848,X19849,X19850,X19851,X19852,X19853,X19854)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19854),X19848),X19850))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19854,X19853,X19852,X19851,X19850),X19849))
        | ~ c_Finite__Set_Ofun__left__comm(X19854,X19853,X19852) ) ),
    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_6205,plain,
    ! [X19933,X19934,X19935,X19936,X19937,X19938,X19939] :
      ( ( X19933 = hAPP(hAPP(X19937,X19935),esk51_7(X19933,X19934,X19935,X19936,X19937,X19938,X19939))
        | hBOOL(hAPP(hAPP(c_member(X19939),X19935),X19934))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19939,X19938,X19937,X19936,hAPP(hAPP(c_Set_Oinsert(X19939),X19935),X19934)),X19933))
        | ~ c_Finite__Set_Ofun__left__comm(X19939,X19938,X19937) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19939,X19938,X19937,X19936,X19934),esk51_7(X19933,X19934,X19935,X19936,X19937,X19938,X19939)))
        | hBOOL(hAPP(hAPP(c_member(X19939),X19935),X19934))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19939,X19938,X19937,X19936,hAPP(hAPP(c_Set_Oinsert(X19939),X19935),X19934)),X19933))
        | ~ c_Finite__Set_Ofun__left__comm(X19939,X19938,X19937) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5264])])])]) ).

fof(i_0_6206,plain,
    ! [X29965,X29966,X29967,X29968,X29969] : hAPP(hAPP(c_List_Ozip(X29969,X29968),hAPP(hAPP(c_List_Olist_OCons(X29969),X29967),X29966)),X29965) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(X29969,X29968)),X29968,c_List_Olist_ONil(tc_prod(X29969,X29968)),hAPP(hAPP(c_COMBC(X29968,tc_fun(tc_List_Olist(X29968),tc_List_Olist(tc_prod(X29969,X29968))),tc_fun(tc_List_Olist(X29968),tc_List_Olist(tc_prod(X29969,X29968)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(X29969,X29968)),tc_List_Olist(tc_prod(X29969,X29968))),tc_fun(tc_fun(tc_List_Olist(X29968),tc_List_Olist(tc_prod(X29969,X29968))),tc_fun(tc_List_Olist(X29968),tc_List_Olist(tc_prod(X29969,X29968)))),X29968),c_COMBB(tc_List_Olist(tc_prod(X29969,X29968)),tc_List_Olist(tc_prod(X29969,X29968)),tc_List_Olist(X29968))),hAPP(hAPP(c_COMBB(tc_prod(X29969,X29968),tc_fun(tc_List_Olist(tc_prod(X29969,X29968)),tc_List_Olist(tc_prod(X29969,X29968))),X29968),c_List_Olist_OCons(tc_prod(X29969,X29968))),hAPP(c_Product__Type_OPair(X29969,X29968),X29967)))),hAPP(c_List_Ozip(X29969,X29968),X29966))),X29965),
    inference(variable_rename,[status(thm)],[fact_zip__Cons1]) ).

cnf(i_0_6207,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_5265]) ).

cnf(i_0_6208,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_5254]) ).

cnf(i_0_6209,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_5254]) ).

cnf(i_0_6210,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_5266]) ).

fof(i_0_6211,plain,
    ! [X28054,X28055,X28056,X28057] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28057),esk289_4(X28054,X28055,X28056,X28057)),X28056))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28055),hAPP(c_Set_Oimage(X28057,X28055,X28054),X28056)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X28057),X28056)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28057),hAPP(c_Set_OCollect(X28057),hAPP(hAPP(c_COMBS(X28057,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28057),c_fconj),hAPP(hAPP(c_COMBC(X28057,tc_fun(X28057,tc_HOL_Obool),tc_HOL_Obool),c_member(X28057)),X28056))),hAPP(hAPP(c_COMBC(X28057,X28055,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28055,tc_fun(X28055,tc_HOL_Obool),X28057),c_fequal),X28054)),hAPP(X28054,esk289_4(X28054,X28055,X28056,X28057)))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28055),hAPP(c_Set_Oimage(X28057,X28055,X28054),X28056)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X28057),X28056)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5267])])])]) ).

fof(i_0_6212,plain,
    ! [X28241,X28242,X28243,X28244] :
      ( ( hBOOL(hAPP(X28244,esk297_4(X28241,X28242,X28243,X28244)))
        | c_Wellfounded_Owf(X28241,hAPP(c_Set_OCollect(tc_prod(X28241,X28241)),hAPP(c_Product__Type_Oprod_Oprod__case(X28241,X28241,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28241,tc_HOL_Obool),tc_fun(X28241,tc_HOL_Obool),X28241),hAPP(c_COMBS(X28241,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28241),c_fconj),X28244))),hAPP(hAPP(c_COMBC(X28241,tc_fun(X28241,X28241),tc_fun(X28241,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28241,tc_HOL_Obool),tc_fun(tc_fun(X28241,X28241),tc_fun(X28241,tc_HOL_Obool)),X28241),c_COMBB(X28241,tc_HOL_Obool,X28241)),c_fequal)),X28242))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X28243,hAPP(X28242,esk297_4(X28241,X28242,X28243,X28244)))),hAPP(X28243,esk297_4(X28241,X28242,X28243,X28244))))
        | c_Wellfounded_Owf(X28241,hAPP(c_Set_OCollect(tc_prod(X28241,X28241)),hAPP(c_Product__Type_Oprod_Oprod__case(X28241,X28241,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28241,tc_HOL_Obool),tc_fun(X28241,tc_HOL_Obool),X28241),hAPP(c_COMBS(X28241,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28241),c_fconj),X28244))),hAPP(hAPP(c_COMBC(X28241,tc_fun(X28241,X28241),tc_fun(X28241,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28241,tc_HOL_Obool),tc_fun(tc_fun(X28241,X28241),tc_fun(X28241,tc_HOL_Obool)),X28241),c_COMBB(X28241,tc_HOL_Obool,X28241)),c_fequal)),X28242))))) ) ),
    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_6213,plain,
    ! [X27987,X27988,X27989] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27989,X27989),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27989,X27989,X27989),X27988),X27987)),X27988))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X27989,tc_HOL_Obool),tc_fun(X27989,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X27989,tc_HOL_Obool),tc_fun(X27989,tc_HOL_Obool),tc_fun(X27989,tc_HOL_Obool)),c_Wellfounded_Omax__ext(X27989,X27988)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X27989,tc_HOL_Obool),tc_fun(X27989,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(X27989,X27987)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X27989,tc_HOL_Obool),tc_fun(X27989,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27989,tc_HOL_Obool),tc_fun(X27989,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X27989,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X27989,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X27989,tc_HOL_Obool),tc_fun(X27989,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(X27989,X27988))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__compat])]) ).

fof(i_0_6214,plain,
    ! [X27990,X27991,X27992] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27992,X27992),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27992,X27992,X27992),X27991),X27990)),X27991))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(X27992,tc_HOL_Obool),tc_fun(X27992,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(X27992,tc_HOL_Obool),tc_fun(X27992,tc_HOL_Obool),tc_fun(X27992,tc_HOL_Obool)),c_Wellfounded_Omin__ext(X27992,X27991)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(X27992,tc_HOL_Obool),tc_fun(X27992,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(X27992,X27990)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(X27992,tc_HOL_Obool),tc_fun(X27992,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X27992,tc_HOL_Obool),tc_fun(X27992,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X27992,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(X27992,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(X27992,tc_HOL_Obool),tc_fun(X27992,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(X27992,X27991))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__compat])]) ).

cnf(i_0_6215,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)))),esk423_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5268]) ).

cnf(i_0_6216,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)))),esk422_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_5269]) ).

fof(i_0_6217,plain,
    ! [X27686,X27687,X27688,X27689,X27690] :
      ( ~ class_Groups_Ocomm__monoid__add(X27690)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27689),X27688))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27689,X27690),X27687),hAPP(c_Set_OCollect(X27689),hAPP(hAPP(c_COMBS(X27689,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27689),c_fconj),hAPP(hAPP(c_COMBC(X27689,tc_fun(X27689,tc_HOL_Obool),tc_HOL_Obool),c_member(X27689)),X27688))),hAPP(hAPP(c_COMBC(X27689,tc_fun(X27689,tc_HOL_Obool),tc_HOL_Obool),c_member(X27689)),X27686)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27689,X27690),hAPP(hAPP(c_COMBC(X27689,X27690,X27690),hAPP(hAPP(c_COMBS(X27689,X27690,tc_fun(X27690,X27690)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27690,tc_fun(X27690,X27690)),X27689),c_If(X27690)),hAPP(hAPP(c_COMBC(X27689,tc_fun(X27689,tc_HOL_Obool),tc_HOL_Obool),c_member(X27689)),X27686))),X27687)),c_Groups_Ozero__class_Ozero(X27690))),X27688) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set_H])]) ).

cnf(i_0_6218,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_5270]) ).

cnf(i_0_6219,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_5271]) ).

cnf(i_0_6220,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_5272]) ).

fof(i_0_6221,plain,
    ! [X30686,X30687,X30688,X30689,X30690,X30691,X30692,X30693] : hAPP(hAPP(c_List_Ozip(X30693,X30692),hAPP(hAPP(c_List_Omap(X30691,X30693),X30690),X30689)),hAPP(hAPP(c_List_Omap(X30688,X30692),X30687),X30686)) = hAPP(hAPP(c_List_Omap(tc_prod(X30691,X30688),tc_prod(X30693,X30692)),hAPP(c_Product__Type_Oprod_Oprod__case(X30691,X30688,tc_prod(X30693,X30692)),hAPP(hAPP(c_COMBC(X30691,tc_fun(X30688,X30692),tc_fun(X30688,tc_prod(X30693,X30692))),hAPP(hAPP(c_COMBB(tc_fun(X30692,tc_prod(X30693,X30692)),tc_fun(tc_fun(X30688,X30692),tc_fun(X30688,tc_prod(X30693,X30692))),X30691),c_COMBB(X30692,tc_prod(X30693,X30692),X30688)),hAPP(hAPP(c_COMBB(X30693,tc_fun(X30692,tc_prod(X30693,X30692)),X30691),c_Product__Type_OPair(X30693,X30692)),X30690))),X30687))),hAPP(hAPP(c_List_Ozip(X30691,X30688),X30689),X30686)),
    inference(variable_rename,[status(thm)],[fact_zip__map__map]) ).

cnf(i_0_6222,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_5273]) ).

cnf(i_0_6223,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_5274]) ).

fof(i_0_6224,plain,
    ! [X27741] : c_Wellfounded_Ofinite__psubset(X27741) = hAPP(c_Set_OCollect(tc_prod(tc_fun(X27741,tc_HOL_Obool),tc_fun(X27741,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(X27741,tc_HOL_Obool),tc_fun(X27741,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(X27741,tc_HOL_Obool),tc_fun(tc_fun(X27741,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27741,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27741,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(X27741,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27741,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(X27741,tc_HOL_Obool)),c_COMBS(tc_fun(X27741,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X27741,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X27741,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(X27741,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X27741,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(X27741,tc_HOL_Obool))))),c_Finite__Set_Ofinite(X27741)))),
    inference(variable_rename,[status(thm)],[fact_finite__psubset__def]) ).

cnf(i_0_6225,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_5275]) ).

cnf(i_0_6226,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_5276]) ).

fof(i_0_6227,plain,
    ! [X29808,X29809] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29809),X29808))
        | c_Nitpick_Ocard_H(X29809,X29808) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29809)),c_Hilbert__Choice_OEps(tc_List_Olist(X29809),hAPP(hAPP(c_COMBS(tc_List_Olist(X29809),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X29809)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X29809),tc_fun(X29809,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29809,tc_HOL_Obool),tc_fun(tc_fun(X29809,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29809)),c_fequal),c_List_Oset(X29809))),X29808))),c_List_Odistinct(X29809)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X29809),X29808))
        | c_Nitpick_Ocard_H(X29809,X29808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5277])]) ).

fof(i_0_6228,plain,
    ! [X27707,X27708] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27708))
      | 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)),X27708))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X27707)))) = 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)),X27708))),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,X27707))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5278])]) ).

fof(i_0_6229,plain,
    ! [X27382,X27383,X27384,X27385,X27386,X27387,X27388,X27389,X27390] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27390,X27389)),hAPP(hAPP(c_Product__Type_OPair(X27390,X27389),X27388),X27387)),X27386))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27385,X27384)),hAPP(hAPP(c_Product__Type_OPair(X27385,X27384),hAPP(X27383,X27388)),hAPP(X27382,X27387))),hAPP(c_Set_Oimage(tc_prod(X27390,X27389),tc_prod(X27385,X27384),c_Product__Type_Omap__pair(X27390,X27385,X27389,X27384,X27383,X27382)),X27386))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__imageI])]) ).

cnf(i_0_6230,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_5279]) ).

cnf(i_0_6231,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_5280]) ).

fof(i_0_6232,plain,
    ! [X32374,X32375,X32376,X32377,X32378,X32379,X32380] : c_New__Random__Sequence_Oneg__decr__bind(X32380,X32379,X32378,X32377,X32376,X32375,X32374) = c_New__DSequence_Oneg__decr__bind(X32380,X32379,hAPP(hAPP(hAPP(X32378,X32376),X32375),X32374),hAPP(hAPP(c_COMBC(X32380,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(X32379)))),hAPP(hAPP(c_COMBC(X32380,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(X32379))))),hAPP(hAPP(c_COMBC(X32380,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(X32379)))))),X32377),X32376)),X32375)),X32374)),
    inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Oneg__decr__bind__def]) ).

fof(i_0_6233,plain,
    ! [X28311,X28312,X28313,X28314] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28314,tc_fun(X28313,tc_HOL_Obool)),X28312),X28311) = hAPP(c_Set_OCollect(X28313),hAPP(hAPP(c_COMBB(tc_fun(X28314,tc_HOL_Obool),tc_HOL_Obool,X28313),c_HOL_OAll(X28314)),hAPP(hAPP(c_COMBB(tc_fun(X28314,tc_HOL_Obool),tc_fun(X28314,tc_HOL_Obool),X28313),hAPP(c_COMBS(X28314,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28314),c_fimplies),hAPP(hAPP(c_COMBC(X28314,tc_fun(X28314,tc_HOL_Obool),tc_HOL_Obool),c_member(X28314)),X28312)))),hAPP(hAPP(c_COMBC(X28313,tc_fun(X28314,tc_fun(X28313,tc_HOL_Obool)),tc_fun(X28314,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28313,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X28314,tc_fun(X28313,tc_HOL_Obool)),tc_fun(X28314,tc_HOL_Obool)),X28313),c_COMBB(tc_fun(X28313,tc_HOL_Obool),tc_HOL_Obool,X28314)),c_member(X28313))),X28311)))),
    inference(variable_rename,[status(thm)],[fact_INTER__def]) ).

fof(i_0_6234,plain,
    ! [X28301,X28302,X28303,X28304,X28305,X28306,X28307,X28308,X28309] :
      ( ( ~ c_Equiv__Relations_Ocongruent(X28304,X28303,X28302,X28301)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28304,X28304)),X28305),X28302))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28304,X28304,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28304,tc_fun(X28304,X28303),tc_fun(X28304,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28303,tc_HOL_Obool),tc_fun(tc_fun(X28304,X28303),tc_fun(X28304,tc_HOL_Obool)),X28304),c_COMBB(X28303,tc_HOL_Obool,X28304)),hAPP(hAPP(c_COMBB(X28303,tc_fun(X28303,tc_HOL_Obool),X28304),c_fequal),X28301))),X28301)),X28305)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28309,X28309)),esk303_4(X28306,X28307,X28308,X28309)),X28307))
        | c_Equiv__Relations_Ocongruent(X28309,X28308,X28307,X28306) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28309,X28309,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28309,tc_fun(X28309,X28308),tc_fun(X28309,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X28308,tc_HOL_Obool),tc_fun(tc_fun(X28309,X28308),tc_fun(X28309,tc_HOL_Obool)),X28309),c_COMBB(X28308,tc_HOL_Obool,X28309)),hAPP(hAPP(c_COMBB(X28308,tc_fun(X28308,tc_HOL_Obool),X28309),c_fequal),X28306))),X28306)),esk303_4(X28306,X28307,X28308,X28309)))
        | c_Equiv__Relations_Ocongruent(X28309,X28308,X28307,X28306) ) ),
    inference(distribute,[status(thm)],[inference(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_6235,plain,
    ! [X27732,X27733,X27734,X27735,X27736] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27733),hAPP(c_Set_OCollect(X27733),hAPP(hAPP(c_COMBB(tc_fun(X27735,tc_HOL_Obool),tc_HOL_Obool,X27733),c_HOL_OEx(X27735)),hAPP(hAPP(c_COMBB(tc_fun(X27735,tc_HOL_Obool),tc_fun(X27735,tc_HOL_Obool),X27733),hAPP(c_COMBS(X27735,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27735),c_fconj),X27734))),X27732)))))
        | ~ hBOOL(hAPP(X27734,X27736))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27733),hAPP(c_Set_OCollect(X27733),hAPP(hAPP(c_COMBC(X27733,X27735,tc_HOL_Obool),X27732),X27736))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27735),hAPP(c_Set_OCollect(X27735),X27734))) )
      & ( hBOOL(hAPP(X27734,esk281_4(X27732,X27733,X27734,X27735)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27733),hAPP(c_Set_OCollect(X27733),hAPP(hAPP(c_COMBB(tc_fun(X27735,tc_HOL_Obool),tc_HOL_Obool,X27733),c_HOL_OEx(X27735)),hAPP(hAPP(c_COMBB(tc_fun(X27735,tc_HOL_Obool),tc_fun(X27735,tc_HOL_Obool),X27733),hAPP(c_COMBS(X27735,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27735),c_fconj),X27734))),X27732)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27735),hAPP(c_Set_OCollect(X27735),X27734))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27733),hAPP(c_Set_OCollect(X27733),hAPP(hAPP(c_COMBC(X27733,X27735,tc_HOL_Obool),X27732),esk281_4(X27732,X27733,X27734,X27735)))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27733),hAPP(c_Set_OCollect(X27733),hAPP(hAPP(c_COMBB(tc_fun(X27735,tc_HOL_Obool),tc_HOL_Obool,X27733),c_HOL_OEx(X27735)),hAPP(hAPP(c_COMBB(tc_fun(X27735,tc_HOL_Obool),tc_fun(X27735,tc_HOL_Obool),X27733),hAPP(c_COMBS(X27735,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27735),c_fconj),X27734))),X27732)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27735),hAPP(c_Set_OCollect(X27735),X27734))) ) ),
    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_6236,plain,
    ! [X27349,X27350,X27351,X27352,X27353,X27354] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27353),esk261_6(X27349,X27350,X27351,X27352,X27353,X27354)),X27352))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27353,X27354),hAPP(hAPP(c_COMBS(X27353,tc_fun(X27351,tc_HOL_Obool),X27354),hAPP(hAPP(c_COMBB(tc_fun(X27351,X27354),tc_fun(tc_fun(X27351,tc_HOL_Obool),X27354),X27353),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27351,X27354)),X27349)),X27350)),X27352) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27353,X27351),X27354),hAPP(c_Product__Type_Oprod_Oprod__case(X27353,X27351,X27354),X27349)),hAPP(hAPP(c_Product__Type_OSigma(X27353,X27351),X27352),X27350))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27353),X27352))
        | ~ class_Groups_Ocomm__monoid__add(X27354) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27351),hAPP(X27350,esk261_6(X27349,X27350,X27351,X27352,X27353,X27354))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27353,X27354),hAPP(hAPP(c_COMBS(X27353,tc_fun(X27351,tc_HOL_Obool),X27354),hAPP(hAPP(c_COMBB(tc_fun(X27351,X27354),tc_fun(tc_fun(X27351,tc_HOL_Obool),X27354),X27353),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27351,X27354)),X27349)),X27350)),X27352) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27353,X27351),X27354),hAPP(c_Product__Type_Oprod_Oprod__case(X27353,X27351,X27354),X27349)),hAPP(hAPP(c_Product__Type_OSigma(X27353,X27351),X27352),X27350))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27353),X27352))
        | ~ class_Groups_Ocomm__monoid__add(X27354) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Sigma])])])]) ).

fof(i_0_6237,plain,
    ! [X27342,X27343,X27344,X27345,X27346,X27347] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27346),esk260_6(X27342,X27343,X27344,X27345,X27346,X27347)),X27345))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27346,X27347),hAPP(hAPP(c_COMBS(X27346,tc_fun(X27344,tc_HOL_Obool),X27347),hAPP(hAPP(c_COMBB(tc_fun(X27344,X27347),tc_fun(tc_fun(X27344,tc_HOL_Obool),X27347),X27346),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27344,X27347)),X27342)),X27343)),X27345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27346,X27344),X27347),hAPP(c_Product__Type_Oprod_Oprod__case(X27346,X27344,X27347),X27342)),hAPP(hAPP(c_Product__Type_OSigma(X27346,X27344),X27345),X27343))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27346),X27345))
        | ~ class_Groups_Ocomm__monoid__mult(X27347) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27344),hAPP(X27343,esk260_6(X27342,X27343,X27344,X27345,X27346,X27347))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27346,X27347),hAPP(hAPP(c_COMBS(X27346,tc_fun(X27344,tc_HOL_Obool),X27347),hAPP(hAPP(c_COMBB(tc_fun(X27344,X27347),tc_fun(tc_fun(X27344,tc_HOL_Obool),X27347),X27346),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27344,X27347)),X27342)),X27343)),X27345) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27346,X27344),X27347),hAPP(c_Product__Type_Oprod_Oprod__case(X27346,X27344,X27347),X27342)),hAPP(hAPP(c_Product__Type_OSigma(X27346,X27344),X27345),X27343))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27346),X27345))
        | ~ class_Groups_Ocomm__monoid__mult(X27347) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Sigma])])])]) ).

fof(i_0_6238,plain,
    ! [X25431,X25432,X25433,X25434,X25435] :
      ( ~ class_Groups_Ocomm__monoid__add(X25435)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25434),X25433))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25434,X25435),X25432),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25434,tc_HOL_Obool)),X25433),X25431)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25434,X25435),hAPP(hAPP(c_COMBC(X25434,X25435,X25435),hAPP(hAPP(c_COMBS(X25434,X25435,tc_fun(X25435,X25435)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X25435,tc_fun(X25435,X25435)),X25434),c_If(X25435)),hAPP(hAPP(c_COMBC(X25434,tc_fun(X25434,tc_HOL_Obool),tc_HOL_Obool),c_member(X25434)),X25431))),X25432)),c_Groups_Ozero__class_Ozero(X25435))),X25433) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__restrict__set])]) ).

fof(i_0_6239,plain,
    ! [X26957,X26958,X26959,X26960,X26961,X26962] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26962),X26959),X26960))
        | hAPP(c_Set_Ovimage(X26958,X26962,hAPP(hAPP(c_COMBC(X26958,X26962,X26962),hAPP(hAPP(c_COMBC(X26958,X26962,tc_fun(X26962,X26962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26962,tc_fun(X26962,X26962)),X26958),c_If(X26962)),hAPP(hAPP(c_COMBC(X26958,tc_fun(X26958,tc_HOL_Obool),tc_HOL_Obool),c_member(X26958)),X26957))),X26961)),X26959)),X26960) = c_Orderings_Otop__class_Otop(tc_fun(X26958,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X26962),X26961),X26960)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26962),X26959),X26960))
        | hAPP(c_Set_Ovimage(X26958,X26962,hAPP(hAPP(c_COMBC(X26958,X26962,X26962),hAPP(hAPP(c_COMBC(X26958,X26962,tc_fun(X26962,X26962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26962,tc_fun(X26962,X26962)),X26958),c_If(X26962)),hAPP(hAPP(c_COMBC(X26958,tc_fun(X26958,tc_HOL_Obool),tc_HOL_Obool),c_member(X26958)),X26957))),X26961)),X26959)),X26960) = X26957
        | ~ hBOOL(hAPP(hAPP(c_member(X26962),X26961),X26960)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26962),X26959),X26960))
        | hAPP(c_Set_Ovimage(X26958,X26962,hAPP(hAPP(c_COMBC(X26958,X26962,X26962),hAPP(hAPP(c_COMBC(X26958,X26962,tc_fun(X26962,X26962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26962,tc_fun(X26962,X26962)),X26958),c_If(X26962)),hAPP(hAPP(c_COMBC(X26958,tc_fun(X26958,tc_HOL_Obool),tc_HOL_Obool),c_member(X26958)),X26957))),X26961)),X26959)),X26960) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26958,tc_HOL_Obool)),X26957)
        | hBOOL(hAPP(hAPP(c_member(X26962),X26961),X26960)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26962),X26959),X26960))
        | hAPP(c_Set_Ovimage(X26958,X26962,hAPP(hAPP(c_COMBC(X26958,X26962,X26962),hAPP(hAPP(c_COMBC(X26958,X26962,tc_fun(X26962,X26962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X26962,tc_fun(X26962,X26962)),X26958),c_If(X26962)),hAPP(hAPP(c_COMBC(X26958,tc_fun(X26958,tc_HOL_Obool),tc_HOL_Obool),c_member(X26958)),X26957))),X26961)),X26959)),X26960) = c_Orderings_Obot__class_Obot(tc_fun(X26958,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X26962),X26961),X26960)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5281])])]) ).

fof(i_0_6240,plain,
    ! [X26285,X26286,X26287,X26288] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26288,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk227_4(X26285,X26286,X26287,X26288))),X26287)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26288,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(X26285,X26286,X26287,X26288)),X26286))),X26285)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26288,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26288,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26287)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26288,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26285))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__subset])])]) ).

cnf(i_0_6241,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_5282]) ).

fof(i_0_6242,plain,
    ! [X32381,X32382,X32383,X32384,X32385,X32386,X32387] : c_New__Random__Sequence_Opos__decr__bind(X32387,X32386,X32385,X32384,X32383,X32382,X32381) = c_New__DSequence_Opos__decr__bind(X32387,X32386,hAPP(hAPP(hAPP(X32385,X32383),X32382),X32381),hAPP(hAPP(c_COMBC(X32387,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32386))),hAPP(hAPP(c_COMBC(X32387,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(X32386)))),hAPP(hAPP(c_COMBC(X32387,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(X32386))))),X32384),X32383)),X32382)),X32381)),
    inference(variable_rename,[status(thm)],[fact_New__Random__Sequence_Opos__decr__bind__def]) ).

cnf(i_0_6243,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_5283]) ).

cnf(i_0_6244,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_5284]) ).

cnf(i_0_6245,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_5285]) ).

cnf(i_0_6246,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_5286]) ).

cnf(i_0_6247,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_5287]) ).

fof(i_0_6248,plain,
    ! [X27124,X27125,X27126,X27127,X27128,X27129] : hAPP(c_Set_Oimage(X27129,tc_prod(X27128,X27127),hAPP(hAPP(c_COMBS(X27129,X27127,tc_prod(X27128,X27127)),hAPP(hAPP(c_COMBB(X27128,tc_fun(X27127,tc_prod(X27128,X27127)),X27129),c_Product__Type_OPair(X27128,X27127)),X27126)),X27125)),X27124) = hAPP(hAPP(c_Product__Type_OSigma(X27128,X27127),hAPP(c_Set_Oimage(X27129,X27128,X27126),X27124)),hAPP(hAPP(c_COMBB(tc_fun(X27129,tc_HOL_Obool),tc_fun(X27127,tc_HOL_Obool),X27128),c_Set_Oimage(X27129,X27127,X27125)),hAPP(hAPP(c_COMBC(X27128,tc_fun(X27129,tc_HOL_Obool),tc_fun(X27129,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27129,tc_HOL_Obool),tc_fun(tc_fun(X27129,tc_HOL_Obool),tc_fun(X27129,tc_HOL_Obool)),X27128),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27129,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X27128,tc_HOL_Obool),tc_fun(X27129,tc_HOL_Obool),X27128),c_Set_Ovimage(X27129,X27128,X27126)),hAPP(hAPP(c_COMBC(X27128,tc_fun(X27128,tc_HOL_Obool),tc_fun(X27128,tc_HOL_Obool)),c_Set_Oinsert(X27128)),c_Orderings_Obot__class_Obot(tc_fun(X27128,tc_HOL_Obool)))))),X27124))),
    inference(variable_rename,[status(thm)],[fact_image__split__eq__Sigma]) ).

cnf(i_0_6249,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_5288]) ).

fof(i_0_6250,plain,
    ! [X32626,X32627] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X32627)
      | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X32627),X32626) = c_Lazy__Sequence_Oappend(tc_List_Olist(X32627),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(X32627)),c_List_Olist_ONil(X32627)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X32627))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X32626)),hAPP(c_Lazy__Sequence_Obind(tc_prod(X32627,tc_List_Olist(X32627)),tc_List_Olist(X32627),c_Lazy__Sequence_Oproduct(X32627,tc_List_Olist(X32627),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X32627,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32626),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(X32627),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X32626),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(X32627,tc_List_Olist(X32627),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X32627))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X32627),tc_List_Olist(X32627)),tc_fun(tc_List_Olist(X32627),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X32627))),X32627),hAPP(c_COMBB(tc_List_Olist(X32627),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(X32627)),tc_List_Olist(X32627)),c_Lazy__Sequence_Osingle(tc_List_Olist(X32627)))),c_List_Olist_OCons(X32627))))),c_Lazy__Sequence_Oempty(tc_List_Olist(X32627)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__list_Osimps])]) ).

fof(i_0_6251,plain,
    ! [X28319,X28320] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X28320)
      | c_Complete__Lattice_OSup__class_OSup(X28320,X28319) = c_Complete__Lattice_OInf__class_OInf(X28320,hAPP(c_Set_OCollect(X28320),hAPP(hAPP(c_COMBB(tc_fun(X28320,tc_HOL_Obool),tc_HOL_Obool,X28320),c_HOL_OAll(X28320)),hAPP(hAPP(c_COMBB(tc_fun(X28320,tc_HOL_Obool),tc_fun(X28320,tc_HOL_Obool),X28320),hAPP(c_COMBS(X28320,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28320),c_fimplies),hAPP(hAPP(c_COMBC(X28320,tc_fun(X28320,tc_HOL_Obool),tc_HOL_Obool),c_member(X28320)),X28319)))),hAPP(c_COMBC(X28320,X28320,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X28320)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__Inf])]) ).

fof(i_0_6252,plain,
    ! [X25636,X25637,X25638,X25639,X25640,X25641] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25640),esk209_6(X25636,X25637,X25638,X25639,X25640,X25641)),X25639))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25640,X25641),X25638),X25639) != X25637
        | ~ hBOOL(hAPP(hAPP(c_member(X25640),X25636),X25639))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25641),hAPP(X25638,X25636)),X25637))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25640),X25639))
        | ~ class_Groups_Oordered__ab__group__add(X25641) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25641),c_Groups_Ozero__class_Ozero(X25641)),hAPP(X25638,esk209_6(X25636,X25637,X25638,X25639,X25640,X25641))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25640,X25641),X25638),X25639) != X25637
        | ~ hBOOL(hAPP(hAPP(c_member(X25640),X25636),X25639))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25641),hAPP(X25638,X25636)),X25637))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25640),X25639))
        | ~ class_Groups_Oordered__ab__group__add(X25641) ) ),
    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_6253,plain,
    ! [X21839,X21840,X21841,X21842,X21843,X21844] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21843),X21841),X21842))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21843,X21844),hAPP(hAPP(c_COMBC(X21843,X21844,X21844),hAPP(hAPP(c_COMBS(X21843,X21844,tc_fun(X21844,X21844)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21844,tc_fun(X21844,X21844)),X21843),c_If(X21844)),hAPP(hAPP(c_COMBC(X21843,X21843,tc_HOL_Obool),c_fequal),X21841))),X21840)),X21839)),X21842) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21844),hAPP(X21840,X21841)),hAPP(hAPP(c_Power_Opower__class_Opower(X21844),X21839),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X21843),X21842)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21843),X21842))
        | ~ class_Groups_Ocomm__monoid__mult(X21844) )
      & ( hBOOL(hAPP(hAPP(c_member(X21843),X21841),X21842))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21843,X21844),hAPP(hAPP(c_COMBC(X21843,X21844,X21844),hAPP(hAPP(c_COMBS(X21843,X21844,tc_fun(X21844,X21844)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21844,tc_fun(X21844,X21844)),X21843),c_If(X21844)),hAPP(hAPP(c_COMBC(X21843,X21843,tc_HOL_Obool),c_fequal),X21841))),X21840)),X21839)),X21842) = hAPP(hAPP(c_Power_Opower__class_Opower(X21844),X21839),hAPP(c_Finite__Set_Ocard(X21843),X21842))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21843),X21842))
        | ~ class_Groups_Ocomm__monoid__mult(X21844) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5289])])]) ).

fof(i_0_6254,plain,
    ! [X24543,X24544,X24545,X24546,X24547] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24546),X24544),X24545))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24546,X24547),hAPP(hAPP(c_COMBC(X24546,X24547,X24547),hAPP(hAPP(c_COMBS(X24546,X24547,tc_fun(X24547,X24547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24547,tc_fun(X24547,X24547)),X24546),c_If(X24547)),hAPP(hAPP(c_COMBC(X24546,X24546,tc_HOL_Obool),c_fequal),X24544))),X24543)),c_Groups_Ozero__class_Ozero(X24547))),X24545) = hAPP(X24543,X24544)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24546),X24545))
        | ~ class_Groups_Ocomm__monoid__add(X24547) )
      & ( hBOOL(hAPP(hAPP(c_member(X24546),X24544),X24545))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24546,X24547),hAPP(hAPP(c_COMBC(X24546,X24547,X24547),hAPP(hAPP(c_COMBS(X24546,X24547,tc_fun(X24547,X24547)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24547,tc_fun(X24547,X24547)),X24546),c_If(X24547)),hAPP(hAPP(c_COMBC(X24546,X24546,tc_HOL_Obool),c_fequal),X24544))),X24543)),c_Groups_Ozero__class_Ozero(X24547))),X24545) = c_Groups_Ozero__class_Ozero(X24547)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24546),X24545))
        | ~ class_Groups_Ocomm__monoid__add(X24547) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5290])])]) ).

fof(i_0_6255,plain,
    ! [X21963,X21964,X21965,X21966,X21967] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21966),X21964),X21965))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21966,X21967),hAPP(hAPP(c_COMBC(X21966,X21967,X21967),hAPP(hAPP(c_COMBS(X21966,X21967,tc_fun(X21967,X21967)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21967,tc_fun(X21967,X21967)),X21966),c_If(X21967)),hAPP(hAPP(c_COMBC(X21966,X21966,tc_HOL_Obool),c_fequal),X21964))),X21963)),c_Groups_Oone__class_Oone(X21967))),X21965) = hAPP(X21963,X21964)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21966),X21965))
        | ~ class_Groups_Ocomm__monoid__mult(X21967) )
      & ( hBOOL(hAPP(hAPP(c_member(X21966),X21964),X21965))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21966,X21967),hAPP(hAPP(c_COMBC(X21966,X21967,X21967),hAPP(hAPP(c_COMBS(X21966,X21967,tc_fun(X21967,X21967)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21967,tc_fun(X21967,X21967)),X21966),c_If(X21967)),hAPP(hAPP(c_COMBC(X21966,X21966,tc_HOL_Obool),c_fequal),X21964))),X21963)),c_Groups_Oone__class_Oone(X21967))),X21965) = c_Groups_Oone__class_Oone(X21967)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21966),X21965))
        | ~ class_Groups_Ocomm__monoid__mult(X21967) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5291])])]) ).

fof(i_0_6256,plain,
    ! [X28321,X28322] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X28322)
      | c_Complete__Lattice_OInf__class_OInf(X28322,X28321) = c_Complete__Lattice_OSup__class_OSup(X28322,hAPP(c_Set_OCollect(X28322),hAPP(hAPP(c_COMBB(tc_fun(X28322,tc_HOL_Obool),tc_HOL_Obool,X28322),c_HOL_OAll(X28322)),hAPP(hAPP(c_COMBB(tc_fun(X28322,tc_HOL_Obool),tc_fun(X28322,tc_HOL_Obool),X28322),hAPP(c_COMBS(X28322,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28322),c_fimplies),hAPP(hAPP(c_COMBC(X28322,tc_fun(X28322,tc_HOL_Obool),tc_HOL_Obool),c_member(X28322)),X28321)))),c_Orderings_Oord__class_Oless__eq(X28322))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__Sup])]) ).

fof(i_0_6257,plain,
    ! [X25193,X25194,X25195,X25196,X25197,X25198,X25199] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25199,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25198,tc_fun(X25199,tc_HOL_Obool)),X25197),X25196)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25195,tc_fun(X25199,tc_HOL_Obool)),X25194),X25193)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25198,tc_fun(X25199,tc_HOL_Obool)),X25197),hAPP(hAPP(c_COMBB(tc_fun(X25195,tc_fun(X25199,tc_HOL_Obool)),tc_fun(X25199,tc_HOL_Obool),X25198),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25195,tc_fun(X25199,tc_HOL_Obool)),X25194)),hAPP(hAPP(c_COMBC(X25198,tc_fun(X25195,tc_fun(X25199,tc_HOL_Obool)),tc_fun(X25195,tc_fun(X25199,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X25199,tc_HOL_Obool),tc_fun(X25199,tc_HOL_Obool)),tc_fun(tc_fun(X25195,tc_fun(X25199,tc_HOL_Obool)),tc_fun(X25195,tc_fun(X25199,tc_HOL_Obool))),X25198),c_COMBB(tc_fun(X25199,tc_HOL_Obool),tc_fun(X25199,tc_HOL_Obool),X25195)),hAPP(hAPP(c_COMBB(tc_fun(X25199,tc_HOL_Obool),tc_fun(tc_fun(X25199,tc_HOL_Obool),tc_fun(X25199,tc_HOL_Obool)),X25198),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25199,tc_HOL_Obool))),X25196))),X25193))),
    inference(variable_rename,[status(thm)],[fact_Int__UN__distrib2]) ).

fof(i_0_6258,plain,
    ! [X26444,X26445,X26446,X26447,X26448,X26449,X26450] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26450,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26449,tc_fun(X26450,tc_HOL_Obool)),X26448),X26447)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26446,tc_fun(X26450,tc_HOL_Obool)),X26445),X26444)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26449,tc_fun(X26450,tc_HOL_Obool)),X26448),hAPP(hAPP(c_COMBB(tc_fun(X26446,tc_fun(X26450,tc_HOL_Obool)),tc_fun(X26450,tc_HOL_Obool),X26449),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26446,tc_fun(X26450,tc_HOL_Obool)),X26445)),hAPP(hAPP(c_COMBC(X26449,tc_fun(X26446,tc_fun(X26450,tc_HOL_Obool)),tc_fun(X26446,tc_fun(X26450,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X26450,tc_HOL_Obool),tc_fun(X26450,tc_HOL_Obool)),tc_fun(tc_fun(X26446,tc_fun(X26450,tc_HOL_Obool)),tc_fun(X26446,tc_fun(X26450,tc_HOL_Obool))),X26449),c_COMBB(tc_fun(X26450,tc_HOL_Obool),tc_fun(X26450,tc_HOL_Obool),X26446)),hAPP(hAPP(c_COMBB(tc_fun(X26450,tc_HOL_Obool),tc_fun(tc_fun(X26450,tc_HOL_Obool),tc_fun(X26450,tc_HOL_Obool)),X26449),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26450,tc_HOL_Obool))),X26447))),X26444))),
    inference(variable_rename,[status(thm)],[fact_Un__INT__distrib2]) ).

cnf(i_0_6259,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_5292]) ).

cnf(i_0_6260,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_5293]) ).

cnf(i_0_6261,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_5294]) ).

cnf(i_0_6262,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_5295]) ).

fof(i_0_6263,plain,
    ! [X32399,X32400,X32401,X32402,X32403,X32404,X32405] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(X32405,X32404,X32403,X32402),X32401),X32400),X32399) = c_New__DSequence_Oneg__bind(X32405,X32404,hAPP(hAPP(hAPP(X32403,X32401),X32400),X32399),hAPP(hAPP(c_COMBC(X32405,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(X32404)))),hAPP(hAPP(c_COMBC(X32405,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(X32404))))),hAPP(hAPP(c_COMBC(X32405,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(X32404)))))),X32402),X32401)),X32400)),X32399)),
    inference(variable_rename,[status(thm)],[fact_neg__bind__def]) ).

fof(i_0_6264,plain,
    ! [X30216,X30217,X30218,X30219,X30220] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30220),tc_List_Olist(X30220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30220),tc_List_Olist(X30220)),hAPP(hAPP(c_List_Oappend(X30220),X30219),X30218)),hAPP(hAPP(c_List_Oappend(X30220),X30219),X30217))),c_List_Olexord(X30220,X30216)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X30220,X30220)),hAPP(hAPP(c_Product__Type_OPair(X30220,X30220),esk407_5(X30216,X30217,X30218,X30219,X30220)),esk407_5(X30216,X30217,X30218,X30219,X30220))),X30216))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30220),tc_List_Olist(X30220))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30220),tc_List_Olist(X30220)),X30218),X30217)),c_List_Olexord(X30220,X30216))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5296])])]) ).

fof(i_0_6265,plain,
    ! [X32845,X32846] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X32846,tc_HOL_Obool),X32845) = hAPP(c_Set_OCollect(X32846),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32846,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X32846),c_HOL_OEx(tc_fun(X32846,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32846,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X32846,tc_HOL_Obool),tc_HOL_Obool),X32846),hAPP(c_COMBS(tc_fun(X32846,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(X32846,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X32846,tc_HOL_Obool),tc_fun(tc_fun(X32846,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X32846,tc_HOL_Obool))),X32845)))),c_member(X32846)))),
    inference(variable_rename,[status(thm)],[fact_Union__eq]) ).

fof(i_0_6266,plain,
    ! [X28332,X28333] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X28333,tc_HOL_Obool),X28332) = hAPP(c_Set_OCollect(X28333),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28333,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X28333),c_HOL_OAll(tc_fun(X28333,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X28333,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X28333,tc_HOL_Obool),tc_HOL_Obool),X28333),hAPP(c_COMBS(tc_fun(X28333,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(X28333,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(X28333,tc_HOL_Obool),tc_fun(tc_fun(X28333,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X28333,tc_HOL_Obool))),X28332)))),c_member(X28333)))),
    inference(variable_rename,[status(thm)],[fact_Inter__eq]) ).

fof(i_0_6267,plain,
    ! [X29055,X29056,X29057,X29058,X29059] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29059,X29059)),hAPP(hAPP(c_Product__Type_OPair(X29059,X29059),X29058),esk349_5(X29055,X29056,X29057,X29058,X29059))),c_Transitive__Closure_Ortrancl(X29059,X29056)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29059,X29059)),hAPP(hAPP(c_Product__Type_OPair(X29059,X29059),X29058),X29057)),c_Transitive__Closure_Ortrancl(X29059,X29056)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29059,X29059)),hAPP(hAPP(c_Product__Type_OPair(X29059,X29059),X29058),X29057)),c_Transitive__Closure_Ortrancl(X29059,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29059,X29059),tc_HOL_Obool)),X29056),X29055)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29059,X29059)),hAPP(hAPP(c_Product__Type_OPair(X29059,X29059),esk349_5(X29055,X29056,X29057,X29058,X29059)),esk350_5(X29055,X29056,X29057,X29058,X29059))),X29055))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29059,X29059)),hAPP(hAPP(c_Product__Type_OPair(X29059,X29059),X29058),X29057)),c_Transitive__Closure_Ortrancl(X29059,X29056)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29059,X29059)),hAPP(hAPP(c_Product__Type_OPair(X29059,X29059),X29058),X29057)),c_Transitive__Closure_Ortrancl(X29059,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29059,X29059),tc_HOL_Obool)),X29056),X29055)))) )
      & ( esk349_5(X29055,X29056,X29057,X29058,X29059) != esk350_5(X29055,X29056,X29057,X29058,X29059)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29059,X29059)),hAPP(hAPP(c_Product__Type_OPair(X29059,X29059),X29058),X29057)),c_Transitive__Closure_Ortrancl(X29059,X29056)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29059,X29059)),hAPP(hAPP(c_Product__Type_OPair(X29059,X29059),X29058),X29057)),c_Transitive__Closure_Ortrancl(X29059,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29059,X29059),tc_HOL_Obool)),X29056),X29055)))) ) ),
    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_6268,plain,
    ! [X29048,X29049,X29050,X29051,X29052] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29052,X29052)),hAPP(hAPP(c_Product__Type_OPair(X29052,X29052),esk347_5(X29048,X29049,X29050,X29051,X29052)),X29050)),c_Transitive__Closure_Ortrancl(X29052,X29049)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29052,X29052)),hAPP(hAPP(c_Product__Type_OPair(X29052,X29052),X29051),X29050)),c_Transitive__Closure_Ortrancl(X29052,X29049)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29052,X29052)),hAPP(hAPP(c_Product__Type_OPair(X29052,X29052),X29051),X29050)),c_Transitive__Closure_Ortrancl(X29052,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29052,X29052),tc_HOL_Obool)),X29049),X29048)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29052,X29052)),hAPP(hAPP(c_Product__Type_OPair(X29052,X29052),esk348_5(X29048,X29049,X29050,X29051,X29052)),esk347_5(X29048,X29049,X29050,X29051,X29052))),X29048))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29052,X29052)),hAPP(hAPP(c_Product__Type_OPair(X29052,X29052),X29051),X29050)),c_Transitive__Closure_Ortrancl(X29052,X29049)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29052,X29052)),hAPP(hAPP(c_Product__Type_OPair(X29052,X29052),X29051),X29050)),c_Transitive__Closure_Ortrancl(X29052,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29052,X29052),tc_HOL_Obool)),X29049),X29048)))) )
      & ( esk348_5(X29048,X29049,X29050,X29051,X29052) != esk347_5(X29048,X29049,X29050,X29051,X29052)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29052,X29052)),hAPP(hAPP(c_Product__Type_OPair(X29052,X29052),X29051),X29050)),c_Transitive__Closure_Ortrancl(X29052,X29049)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29052,X29052)),hAPP(hAPP(c_Product__Type_OPair(X29052,X29052),X29051),X29050)),c_Transitive__Closure_Ortrancl(X29052,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X29052,X29052),tc_HOL_Obool)),X29049),X29048)))) ) ),
    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_6269,plain,
    ! [X30716,X30717,X30718,X30719,X30720,X30721] : hAPP(hAPP(c_List_Ozip(X30721,X30720),X30719),hAPP(hAPP(c_List_Omap(X30718,X30720),X30717),X30716)) = hAPP(hAPP(c_List_Omap(tc_prod(X30721,X30718),tc_prod(X30721,X30720)),hAPP(c_Product__Type_Oprod_Oprod__case(X30721,X30718,tc_prod(X30721,X30720)),hAPP(hAPP(c_COMBC(X30721,tc_fun(X30718,X30720),tc_fun(X30718,tc_prod(X30721,X30720))),hAPP(hAPP(c_COMBB(tc_fun(X30720,tc_prod(X30721,X30720)),tc_fun(tc_fun(X30718,X30720),tc_fun(X30718,tc_prod(X30721,X30720))),X30721),c_COMBB(X30720,tc_prod(X30721,X30720),X30718)),c_Product__Type_OPair(X30721,X30720))),X30717))),hAPP(hAPP(c_List_Ozip(X30721,X30718),X30719),X30716)),
    inference(variable_rename,[status(thm)],[fact_zip__map2]) ).

cnf(i_0_6270,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_5297]) ).

cnf(i_0_6271,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_5275]) ).

cnf(i_0_6272,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_5276]) ).

fof(i_0_6273,plain,
    ! [X27529,X27530,X27531] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk272_3(X27529,X27530,X27531)),X27531))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27529),hAPP(X27530,X27531)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27530,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27529))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk271_3(X27529,X27530,X27531)),X27531)) )
      & ( hAPP(X27530,esk272_3(X27529,X27530,X27531)) = X27529
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27529),hAPP(X27530,X27531)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27530,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27529))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk271_3(X27529,X27530,X27531)),X27531)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk272_3(X27529,X27530,X27531)),X27531))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27529),hAPP(X27530,X27531)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27530,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27529))
        | ~ 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(X27530,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk271_3(X27529,X27530,X27531)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X27530,esk271_3(X27529,X27530,X27531))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X27530,esk272_3(X27529,X27530,X27531)) = X27529
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27529),hAPP(X27530,X27531)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27530,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27529))
        | ~ 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(X27530,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk271_3(X27529,X27530,X27531)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X27530,esk271_3(X27529,X27530,X27531))))),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_6274,plain,
    ! [X27493,X27494,X27495] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk269_3(X27493,X27494,X27495)),X27495))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27493),hAPP(X27494,X27495)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27494,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27493))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk268_3(X27493,X27494,X27495)),X27495)) )
      & ( hAPP(X27494,esk269_3(X27493,X27494,X27495)) = X27493
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27493),hAPP(X27494,X27495)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27494,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27493))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk268_3(X27493,X27494,X27495)),X27495)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk269_3(X27493,X27494,X27495)),X27495))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27493),hAPP(X27494,X27495)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27494,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27493))
        | ~ 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(X27494,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk268_3(X27493,X27494,X27495)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X27494,esk268_3(X27493,X27494,X27495))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
      & ( hAPP(X27494,esk269_3(X27493,X27494,X27495)) = X27493
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27493),hAPP(X27494,X27495)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(X27494,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X27493))
        | ~ 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(X27494,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk268_3(X27493,X27494,X27495)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X27494,esk268_3(X27493,X27494,X27495))))),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_6275,plain,
    ! [X29031,X29032,X29033,X29034,X29035] :
      ( ( X29032 = hAPP(c_Nat_OSuc,esk343_5(X29031,X29032,X29033,X29034,X29035))
        | X29032 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),X29034),X29033)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29035,X29035),tc_HOL_Obool),X29032),X29031))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),X29034),esk342_5(X29031,X29032,X29033,X29034,X29035))),X29031))
        | X29032 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),X29034),X29033)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29035,X29035),tc_HOL_Obool),X29032),X29031))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),esk342_5(X29031,X29032,X29033,X29034,X29035)),X29033)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29035,X29035),tc_HOL_Obool),esk343_5(X29031,X29032,X29033,X29034,X29035)),X29031)))
        | X29032 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),X29034),X29033)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29035,X29035),tc_HOL_Obool),X29032),X29031))) )
      & ( X29032 = hAPP(c_Nat_OSuc,esk343_5(X29031,X29032,X29033,X29034,X29035))
        | X29034 = X29033
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),X29034),X29033)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29035,X29035),tc_HOL_Obool),X29032),X29031))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),X29034),esk342_5(X29031,X29032,X29033,X29034,X29035))),X29031))
        | X29034 = X29033
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),X29034),X29033)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29035,X29035),tc_HOL_Obool),X29032),X29031))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),esk342_5(X29031,X29032,X29033,X29034,X29035)),X29033)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29035,X29035),tc_HOL_Obool),esk343_5(X29031,X29032,X29033,X29034,X29035)),X29031)))
        | X29034 = X29033
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29035,X29035)),hAPP(hAPP(c_Product__Type_OPair(X29035,X29035),X29034),X29033)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29035,X29035),tc_HOL_Obool),X29032),X29031))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5298])])])]) ).

fof(i_0_6276,plain,
    ! [X26741,X26742,X26743,X26744] :
      ( ~ c_Fun_Oinj__on(X26744,X26743,X26742,c_Orderings_Otop__class_Otop(tc_fun(X26744,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26744,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26744,X26743,X26742),hAPP(hAPP(c_Set_Oinsert(X26743),X26741),c_Orderings_Obot__class_Obot(tc_fun(X26743,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X26744),c_HOL_OThe(X26744,hAPP(hAPP(c_COMBC(X26744,X26743,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X26743,tc_fun(X26743,tc_HOL_Obool),X26744),c_fequal),X26742)),X26741))),c_Orderings_Obot__class_Obot(tc_fun(X26744,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__singleton])]) ).

fof(i_0_6277,plain,
    ! [X32420,X32421,X32422,X32423,X32424,X32425,X32426] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(X32426,X32425,X32424,X32423),X32422),X32421),X32420) = c_New__DSequence_Opos__bind(X32426,X32425,hAPP(hAPP(hAPP(X32424,X32422),X32421),X32420),hAPP(hAPP(c_COMBC(X32426,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32425))),hAPP(hAPP(c_COMBC(X32426,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(X32425)))),hAPP(hAPP(c_COMBC(X32426,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(X32425))))),X32423),X32422)),X32421)),X32420)),
    inference(variable_rename,[status(thm)],[fact_pos__bind__def]) ).

fof(i_0_6278,plain,
    ! [X33825,X33826] :
      ( ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33826,X33825) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33826),X33825))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33825),X33826)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33826),X33825))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33826,X33825) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33825),X33826))
        | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33826,X33825) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5299])])]) ).

fof(i_0_6279,plain,
    ! [X33823,X33824] :
      ( ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33824,X33823) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33824),X33823))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33823),X33824)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33824),X33823))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33824,X33823) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33823),X33824))
        | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33824,X33823) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5300])])]) ).

fof(i_0_6280,plain,
    ! [X33829,X33830] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33830,X33829)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33830),X33829))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33829),X33830)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33830),X33829))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33830,X33829) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33829),X33830))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33830,X33829) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5301])])]) ).

fof(i_0_6281,plain,
    ! [X33827,X33828] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33828,X33827)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33828),X33827))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33827),X33828)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33828),X33827))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33828,X33827) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33827),X33828))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33828,X33827) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5302])])]) ).

fof(i_0_6282,plain,
    ! [X27772,X27773,X27774,X27775] : c_Nitpick_Oprod(X27775,X27774,X27773,X27772) = hAPP(c_Set_OCollect(tc_prod(X27775,X27774)),hAPP(c_Product__Type_Oprod_Oprod__case(X27775,X27774,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27775,tc_fun(X27774,tc_HOL_Obool),tc_fun(X27774,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27774,tc_HOL_Obool),tc_fun(X27774,tc_HOL_Obool)),X27775),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27774)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27775),c_fconj),hAPP(hAPP(c_COMBC(X27775,tc_fun(X27775,tc_HOL_Obool),tc_HOL_Obool),c_member(X27775)),X27773)))),hAPP(hAPP(c_COMBC(X27774,tc_fun(X27774,tc_HOL_Obool),tc_HOL_Obool),c_member(X27774)),X27772)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oprod__def]) ).

fof(i_0_6283,plain,
    ! [X33935,X33936,X33937,X33938] :
      ( ~ class_Orderings_Oorder(X33938)
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X33938,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33937)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33936),X33935))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33935),X33936))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X33938),hAPP(X33937,X33936)),hAPP(X33937,X33935))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5303])]) ).

cnf(i_0_6284,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_5304]) ).

fof(i_0_6285,plain,
    ! [X27448,X27449,X27450,X27451,X27452,X27453,X27454,X27455,X27456,X27457,X27458] : hAPP(c_Product__Type_Omap__pair(X27458,X27457,X27456,X27455,X27454,X27453),hAPP(c_Product__Type_Omap__pair(X27452,X27458,X27451,X27456,X27450,X27449),X27448)) = hAPP(c_Product__Type_Omap__pair(X27452,X27457,X27451,X27455,hAPP(c_Fun_Ocomp(X27458,X27457,X27452,X27454),X27450),hAPP(c_Fun_Ocomp(X27456,X27455,X27451,X27453),X27449)),X27448),
    inference(variable_rename,[status(thm)],[fact_map__pair_Ocompositionality]) ).

fof(i_0_6286,plain,
    ! [X24234,X24235,X24236,X24237] :
      ( ( ~ 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),X24237),X24236)),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),X24235),X24234)),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),X24237),X24234)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24235),X24236))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24237),X24234)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24235),X24236)))
        | 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),X24237),X24236)),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),X24235),X24234)),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_6287,plain,
    ! [X24219,X24220,X24221,X24222] :
      ( ( ~ 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),X24222),X24221)),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),X24220),X24219)),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),X24222),X24219)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24220),X24221))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24222),X24219)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24220),X24221)))
        | 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),X24222),X24221)),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),X24220),X24219)),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_6288,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_5305]) ).

cnf(i_0_6289,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_5306]) ).

fof(i_0_6290,plain,
    ! [X24837,X24838,X24839,X24840,X24841,X24842] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24841),esk195_6(X24837,X24838,X24839,X24840,X24841,X24842)),X24840))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24837,X24842),X24838),hAPP(c_Set_Oimage(X24841,X24837,X24839),X24840)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24841,X24842),hAPP(c_Fun_Ocomp(X24837,X24842,X24841,X24838),X24839)),X24840)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24841),X24840))
        | ~ class_Groups_Ocomm__monoid__add(X24842) )
      & ( hBOOL(hAPP(hAPP(c_member(X24841),esk196_6(X24837,X24838,X24839,X24840,X24841,X24842)),X24840))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24837,X24842),X24838),hAPP(c_Set_Oimage(X24841,X24837,X24839),X24840)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24841,X24842),hAPP(c_Fun_Ocomp(X24837,X24842,X24841,X24838),X24839)),X24840)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24841),X24840))
        | ~ class_Groups_Ocomm__monoid__add(X24842) )
      & ( esk195_6(X24837,X24838,X24839,X24840,X24841,X24842) != esk196_6(X24837,X24838,X24839,X24840,X24841,X24842)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24837,X24842),X24838),hAPP(c_Set_Oimage(X24841,X24837,X24839),X24840)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24841,X24842),hAPP(c_Fun_Ocomp(X24837,X24842,X24841,X24838),X24839)),X24840)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24841),X24840))
        | ~ class_Groups_Ocomm__monoid__add(X24842) )
      & ( hAPP(X24839,esk195_6(X24837,X24838,X24839,X24840,X24841,X24842)) = hAPP(X24839,esk196_6(X24837,X24838,X24839,X24840,X24841,X24842))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24837,X24842),X24838),hAPP(c_Set_Oimage(X24841,X24837,X24839),X24840)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24841,X24842),hAPP(c_Fun_Ocomp(X24837,X24842,X24841,X24838),X24839)),X24840)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24841),X24840))
        | ~ class_Groups_Ocomm__monoid__add(X24842) )
      & ( hAPP(X24838,hAPP(X24839,esk195_6(X24837,X24838,X24839,X24840,X24841,X24842))) != c_Groups_Ozero__class_Ozero(X24842)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24837,X24842),X24838),hAPP(c_Set_Oimage(X24841,X24837,X24839),X24840)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24841,X24842),hAPP(c_Fun_Ocomp(X24837,X24842,X24841,X24838),X24839)),X24840)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24841),X24840))
        | ~ class_Groups_Ocomm__monoid__add(X24842) ) ),
    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_6291,plain,
    ! [X27676,X27677,X27678,X27679,X27680,X27681] : hAPP(c_Set_Oimage(X27681,X27680,hAPP(hAPP(c_COMBS(X27681,X27680,X27680),hAPP(hAPP(c_COMBS(X27681,X27680,tc_fun(X27680,X27680)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27680,tc_fun(X27680,X27680)),X27681),c_If(X27680)),X27679)),X27678)),X27677)),X27676) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27680,tc_HOL_Obool)),hAPP(c_Set_Oimage(X27681,X27680,X27678),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27681,tc_HOL_Obool)),X27676),hAPP(c_Set_OCollect(X27681),X27679)))),hAPP(c_Set_Oimage(X27681,X27680,X27677),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27681,tc_HOL_Obool)),X27676),hAPP(c_Set_OCollect(X27681),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27681),c_fNot),X27679))))),
    inference(variable_rename,[status(thm)],[fact_if__image__distrib]) ).

cnf(i_0_6292,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_5307]) ).

cnf(i_0_6293,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_5308]) ).

fof(i_0_6294,plain,
    ! [X24215,X24216,X24217,X24218] : 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),X24218),X24217)),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),X24216),X24215)),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),X24218),X24216)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24217),X24215))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24218),X24215)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24217),X24216)))),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_6295,plain,
    ! [X19401,X19402,X19403,X19404,X19405,X19406] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19405),esk49_6(X19401,X19402,X19403,X19404,X19405,X19406)),X19404))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19406,X19405,c_Groups_Otimes__class_Otimes(X19406)),X19403),X19401),X19404) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19406,X19405,c_Groups_Otimes__class_Otimes(X19406)),X19402),X19401),X19404)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19405),X19404))
        | ~ class_Groups_Oab__semigroup__mult(X19406) )
      & ( hAPP(X19403,esk49_6(X19401,X19402,X19403,X19404,X19405,X19406)) != hAPP(X19402,esk49_6(X19401,X19402,X19403,X19404,X19405,X19406))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19406,X19405,c_Groups_Otimes__class_Otimes(X19406)),X19403),X19401),X19404) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19406,X19405,c_Groups_Otimes__class_Otimes(X19406)),X19402),X19401),X19404)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19405),X19404))
        | ~ class_Groups_Oab__semigroup__mult(X19406) ) ),
    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_6296,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_5309]) ).

cnf(i_0_6297,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_5309]) ).

fof(i_0_6298,plain,
    ! [X28194,X28195,X28196,X28197] :
      ( ~ c_Wellfounded_Owf(X28197,X28196)
      | ~ c_Fun_Oinj__on(X28197,X28195,X28194,c_Orderings_Otop__class_Otop(tc_fun(X28197,tc_HOL_Obool)))
      | c_Wellfounded_Owf(X28195,hAPP(c_Set_Oimage(tc_prod(X28197,X28197),tc_prod(X28195,X28195),c_Product__Type_Omap__pair(X28197,X28195,X28197,X28195,X28194,X28194)),X28196)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__map__pair__image])]) ).

fof(i_0_6299,plain,
    ! [X27552,X27553,X27554,X27555,X27556,X27557] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27556),esk277_6(X27552,X27553,X27554,X27555,X27556,X27557)),X27557))
        | c_Fun_Oinj__on(X27555,X27554,X27553,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X27556,tc_fun(X27555,tc_HOL_Obool)),X27557),X27552))
        | X27557 = c_Orderings_Obot__class_Obot(tc_fun(X27556,tc_HOL_Obool)) )
      & ( ~ c_Fun_Oinj__on(X27555,X27554,X27553,hAPP(X27552,esk277_6(X27552,X27553,X27554,X27555,X27556,X27557)))
        | c_Fun_Oinj__on(X27555,X27554,X27553,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X27556,tc_fun(X27555,tc_HOL_Obool)),X27557),X27552))
        | X27557 = c_Orderings_Obot__class_Obot(tc_fun(X27556,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_6300,plain,
    ! [X31002,X31003,X31004,X31005,X31006] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31005),esk414_5(X31002,X31003,X31004,X31005,X31006)),hAPP(c_List_Oset(X31005),X31004)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31006),hAPP(c_List_Omonoid__add__class_Olistsum(X31006),hAPP(hAPP(c_List_Omap(X31005,X31006),X31003),X31004))),hAPP(c_List_Omonoid__add__class_Olistsum(X31006),hAPP(hAPP(c_List_Omap(X31005,X31006),X31002),X31004))))
        | ~ class_Groups_Omonoid__add(X31006)
        | ~ class_Groups_Oordered__ab__semigroup__add(X31006) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31006),hAPP(X31003,esk414_5(X31002,X31003,X31004,X31005,X31006))),hAPP(X31002,esk414_5(X31002,X31003,X31004,X31005,X31006))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31006),hAPP(c_List_Omonoid__add__class_Olistsum(X31006),hAPP(hAPP(c_List_Omap(X31005,X31006),X31003),X31004))),hAPP(c_List_Omonoid__add__class_Olistsum(X31006),hAPP(hAPP(c_List_Omap(X31005,X31006),X31002),X31004))))
        | ~ class_Groups_Omonoid__add(X31006)
        | ~ class_Groups_Oordered__ab__semigroup__add(X31006) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mono])])])]) ).

fof(i_0_6301,plain,
    ! [X32154,X32155,X32156,X32157,X32158] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_5(X32154,X32155,X32156,X32157,X32158)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32158)),X32157)))
        | c_List_Olist__all2(X32158,X32156,X32154,X32157,X32155)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32158)),X32157) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32156)),X32155) )
      & ( ~ hBOOL(hAPP(hAPP(X32154,hAPP(hAPP(c_List_Onth(X32158),X32157),esk452_5(X32154,X32155,X32156,X32157,X32158))),hAPP(hAPP(c_List_Onth(X32156),X32155),esk452_5(X32154,X32155,X32156,X32157,X32158))))
        | c_List_Olist__all2(X32158,X32156,X32154,X32157,X32155)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32158)),X32157) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32156)),X32155) ) ),
    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_6302,plain,
    ! [X31167,X31168,X31169,X31170,X31171,X31172,X31173,X31174,X31175,X31176,X31177] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31171)),X31168) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31170)),X31167)
        | ~ c_List_Olist__all2(X31171,X31170,X31169,X31168,X31167) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31172),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31171)),X31168)))
        | hBOOL(hAPP(hAPP(X31169,hAPP(hAPP(c_List_Onth(X31171),X31168),X31172)),hAPP(hAPP(c_List_Onth(X31170),X31167),X31172)))
        | ~ c_List_Olist__all2(X31171,X31170,X31169,X31168,X31167) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk417_5(X31173,X31174,X31175,X31176,X31177)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31177)),X31174)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31177)),X31174) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31176)),X31173)
        | c_List_Olist__all2(X31177,X31176,X31175,X31174,X31173) )
      & ( ~ hBOOL(hAPP(hAPP(X31175,hAPP(hAPP(c_List_Onth(X31177),X31174),esk417_5(X31173,X31174,X31175,X31176,X31177))),hAPP(hAPP(c_List_Onth(X31176),X31173),esk417_5(X31173,X31174,X31175,X31176,X31177))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31177)),X31174) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31176)),X31173)
        | c_List_Olist__all2(X31177,X31176,X31175,X31174,X31173) ) ),
    inference(distribute,[status(thm)],[inference(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_6303,plain,
    ! [X25713,X25714,X25715,X25716,X25717] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25716),esk218_5(X25713,X25714,X25715,X25716,X25717)),X25715))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25717),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25716,X25717),X25714),X25715)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25716,X25717),X25713),X25715)))
        | X25715 = c_Orderings_Obot__class_Obot(tc_fun(X25716,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25716),X25715))
        | ~ class_Groups_Ocomm__monoid__add(X25717)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X25717) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25717),hAPP(X25714,esk218_5(X25713,X25714,X25715,X25716,X25717))),hAPP(X25713,esk218_5(X25713,X25714,X25715,X25716,X25717))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25717),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25716,X25717),X25714),X25715)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25716,X25717),X25713),X25715)))
        | X25715 = c_Orderings_Obot__class_Obot(tc_fun(X25716,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25716),X25715))
        | ~ class_Groups_Ocomm__monoid__add(X25717)
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X25717) ) ),
    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_6304,plain,
    ! [X27701,X27702,X27703,X27704,X27705,X27706] :
      ( ~ class_Groups_Ocomm__monoid__add(X27706)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27705),X27704))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27705,X27706),hAPP(hAPP(c_COMBS(X27705,X27706,X27706),hAPP(hAPP(c_COMBS(X27705,X27706,tc_fun(X27706,X27706)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X27706,tc_fun(X27706,X27706)),X27705),c_If(X27706)),X27703)),X27702)),X27701)),X27704) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X27706),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27705,X27706),X27702),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27705,tc_HOL_Obool)),X27704),hAPP(c_Set_OCollect(X27705),X27703)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27705,X27706),X27701),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27705,tc_HOL_Obool)),X27704),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27705,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27705),X27703))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cases])]) ).

cnf(i_0_6305,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_5292]) ).

cnf(i_0_6306,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_5293]) ).

fof(i_0_6307,plain,
    ! [X17543,X17544,X17545,X17546,X17547] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17547,X17546,X17545)
      | hAPP(X17544,hAPP(hAPP(X17546,esk14_5(X17543,X17544,X17545,X17546,X17547)),esk15_5(X17543,X17544,X17545,X17546,X17547))) != hAPP(hAPP(X17546,hAPP(X17544,esk14_5(X17543,X17544,X17545,X17546,X17547))),hAPP(X17544,esk15_5(X17543,X17544,X17545,X17546,X17547)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17547),X17543))
      | X17543 = c_Orderings_Obot__class_Obot(tc_fun(X17547,tc_HOL_Obool))
      | hAPP(X17544,hAPP(X17545,X17543)) = hAPP(X17545,hAPP(c_Set_Oimage(X17547,X17547,X17544),X17543)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ohom__commute])])]) ).

cnf(i_0_6308,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk427_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_5310]) ).

cnf(i_0_6309,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk427_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_5310]) ).

cnf(i_0_6310,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),esk427_3(X3,X1,X2))) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_5310]) ).

cnf(i_0_6311,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),esk427_3(X3,X1,X2))) != X3
    | X3 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_5310]) ).

cnf(i_0_6312,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_5311]) ).

cnf(i_0_6313,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),esk93_3(X1,X2,X3)),esk94_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk94_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X1,esk93_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)))),esk94_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_5312]) ).

fof(i_0_6314,plain,
    ! [X24548,X24549,X24550,X24551,X24552] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24551),X24549),X24550))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24551,X24552),hAPP(hAPP(c_COMBC(X24551,X24552,X24552),hAPP(hAPP(c_COMBS(X24551,X24552,tc_fun(X24552,X24552)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24552,tc_fun(X24552,X24552)),X24551),c_If(X24552)),hAPP(c_fequal,X24549))),X24548)),c_Groups_Ozero__class_Ozero(X24552))),X24550) = hAPP(X24548,X24549)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24551),X24550))
        | ~ class_Groups_Ocomm__monoid__add(X24552) )
      & ( hBOOL(hAPP(hAPP(c_member(X24551),X24549),X24550))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24551,X24552),hAPP(hAPP(c_COMBC(X24551,X24552,X24552),hAPP(hAPP(c_COMBS(X24551,X24552,tc_fun(X24552,X24552)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X24552,tc_fun(X24552,X24552)),X24551),c_If(X24552)),hAPP(c_fequal,X24549))),X24548)),c_Groups_Ozero__class_Ozero(X24552))),X24550) = c_Groups_Ozero__class_Ozero(X24552)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24551),X24550))
        | ~ class_Groups_Ocomm__monoid__add(X24552) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5313])])]) ).

fof(i_0_6315,plain,
    ! [X21958,X21959,X21960,X21961,X21962] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21961),X21959),X21960))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21961,X21962),hAPP(hAPP(c_COMBC(X21961,X21962,X21962),hAPP(hAPP(c_COMBS(X21961,X21962,tc_fun(X21962,X21962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21962,tc_fun(X21962,X21962)),X21961),c_If(X21962)),hAPP(c_fequal,X21959))),X21958)),c_Groups_Oone__class_Oone(X21962))),X21960) = hAPP(X21958,X21959)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21961),X21960))
        | ~ class_Groups_Ocomm__monoid__mult(X21962) )
      & ( hBOOL(hAPP(hAPP(c_member(X21961),X21959),X21960))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21961,X21962),hAPP(hAPP(c_COMBC(X21961,X21962,X21962),hAPP(hAPP(c_COMBS(X21961,X21962,tc_fun(X21962,X21962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X21962,tc_fun(X21962,X21962)),X21961),c_If(X21962)),hAPP(c_fequal,X21959))),X21958)),c_Groups_Oone__class_Oone(X21962))),X21960) = c_Groups_Oone__class_Oone(X21962)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21961),X21960))
        | ~ class_Groups_Ocomm__monoid__mult(X21962) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5314])])]) ).

fof(i_0_6316,plain,
    ! [X31213,X31214,X31215] : hAPP(c_List_Oset(tc_List_Olist(X31215)),c_Enum_On__lists(X31215,X31214,X31213)) = hAPP(c_Set_OCollect(tc_List_Olist(X31215)),hAPP(hAPP(c_COMBS(tc_List_Olist(X31215),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X31215)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X31215),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(X31215)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(X31215)))),X31214))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31215),tc_fun(X31215,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X31215,tc_HOL_Obool),tc_fun(tc_fun(X31215,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X31215)),c_Orderings_Oord__class_Oless__eq(tc_fun(X31215,tc_HOL_Obool))),c_List_Oset(X31215))),hAPP(c_List_Oset(X31215),X31213)))),
    inference(variable_rename,[status(thm)],[fact_set__n__lists]) ).

fof(i_0_6317,plain,
    ! [X27428,X27429,X27430,X27431,X27432,X27433,X27434,X27435,X27436,X27437] : hAPP(c_Fun_Ocomp(tc_prod(X27437,X27436),tc_prod(X27435,X27434),tc_prod(X27433,X27432),c_Product__Type_Omap__pair(X27437,X27435,X27436,X27434,X27431,X27430)),c_Product__Type_Omap__pair(X27433,X27437,X27432,X27436,X27429,X27428)) = c_Product__Type_Omap__pair(X27433,X27435,X27432,X27434,hAPP(c_Fun_Ocomp(X27437,X27435,X27433,X27431),X27429),hAPP(c_Fun_Ocomp(X27436,X27434,X27432,X27430),X27428)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Ocomp]) ).

fof(i_0_6318,plain,
    ! [X27438,X27439,X27440,X27441,X27442,X27443,X27444,X27445,X27446,X27447] : c_Product__Type_Omap__pair(X27447,X27446,X27445,X27444,hAPP(c_Fun_Ocomp(X27443,X27446,X27447,X27442),X27441),hAPP(c_Fun_Ocomp(X27440,X27444,X27445,X27439),X27438)) = hAPP(c_Fun_Ocomp(tc_prod(X27443,X27440),tc_prod(X27446,X27444),tc_prod(X27447,X27445),c_Product__Type_Omap__pair(X27443,X27446,X27440,X27444,X27442,X27439)),c_Product__Type_Omap__pair(X27447,X27443,X27445,X27440,X27441,X27438)),
    inference(variable_rename,[status(thm)],[fact_map__pair__compose]) ).

fof(i_0_6319,plain,
    ! [X29400,X29401,X29402,X29403,X29404,X29405,X29406,X29407,X29408] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29403)),X29402) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29403)),X29401)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29403),tc_List_Olist(X29403))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29403),tc_List_Olist(X29403)),X29402),X29401)),c_List_Olistrel(X29403,X29400))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29404),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29403)),X29402)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29403,X29403)),hAPP(hAPP(c_Product__Type_OPair(X29403,X29403),hAPP(hAPP(c_List_Onth(X29403),X29402),X29404)),hAPP(hAPP(c_List_Onth(X29403),X29401),X29404))),X29400))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29403),tc_List_Olist(X29403))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29403),tc_List_Olist(X29403)),X29402),X29401)),c_List_Olistrel(X29403,X29400))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk380_4(X29405,X29406,X29407,X29408)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29408)),X29407)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29408)),X29407) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29408)),X29406)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29408),tc_List_Olist(X29408))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29408),tc_List_Olist(X29408)),X29407),X29406)),c_List_Olistrel(X29408,X29405))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29408,X29408)),hAPP(hAPP(c_Product__Type_OPair(X29408,X29408),hAPP(hAPP(c_List_Onth(X29408),X29407),esk380_4(X29405,X29406,X29407,X29408))),hAPP(hAPP(c_List_Onth(X29408),X29406),esk380_4(X29405,X29406,X29407,X29408)))),X29405))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29408)),X29407) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29408)),X29406)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29408),tc_List_Olist(X29408))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29408),tc_List_Olist(X29408)),X29407),X29406)),c_List_Olistrel(X29408,X29405))) ) ),
    inference(distribute,[status(thm)],[inference(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_6320,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk95_3(X1,X2,X3)),esk96_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk96_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(X1,esk95_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)))),esk96_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_5315]) ).

fof(i_0_6321,plain,
    ! [X29370,X29371,X29372,X29373,X29374] :
      ( ( X29373 = hAPP(hAPP(c_List_Olist_OCons(X29374),esk378_5(X29370,X29371,X29372,X29373,X29374)),esk379_5(X29370,X29371,X29372,X29373,X29374))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29374),tc_List_Olist(X29374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29374),tc_List_Olist(X29374)),X29373),hAPP(hAPP(c_List_Olist_OCons(X29374),X29372),X29371))),c_List_Olistrel(X29374,X29370))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29374,X29374)),hAPP(hAPP(c_Product__Type_OPair(X29374,X29374),esk378_5(X29370,X29371,X29372,X29373,X29374)),X29372)),X29370))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29374),tc_List_Olist(X29374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29374),tc_List_Olist(X29374)),X29373),hAPP(hAPP(c_List_Olist_OCons(X29374),X29372),X29371))),c_List_Olistrel(X29374,X29370))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29374),tc_List_Olist(X29374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29374),tc_List_Olist(X29374)),esk379_5(X29370,X29371,X29372,X29373,X29374)),X29371)),c_List_Olistrel(X29374,X29370)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29374),tc_List_Olist(X29374))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29374),tc_List_Olist(X29374)),X29373),hAPP(hAPP(c_List_Olist_OCons(X29374),X29372),X29371))),c_List_Olistrel(X29374,X29370))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5316])])])]) ).

cnf(i_0_6322,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_5311]) ).

fof(i_0_6323,plain,
    ! [X29068,X29069,X29070,X29071,X29072] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29072,X29072)),hAPP(hAPP(c_Product__Type_OPair(X29072,X29072),X29071),esk352_5(X29068,X29069,X29070,X29071,X29072))),X29068))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29072,X29072)),hAPP(hAPP(c_Product__Type_OPair(X29072,X29072),X29071),X29070)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29072,X29072),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29069)),X29068))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29072,X29072)),hAPP(hAPP(c_Product__Type_OPair(X29072,X29072),esk352_5(X29068,X29069,X29070,X29071,X29072)),X29070)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29072,X29072),tc_HOL_Obool),X29069),X29068)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29072,X29072)),hAPP(hAPP(c_Product__Type_OPair(X29072,X29072),X29071),X29070)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29072,X29072),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29069)),X29068))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5317])])])]) ).

fof(i_0_6324,plain,
    ! [X29062,X29063,X29064,X29065,X29066] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29066,X29066)),hAPP(hAPP(c_Product__Type_OPair(X29066,X29066),X29065),esk351_5(X29062,X29063,X29064,X29065,X29066))),X29062))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29066,X29066)),hAPP(hAPP(c_Product__Type_OPair(X29066,X29066),X29065),X29064)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29066,X29066),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29063)),X29062))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29066,X29066)),hAPP(hAPP(c_Product__Type_OPair(X29066,X29066),esk351_5(X29062,X29063,X29064,X29065,X29066)),X29064)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29066,X29066),tc_HOL_Obool),X29063),X29062)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29066,X29066)),hAPP(hAPP(c_Product__Type_OPair(X29066,X29066),X29065),X29064)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29066,X29066),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29063)),X29062))) ) ),
    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_6325,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_5318]) ).

fof(i_0_6326,plain,
    ! [X29038,X29039,X29040,X29041,X29042] :
      ( ( X29039 = hAPP(c_Nat_OSuc,esk345_5(X29038,X29039,X29040,X29041,X29042))
        | X29039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),X29041),X29040)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29042,X29042),tc_HOL_Obool),X29039),X29038))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),X29041),esk344_5(X29038,X29039,X29040,X29041,X29042))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29042,X29042),tc_HOL_Obool),esk345_5(X29038,X29039,X29040,X29041,X29042)),X29038)))
        | X29039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),X29041),X29040)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29042,X29042),tc_HOL_Obool),X29039),X29038))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),esk344_5(X29038,X29039,X29040,X29041,X29042)),X29040)),X29038))
        | X29039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),X29041),X29040)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29042,X29042),tc_HOL_Obool),X29039),X29038))) )
      & ( X29039 = hAPP(c_Nat_OSuc,esk345_5(X29038,X29039,X29040,X29041,X29042))
        | X29041 = X29040
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),X29041),X29040)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29042,X29042),tc_HOL_Obool),X29039),X29038))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),X29041),esk344_5(X29038,X29039,X29040,X29041,X29042))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29042,X29042),tc_HOL_Obool),esk345_5(X29038,X29039,X29040,X29041,X29042)),X29038)))
        | X29041 = X29040
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),X29041),X29040)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29042,X29042),tc_HOL_Obool),X29039),X29038))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),esk344_5(X29038,X29039,X29040,X29041,X29042)),X29040)),X29038))
        | X29041 = X29040
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29042,X29042)),hAPP(hAPP(c_Product__Type_OPair(X29042,X29042),X29041),X29040)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29042,X29042),tc_HOL_Obool),X29039),X29038))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5319])])])]) ).

fof(i_0_6327,plain,
    ! [X29074,X29075,X29076,X29077,X29078] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29078,X29078)),hAPP(hAPP(c_Product__Type_OPair(X29078,X29078),X29077),esk353_5(X29074,X29075,X29076,X29077,X29078))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29078,X29078),tc_HOL_Obool),X29075),X29074)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29078,X29078)),hAPP(hAPP(c_Product__Type_OPair(X29078,X29078),X29077),X29076)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29078,X29078),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29075)),X29074))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29078,X29078)),hAPP(hAPP(c_Product__Type_OPair(X29078,X29078),esk353_5(X29074,X29075,X29076,X29077,X29078)),X29076)),X29074))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29078,X29078)),hAPP(hAPP(c_Product__Type_OPair(X29078,X29078),X29077),X29076)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29078,X29078),tc_HOL_Obool),hAPP(c_Nat_OSuc,X29075)),X29074))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5320])])])]) ).

cnf(i_0_6328,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_5321]) ).

cnf(i_0_6329,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_5322]) ).

cnf(i_0_6330,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_5323]) ).

cnf(i_0_6331,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_5324]) ).

cnf(i_0_6332,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_5325]) ).

cnf(i_0_6333,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_5326]) ).

cnf(i_0_6334,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_5327]) ).

cnf(i_0_6335,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_5328]) ).

cnf(i_0_6336,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_5329]) ).

cnf(i_0_6337,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_5330]) ).

fof(i_0_6338,plain,
    ! [X24397,X24398,X24399] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X24399),X24398),X24397) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24399,tc_fun(tc_fun(X24399,tc_HOL_Obool),tc_HOL_Obool)),X24398),hAPP(hAPP(c_COMBC(X24399,tc_fun(tc_fun(X24399,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X24399,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24399,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X24399,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X24399,tc_HOL_Obool),tc_HOL_Obool)),X24399),c_Set_Oinsert(tc_fun(X24399,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X24399,tc_HOL_Obool),tc_fun(X24399,tc_HOL_Obool),X24399),c_Relation_OImage(X24399,X24399,X24397)),hAPP(hAPP(c_COMBC(X24399,tc_fun(X24399,tc_HOL_Obool),tc_fun(X24399,tc_HOL_Obool)),c_Set_Oinsert(X24399)),c_Orderings_Obot__class_Obot(tc_fun(X24399,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24399,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_quotient__def]) ).

cnf(i_0_6339,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_5331]) ).

cnf(i_0_6340,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_5332]) ).

cnf(i_0_6341,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_5333]) ).

cnf(i_0_6342,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_5334]) ).

cnf(i_0_6343,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_5335]) ).

cnf(i_0_6344,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_5336]) ).

cnf(i_0_6345,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_5337]) ).

cnf(i_0_6346,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_5338]) ).

cnf(i_0_6347,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_5339]) ).

cnf(i_0_6348,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_6349,plain,
    ! [X25695,X25696,X25697,X25698,X25699] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X25697,X25699)),hAPP(hAPP(c_Product__Type_OPair(X25697,X25699),esk215_5(X25695,X25696,X25697,X25698,X25699)),X25698)),X25696))
        | ~ hBOOL(hAPP(hAPP(c_member(X25699),X25698),hAPP(c_Relation_OImage(X25697,X25699,X25696),X25695))) )
      & ( hBOOL(hAPP(hAPP(c_member(X25697),esk215_5(X25695,X25696,X25697,X25698,X25699)),X25695))
        | ~ hBOOL(hAPP(hAPP(c_member(X25699),X25698),hAPP(c_Relation_OImage(X25697,X25699,X25696),X25695))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5340])])])]) ).

fof(i_0_6350,plain,
    ! [X24138,X24139,X24140,X24141,X24142,X24144,X24145,X24146,X24147,X24148,X24149] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24140),esk141_5(X24138,X24139,X24140,X24141,X24142)),X24138))
        | ~ hBOOL(hAPP(hAPP(c_member(X24142),X24141),hAPP(c_Relation_OImage(X24140,X24142,X24139),X24138))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X24140,X24142)),hAPP(hAPP(c_Product__Type_OPair(X24140,X24142),esk141_5(X24138,X24139,X24140,X24141,X24142)),X24141)),X24139))
        | ~ hBOOL(hAPP(hAPP(c_member(X24142),X24141),hAPP(c_Relation_OImage(X24140,X24142,X24139),X24138))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X24146),X24149),X24144))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24146,X24148)),hAPP(hAPP(c_Product__Type_OPair(X24146,X24148),X24149),X24147)),X24145))
        | hBOOL(hAPP(hAPP(c_member(X24148),X24147),hAPP(c_Relation_OImage(X24146,X24148,X24145),X24144))) ) ),
    inference(distribute,[status(thm)],[inference(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_6351,plain,
    ! [X17521,X17522,X17523,X17524] :
      ( ~ c_Finite__Set_Ofolding__one(X17524,X17523,X17522)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17524),X17521))
      | X17521 = c_Orderings_Obot__class_Obot(tc_fun(X17524,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X17524),hAPP(hAPP(X17523,esk10_4(X17521,X17522,X17523,X17524)),esk11_4(X17521,X17522,X17523,X17524))),hAPP(hAPP(c_Set_Oinsert(X17524),esk10_4(X17521,X17522,X17523,X17524)),hAPP(hAPP(c_Set_Oinsert(X17524),esk11_4(X17521,X17522,X17523,X17524)),c_Orderings_Obot__class_Obot(tc_fun(X17524,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X17524),hAPP(X17522,X17521)),X17521)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oclosed])])]) ).

cnf(i_0_6352,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_5341]) ).

cnf(i_0_6353,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_5342]) ).

fof(i_0_6354,plain,
    ! [X32817,X32818,X32819,X32820] : hAPP(c_Relation_OImage(X32820,X32819,hAPP(c_Set_OCollect(tc_prod(X32820,X32819)),hAPP(c_Product__Type_Oprod_Oprod__case(X32820,X32819,tc_HOL_Obool),X32818))),X32817) = hAPP(c_Set_OCollect(X32819),hAPP(hAPP(c_COMBB(tc_fun(X32820,tc_HOL_Obool),tc_HOL_Obool,X32819),c_HOL_OEx(X32820)),hAPP(hAPP(c_COMBB(tc_fun(X32820,tc_HOL_Obool),tc_fun(X32820,tc_HOL_Obool),X32819),hAPP(c_COMBS(X32820,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32820),c_fconj),hAPP(hAPP(c_COMBC(X32820,tc_fun(X32820,tc_HOL_Obool),tc_HOL_Obool),c_member(X32820)),X32817)))),hAPP(c_COMBC(X32820,X32819,tc_HOL_Obool),X32818)))),
    inference(variable_rename,[status(thm)],[fact_Image__Collect__split]) ).

cnf(i_0_6355,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_5265]) ).

fof(i_0_6356,plain,
    ! [X24588,X24589,X24590,X24591] :
      ( ~ c_Fun_Oinj__on(X24591,tc_fun(tc_fun(X24591,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X24591,tc_fun(tc_prod(X24591,X24591),tc_HOL_Obool),tc_fun(tc_fun(X24591,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24591,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X24591,X24591),tc_HOL_Obool),tc_fun(tc_fun(X24591,tc_HOL_Obool),tc_HOL_Obool)),X24591),c_Equiv__Relations_Oquotient(X24591)),hAPP(hAPP(c_COMBC(X24591,tc_fun(X24591,tc_HOL_Obool),tc_fun(X24591,tc_HOL_Obool)),c_Set_Oinsert(X24591)),c_Orderings_Obot__class_Obot(tc_fun(X24591,tc_HOL_Obool))))),X24590),X24589)
      | ~ hBOOL(hAPP(hAPP(c_member(X24591),X24588),X24589))
      | hAPP(hAPP(c_Equiv__Relations_Oquotient(X24591),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24591,tc_HOL_Obool)),X24589),hAPP(hAPP(c_Set_Oinsert(X24591),X24588),c_Orderings_Obot__class_Obot(tc_fun(X24591,tc_HOL_Obool))))),X24590) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(X24591,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24591),X24589),X24590)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24591),hAPP(hAPP(c_Set_Oinsert(X24591),X24588),c_Orderings_Obot__class_Obot(tc_fun(X24591,tc_HOL_Obool)))),X24590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__diff1])]) ).

fof(i_0_6357,plain,
    ! [X28297,X28298,X28299,X28300] : hAPP(c_Set_OCollect(X28300),hAPP(hAPP(c_COMBB(tc_fun(X28299,tc_HOL_Obool),tc_HOL_Obool,X28300),c_HOL_OAll(X28299)),hAPP(hAPP(c_COMBB(tc_fun(X28299,tc_HOL_Obool),tc_fun(X28299,tc_HOL_Obool),X28300),hAPP(c_COMBS(X28299,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28299),c_fimplies),hAPP(hAPP(c_COMBC(X28299,tc_fun(X28299,tc_HOL_Obool),tc_HOL_Obool),c_member(X28299)),X28298)))),X28297))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28299,tc_fun(X28300,tc_HOL_Obool)),X28298),hAPP(hAPP(c_COMBB(tc_fun(X28300,tc_HOL_Obool),tc_fun(X28300,tc_HOL_Obool),X28299),c_Set_OCollect(X28300)),hAPP(c_COMBC(X28300,X28299,tc_HOL_Obool),X28297))),
    inference(variable_rename,[status(thm)],[fact_Collect__ball__eq]) ).

fof(i_0_6358,plain,
    ! [X30180,X30181,X30182,X30183] : c_List_Osublist(X30183,hAPP(hAPP(c_List_Oappend(X30183),X30182),X30181),X30180) = hAPP(hAPP(c_List_Oappend(X30183),c_List_Osublist(X30183,X30182,X30180)),c_List_Osublist(X30183,X30181,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(X30183)),X30182)))),X30180)))),
    inference(variable_rename,[status(thm)],[fact_sublist__append]) ).

fof(i_0_6359,plain,
    ! [X32140,X32141,X32142,X32143,X32144] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32144)),hAPP(hAPP(c_List_Otake(X32144),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32144)),X32143)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32142)),X32141))),X32143)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32142)),hAPP(hAPP(c_List_Otake(X32142),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32144)),X32143)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32142)),X32141))),X32141))
        | hBOOL(hAPP(X32140,hAPP(hAPP(c_List_Ozip(X32144,X32142),X32143),X32141))) )
      & ( ~ hBOOL(hAPP(X32140,hAPP(hAPP(c_List_Ozip(X32144,X32142),hAPP(hAPP(c_List_Otake(X32144),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32144)),X32143)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32142)),X32141))),X32143)),hAPP(hAPP(c_List_Otake(X32142),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32144)),X32143)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32142)),X32141))),X32141))))
        | hBOOL(hAPP(X32140,hAPP(hAPP(c_List_Ozip(X32144,X32142),X32143),X32141))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__obtain__same__length])])]) ).

cnf(i_0_6360,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_5343]) ).

cnf(i_0_6361,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_5344]) ).

cnf(i_0_6362,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_5345]) ).

cnf(i_0_6363,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_5346]) ).

cnf(i_0_6364,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_5347]) ).

cnf(i_0_6365,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_5348]) ).

fof(i_0_6366,plain,
    ! [X24660,X24661,X24662] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24662),X24661))
      | ~ c_Fun_Oinj__on(X24662,tc_fun(tc_fun(X24662,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(X24662,tc_fun(tc_prod(X24662,X24662),tc_HOL_Obool),tc_fun(tc_fun(X24662,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24662,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X24662,X24662),tc_HOL_Obool),tc_fun(tc_fun(X24662,tc_HOL_Obool),tc_HOL_Obool)),X24662),c_Equiv__Relations_Oquotient(X24662)),hAPP(hAPP(c_COMBC(X24662,tc_fun(X24662,tc_HOL_Obool),tc_fun(X24662,tc_HOL_Obool)),c_Set_Oinsert(X24662)),c_Orderings_Obot__class_Obot(tc_fun(X24662,tc_HOL_Obool))))),X24660),X24661)
      | hAPP(c_Finite__Set_Ocard(tc_fun(X24662,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24662),X24661),X24660)) = hAPP(c_Finite__Set_Ocard(X24662),X24661) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__quotient__disjoint])]) ).

fof(i_0_6367,plain,
    ! [X24393,X24394,X24395,X24396] :
      ( ~ class_Rings_Ocomm__semiring__1(X24396)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24396),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24396),c_Groups_Oone__class_Oone(X24396)),c_Groups_Oone__class_Oone(X24396))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24396),hAPP(hAPP(c_COMBB(X24396,X24396,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(X24396),X24395)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X24396,X24396),hAPP(hAPP(c_COMBB(X24396,tc_fun(X24396,X24396),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(X24396)),c_Nat_Osemiring__1__class_Oof__nat(X24396))),X24394))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24393))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24396),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24396),X24393)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24396),X24395),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24396),X24395),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24396),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24396),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24393),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),X24394)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__series__general])]) ).

fof(i_0_6368,plain,
    ! [X33821,X33822] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33822),X33821))
      | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33821,X33822) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastLessThan__empty])]) ).

fof(i_0_6369,plain,
    ! [X33819,X33820] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33820),X33819))
      | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33819,X33820) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanAtMost__empty])]) ).

fof(i_0_6370,plain,
    ! [X33817,X33818] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33818),X33817))
      | c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X33817,X33818) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OgreaterThanLessThan__empty])]) ).

cnf(i_0_6371,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_5349]) ).

fof(i_0_6372,plain,
    ! [X28178,X28179] :
      ( ( c_Wellfounded_Owf(X28179,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool),tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),X28178))
        | ~ c_FunDef_Oreduction__pair(X28179,X28178) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28179,X28179,X28179),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool),tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),X28178)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool),tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),X28178))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool),tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),X28178)))
        | ~ c_FunDef_Oreduction__pair(X28179,X28178) )
      & ( ~ c_Wellfounded_Owf(X28179,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool),tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),X28178))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28179,X28179,X28179),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool),tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),X28178)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool),tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),X28178))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool),tc_fun(tc_prod(X28179,X28179),tc_HOL_Obool)),X28178)))
        | c_FunDef_Oreduction__pair(X28179,X28178) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__def])])]) ).

cnf(i_0_6373,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_5350]) ).

cnf(i_0_6374,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_5351]) ).

cnf(i_0_6375,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_5352]) ).

fof(i_0_6376,plain,
    ! [X23793,X23794,X23795,X23796,X23797,X23798,X23799,X23800,X23801,X23802,X23803] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23797,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23796,tc_fun(X23797,tc_HOL_Obool)),X23795),X23794)),X23793))
        | ~ hBOOL(hAPP(hAPP(c_member(X23796),X23798),X23795))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23797,tc_HOL_Obool)),hAPP(X23794,X23798)),X23793)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23802),esk136_5(X23799,X23800,X23801,X23802,X23803)),X23801))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23803,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23802,tc_fun(X23803,tc_HOL_Obool)),X23801),X23800)),X23799)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23803,tc_HOL_Obool)),hAPP(X23800,esk136_5(X23799,X23800,X23801,X23802,X23803))),X23799))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23803,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23802,tc_fun(X23803,tc_HOL_Obool)),X23801),X23800)),X23799)) ) ),
    inference(distribute,[status(thm)],[inference(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_6377,plain,
    ! [X24762,X24763,X24764,X24765,X24766] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24765),esk188_5(X24762,X24763,X24764,X24765,X24766)),X24764))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24766),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24765,X24766),X24763),X24764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24766),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24766),hAPP(c_Finite__Set_Ocard(X24765),X24764))),X24762)))
        | ~ class_Groups_Oordered__ab__semigroup__add(X24766)
        | ~ class_Rings_Osemiring__1(X24766) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24766),hAPP(X24763,esk188_5(X24762,X24763,X24764,X24765,X24766))),X24762))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24766),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24765,X24766),X24763),X24764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24766),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24766),hAPP(c_Finite__Set_Ocard(X24765),X24764))),X24762)))
        | ~ class_Groups_Oordered__ab__semigroup__add(X24766)
        | ~ class_Rings_Osemiring__1(X24766) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__bounded])])])]) ).

cnf(i_0_6378,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_5353]) ).

fof(i_0_6379,plain,
    ! [X27459,X27460,X27461,X27462,X27463,X27464] : c_Product__Type_Omap__pair(X27464,X27463,X27462,X27461,X27460,X27459) = hAPP(c_Product__Type_Oprod_Oprod__case(X27464,X27462,tc_prod(X27463,X27461)),hAPP(hAPP(c_COMBC(X27464,tc_fun(X27462,X27461),tc_fun(X27462,tc_prod(X27463,X27461))),hAPP(hAPP(c_COMBB(tc_fun(X27461,tc_prod(X27463,X27461)),tc_fun(tc_fun(X27462,X27461),tc_fun(X27462,tc_prod(X27463,X27461))),X27464),c_COMBB(X27461,tc_prod(X27463,X27461),X27462)),hAPP(hAPP(c_COMBB(X27463,tc_fun(X27461,tc_prod(X27463,X27461)),X27464),c_Product__Type_OPair(X27463,X27461)),X27460))),X27459)),
    inference(variable_rename,[status(thm)],[fact_map__pair__def]) ).

fof(i_0_6380,plain,
    ! [X25829,X25830,X25831] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25831))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X25830),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),X25830),X25829))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25831))),X25829)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_decr__lemma])]) ).

fof(i_0_6381,plain,
    ! [X23883,X23884,X23885,X23886,X23887,X23888] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23887),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23886,X23887),X23885),X23884)),X23883))
        | ~ hBOOL(hAPP(hAPP(c_member(X23886),X23888),X23885))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23887),hAPP(X23884,X23888)),X23883))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X23887) )
      & ( hBOOL(hAPP(hAPP(c_member(X23886),esk137_5(X23883,X23884,X23885,X23886,X23887)),X23885))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23887),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23886,X23887),X23885),X23884)),X23883))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X23887) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23887),hAPP(X23884,esk137_5(X23883,X23884,X23885,X23886,X23887))),X23883))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23887),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23886,X23887),X23885),X23884)),X23883))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X23887) ) ),
    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_6382,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_5309]) ).

cnf(i_0_6383,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_6384,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_6385,plain,
    ! [X29442,X29443,X29444,X29445,X29447,X29448,X29449,X29450,X29451] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk383_4(X29442,X29443,X29444,X29445)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29444)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29443))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29444)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29443)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29445),tc_List_Olist(X29445))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29445),tc_List_Olist(X29445)),X29444),X29443)),c_List_Olexord(X29445,X29442))) )
      & ( hAPP(hAPP(c_List_Otake(X29445),esk383_4(X29442,X29443,X29444,X29445)),X29444) = hAPP(hAPP(c_List_Otake(X29445),esk383_4(X29442,X29443,X29444,X29445)),X29443)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29444)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29443)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29445),tc_List_Olist(X29445))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29445),tc_List_Olist(X29445)),X29444),X29443)),c_List_Olexord(X29445,X29442))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29445,X29445)),hAPP(hAPP(c_Product__Type_OPair(X29445,X29445),hAPP(hAPP(c_List_Onth(X29445),X29444),esk383_4(X29442,X29443,X29444,X29445))),hAPP(hAPP(c_List_Onth(X29445),X29443),esk383_4(X29442,X29443,X29444,X29445)))),X29442))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29444)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29443)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29445),tc_List_Olist(X29445))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29445),tc_List_Olist(X29445)),X29444),X29443)),c_List_Olexord(X29445,X29442))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk383_4(X29442,X29443,X29444,X29445)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29444)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29443))))
        | hAPP(hAPP(c_List_Otake(X29445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29444)),X29443) = X29444
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29445),tc_List_Olist(X29445))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29445),tc_List_Olist(X29445)),X29444),X29443)),c_List_Olexord(X29445,X29442))) )
      & ( hAPP(hAPP(c_List_Otake(X29445),esk383_4(X29442,X29443,X29444,X29445)),X29444) = hAPP(hAPP(c_List_Otake(X29445),esk383_4(X29442,X29443,X29444,X29445)),X29443)
        | hAPP(hAPP(c_List_Otake(X29445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29444)),X29443) = X29444
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29445),tc_List_Olist(X29445))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29445),tc_List_Olist(X29445)),X29444),X29443)),c_List_Olexord(X29445,X29442))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29445,X29445)),hAPP(hAPP(c_Product__Type_OPair(X29445,X29445),hAPP(hAPP(c_List_Onth(X29445),X29444),esk383_4(X29442,X29443,X29444,X29445))),hAPP(hAPP(c_List_Onth(X29445),X29443),esk383_4(X29442,X29443,X29444,X29445)))),X29442))
        | hAPP(hAPP(c_List_Otake(X29445),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29445)),X29444)),X29443) = X29444
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29445),tc_List_Olist(X29445))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29445),tc_List_Olist(X29445)),X29444),X29443)),c_List_Olexord(X29445,X29442))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29450)),X29449)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29450)),X29448)))
        | hAPP(hAPP(c_List_Otake(X29450),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29450)),X29449)),X29448) != X29449
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29450),tc_List_Olist(X29450))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29450),tc_List_Olist(X29450)),X29449),X29448)),c_List_Olexord(X29450,X29447))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29451),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29450)),X29449)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29450)),X29448))))
        | hAPP(hAPP(c_List_Otake(X29450),X29451),X29449) != hAPP(hAPP(c_List_Otake(X29450),X29451),X29448)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29450,X29450)),hAPP(hAPP(c_Product__Type_OPair(X29450,X29450),hAPP(hAPP(c_List_Onth(X29450),X29449),X29451)),hAPP(hAPP(c_List_Onth(X29450),X29448),X29451))),X29447))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29450),tc_List_Olist(X29450))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29450),tc_List_Olist(X29450)),X29449),X29448)),c_List_Olexord(X29450,X29447))) ) ),
    inference(distribute,[status(thm)],[inference(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_6386,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_5354]) ).

fof(i_0_6387,plain,
    ! [X27620,X27621,X27622,X27623] : hAPP(c_Set_OCollect(tc_prod(X27623,X27622)),hAPP(c_Product__Type_Oprod_Oprod__case(X27623,X27622,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X27623,tc_fun(X27622,tc_HOL_Obool),tc_fun(X27622,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27622,tc_HOL_Obool),tc_fun(X27622,tc_HOL_Obool)),X27623),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27622)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27623),c_fconj),X27621))),X27620))) = hAPP(hAPP(c_Product__Type_OSigma(X27623,X27622),hAPP(c_Set_OCollect(X27623),X27621)),hAPP(hAPP(c_COMBB(tc_fun(X27622,tc_HOL_Obool),tc_fun(X27622,tc_HOL_Obool),X27623),c_Set_OCollect(X27622)),X27620)),
    inference(variable_rename,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(i_0_6388,plain,
    ! [X27561,X27562] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X27562))
      | 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)),X27562))),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,X27561))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__less])]) ).

fof(i_0_6389,plain,
    ! [X28391,X28392,X28393,X28394] : c_Hilbert__Choice_OEps(tc_prod(X28394,X28393),hAPP(c_Product__Type_Oprod_Oprod__case(X28394,X28393,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X28394,tc_fun(X28393,tc_HOL_Obool),tc_fun(X28393,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X28393,tc_HOL_Obool),tc_fun(X28393,tc_HOL_Obool)),X28394),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X28393)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X28394),c_fconj),hAPP(c_fequal,X28392)))),hAPP(c_fequal,X28391)))) = hAPP(hAPP(c_Product__Type_OPair(X28394,X28393),X28392),X28391),
    inference(variable_rename,[status(thm)],[fact_Eps__split__eq]) ).

fof(i_0_6390,plain,
    ! [X22161,X22162,X22163,X22164] : c_HOL_OThe(tc_prod(X22164,X22163),hAPP(c_Product__Type_Oprod_Oprod__case(X22164,X22163,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X22164,tc_fun(X22163,tc_HOL_Obool),tc_fun(X22163,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X22163,tc_HOL_Obool),tc_fun(X22163,tc_HOL_Obool)),X22164),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X22163)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X22164),c_fconj),hAPP(c_fequal,X22162)))),hAPP(c_fequal,X22161)))) = hAPP(hAPP(c_Product__Type_OPair(X22164,X22163),X22162),X22161),
    inference(variable_rename,[status(thm)],[fact_The__split__eq]) ).

cnf(i_0_6391,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_5343]) ).

fof(i_0_6392,plain,
    ! [X24411,X24412,X24413,X24414,X24415,X24416] :
      ( ~ class_Groups_Ocomm__monoid__add(X24416)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24415,X24416),hAPP(hAPP(c_COMBC(X24415,tc_fun(X24414,tc_HOL_Obool),X24416),hAPP(hAPP(c_COMBB(tc_fun(X24414,X24416),tc_fun(tc_fun(X24414,tc_HOL_Obool),X24416),X24415),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24414,X24416)),X24413)),X24412)),X24411) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24414,X24416),hAPP(hAPP(c_COMBC(X24414,tc_fun(X24415,tc_HOL_Obool),X24416),hAPP(hAPP(c_COMBB(tc_fun(X24415,X24416),tc_fun(tc_fun(X24415,tc_HOL_Obool),X24416),X24414),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24415,X24416)),hAPP(c_COMBC(X24415,X24414,X24416),X24413))),X24411)),X24412) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__commute])]) ).

fof(i_0_6393,plain,
    ! [X27616,X27617,X27618,X27619] : hAPP(c_Set_OCollect(tc_prod(X27619,X27618)),hAPP(c_Product__Type_Oprod_Oprod__case(X27619,X27618,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X27619,tc_fun(X27618,tc_HOL_Obool),tc_fun(X27618,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X27618,tc_HOL_Obool),tc_fun(X27618,tc_HOL_Obool)),X27619),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27618)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27619),c_fconj),X27617))),X27616))) = hAPP(hAPP(c_Product__Type_OSigma(X27619,X27618),hAPP(c_Set_OCollect(X27619),X27617)),hAPP(c_COMBK(tc_fun(X27618,tc_HOL_Obool),X27619),hAPP(c_Set_OCollect(X27618),X27616))),
    inference(variable_rename,[status(thm)],[fact_Collect__split]) ).

fof(i_0_6394,plain,
    ! [X23456,X23457,X23458,X23459] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23459),X23458))
      | hAPP(c_Set_Oimage(X23459,X23457,X23456),X23458) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(X23457,tc_HOL_Obool),X23459,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23457,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X23459,tc_fun(X23457,tc_HOL_Obool),tc_fun(X23457,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X23457,tc_fun(tc_fun(X23457,tc_HOL_Obool),tc_fun(X23457,tc_HOL_Obool)),X23459),c_Set_Oinsert(X23457)),X23456)),c_Orderings_Obot__class_Obot(tc_fun(X23457,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(X23457,tc_HOL_Obool))),X23458) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eq__fold__image])]) ).

cnf(i_0_6395,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_5355]) ).

fof(i_0_6396,plain,
    ! [X17531,X17532,X17533,X17534] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17534),X17533))
      | ~ hBOOL(hAPP(hAPP(c_member(X17534),X17532),X17533))
      | ~ hBOOL(hAPP(hAPP(c_member(X17534),X17531),X17533))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17534),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17534,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17534,tc_HOL_Obool)),X17533),hAPP(hAPP(c_Set_Oinsert(X17534),X17532),c_Orderings_Obot__class_Obot(tc_fun(X17534,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(X17534),X17531),c_Orderings_Obot__class_Obot(tc_fun(X17534,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X17534),X17533))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff2__less])]) ).

cnf(i_0_6397,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_5356]) ).

fof(i_0_6398,plain,
    ! [X24359,X24360] : c_Relation_OId__on(X24360,X24359) = hAPP(c_Product__Type_Oprod_Oprod__case(X24360,X24360,tc_HOL_Obool),hAPP(hAPP(c_COMBS(X24360,tc_HOL_Obool,tc_fun(X24360,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24360,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(X24360,tc_HOL_Obool)),X24360),c_COMBC(X24360,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X24360,tc_HOL_Obool),tc_fun(X24360,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),X24360),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X24360),c_fconj)),c_fequal))),X24359)),
    inference(variable_rename,[status(thm)],[fact_Id__on__def_H]) ).

fof(i_0_6399,plain,
    ! [X27776] : c_Int_Oint__ge__less__than(X27776) = 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),X27776)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_int__ge__less__than__def]) ).

fof(i_0_6400,plain,
    ! [X28495,X28496,X28497,X28498,X28499,X28500,X28501,X28502,X28503] : hAPP(hAPP(c_Product__Type_Oscomp(X28503,X28502,X28501,X28500),hAPP(hAPP(c_Product__Type_Oscomp(X28503,X28499,X28498,tc_prod(X28502,X28501)),X28497),X28496)),X28495) = hAPP(hAPP(c_Product__Type_Oscomp(X28503,X28499,X28498,X28500),X28497),hAPP(hAPP(c_COMBC(X28499,tc_fun(X28502,tc_fun(X28501,X28500)),tc_fun(X28498,X28500)),hAPP(hAPP(c_COMBB(tc_fun(X28498,tc_prod(X28502,X28501)),tc_fun(tc_fun(X28502,tc_fun(X28501,X28500)),tc_fun(X28498,X28500)),X28499),c_Product__Type_Oscomp(X28498,X28502,X28501,X28500)),X28496)),X28495)),
    inference(variable_rename,[status(thm)],[fact_scomp__scomp]) ).

fof(i_0_6401,plain,
    ! [X23085,X23086,X23087,X23088] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23088),X23087))
      | ~ 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)),X23086),X23088)),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)),X23085),X23087)),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)),X23086),X23085)),X23087)),c_FunDef_Omax__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__insertI])]) ).

fof(i_0_6402,plain,
    ! [X23071,X23072,X23073,X23074] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23074),X23073))
      | ~ 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)),X23072),X23074)),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)),X23071),X23073)),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)),X23072),X23071)),X23073)),c_FunDef_Omax__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__insertI])]) ).

cnf(i_0_6403,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_5328]) ).

cnf(i_0_6404,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_5329]) ).

fof(i_0_6405,plain,
    ! [X31717,X31718,X31719,X31720,X31721] :
      ( ~ class_Orderings_Olinorder(X31721)
      | c_List_Olinorder__class_Osorted(X31721,hAPP(hAPP(c_List_Omap(X31720,X31721),X31719),hAPP(c_List_Ofilter(X31720,hAPP(hAPP(c_COMBC(X31720,X31721,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X31721,tc_fun(X31721,tc_HOL_Obool),X31720),c_fequal),X31719)),hAPP(X31718,X31717))),X31717))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__same])]) ).

fof(i_0_6406,plain,
    ! [X29351,X29352,X29353,X29354,X29355] :
      ( ( X29352 = hAPP(hAPP(c_List_Olist_OCons(X29355),esk376_5(X29351,X29352,X29353,X29354,X29355)),esk377_5(X29351,X29352,X29353,X29354,X29355))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29355),tc_List_Olist(X29355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29355),tc_List_Olist(X29355)),hAPP(hAPP(c_List_Olist_OCons(X29355),X29354),X29353)),X29352)),c_List_Olistrel(X29355,X29351))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29355,X29355)),hAPP(hAPP(c_Product__Type_OPair(X29355,X29355),X29354),esk376_5(X29351,X29352,X29353,X29354,X29355))),X29351))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29355),tc_List_Olist(X29355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29355),tc_List_Olist(X29355)),hAPP(hAPP(c_List_Olist_OCons(X29355),X29354),X29353)),X29352)),c_List_Olistrel(X29355,X29351))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29355),tc_List_Olist(X29355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29355),tc_List_Olist(X29355)),X29353),esk377_5(X29351,X29352,X29353,X29354,X29355))),c_List_Olistrel(X29355,X29351)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29355),tc_List_Olist(X29355))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29355),tc_List_Olist(X29355)),hAPP(hAPP(c_List_Olist_OCons(X29355),X29354),X29353)),X29352)),c_List_Olistrel(X29355,X29351))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5357])])])]) ).

cnf(i_0_6407,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_5358]) ).

cnf(i_0_6408,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_5359]) ).

fof(i_0_6409,plain,
    ! [X28416,X28417,X28418,X28419,X28420,X28422,X28423,X28424,X28425,X28427] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28419),X28418))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool)),X28418),X28417)),c_Wellfounded_Omax__ext(X28419,X28416))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X28419),X28417))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool)),X28418),X28417)),c_Wellfounded_Omax__ext(X28419,X28416))) )
      & ( X28417 != c_Orderings_Obot__class_Obot(tc_fun(X28419,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool)),X28418),X28417)),c_Wellfounded_Omax__ext(X28419,X28416))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28419),esk320_5(X28416,X28417,X28418,X28419,X28420)),X28417))
        | ~ hBOOL(hAPP(hAPP(c_member(X28419),X28420),X28418))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool)),X28418),X28417)),c_Wellfounded_Omax__ext(X28419,X28416))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28419,X28419)),hAPP(hAPP(c_Product__Type_OPair(X28419,X28419),X28420),esk320_5(X28416,X28417,X28418,X28419,X28420))),X28416))
        | ~ hBOOL(hAPP(hAPP(c_member(X28419),X28420),X28418))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28419,tc_HOL_Obool),tc_fun(X28419,tc_HOL_Obool)),X28418),X28417)),c_Wellfounded_Omax__ext(X28419,X28416))) )
      & ( hBOOL(hAPP(hAPP(c_member(X28425),esk321_4(X28422,X28423,X28424,X28425)),X28424))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28425),X28424))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28425),X28423))
        | X28423 = c_Orderings_Obot__class_Obot(tc_fun(X28425,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28425,tc_HOL_Obool),tc_fun(X28425,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28425,tc_HOL_Obool),tc_fun(X28425,tc_HOL_Obool)),X28424),X28423)),c_Wellfounded_Omax__ext(X28425,X28422))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28425),X28427),X28423))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28425,X28425)),hAPP(hAPP(c_Product__Type_OPair(X28425,X28425),esk321_4(X28422,X28423,X28424,X28425)),X28427)),X28422))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28425),X28424))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28425),X28423))
        | X28423 = c_Orderings_Obot__class_Obot(tc_fun(X28425,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X28425,tc_HOL_Obool),tc_fun(X28425,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X28425,tc_HOL_Obool),tc_fun(X28425,tc_HOL_Obool)),X28424),X28423)),c_Wellfounded_Omax__ext(X28425,X28422))) ) ),
    inference(distribute,[status(thm)],[inference(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_6410,plain,
    ! [X28126,X28127,X28128] :
      ( ( ~ c_Wellfounded_Owf(X28128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28128,X28128),tc_HOL_Obool)),X28127),X28126))
        | c_Wellfounded_Owf(X28128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28128,X28128),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28128,X28128),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28128,X28128,X28128),X28127),X28127)),hAPP(hAPP(c_Relation_Orel__comp(X28128,X28128,X28128),X28126),X28127))),X28126)) )
      & ( ~ c_Wellfounded_Owf(X28128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28128,X28128),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28128,X28128),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28128,X28128,X28128),X28127),X28127)),hAPP(hAPP(c_Relation_Orel__comp(X28128,X28128,X28128),X28126),X28127))),X28126))
        | c_Wellfounded_Owf(X28128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28128,X28128),tc_HOL_Obool)),X28127),X28126)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__merge])]) ).

fof(i_0_6411,plain,
    ! [X27465,X27466,X27467,X27468,X27469,X27470,X27471,X27472,X27473,X27474] :
      ( hAPP(c_Set_Oimage(X27474,X27473,X27472),X27471) != X27470
      | hAPP(c_Set_Oimage(X27469,X27468,X27467),X27466) != X27465
      | hAPP(c_Set_Oimage(tc_prod(X27474,X27469),tc_prod(X27473,X27468),c_Product__Type_Omap__pair(X27474,X27473,X27469,X27468,X27472,X27467)),hAPP(hAPP(c_Product__Type_OSigma(X27474,X27469),X27471),hAPP(c_COMBK(tc_fun(X27469,tc_HOL_Obool),X27474),X27466))) = hAPP(hAPP(c_Product__Type_OSigma(X27473,X27468),X27470),hAPP(c_COMBK(tc_fun(X27468,tc_HOL_Obool),X27473),X27465)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj__on])]) ).

fof(i_0_6412,plain,
    ! [X23089,X23090,X23091,X23092] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23092),X23091))
      | ~ 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)),X23092),X23090)),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)),X23091),X23089)),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)),X23091),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23090),X23089))),c_FunDef_Omin__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmin__insertI])]) ).

fof(i_0_6413,plain,
    ! [X23067,X23068,X23069,X23070] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23070),X23069))
      | ~ 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)),X23070),X23068)),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)),X23069),X23067)),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)),X23069),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23068),X23067))),c_FunDef_Omin__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smin__insertI])]) ).

fof(i_0_6414,plain,
    ! [X19263,X19264,X19265,X19266,X19267,X19270,X19271,X19272,X19273,X19274,X19275,X19276] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X19267),X19265),X19264) = hAPP(hAPP(c_Set_Oinsert(X19267),esk40_5(X19263,X19264,X19265,X19266,X19267)),esk41_5(X19263,X19264,X19265,X19266,X19267))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19267,X19266,hAPP(hAPP(c_Set_Oinsert(X19267),X19265),X19264)),X19263)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19267,X19267,X19266,esk40_5(X19263,X19264,X19265,X19266,X19267),esk41_5(X19263,X19264,X19265,X19266,X19267)),X19263))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19267,X19266,hAPP(hAPP(c_Set_Oinsert(X19267),X19265),X19264)),X19263)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19267),esk40_5(X19263,X19264,X19265,X19266,X19267)),esk41_5(X19263,X19264,X19265,X19266,X19267)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19267,X19266,hAPP(hAPP(c_Set_Oinsert(X19267),X19265),X19264)),X19263)) )
      & ( hAPP(hAPP(c_Set_Oinsert(X19274),X19272),X19271) != hAPP(hAPP(c_Set_Oinsert(X19274),X19275),X19276)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19274,X19274,X19273,X19275,X19276),X19270))
        | hBOOL(hAPP(hAPP(c_member(X19274),X19275),X19276))
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19274,X19273,hAPP(hAPP(c_Set_Oinsert(X19274),X19272),X19271)),X19270)) ) ),
    inference(distribute,[status(thm)],[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_5360])])])])])]) ).

fof(i_0_6415,plain,
    ! [X19256,X19257,X19258,X19259,X19260] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X19260),X19258),X19257) = hAPP(hAPP(c_Set_Oinsert(X19260),esk38_5(X19256,X19257,X19258,X19259,X19260)),esk39_5(X19256,X19257,X19258,X19259,X19260))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19260,X19259,hAPP(hAPP(c_Set_Oinsert(X19260),X19258),X19257)),X19256)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19260,X19260,X19259,esk38_5(X19256,X19257,X19258,X19259,X19260),esk39_5(X19256,X19257,X19258,X19259,X19260)),X19256))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19260,X19259,hAPP(hAPP(c_Set_Oinsert(X19260),X19258),X19257)),X19256)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X19260),esk38_5(X19256,X19257,X19258,X19259,X19260)),esk39_5(X19256,X19257,X19258,X19259,X19260)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X19260,X19259,hAPP(hAPP(c_Set_Oinsert(X19260),X19258),X19257)),X19256)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__fold1SetE])])])]) ).

fof(i_0_6416,plain,
    ! [X29755,X29756,X29757,X29758,X29761,X29762,X29763,X29764,X29765,X29766] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29758,X29758)),hAPP(hAPP(c_Product__Type_OPair(X29758,X29758),hAPP(hAPP(c_List_Onth(X29758),X29757),esk393_4(X29755,X29756,X29757,X29758))),esk392_4(X29755,X29756,X29757,X29758))),X29755))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29758),tc_List_Olist(X29758))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29758),tc_List_Olist(X29758)),X29757),X29756)),c_List_Olistrel1(X29758,X29755))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk393_4(X29755,X29756,X29757,X29758)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29758)),X29757)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29758),tc_List_Olist(X29758))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29758),tc_List_Olist(X29758)),X29757),X29756)),c_List_Olistrel1(X29758,X29755))) )
      & ( X29756 = hAPP(hAPP(c_List_Olist__update(X29758,X29757),esk393_4(X29755,X29756,X29757,X29758)),esk392_4(X29755,X29756,X29757,X29758))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29758),tc_List_Olist(X29758))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29758),tc_List_Olist(X29758)),X29757),X29756)),c_List_Olistrel1(X29758,X29755))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29764,X29764)),hAPP(hAPP(c_Product__Type_OPair(X29764,X29764),hAPP(hAPP(c_List_Onth(X29764),X29763),X29766)),X29765)),X29761))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29766),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29764)),X29763)))
        | X29762 != hAPP(hAPP(c_List_Olist__update(X29764,X29763),X29766),X29765)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29764),tc_List_Olist(X29764))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29764),tc_List_Olist(X29764)),X29763),X29762)),c_List_Olistrel1(X29764,X29761))) ) ),
    inference(distribute,[status(thm)],[inference(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_6417,plain,
    ! [X27368,X27369,X27370,X27371,X27372,X27373] :
      ( hAPP(c_Set_Oimage(X27373,X27372,X27371),c_Orderings_Otop__class_Otop(tc_fun(X27373,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27372,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X27370,X27369,X27368),c_Orderings_Otop__class_Otop(tc_fun(X27370,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X27369,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(tc_prod(X27373,X27370),tc_prod(X27372,X27369),c_Product__Type_Omap__pair(X27373,X27372,X27370,X27369,X27371,X27368)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27373,X27370),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27372,X27369),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__surj])]) ).

fof(i_0_6418,plain,
    ! [X19643,X19644,X19645] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19645),X19644))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19645,tc_HOL_Obool)),X19643),X19644) = hAPP(hAPP(c_Finite__Set_Ofold(X19645,tc_fun(X19645,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X19645,tc_HOL_Obool),tc_fun(tc_fun(X19645,tc_HOL_Obool),tc_fun(X19645,tc_HOL_Obool)),X19645),hAPP(c_COMBC(tc_fun(X19645,tc_HOL_Obool),tc_fun(X19645,tc_HOL_Obool),tc_fun(X19645,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X19645,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X19645,tc_fun(X19645,tc_HOL_Obool),tc_fun(X19645,tc_HOL_Obool)),c_Set_Oinsert(X19645)),c_Orderings_Obot__class_Obot(tc_fun(X19645,tc_HOL_Obool))))),X19643),X19644) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__fold__remove])]) ).

cnf(i_0_6419,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_5344]) ).

cnf(i_0_6420,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_5345]) ).

cnf(i_0_6421,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_5361]) ).

cnf(i_0_6422,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_5362]) ).

cnf(i_0_6423,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_5363]) ).

fof(i_0_6424,plain,
    ! [X27409,X27410,X27411,X27412,X27413,X27414,X27415] : hAPP(c_Product__Type_Ofst(X27415,X27414),hAPP(c_Product__Type_Omap__pair(X27413,X27415,X27412,X27414,X27411,X27410),X27409)) = hAPP(X27411,hAPP(c_Product__Type_Ofst(X27413,X27412),X27409)),
    inference(variable_rename,[status(thm)],[fact_fst__map__pair]) ).

fof(i_0_6425,plain,
    ! [X27402,X27403,X27404,X27405,X27406,X27407,X27408] : hAPP(c_Product__Type_Osnd(X27408,X27407),hAPP(c_Product__Type_Omap__pair(X27406,X27408,X27405,X27407,X27404,X27403),X27402)) = hAPP(X27403,hAPP(c_Product__Type_Osnd(X27406,X27405),X27402)),
    inference(variable_rename,[status(thm)],[fact_snd__prod__fun]) ).

cnf(i_0_6426,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_5364]) ).

cnf(i_0_6427,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_5365]) ).

fof(i_0_6428,plain,
    ! [X29305,X29306,X29307,X29308] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29308,X29308)),hAPP(hAPP(c_Product__Type_OPair(X29308,X29308),esk374_4(X29305,X29306,X29307,X29308)),esk375_4(X29305,X29306,X29307,X29308))),X29307))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29308),tc_List_Olist(X29308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29308),tc_List_Olist(X29308)),X29306),X29305)),c_List_Olexord(X29308,X29307)))
        | X29306 = X29305
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29308),tc_List_Olist(X29308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29308),tc_List_Olist(X29308)),X29305),X29306)),c_List_Olexord(X29308,X29307))) )
      & ( esk374_4(X29305,X29306,X29307,X29308) != esk375_4(X29305,X29306,X29307,X29308)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29308),tc_List_Olist(X29308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29308),tc_List_Olist(X29308)),X29306),X29305)),c_List_Olexord(X29308,X29307)))
        | X29306 = X29305
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29308),tc_List_Olist(X29308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29308),tc_List_Olist(X29308)),X29305),X29306)),c_List_Olexord(X29308,X29307))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29308,X29308)),hAPP(hAPP(c_Product__Type_OPair(X29308,X29308),esk375_4(X29305,X29306,X29307,X29308)),esk374_4(X29305,X29306,X29307,X29308))),X29307))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29308),tc_List_Olist(X29308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29308),tc_List_Olist(X29308)),X29306),X29305)),c_List_Olexord(X29308,X29307)))
        | X29306 = X29305
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29308),tc_List_Olist(X29308))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29308),tc_List_Olist(X29308)),X29305),X29306)),c_List_Olexord(X29308,X29307))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__linear])])])]) ).

fof(i_0_6429,plain,
    ! [X24227,X24228,X24229,X24230] : 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),X24230),X24229)),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),X24228),X24227)),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),X24230),X24228)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24229),X24227))),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_6430,plain,
    ! [X24352,X24353] : c_Relation_OId__on(X24353,X24352) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24353,tc_fun(tc_prod(X24353,X24353),tc_HOL_Obool)),X24352),hAPP(hAPP(c_COMBC(X24353,tc_fun(tc_prod(X24353,X24353),tc_HOL_Obool),tc_fun(tc_prod(X24353,X24353),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(X24353,X24353),tc_fun(tc_fun(tc_prod(X24353,X24353),tc_HOL_Obool),tc_fun(tc_prod(X24353,X24353),tc_HOL_Obool)),X24353),c_Set_Oinsert(tc_prod(X24353,X24353))),hAPP(hAPP(c_COMBS(X24353,X24353,tc_prod(X24353,X24353)),c_Product__Type_OPair(X24353,X24353)),c_COMBI(X24353)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X24353,X24353),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Id__on__def]) ).

cnf(i_0_6431,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_5366]) ).

fof(i_0_6432,plain,
    ! [X32467,X32468,X32469] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32469,X32469,hAPP(hAPP(c_COMBB(tc_fun(X32469,tc_HOL_Obool),tc_fun(X32469,tc_HOL_Obool),X32469),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32469),c_fNot)),c_fequal)),X32468),X32467))
        | X32468 != X32467 )
      & ( X32468 = X32467
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32469,X32469,hAPP(hAPP(c_COMBB(tc_fun(X32469,tc_HOL_Obool),tc_fun(X32469,tc_HOL_Obool),X32469),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32469),c_fNot)),c_fequal)),X32468),X32467)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__noteq])]) ).

cnf(i_0_6433,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_5367]) ).

cnf(i_0_6434,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_5368]) ).

fof(i_0_6435,plain,
    ! [X30700,X30701,X30702,X30703,X30704,X30705,X30706,X30707] : hAPP(hAPP(c_List_Omap(tc_prod(X30707,X30706),X30705),X30704),hAPP(hAPP(c_List_Ozip(X30707,X30706),hAPP(hAPP(c_List_Omap(X30703,X30707),X30702),X30701)),X30700)) = hAPP(hAPP(c_List_Omap(tc_prod(X30703,X30706),X30705),hAPP(c_Product__Type_Oprod_Oprod__case(X30703,X30706,X30705),hAPP(hAPP(c_COMBB(tc_fun(X30706,tc_prod(X30707,X30706)),tc_fun(X30706,X30705),X30703),hAPP(c_COMBB(tc_prod(X30707,X30706),X30705,X30706),X30704)),hAPP(hAPP(c_COMBB(X30707,tc_fun(X30706,tc_prod(X30707,X30706)),X30703),c_Product__Type_OPair(X30707,X30706)),X30702)))),hAPP(hAPP(c_List_Ozip(X30703,X30706),X30701),X30700)),
    inference(variable_rename,[status(thm)],[fact_map__zip__map]) ).

fof(i_0_6436,plain,
    ! [X32125,X32126,X32127,X32128] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32127,X32128)),X32126),X32125))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X32127,X32128)),X32126),X32125))
        | ~ class_Orderings_Oorder(X32128)
        | ~ class_Enum_Oenum(X32127) )
      & ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32127),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32127),c_fNot),hAPP(hAPP(c_COMBS(X32127,X32128,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32128,tc_fun(X32128,tc_HOL_Obool),X32127),c_fequal),X32126)),X32125))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X32127,X32128)),X32126),X32125))
        | ~ class_Orderings_Oorder(X32128)
        | ~ class_Enum_Oenum(X32127) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32127,X32128)),X32126),X32125))
        | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32127),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32127),c_fNot),hAPP(hAPP(c_COMBS(X32127,X32128,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32128,tc_fun(X32128,tc_HOL_Obool),X32127),c_fequal),X32126)),X32125))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X32127,X32128)),X32126),X32125))
        | ~ class_Orderings_Oorder(X32128)
        | ~ class_Enum_Oenum(X32127) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I2_J])])]) ).

fof(i_0_6437,plain,
    ! [X30002,X30003,X30004,X30005] : c_List_Osublist(X30005,hAPP(hAPP(c_List_Olist_OCons(X30005),X30004),X30003),X30002) = hAPP(hAPP(c_List_Oappend(X30005),hAPP(hAPP(hAPP(c_If(tc_List_Olist(X30005)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30002)),hAPP(hAPP(c_List_Olist_OCons(X30005),X30004),c_List_Olist_ONil(X30005))),c_List_Olist_ONil(X30005))),c_List_Osublist(X30005,X30003,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)),X30002)))),
    inference(variable_rename,[status(thm)],[fact_sublist__Cons]) ).

cnf(i_0_6438,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_5369]) ).

fof(i_0_6439,plain,
    ! [X31776,X31777,X31778,X31779] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31779),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31779))),X31778)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31777),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31779))),c_List_Otranspose(X31779,X31778))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31779))),hAPP(c_List_Ofilter(tc_List_Olist(X31779),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31779)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31777)),c_Nat_Osize__class_Osize(tc_List_Olist(X31779)))),X31778))))
      | hAPP(hAPP(c_List_Onth(X31779),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31779)),c_List_Otranspose(X31779,X31778)),X31777)),X31776) = hAPP(hAPP(c_List_Onth(X31779),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31779)),X31778),X31776)),X31777) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted])]) ).

cnf(i_0_6440,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_5370]) ).

cnf(i_0_6441,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_5349]) ).

cnf(i_0_6442,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_5371]) ).

cnf(i_0_6443,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_5372]) ).

cnf(i_0_6444,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_5373]) ).

cnf(i_0_6445,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_5351]) ).

cnf(i_0_6446,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_5374]) ).

cnf(i_0_6447,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_5375]) ).

cnf(i_0_6448,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_5376]) ).

fof(i_0_6449,plain,
    ! [X26501,X26502,X26503,X26504,X26505,X26507] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26504),esk234_5(X26501,X26502,X26503,X26504,X26505)),X26503))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26505),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26504,X26505),X26503),X26502)),X26501))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26505)
        | ~ class_Orderings_Olinorder(X26505) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26505),hAPP(X26502,esk234_5(X26501,X26502,X26503,X26504,X26505))),X26501))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26505),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26504,X26505),X26503),X26502)),X26501))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26505)
        | ~ class_Orderings_Olinorder(X26505) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26504),X26507),X26503))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26505),hAPP(X26502,X26507)),X26501))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26505),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26504,X26505),X26503),X26502)),X26501))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26505)
        | ~ class_Orderings_Olinorder(X26505) ) ),
    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_6450,plain,
    ! [X23738,X23739,X23740,X23741,X23742,X23744,X23745,X23746,X23747,X23748,X23749,X23750,X23753] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23742),esk130_5(X23738,X23739,X23740,X23741,X23742)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23741,tc_fun(X23742,tc_HOL_Obool)),X23740),X23739)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23741),X23744),X23740))
        | ~ hBOOL(hAPP(hAPP(c_member(X23742),X23745),hAPP(X23739,X23744)))
        | hBOOL(hAPP(X23738,X23745)) )
      & ( ~ hBOOL(hAPP(X23738,esk130_5(X23738,X23739,X23740,X23741,X23742)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23741),X23744),X23740))
        | ~ hBOOL(hAPP(hAPP(c_member(X23742),X23745),hAPP(X23739,X23744)))
        | hBOOL(hAPP(X23738,X23745)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23749),esk131_5(X23746,X23747,X23748,X23749,X23750)),X23748))
        | ~ hBOOL(hAPP(hAPP(c_member(X23750),X23753),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23749,tc_fun(X23750,tc_HOL_Obool)),X23748),X23747)))
        | hBOOL(hAPP(X23746,X23753)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23750),esk132_5(X23746,X23747,X23748,X23749,X23750)),hAPP(X23747,esk131_5(X23746,X23747,X23748,X23749,X23750))))
        | ~ hBOOL(hAPP(hAPP(c_member(X23750),X23753),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23749,tc_fun(X23750,tc_HOL_Obool)),X23748),X23747)))
        | hBOOL(hAPP(X23746,X23753)) )
      & ( ~ hBOOL(hAPP(X23746,esk132_5(X23746,X23747,X23748,X23749,X23750)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23750),X23753),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23749,tc_fun(X23750,tc_HOL_Obool)),X23748),X23747)))
        | hBOOL(hAPP(X23746,X23753)) ) ),
    inference(distribute,[status(thm)],[inference(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_6451,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_6452,plain,
    ! [X23543,X23544,X23545,X23546,X23547,X23548] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23548,tc_HOL_Obool),tc_fun(X23548,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23548,tc_HOL_Obool),tc_fun(X23548,tc_HOL_Obool)),X23547),X23546)),c_Wellfounded_Omax__ext(X23548,X23545)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23548,tc_HOL_Obool),tc_fun(X23548,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23548,tc_HOL_Obool),tc_fun(X23548,tc_HOL_Obool)),X23544),X23543)),c_Wellfounded_Omax__ext(X23548,X23545)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X23548,tc_HOL_Obool),tc_fun(X23548,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X23548,tc_HOL_Obool),tc_fun(X23548,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23548,tc_HOL_Obool)),X23547),X23544)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23548,tc_HOL_Obool)),X23546),X23543))),c_Wellfounded_Omax__ext(X23548,X23545))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__additive])]) ).

fof(i_0_6453,plain,
    ! [X27361,X27362,X27363,X27364,X27365] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27365),esk263_5(X27361,X27362,X27363,X27364,X27365)),X27362))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27365,X27364)),X27363),hAPP(hAPP(c_Product__Type_OSigma(X27365,X27364),X27362),X27361))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27364),esk264_5(X27361,X27362,X27363,X27364,X27365)),hAPP(X27361,esk263_5(X27361,X27362,X27363,X27364,X27365))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27365,X27364)),X27363),hAPP(hAPP(c_Product__Type_OSigma(X27365,X27364),X27362),X27361))) )
      & ( X27363 = hAPP(hAPP(c_Product__Type_OPair(X27365,X27364),esk263_5(X27361,X27362,X27363,X27364,X27365)),esk264_5(X27361,X27362,X27363,X27364,X27365))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27365,X27364)),X27363),hAPP(hAPP(c_Product__Type_OSigma(X27365,X27364),X27362),X27361))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaE])])])]) ).

fof(i_0_6454,plain,
    ! [X30668,X30669,X30670,X30671,X30672,X30673,X30674] : hAPP(c_List_Ofoldl(X30674,X30673,X30672,X30671),hAPP(hAPP(c_List_Omap(X30670,X30673),X30669),X30668)) = hAPP(c_List_Ofoldl(X30674,X30670,hAPP(hAPP(c_COMBC(X30674,tc_fun(X30670,X30673),tc_fun(X30670,X30674)),hAPP(hAPP(c_COMBB(tc_fun(X30673,X30674),tc_fun(tc_fun(X30670,X30673),tc_fun(X30670,X30674)),X30674),c_COMBB(X30673,X30674,X30670)),X30672)),X30669),X30671),X30668),
    inference(variable_rename,[status(thm)],[fact_foldl__map]) ).

fof(i_0_6455,plain,
    ! [X27923,X27924,X27925,X27926,X27927,X27928,X27929] : hAPP(hAPP(c_Relation_Orel__comp(X27929,X27928,X27927),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27926,tc_fun(tc_prod(X27929,X27928),tc_HOL_Obool)),X27925),X27924)),X27923) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27926,tc_fun(tc_prod(X27929,X27927),tc_HOL_Obool)),X27925),hAPP(hAPP(c_COMBC(X27926,tc_fun(tc_prod(X27928,X27927),tc_HOL_Obool),tc_fun(tc_prod(X27929,X27927),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27929,X27928),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(X27928,X27927),tc_HOL_Obool),tc_fun(tc_prod(X27929,X27927),tc_HOL_Obool)),X27926),c_Relation_Orel__comp(X27929,X27928,X27927)),X27924)),X27923)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib2]) ).

fof(i_0_6456,plain,
    ! [X21088,X21089] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21089),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21088)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21089)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21088) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21089),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21088)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21089)) = 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),X21088),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21089)))),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_5377])]) ).

cnf(i_0_6457,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_5378]) ).

fof(i_0_6458,plain,
    ! [X27583,X27584,X27585] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27585),hAPP(c_Set_OCollect(X27585),X27584)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27585),hAPP(c_Set_OCollect(X27585),hAPP(hAPP(c_COMBS(X27585,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27585),c_fdisj),X27584)),X27583)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X27585),hAPP(c_Set_OCollect(X27585),X27583)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27585),hAPP(c_Set_OCollect(X27585),hAPP(hAPP(c_COMBS(X27585,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27585),c_fdisj),X27584)),X27583)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27585),hAPP(c_Set_OCollect(X27585),X27584)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27585),hAPP(c_Set_OCollect(X27585),X27583)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27585),hAPP(c_Set_OCollect(X27585),hAPP(hAPP(c_COMBS(X27585,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27585),c_fdisj),X27584)),X27583)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI])])]) ).

fof(i_0_6459,plain,
    ! [X33203,X33204,X33205,X33206,X33207] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33206),esk522_5(X33203,X33204,X33205,X33206,X33207)),hAPP(c_Set_Oimage(X33207,X33206,X33205),c_Orderings_Otop__class_Otop(tc_fun(X33207,tc_HOL_Obool)))))
        | hBOOL(hAPP(X33204,X33203))
        | ~ c_Fun_Oinj__on(X33207,X33206,X33205,c_Orderings_Otop__class_Otop(tc_fun(X33207,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(X33204,hAPP(c_Hilbert__Choice_Oinv__into(X33207,X33206,c_Orderings_Otop__class_Otop(tc_fun(X33207,tc_HOL_Obool)),X33205),esk522_5(X33203,X33204,X33205,X33206,X33207))))
        | hBOOL(hAPP(X33204,X33203))
        | ~ c_Fun_Oinj__on(X33207,X33206,X33205,c_Orderings_Otop__class_Otop(tc_fun(X33207,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_6460,plain,
    ! [X32219,X32220,X32221] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X32220,X32221)),X32219))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32220),hAPP(hAPP(c_COMBB(tc_fun(X32221,tc_HOL_Obool),tc_HOL_Obool,X32220),c_Enum_Oenum__class_Oenum__all(X32221)),hAPP(hAPP(c_COMBB(tc_fun(X32221,tc_prod(X32220,X32221)),tc_fun(X32221,tc_HOL_Obool),X32220),hAPP(c_COMBB(tc_prod(X32220,X32221),tc_HOL_Obool,X32221),X32219)),c_Product__Type_OPair(X32220,X32221)))))
        | ~ class_Enum_Oenum(X32221)
        | ~ class_Enum_Oenum(X32220) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32220),hAPP(hAPP(c_COMBB(tc_fun(X32221,tc_HOL_Obool),tc_HOL_Obool,X32220),c_Enum_Oenum__class_Oenum__all(X32221)),hAPP(hAPP(c_COMBB(tc_fun(X32221,tc_prod(X32220,X32221)),tc_fun(X32221,tc_HOL_Obool),X32220),hAPP(c_COMBB(tc_prod(X32220,X32221),tc_HOL_Obool,X32221),X32219)),c_Product__Type_OPair(X32220,X32221)))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(X32220,X32221)),X32219))
        | ~ class_Enum_Oenum(X32221)
        | ~ class_Enum_Oenum(X32220) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__all__prod__def])])]) ).

fof(i_0_6461,plain,
    ! [X32129,X32130,X32131] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X32130,X32131)),X32129))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32130),hAPP(hAPP(c_COMBB(tc_fun(X32131,tc_HOL_Obool),tc_HOL_Obool,X32130),c_Enum_Oenum__class_Oenum__ex(X32131)),hAPP(hAPP(c_COMBB(tc_fun(X32131,tc_prod(X32130,X32131)),tc_fun(X32131,tc_HOL_Obool),X32130),hAPP(c_COMBB(tc_prod(X32130,X32131),tc_HOL_Obool,X32131),X32129)),c_Product__Type_OPair(X32130,X32131)))))
        | ~ class_Enum_Oenum(X32131)
        | ~ class_Enum_Oenum(X32130) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32130),hAPP(hAPP(c_COMBB(tc_fun(X32131,tc_HOL_Obool),tc_HOL_Obool,X32130),c_Enum_Oenum__class_Oenum__ex(X32131)),hAPP(hAPP(c_COMBB(tc_fun(X32131,tc_prod(X32130,X32131)),tc_fun(X32131,tc_HOL_Obool),X32130),hAPP(c_COMBB(tc_prod(X32130,X32131),tc_HOL_Obool,X32131),X32129)),c_Product__Type_OPair(X32130,X32131)))))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(X32130,X32131)),X32129))
        | ~ class_Enum_Oenum(X32131)
        | ~ class_Enum_Oenum(X32130) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_enum__ex__prod__def])])]) ).

fof(i_0_6462,plain,
    ! [X31030,X31031,X31032,X31033] :
      ( ( hBOOL(hAPP(c_List_Olistsp(X31033,X31032),X31030))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31033,hAPP(hAPP(c_COMBS(X31033,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31033),c_fconj),X31032)),X31031)),X31030)) )
      & ( hBOOL(hAPP(c_List_Olistsp(X31033,X31031),X31030))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31033,hAPP(hAPP(c_COMBS(X31033,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31033),c_fconj),X31032)),X31031)),X31030)) )
      & ( ~ hBOOL(hAPP(c_List_Olistsp(X31033,X31032),X31030))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31033,X31031),X31030))
        | hBOOL(hAPP(c_List_Olistsp(X31033,hAPP(hAPP(c_COMBS(X31033,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31033),c_fconj),X31032)),X31031)),X31030)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__conj__eq])])]) ).

fof(i_0_6463,plain,
    ! [X20978,X20979] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X20979))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X20978)),hAPP(c_Int_Onat,X20979)) = hAPP(c_Int_Onat,X20978) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X20979))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X20978)),hAPP(c_Int_Onat,X20979)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20978),X20979)),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_5379])]) ).

cnf(i_0_6464,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_5380]) ).

cnf(i_0_6465,plain,
    ( hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk541_3(X3,X2,X1)),X4)) = hAPP(X2,esk541_3(X3,X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk540_3(X3,X2,X1)))),hAPP(X2,esk540_3(X3,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5381]) ).

fof(i_0_6466,plain,
    ! [X18178,X18179,X18180,X18181,X18182] :
      ( ~ class_Groups_Oab__semigroup__mult(X18182)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18182,X18182,c_Groups_Otimes__class_Otimes(X18182),X18181,X18180),X18179))
      | ~ hBOOL(hAPP(hAPP(c_member(X18182),X18178),X18180))
      | hBOOL(hAPP(hAPP(c_member(X18182),X18181),X18180))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18182,X18182,c_Groups_Otimes__class_Otimes(X18182),X18178,hAPP(hAPP(c_Set_Oinsert(X18182),X18181),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18182,tc_HOL_Obool)),X18180),hAPP(hAPP(c_Set_Oinsert(X18182),X18178),c_Orderings_Obot__class_Obot(tc_fun(X18182,tc_HOL_Obool)))))),X18179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5382])]) ).

fof(i_0_6467,plain,
    ! [X31068,X31069,X31070,X31071] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31071)),X31070),c_List_Olists(X31071,X31069)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31071)),X31070),c_List_Olists(X31071,X31068)))
      | hBOOL(hAPP(c_List_Olistsp(X31071,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31071,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X31071,tc_fun(X31071,tc_HOL_Obool),tc_HOL_Obool),c_member(X31071)),X31069)),hAPP(hAPP(c_COMBC(X31071,tc_fun(X31071,tc_HOL_Obool),tc_HOL_Obool),c_member(X31071)),X31068))),X31070)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__IntI])]) ).

fof(i_0_6468,plain,
    ! [X24746,X24747,X24748,X24749,X24750,X24751,X24752,X24753,X24754,X24755] :
      ( ~ c_Equiv__Relations_Oequiv(X24755,X24754,X24753)
      | ~ c_Equiv__Relations_Oequiv(X24752,X24751,X24750)
      | ~ c_Equiv__Relations_Ocongruent2(X24755,X24752,tc_fun(X24749,tc_HOL_Obool),X24753,X24750,X24748)
      | ~ hBOOL(hAPP(hAPP(c_member(X24755),X24747),X24754))
      | ~ hBOOL(hAPP(hAPP(c_member(X24752),X24746),X24751))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24755,tc_fun(X24749,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24755,X24755,X24753),hAPP(hAPP(c_Set_Oinsert(X24755),X24747),c_Orderings_Obot__class_Obot(tc_fun(X24755,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(X24752,tc_fun(X24749,tc_HOL_Obool)),tc_fun(X24749,tc_HOL_Obool),X24755),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24752,tc_fun(X24749,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24752,X24752,X24750),hAPP(hAPP(c_Set_Oinsert(X24752),X24746),c_Orderings_Obot__class_Obot(tc_fun(X24752,tc_HOL_Obool)))))),X24748)) = hAPP(hAPP(X24748,X24747),X24746) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class2])]) ).

fof(i_0_6469,plain,
    ! [X29197,X29198,X29199] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29199)),c_List_Osublist(X29199,X29198,X29197)) = 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(X29199)),X29198)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),X29197)))),
    inference(variable_rename,[status(thm)],[fact_length__sublist]) ).

cnf(i_0_6470,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_5383]) ).

fof(i_0_6471,plain,
    ! [X31511,X31512,X31513] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31513)),hAPP(c_List_Ofilter(X31513,X31512),X31511)) = 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(X31513)),X31511)))),hAPP(hAPP(c_COMBB(X31513,tc_HOL_Obool,tc_Nat_Onat),X31512),hAPP(c_List_Onth(X31513),X31511))))),
    inference(variable_rename,[status(thm)],[fact_length__filter__conv__card]) ).

fof(i_0_6472,plain,
    ! [X19373,X19374,X19375,X19376,X19377] :
      ( ~ class_Groups_Ocomm__monoid__mult(X19377)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19376),X19375))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19377,X19376,c_Groups_Otimes__class_Otimes(X19377)),hAPP(hAPP(c_COMBS(X19376,X19377,X19377),hAPP(hAPP(c_COMBB(X19377,tc_fun(X19377,X19377),X19376),c_Groups_Otimes__class_Otimes(X19377)),X19374)),X19373)),c_Groups_Oone__class_Oone(X19377)),X19375) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19377),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19377,X19376,c_Groups_Otimes__class_Otimes(X19377)),X19374),c_Groups_Oone__class_Oone(X19377)),X19375)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19377,X19376,c_Groups_Otimes__class_Otimes(X19377)),X19373),c_Groups_Oone__class_Oone(X19377)),X19375)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__distrib])]) ).

fof(i_0_6473,plain,
    ! [X33443,X33444,X33445,X33446,X33447,X33448] :
      ( ~ c_Fun_Oinj__on(X33448,X33447,X33446,X33445)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33447,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33448,X33447,X33446),X33445)),X33444))
      | ~ c_Fun_Oinj__on(X33447,X33448,X33443,X33444)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33448,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33447,X33448,X33443),X33444)),X33445))
      | c_Fun_Obij__betw(X33448,X33447,esk532_6(X33443,X33444,X33445,X33446,X33447,X33448),X33445,X33444) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantor__Bernstein])])]) ).

fof(i_0_6474,plain,
    ! [X30202,X30203,X30204,X30205,X30206,X30207] :
      ( ( X30206 = X30204
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),X30206),X30204)),c_List_Olistrel1(X30207,X30202)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),hAPP(hAPP(c_List_Oappend(X30207),X30206),hAPP(hAPP(c_List_Olist_OCons(X30207),X30205),c_List_Olist_ONil(X30207)))),hAPP(hAPP(c_List_Oappend(X30207),X30204),hAPP(hAPP(c_List_Olist_OCons(X30207),X30203),c_List_Olist_ONil(X30207))))),c_List_Olistrel1(X30207,X30202))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30207,X30207)),hAPP(hAPP(c_Product__Type_OPair(X30207,X30207),X30205),X30203)),X30202))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),X30206),X30204)),c_List_Olistrel1(X30207,X30202)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),hAPP(hAPP(c_List_Oappend(X30207),X30206),hAPP(hAPP(c_List_Olist_OCons(X30207),X30205),c_List_Olist_ONil(X30207)))),hAPP(hAPP(c_List_Oappend(X30207),X30204),hAPP(hAPP(c_List_Olist_OCons(X30207),X30203),c_List_Olist_ONil(X30207))))),c_List_Olistrel1(X30207,X30202))) )
      & ( X30206 = X30204
        | X30205 = X30203
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),hAPP(hAPP(c_List_Oappend(X30207),X30206),hAPP(hAPP(c_List_Olist_OCons(X30207),X30205),c_List_Olist_ONil(X30207)))),hAPP(hAPP(c_List_Oappend(X30207),X30204),hAPP(hAPP(c_List_Olist_OCons(X30207),X30203),c_List_Olist_ONil(X30207))))),c_List_Olistrel1(X30207,X30202))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30207,X30207)),hAPP(hAPP(c_Product__Type_OPair(X30207,X30207),X30205),X30203)),X30202))
        | X30205 = X30203
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),hAPP(hAPP(c_List_Oappend(X30207),X30206),hAPP(hAPP(c_List_Olist_OCons(X30207),X30205),c_List_Olist_ONil(X30207)))),hAPP(hAPP(c_List_Oappend(X30207),X30204),hAPP(hAPP(c_List_Olist_OCons(X30207),X30203),c_List_Olist_ONil(X30207))))),c_List_Olistrel1(X30207,X30202))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),X30206),X30204)),c_List_Olistrel1(X30207,X30202)))
        | X30205 != X30203
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),hAPP(hAPP(c_List_Oappend(X30207),X30206),hAPP(hAPP(c_List_Olist_OCons(X30207),X30205),c_List_Olist_ONil(X30207)))),hAPP(hAPP(c_List_Oappend(X30207),X30204),hAPP(hAPP(c_List_Olist_OCons(X30207),X30203),c_List_Olist_ONil(X30207))))),c_List_Olistrel1(X30207,X30202))) )
      & ( X30206 != X30204
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30207,X30207)),hAPP(hAPP(c_Product__Type_OPair(X30207,X30207),X30205),X30203)),X30202))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30207),tc_List_Olist(X30207))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30207),tc_List_Olist(X30207)),hAPP(hAPP(c_List_Oappend(X30207),X30206),hAPP(hAPP(c_List_Olist_OCons(X30207),X30205),c_List_Olist_ONil(X30207)))),hAPP(hAPP(c_List_Oappend(X30207),X30204),hAPP(hAPP(c_List_Olist_OCons(X30207),X30203),c_List_Olist_ONil(X30207))))),c_List_Olistrel1(X30207,X30202))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__listrel1__snoc__iff])])]) ).

fof(i_0_6475,plain,
    ! [X31096,X31097,X31098,X31099,X31100,X31101,X31102] :
      ( ( ~ c_List_Olist__all2(X31102,X31101,X31100,X31099,hAPP(hAPP(c_List_Omap(X31098,X31101),X31097),X31096))
        | c_List_Olist__all2(X31102,X31098,hAPP(hAPP(c_COMBC(X31102,tc_fun(X31098,X31101),tc_fun(X31098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31101,tc_HOL_Obool),tc_fun(tc_fun(X31098,X31101),tc_fun(X31098,tc_HOL_Obool)),X31102),c_COMBB(X31101,tc_HOL_Obool,X31098)),X31100)),X31097),X31099,X31096) )
      & ( ~ c_List_Olist__all2(X31102,X31098,hAPP(hAPP(c_COMBC(X31102,tc_fun(X31098,X31101),tc_fun(X31098,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X31101,tc_HOL_Obool),tc_fun(tc_fun(X31098,X31101),tc_fun(X31098,tc_HOL_Obool)),X31102),c_COMBB(X31101,tc_HOL_Obool,X31098)),X31100)),X31097),X31099,X31096)
        | c_List_Olist__all2(X31102,X31101,X31100,X31099,hAPP(hAPP(c_List_Omap(X31098,X31101),X31097),X31096)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map2])]) ).

fof(i_0_6476,plain,
    ! [X26294,X26295,X26296,X26297] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26297,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk228_4(X26294,X26295,X26296,X26297))),X26296) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26297,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),esk228_4(X26294,X26295,X26296,X26297)),X26295))),X26294)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26297,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26296) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26297,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26294) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite2__eq])])]) ).

fof(i_0_6477,plain,
    ! [X26970,X26971,X26972,X26973,X26975] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26973),esk245_4(X26970,X26971,X26972,X26973)),X26972))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26973,tc_HOL_Obool),tc_fun(X26973,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26973,tc_HOL_Obool),tc_fun(X26973,tc_HOL_Obool)),X26972),X26971)),c_Wellfounded_Omax__ext(X26973,X26970)))
        | X26971 = c_Orderings_Obot__class_Obot(tc_fun(X26973,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26973),X26971))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26973),X26972)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26973),X26975),X26971))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26973,X26973)),hAPP(hAPP(c_Product__Type_OPair(X26973,X26973),esk245_4(X26970,X26971,X26972,X26973)),X26975)),X26970))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X26973,tc_HOL_Obool),tc_fun(X26973,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X26973,tc_HOL_Obool),tc_fun(X26973,tc_HOL_Obool)),X26972),X26971)),c_Wellfounded_Omax__ext(X26973,X26970)))
        | X26971 = c_Orderings_Obot__class_Obot(tc_fun(X26973,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26973),X26971))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26973),X26972)) ) ),
    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_6478,plain,
    ! [X28022,X28023,X28024,X28025,X28026,X28027,X28028,X28030,X28031,X28032,X28033,X28034,X28035,X28036,X28037] :
      ( ( hBOOL(hAPP(hAPP(X28025,X28023),esk287_4(X28022,X28023,X28024,X28025)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28028,X28027,X28026,X28025,X28024),X28023),X28022)) )
      & ( hBOOL(hAPP(hAPP(X28024,esk287_4(X28022,X28023,X28024,X28025)),X28022))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28028,X28027,X28026,X28025,X28024),X28023),X28022)) )
      & ( ~ hBOOL(hAPP(hAPP(X28033,X28031),X28034))
        | ~ hBOOL(hAPP(hAPP(X28032,X28034),X28030))
        | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28037,X28036,X28035,X28033,X28032),X28031),X28030)) ) ),
    inference(distribute,[status(thm)],[inference(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_6479,plain,
    ! [X28464,X28465,X28466] :
      ( ~ c_Wellfounded_Owf(X28466,X28465)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28466,X28466)),hAPP(hAPP(c_Product__Type_OPair(X28466,X28466),hAPP(X28464,hAPP(c_Nat_OSuc,esk330_3(X28464,X28465,X28466)))),hAPP(X28464,esk330_3(X28464,X28465,X28466)))),X28465)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__infinite__down__chainE])])]) ).

fof(i_0_6480,plain,
    ! [X28148,X28149,X28150,X28152,X28153,X28155] :
      ( ( ~ c_Wellfounded_Owf(X28149,X28148)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28149,X28149)),hAPP(hAPP(c_Product__Type_OPair(X28149,X28149),hAPP(X28150,hAPP(c_Nat_OSuc,esk291_3(X28148,X28149,X28150)))),hAPP(X28150,esk291_3(X28148,X28149,X28150)))),X28148)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28153,X28153)),hAPP(hAPP(c_Product__Type_OPair(X28153,X28153),hAPP(esk292_2(X28152,X28153),hAPP(c_Nat_OSuc,X28155))),hAPP(esk292_2(X28152,X28153),X28155))),X28152))
        | c_Wellfounded_Owf(X28153,X28152) ) ),
    inference(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_6481,plain,
    ! [X24798,X24799,X24800,X24801,X24802,X24803,X24804,X24805,X24806] :
      ( ~ c_Equiv__Relations_Oequiv(X24806,X24805,X24804)
      | ~ c_Equiv__Relations_Oequiv(X24803,X24802,X24801)
      | ~ c_Equiv__Relations_Ocongruent2(X24806,X24803,tc_fun(X24800,tc_HOL_Obool),X24804,X24801,X24799)
      | ~ hBOOL(hAPP(hAPP(c_member(X24803),X24798),X24802))
      | c_Equiv__Relations_Ocongruent(X24806,tc_fun(X24800,tc_HOL_Obool),X24804,hAPP(hAPP(c_COMBB(tc_fun(X24803,tc_fun(X24800,tc_HOL_Obool)),tc_fun(X24800,tc_HOL_Obool),X24806),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24803,tc_fun(X24800,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24803,X24803,X24801),hAPP(hAPP(c_Set_Oinsert(X24803),X24798),c_Orderings_Obot__class_Obot(tc_fun(X24803,tc_HOL_Obool)))))),X24799)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent__UN])]) ).

cnf(i_0_6482,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_5384]) ).

cnf(i_0_6483,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_5385]) ).

fof(i_0_6484,plain,
    ! [X17805,X17806,X17807,X17808,X17809,X17810,X17811] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17811,X17810,X17809,X17808,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17811,tc_HOL_Obool)),X17807),hAPP(hAPP(c_Set_Oinsert(X17811),X17806),c_Orderings_Obot__class_Obot(tc_fun(X17811,tc_HOL_Obool))))),X17805))
      | ~ hBOOL(hAPP(hAPP(c_member(X17811),X17806),X17807))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X17811,X17810,X17809,X17808,X17807),hAPP(hAPP(X17809,X17806),X17805))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff1__fold__graph])]) ).

fof(i_0_6485,plain,
    ! [X24768,X24769,X24770,X24771,X24772] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24771),esk189_5(X24768,X24769,X24770,X24771,X24772)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24771,tc_HOL_Obool)),X24770),X24769)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24772),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24771,X24772),X24768),X24769)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24771,X24772),X24768),X24770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24771,tc_HOL_Obool)),X24769),X24770))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24771),X24770))
        | ~ class_Groups_Ocomm__monoid__add(X24772)
        | ~ class_Groups_Oordered__ab__semigroup__add(X24772) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24772),c_Groups_Ozero__class_Ozero(X24772)),hAPP(X24768,esk189_5(X24768,X24769,X24770,X24771,X24772))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24772),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24771,X24772),X24768),X24769)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24771,X24772),X24768),X24770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24771,tc_HOL_Obool)),X24769),X24770))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24771),X24770))
        | ~ class_Groups_Ocomm__monoid__add(X24772)
        | ~ class_Groups_Oordered__ab__semigroup__add(X24772) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono3])])])]) ).

fof(i_0_6486,plain,
    ! [X24676,X24677,X24678,X24679,X24680] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24679),esk186_5(X24676,X24677,X24678,X24679,X24680)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24679,tc_HOL_Obool)),X24678),X24677)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24680),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24679,X24680),X24676),X24677)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24679,X24680),X24676),X24678)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24679,tc_HOL_Obool)),X24677),X24678))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24679),X24678))
        | ~ class_Groups_Oordered__comm__monoid__add(X24680) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24680),c_Groups_Ozero__class_Ozero(X24680)),hAPP(X24676,esk186_5(X24676,X24677,X24678,X24679,X24680))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24680),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24679,X24680),X24676),X24677)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24679,X24680),X24676),X24678)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24679,tc_HOL_Obool)),X24677),X24678))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24679),X24678))
        | ~ class_Groups_Oordered__comm__monoid__add(X24680) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__mono2])])])]) ).

fof(i_0_6487,plain,
    ! [X26379,X26380,X26381,X26382] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26382,tc_fun(X26381,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26382,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X26381,tc_HOL_Obool),tc_fun(X26381,tc_HOL_Obool),X26382),hAPP(c_COMBC(X26381,tc_fun(X26381,tc_HOL_Obool),tc_HOL_Obool),c_member(X26381))),X26380)),X26379))
        | hBOOL(hAPP(hAPP(c_member(X26381),X26379),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26382,tc_fun(X26381,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26382,tc_HOL_Obool))),X26380))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26381),X26379),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26382,tc_fun(X26381,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26382,tc_HOL_Obool))),X26380)))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26382,tc_fun(X26381,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26382,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X26381,tc_HOL_Obool),tc_fun(X26381,tc_HOL_Obool),X26382),hAPP(c_COMBC(X26381,tc_fun(X26381,tc_HOL_Obool),tc_HOL_Obool),c_member(X26381))),X26380)),X26379)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__INT__eq])]) ).

fof(i_0_6488,plain,
    ! [X26194,X26195,X26196,X26197] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26197,tc_fun(X26196,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26197,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X26196,tc_HOL_Obool),tc_fun(X26196,tc_HOL_Obool),X26197),hAPP(c_COMBC(X26196,tc_fun(X26196,tc_HOL_Obool),tc_HOL_Obool),c_member(X26196))),X26195)),X26194))
        | hBOOL(hAPP(hAPP(c_member(X26196),X26194),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26197,tc_fun(X26196,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26197,tc_HOL_Obool))),X26195))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26196),X26194),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26197,tc_fun(X26196,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26197,tc_HOL_Obool))),X26195)))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26197,tc_fun(X26196,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26197,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(X26196,tc_HOL_Obool),tc_fun(X26196,tc_HOL_Obool),X26197),hAPP(c_COMBC(X26196,tc_fun(X26196,tc_HOL_Obool),tc_HOL_Obool),c_member(X26196))),X26195)),X26194)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__UN__eq])]) ).

fof(i_0_6489,plain,
    ! [X18703,X18704,X18705,X18706,X18707,X18708] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18708),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18707),X18706)),X18705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18704),X18706)),X18703)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18708),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18708),X18707),X18704)),X18706)),X18705)),X18703))
        | ~ class_Rings_Oordered__ring(X18708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18708),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18708),X18707),X18704)),X18706)),X18705)),X18703))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18708),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18707),X18706)),X18705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18708),X18704),X18706)),X18703)))
        | ~ class_Rings_Oordered__ring(X18708) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff1])])]) ).

fof(i_0_6490,plain,
    ! [X18691,X18692,X18693,X18694,X18695,X18696] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18696),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18696),X18695),X18694)),X18693)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18696),X18692),X18694)),X18691)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18696),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18696),X18695),X18692)),X18694)),X18693)),X18691))
        | ~ class_Rings_Oordered__ring(X18696) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18696),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18696),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18696),X18695),X18692)),X18694)),X18693)),X18691))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18696),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18696),X18695),X18694)),X18693)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18696),X18692),X18694)),X18691)))
        | ~ class_Rings_Oordered__ring(X18696) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff1])])]) ).

cnf(i_0_6491,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_5386]) ).

fof(i_0_6492,plain,
    ! [X17798,X17799,X17800,X17801,X17802,X17803,X17804] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17804),X17803),X17802))
      | ~ c_Nitpick_Ofold__graph_H(X17804,X17801,X17800,X17799,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17804,tc_HOL_Obool)),X17802),hAPP(hAPP(c_Set_Oinsert(X17804),X17803),c_Orderings_Obot__class_Obot(tc_fun(X17804,tc_HOL_Obool)))),X17798)
      | c_Nitpick_Ofold__graph_H(X17804,X17801,X17800,X17799,X17802,hAPP(hAPP(X17800,X17803),X17798)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph_H_Ointros_I2_J])]) ).

fof(i_0_6493,plain,
    ! [X33504,X33505,X33506,X33507,X33508] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33508),esk543_5(X33504,X33505,X33506,X33507,X33508)),X33507))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33506,tc_HOL_Obool)),X33505),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33508,tc_fun(X33506,tc_HOL_Obool)),X33507),X33504))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33506,tc_HOL_Obool)),X33505),hAPP(X33504,esk543_5(X33504,X33505,X33506,X33507,X33508))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33506,tc_HOL_Obool)),X33505),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33508,tc_fun(X33506,tc_HOL_Obool)),X33507),X33504))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__greatest])])])]) ).

fof(i_0_6494,plain,
    ! [X26407,X26408,X26409,X26410,X26411,X26412,X26413,X26414,X26415,X26416,X26417] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26411,tc_HOL_Obool)),X26410),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26409,tc_fun(X26411,tc_HOL_Obool)),X26408),X26407)))
        | ~ hBOOL(hAPP(hAPP(c_member(X26409),X26412),X26408))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26411,tc_HOL_Obool)),X26410),hAPP(X26407,X26412))) )
      & ( hBOOL(hAPP(hAPP(c_member(X26415),esk232_5(X26413,X26414,X26415,X26416,X26417)),X26414))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26417,tc_HOL_Obool)),X26416),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26415,tc_fun(X26417,tc_HOL_Obool)),X26414),X26413))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26417,tc_HOL_Obool)),X26416),hAPP(X26413,esk232_5(X26413,X26414,X26415,X26416,X26417))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26417,tc_HOL_Obool)),X26416),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26415,tc_fun(X26417,tc_HOL_Obool)),X26414),X26413))) ) ),
    inference(distribute,[status(thm)],[inference(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_6495,plain,
    ! [X32690,X32691,X32692,X32693,X32694] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32694),esk485_5(X32690,X32691,X32692,X32693,X32694)),X32693))
        | c_Relation_Orefl__on(X32692,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32694,tc_fun(X32692,tc_HOL_Obool)),X32693),X32691),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32694,tc_fun(tc_prod(X32692,X32692),tc_HOL_Obool)),X32693),X32690)) )
      & ( ~ c_Relation_Orefl__on(X32692,hAPP(X32691,esk485_5(X32690,X32691,X32692,X32693,X32694)),hAPP(X32690,esk485_5(X32690,X32691,X32692,X32693,X32694)))
        | c_Relation_Orefl__on(X32692,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32694,tc_fun(X32692,tc_HOL_Obool)),X32693),X32691),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X32694,tc_fun(tc_prod(X32692,X32692),tc_HOL_Obool)),X32693),X32690)) ) ),
    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_6496,plain,
    ! [X33456,X33457,X33458,X33459,X33460] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33460),esk535_5(X33456,X33457,X33458,X33459,X33460)),X33459))
        | c_Relation_Orefl__on(X33458,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33460,tc_fun(X33458,tc_HOL_Obool)),X33459),X33457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33460,tc_fun(tc_prod(X33458,X33458),tc_HOL_Obool)),X33459),X33456)) )
      & ( ~ c_Relation_Orefl__on(X33458,hAPP(X33457,esk535_5(X33456,X33457,X33458,X33459,X33460)),hAPP(X33456,esk535_5(X33456,X33457,X33458,X33459,X33460)))
        | c_Relation_Orefl__on(X33458,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33460,tc_fun(X33458,tc_HOL_Obool)),X33459),X33457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X33460,tc_fun(tc_prod(X33458,X33458),tc_HOL_Obool)),X33459),X33456)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__UNION])])])]) ).

fof(i_0_6497,plain,
    ! [X22027,X22028,X22029,X22030] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22030,X22029),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22028),X22027)))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22030),X22029),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X22027),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22028)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22028)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,X22027),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),X22029),X22027))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zminus1__lemma])]) ).

cnf(i_0_6498,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_5387]) ).

fof(i_0_6499,plain,
    ! [X26395,X26396,X26397,X26398,X26399,X26400,X26401,X26402,X26403,X26404,X26405] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26399),X26398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26397,tc_fun(X26399,tc_HOL_Obool)),X26396),X26395)))
        | ~ hBOOL(hAPP(hAPP(c_member(X26397),X26400),X26396))
        | hBOOL(hAPP(hAPP(c_member(X26399),X26398),hAPP(X26395,X26400))) )
      & ( hBOOL(hAPP(hAPP(c_member(X26403),esk231_5(X26401,X26402,X26403,X26404,X26405)),X26402))
        | hBOOL(hAPP(hAPP(c_member(X26405),X26404),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26403,tc_fun(X26405,tc_HOL_Obool)),X26402),X26401))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26405),X26404),hAPP(X26401,esk231_5(X26401,X26402,X26403,X26404,X26405))))
        | hBOOL(hAPP(hAPP(c_member(X26405),X26404),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26403,tc_fun(X26405,tc_HOL_Obool)),X26402),X26401))) ) ),
    inference(distribute,[status(thm)],[inference(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_6500,plain,
    ! [X27304,X27305,X27306,X27307,X27308,X27309] : hAPP(c_Set_Ovimage(X27309,tc_prod(X27308,X27307),X27306),hAPP(hAPP(c_Product__Type_OSigma(X27308,X27307),X27305),hAPP(c_COMBK(tc_fun(X27307,tc_HOL_Obool),X27308),X27304))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27309,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X27309,X27308,hAPP(c_Fun_Ocomp(tc_prod(X27308,X27307),X27308,X27309,c_Product__Type_Ofst(X27308,X27307)),X27306)),X27305)),hAPP(c_Set_Ovimage(X27309,X27307,hAPP(c_Fun_Ocomp(tc_prod(X27308,X27307),X27307,X27309,c_Product__Type_Osnd(X27308,X27307)),X27306)),X27304)),
    inference(variable_rename,[status(thm)],[fact_vimage__Times]) ).

fof(i_0_6501,plain,
    ! [X32673,X32674] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X32674)),X32673) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X32674,tc_Lazy__Sequence_Olazy__sequence(X32674)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X32674,tc_Lazy__Sequence_Olazy__sequence(X32674),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X32674),tc_Nat_Onat),X32674),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X32674),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(X32674)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X32674)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X32674),X32673)),
    inference(variable_rename,[status(thm)],[fact_size__code]) ).

fof(i_0_6502,plain,
    ! [X22437,X22438,X22439,X22440,X22441,X22442,X22443,X22444] :
      ( ( X22442 = X22440
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22444,X22444)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22444),X22442),X22440)),X22438))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22444,X22443),tc_prod(X22444,X22443))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22444,X22443),tc_prod(X22444,X22443)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22443),X22442),X22441)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22443),X22440),X22439))),c_Wellfounded_Olex__prod(X22444,X22443,X22438,X22437))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X22443,X22443)),hAPP(hAPP(c_Product__Type_OPair(X22443,X22443),X22441),X22439)),X22437))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22444,X22444)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22444),X22442),X22440)),X22438))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22444,X22443),tc_prod(X22444,X22443))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22444,X22443),tc_prod(X22444,X22443)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22443),X22442),X22441)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22443),X22440),X22439))),c_Wellfounded_Olex__prod(X22444,X22443,X22438,X22437))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22444,X22444)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22444),X22442),X22440)),X22438))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22444,X22443),tc_prod(X22444,X22443))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22444,X22443),tc_prod(X22444,X22443)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22443),X22442),X22441)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22443),X22440),X22439))),c_Wellfounded_Olex__prod(X22444,X22443,X22438,X22437))) )
      & ( X22442 != X22440
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22443,X22443)),hAPP(hAPP(c_Product__Type_OPair(X22443,X22443),X22441),X22439)),X22437))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22444,X22443),tc_prod(X22444,X22443))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22444,X22443),tc_prod(X22444,X22443)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22443),X22442),X22441)),hAPP(hAPP(c_Product__Type_OPair(X22444,X22443),X22440),X22439))),c_Wellfounded_Olex__prod(X22444,X22443,X22438,X22437))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__lex__prod])])]) ).

fof(i_0_6503,plain,
    ! [X26623,X26624,X26625,X26626,X26627,X26628,X26629,X26630,X26631,X26632,X26633] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26627,tc_fun(X26626,tc_HOL_Obool)),X26625),X26624),X26623))
        | ~ hBOOL(hAPP(hAPP(c_member(X26627),X26628),X26625))
        | hBOOL(hAPP(hAPP(X26624,X26628),X26623)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26633),esk236_5(X26629,X26630,X26631,X26632,X26633)),X26631))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26633,tc_fun(X26632,tc_HOL_Obool)),X26631),X26630),X26629)) )
      & ( ~ hBOOL(hAPP(hAPP(X26630,esk236_5(X26629,X26630,X26631,X26632,X26633)),X26629))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26633,tc_fun(X26632,tc_HOL_Obool)),X26631),X26630),X26629)) ) ),
    inference(distribute,[status(thm)],[inference(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_6504,plain,
    ! [X27667,X27668] : 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),X27668)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),X27667))))),
    inference(variable_rename,[status(thm)],[fact_finite__M__bounded__by__nat]) ).

fof(i_0_6505,plain,
    ! [X25832,X25833,X25834] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X25834))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25833),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X25832),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),X25832),X25833))),c_Groups_Oone__class_Oone(tc_Int_Oint))),X25834)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_incr__lemma])]) ).

fof(i_0_6506,plain,
    ! [X26494,X26495,X26496,X26497,X26498,X26499] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26498),X26497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26496,X26498),X26495),X26494)))
        | ~ hBOOL(hAPP(hAPP(c_member(X26496),X26499),X26495))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26498),X26497),hAPP(X26494,X26499)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26498) )
      & ( hBOOL(hAPP(hAPP(c_member(X26496),esk233_5(X26494,X26495,X26496,X26497,X26498)),X26495))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26498),X26497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26496,X26498),X26495),X26494)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26498) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26498),X26497),hAPP(X26494,esk233_5(X26494,X26495,X26496,X26497,X26498))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26498),X26497),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26496,X26498),X26495),X26494)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26498) ) ),
    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_6507,plain,
    ! [X32169,X32170,X32171,X32172,X32173] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32172),esk455_5(X32169,X32170,X32171,X32172,X32173)),hAPP(c_List_Oset(X32172),X32171)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32172,X32173,X32170),X32169),X32171) = hAPP(hAPP(c_List_Olist_OCons(X32172),X32169),X32171)
        | ~ class_Orderings_Olinorder(X32173) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32173),hAPP(X32170,X32169)),hAPP(X32170,esk455_5(X32169,X32170,X32171,X32172,X32173))))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X32172,X32173,X32170),X32169),X32171) = hAPP(hAPP(c_List_Olist_OCons(X32172),X32169),X32171)
        | ~ class_Orderings_Olinorder(X32173) ) ),
    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_6508,plain,
    ! [X24856,X24857,X24858,X24859,X24860] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24859),esk198_5(X24856,X24857,X24858,X24859,X24860)),X24858))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24859,X24860),X24857),X24858) != c_Groups_Ozero__class_Ozero(X24860)
        | ~ hBOOL(hAPP(hAPP(c_member(X24859),X24856),X24858))
        | hAPP(X24857,X24856) = c_Groups_Ozero__class_Ozero(X24860)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24859),X24858))
        | ~ class_Groups_Oordered__ab__group__add(X24860) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24860),c_Groups_Ozero__class_Ozero(X24860)),hAPP(X24857,esk198_5(X24856,X24857,X24858,X24859,X24860))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24859,X24860),X24857),X24858) != c_Groups_Ozero__class_Ozero(X24860)
        | ~ hBOOL(hAPP(hAPP(c_member(X24859),X24856),X24858))
        | hAPP(X24857,X24856) = c_Groups_Ozero__class_Ozero(X24860)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24859),X24858))
        | ~ class_Groups_Oordered__ab__group__add(X24860) ) ),
    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_6509,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_5388]) ).

fof(i_0_6510,plain,
    ! [X33179,X33180,X33181,X33182,X33183] : hAPP(c_Hilbert__Choice_Oinv__into(X33183,X33182,X33181,X33180),X33179) = c_Hilbert__Choice_OEps(X33183,hAPP(hAPP(c_COMBS(X33183,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X33183),c_fconj),hAPP(hAPP(c_COMBC(X33183,tc_fun(X33183,tc_HOL_Obool),tc_HOL_Obool),c_member(X33183)),X33181))),hAPP(hAPP(c_COMBC(X33183,X33182,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X33182,tc_fun(X33182,tc_HOL_Obool),X33183),c_fequal),X33180)),X33179))),
    inference(variable_rename,[status(thm)],[fact_inv__into__def]) ).

fof(i_0_6511,plain,
    ! [X19236,X19237,X19238,X19239,X19240] : hAPP(c_Fun_Othe__inv__into(X19240,X19239,X19238,X19237),X19236) = c_HOL_OThe(X19240,hAPP(hAPP(c_COMBS(X19240,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X19240),c_fconj),hAPP(hAPP(c_COMBC(X19240,tc_fun(X19240,tc_HOL_Obool),tc_HOL_Obool),c_member(X19240)),X19238))),hAPP(hAPP(c_COMBC(X19240,X19239,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X19239,tc_fun(X19239,tc_HOL_Obool),X19240),c_fequal),X19237)),X19236))),
    inference(variable_rename,[status(thm)],[fact_the__inv__into__def]) ).

cnf(i_0_6512,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_5389]) ).

fof(i_0_6513,plain,
    ! [X30208,X30209,X30210,X30211] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X30211,X30211)),hAPP(hAPP(c_Product__Type_OPair(X30211,X30211),esk403_4(X30208,X30209,X30210,X30211)),esk404_4(X30208,X30209,X30210,X30211))),X30208))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30211),tc_List_Olist(X30211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30211),tc_List_Olist(X30211)),X30210),X30209)),c_List_Olistrel1(X30211,X30208))) )
      & ( X30210 = hAPP(hAPP(c_List_Oappend(X30211),esk405_4(X30208,X30209,X30210,X30211)),hAPP(hAPP(c_List_Olist_OCons(X30211),esk403_4(X30208,X30209,X30210,X30211)),esk406_4(X30208,X30209,X30210,X30211)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30211),tc_List_Olist(X30211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30211),tc_List_Olist(X30211)),X30210),X30209)),c_List_Olistrel1(X30211,X30208))) )
      & ( X30209 = hAPP(hAPP(c_List_Oappend(X30211),esk405_4(X30208,X30209,X30210,X30211)),hAPP(hAPP(c_List_Olist_OCons(X30211),esk404_4(X30208,X30209,X30210,X30211)),esk406_4(X30208,X30209,X30210,X30211)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30211),tc_List_Olist(X30211))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30211),tc_List_Olist(X30211)),X30210),X30209)),c_List_Olistrel1(X30211,X30208))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1E])])])]) ).

fof(i_0_6514,plain,
    ! [X19760,X19761,X19762,X19763,X19764,X19765,X19766] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19766,X19765,X19764)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19766,X19765,X19764,X19763,X19762),X19761))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19766,X19765,X19764,X19763,X19762),X19760))
      | X19760 = X19761 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__determ])]) ).

fof(i_0_6515,plain,
    ! [X30780,X30781,X30782,X30783,X30784] :
      ( ~ class_Groups_Ocomm__monoid__add(X30784)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30784),hAPP(hAPP(c_List_Omap(X30783,X30784),hAPP(hAPP(c_COMBS(X30783,X30784,X30784),hAPP(hAPP(c_COMBB(X30784,tc_fun(X30784,X30784),X30783),c_Groups_Oplus__class_Oplus(X30784)),X30782)),X30781)),X30780)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30784),hAPP(c_List_Omonoid__add__class_Olistsum(X30784),hAPP(hAPP(c_List_Omap(X30783,X30784),X30782),X30780))),hAPP(c_List_Omonoid__add__class_Olistsum(X30784),hAPP(hAPP(c_List_Omap(X30783,X30784),X30781),X30780))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__addf])]) ).

fof(i_0_6516,plain,
    ! [X30775,X30776,X30777,X30778,X30779] :
      ( ~ class_Groups_Oab__group__add(X30779)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30779),hAPP(hAPP(c_List_Omap(X30778,X30779),hAPP(hAPP(c_COMBS(X30778,X30779,X30779),hAPP(hAPP(c_COMBB(X30779,tc_fun(X30779,X30779),X30778),c_Groups_Ominus__class_Ominus(X30779)),X30777)),X30776)),X30775)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X30779),hAPP(c_List_Omonoid__add__class_Olistsum(X30779),hAPP(hAPP(c_List_Omap(X30778,X30779),X30777),X30775))),hAPP(c_List_Omonoid__add__class_Olistsum(X30779),hAPP(hAPP(c_List_Omap(X30778,X30779),X30776),X30775))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__subtractf])]) ).

fof(i_0_6517,plain,
    ! [X23974,X23975,X23976,X23977] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X23977,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23976,tc_fun(tc_fun(X23977,tc_HOL_Obool),tc_HOL_Obool)),X23975),hAPP(hAPP(c_COMBB(tc_fun(X23977,tc_HOL_Obool),tc_fun(tc_fun(X23977,tc_HOL_Obool),tc_HOL_Obool),X23976),c_Set_OPow(X23977)),X23974))),hAPP(c_Set_OPow(X23977),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23976,tc_fun(X23977,tc_HOL_Obool)),X23975),X23974)))),
    inference(variable_rename,[status(thm)],[fact_UN__Pow__subset]) ).

fof(i_0_6518,plain,
    ! [X18893,X18894,X18895,X18896,X18897] :
      ( ( ~ 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),X18896),X18895)),X18894)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18897),X18895)),X18893)))
        | 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),X18896),X18897)),X18895)),X18894)),X18893))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18897),X18896)) )
      & ( ~ 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),X18896),X18897)),X18895)),X18894)),X18893))
        | 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),X18896),X18895)),X18894)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18897),X18895)),X18893)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18897),X18896)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff1])])]) ).

fof(i_0_6519,plain,
    ! [X18931,X18932,X18933,X18934,X18935] :
      ( ( ~ 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),X18934),X18933)),X18932)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18935),X18933)),X18931)))
        | 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),X18934),X18935)),X18933)),X18932)),X18931))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18935),X18934)) )
      & ( ~ 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),X18934),X18935)),X18933)),X18932)),X18931))
        | 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),X18934),X18933)),X18932)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18935),X18933)),X18931)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18935),X18934)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1])])]) ).

fof(i_0_6520,plain,
    ! [X30770,X30771,X30772,X30773,X30774] :
      ( ~ class_Rings_Osemiring__0(X30774)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30774),hAPP(hAPP(c_List_Omap(X30773,X30774),hAPP(hAPP(c_COMBC(X30773,X30774,X30774),hAPP(hAPP(c_COMBB(X30774,tc_fun(X30774,X30774),X30773),c_Groups_Otimes__class_Otimes(X30774)),X30772)),X30771)),X30770)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X30774),hAPP(c_List_Omonoid__add__class_Olistsum(X30774),hAPP(hAPP(c_List_Omap(X30773,X30774),X30772),X30770))),X30771) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__mult__const])]) ).

fof(i_0_6521,plain,
    ! [X27777] : c_Int_Oint__ge__less__than2(X27777) = 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),X27777)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_int__ge__less__than2__def]) ).

fof(i_0_6522,plain,
    ! [X25573,X25574,X25575,X25576,X25577] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25576),esk204_5(X25573,X25574,X25575,X25576,X25577)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25576,tc_HOL_Obool)),X25575),X25574)))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25577,X25576,c_Groups_Otimes__class_Otimes(X25577)),X25573),c_Groups_Oone__class_Oone(X25577)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25576,tc_HOL_Obool)),X25575),X25574)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25577),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25577,X25576,c_Groups_Otimes__class_Otimes(X25577)),X25573),c_Groups_Oone__class_Oone(X25577)),X25575)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25577,X25576,c_Groups_Otimes__class_Otimes(X25577)),X25573),c_Groups_Oone__class_Oone(X25577)),X25574))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25576),X25574))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25576),X25575))
        | ~ class_Groups_Ocomm__monoid__mult(X25577) )
      & ( hAPP(X25573,esk204_5(X25573,X25574,X25575,X25576,X25577)) != c_Groups_Oone__class_Oone(X25577)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25577,X25576,c_Groups_Otimes__class_Otimes(X25577)),X25573),c_Groups_Oone__class_Oone(X25577)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25576,tc_HOL_Obool)),X25575),X25574)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25577),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25577,X25576,c_Groups_Otimes__class_Otimes(X25577)),X25573),c_Groups_Oone__class_Oone(X25577)),X25575)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25577,X25576,c_Groups_Otimes__class_Otimes(X25577)),X25573),c_Groups_Oone__class_Oone(X25577)),X25574))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25576),X25574))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25576),X25575))
        | ~ class_Groups_Ocomm__monoid__mult(X25577) ) ),
    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_6523,plain,
    ! [X25164,X25165,X25166,X25167] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25167,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X25167,tc_fun(X25167,tc_HOL_Obool),tc_HOL_Obool),c_member(X25167)),X25166)),hAPP(hAPP(c_COMBC(X25167,tc_fun(X25167,tc_HOL_Obool),tc_HOL_Obool),c_member(X25167)),X25165)),X25164))
        | hBOOL(hAPP(hAPP(c_member(X25167),X25164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25167,tc_HOL_Obool)),X25166),X25165))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25167),X25164),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25167,tc_HOL_Obool)),X25166),X25165)))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25167,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X25167,tc_fun(X25167,tc_HOL_Obool),tc_HOL_Obool),c_member(X25167)),X25166)),hAPP(hAPP(c_COMBC(X25167,tc_fun(X25167,tc_HOL_Obool),tc_HOL_Obool),c_member(X25167)),X25165)),X25164)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Int__eq])]) ).

fof(i_0_6524,plain,
    ! [X23387,X23388,X23389,X23390] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23390,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X23390,tc_fun(X23390,tc_HOL_Obool),tc_HOL_Obool),c_member(X23390)),X23389)),hAPP(hAPP(c_COMBC(X23390,tc_fun(X23390,tc_HOL_Obool),tc_HOL_Obool),c_member(X23390)),X23388)),X23387))
        | hBOOL(hAPP(hAPP(c_member(X23390),X23387),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23390,tc_HOL_Obool)),X23389),X23388))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23390),X23387),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23390,tc_HOL_Obool)),X23389),X23388)))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23390,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X23390,tc_fun(X23390,tc_HOL_Obool),tc_HOL_Obool),c_member(X23390)),X23389)),hAPP(hAPP(c_COMBC(X23390,tc_fun(X23390,tc_HOL_Obool),tc_HOL_Obool),c_member(X23390)),X23388)),X23387)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Un__eq])]) ).

fof(i_0_6525,plain,
    ! [X27589,X27590,X27591] : hAPP(hAPP(c_Set_Oinsert(X27591),X27590),hAPP(c_Set_OCollect(X27591),X27589)) = hAPP(c_Set_OCollect(X27591),hAPP(hAPP(c_COMBS(X27591,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27591),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27591),c_fNot),hAPP(hAPP(c_COMBC(X27591,X27591,tc_HOL_Obool),c_fequal),X27590)))),X27589)),
    inference(variable_rename,[status(thm)],[fact_insert__Collect]) ).

cnf(i_0_6526,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_5390]) ).

fof(i_0_6527,plain,
    ! [X24845,X24846,X24847,X24848,X24849,X24850] :
      ( ~ c_Equiv__Relations_Oequiv(X24850,X24849,X24848)
      | ~ hBOOL(hAPP(hAPP(c_member(X24850),X24847),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24850,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24850,X24850,X24848),hAPP(hAPP(c_Set_Oinsert(X24850),X24846),c_Orderings_Obot__class_Obot(tc_fun(X24850,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X24850,X24850,X24848),hAPP(hAPP(c_Set_Oinsert(X24850),X24845),c_Orderings_Obot__class_Obot(tc_fun(X24850,tc_HOL_Obool)))))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X24850,X24850)),hAPP(hAPP(c_Product__Type_OPair(X24850,X24850),X24846),X24845)),X24848)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__nondisjoint])]) ).

fof(i_0_6528,plain,
    ! [X32104,X32105] : c_List_Omeasures(X32105,X32104) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),X32105),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(X32105,tc_List_Olist(tc_fun(X32105,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X32105,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(X32105,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),X32105),c_List_Omap(tc_fun(X32105,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(X32105,tc_Nat_Onat),X32105,tc_Nat_Onat),c_COMBI(tc_fun(X32105,tc_Nat_Onat))))),X32104)),
    inference(variable_rename,[status(thm)],[fact_measures__def]) ).

fof(i_0_6529,plain,
    ! [X22289,X22290,X22291,X22292,X22293,X22294,X22295] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22295,X22294),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22293),X22292)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22291,X22294),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22290),X22289)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22294))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22295),X22291),X22294),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),X22293),X22290)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22292),X22289)),X22294))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X22292),X22289),X22294)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__add1__eq])]) ).

fof(i_0_6530,plain,
    ! [X32804,X32805,X32806,X32807] : c_Random__Sequence_Omap(X32807,X32806,X32805,X32804) = c_Random__Sequence_Obind(X32807,X32806,X32804,hAPP(c_Fun_Ocomp(X32806,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(X32806)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),X32807,c_Random__Sequence_Osingle(X32806)),X32805)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Omap__def]) ).

fof(i_0_6531,plain,
    ! [X25567,X25568,X25569,X25570,X25571] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25570),esk203_5(X25567,X25568,X25569,X25570,X25571)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25570,tc_HOL_Obool)),X25569),X25568)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25570,X25571),X25567),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25570,tc_HOL_Obool)),X25569),X25568)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25571),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25570,X25571),X25567),X25569)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25570,X25571),X25567),X25568))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25570,X25571),X25567),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25570,tc_HOL_Obool)),X25569),X25568)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25570),X25568))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25570),X25569))
        | ~ class_Fields_Ofield(X25571) )
      & ( hAPP(X25567,esk203_5(X25567,X25568,X25569,X25570,X25571)) = c_Groups_Ozero__class_Ozero(X25571)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25570,X25571),X25567),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25570,tc_HOL_Obool)),X25569),X25568)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25571),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25571),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25570,X25571),X25567),X25569)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25570,X25571),X25567),X25568))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25570,X25571),X25567),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25570,tc_HOL_Obool)),X25569),X25568)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25570),X25568))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25570),X25569))
        | ~ class_Fields_Ofield(X25571) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un])])])]) ).

fof(i_0_6532,plain,
    ! [X22020,X22021,X22022,X22023,X22024,X22025,X22026] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22026,X22025),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22024),X22023)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22022,X22025),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22021),X22020)))
      | X22025 = 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),X22026),X22022),X22025),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),X22024),X22021)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22023),X22020)),X22025))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X22023),X22020),X22025)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd1__lemma])]) ).

fof(i_0_6533,plain,
    ! [X27168,X27169,X27170,X27171,X27172,X27173] :
      ( ~ class_Groups_Ocomm__monoid__add(X27173)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27172,X27173),hAPP(hAPP(c_COMBC(X27172,tc_fun(X27171,tc_HOL_Obool),X27173),hAPP(hAPP(c_COMBB(tc_fun(X27171,X27173),tc_fun(tc_fun(X27171,tc_HOL_Obool),X27173),X27172),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27171,X27173)),X27170)),X27169)),X27168) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(X27172,X27171),X27173),hAPP(c_Product__Type_Oprod_Oprod__case(X27172,X27171,X27173),X27170)),hAPP(hAPP(c_Product__Type_OSigma(X27172,X27171),X27168),hAPP(c_COMBK(tc_fun(X27171,tc_HOL_Obool),X27172),X27169))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__cartesian__product])]) ).

fof(i_0_6534,plain,
    ! [X27187,X27188,X27189,X27190,X27191,X27192] :
      ( ~ class_Groups_Ocomm__monoid__mult(X27192)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27191,X27192),hAPP(hAPP(c_COMBC(X27191,tc_fun(X27190,tc_HOL_Obool),X27192),hAPP(hAPP(c_COMBB(tc_fun(X27190,X27192),tc_fun(tc_fun(X27190,tc_HOL_Obool),X27192),X27191),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27190,X27192)),X27189)),X27188)),X27187) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(X27191,X27190),X27192),hAPP(c_Product__Type_Oprod_Oprod__case(X27191,X27190,X27192),X27189)),hAPP(hAPP(c_Product__Type_OSigma(X27191,X27190),X27187),hAPP(c_COMBK(tc_fun(X27190,tc_HOL_Obool),X27191),X27188))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__cartesian__product])]) ).

fof(i_0_6535,plain,
    ! [X29136,X29137,X29138,X29139] :
      ( ( X29137 = hAPP(hAPP(c_Product__Type_OPair(X29139,X29138),esk370_4(X29136,X29137,X29138,X29139)),esk369_4(X29136,X29137,X29138,X29139))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29139,X29138)),X29137),hAPP(c_Relation_Oconverse(X29138,X29139),X29136))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29138,X29139)),hAPP(hAPP(c_Product__Type_OPair(X29138,X29139),esk369_4(X29136,X29137,X29138,X29139)),esk370_4(X29136,X29137,X29138,X29139))),X29136))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29139,X29138)),X29137),hAPP(c_Relation_Oconverse(X29138,X29139),X29136))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5391])])])]) ).

fof(i_0_6536,plain,
    ! [X27374,X27375,X27376,X27377,X27378,X27379,X27380,X27381] :
      ( ~ c_Fun_Oinj__on(X27381,X27380,X27379,X27378)
      | ~ c_Fun_Oinj__on(X27377,X27376,X27375,X27374)
      | c_Fun_Oinj__on(tc_prod(X27381,X27377),tc_prod(X27380,X27376),c_Product__Type_Omap__pair(X27381,X27380,X27377,X27376,X27379,X27375),hAPP(hAPP(c_Product__Type_OSigma(X27381,X27377),X27378),hAPP(c_COMBK(tc_fun(X27377,tc_HOL_Obool),X27381),X27374))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__pair__inj__on])]) ).

fof(i_0_6537,plain,
    ! [X22258,X22259,X22260,X22261,X22262] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22262,X22261),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22260),X22259)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22261))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22258),X22262),X22261),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),X22258),X22260)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22258),X22259)),X22261))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22258),X22259),X22261)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult1__eq])]) ).

fof(i_0_6538,plain,
    ! [X22035,X22036,X22037,X22038,X22039] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22039,X22038),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22037),X22036)))
      | X22038 = 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),X22035),X22039),X22038),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),X22035),X22037)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22035),X22036)),X22038))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22035),X22036),X22038)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult1__lemma])]) ).

fof(i_0_6539,plain,
    ! [X32504,X32505,X32506,X32507] : c_Lazy__Sequence_Oproduct(X32507,X32506,X32505,X32504) = hAPP(c_Lazy__Sequence_Obind(X32507,tc_prod(X32507,X32506),X32505),hAPP(hAPP(c_COMBB(tc_fun(X32506,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X32507,X32506))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X32507,X32506)),X32507),c_Lazy__Sequence_Obind(X32506,tc_prod(X32507,X32506),X32504)),hAPP(hAPP(c_COMBB(tc_fun(X32506,tc_prod(X32507,X32506)),tc_fun(X32506,tc_Lazy__Sequence_Olazy__sequence(tc_prod(X32507,X32506))),X32507),hAPP(c_COMBB(tc_prod(X32507,X32506),tc_Lazy__Sequence_Olazy__sequence(tc_prod(X32507,X32506)),X32506),c_Lazy__Sequence_Osingle(tc_prod(X32507,X32506)))),c_Product__Type_OPair(X32507,X32506)))),
    inference(variable_rename,[status(thm)],[fact_]) ).

fof(i_0_6540,plain,
    ! [X24668,X24669,X24670,X24671] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24670),X24669))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24671),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X24671,X24671),hAPP(hAPP(c_COMBB(X24671,tc_fun(X24671,X24671),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X24671)),X24668)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24671,tc_Nat_Onat),X24668),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,X24670,X24669)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24671),hAPP(X24668,X24670)),hAPP(X24668,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24669),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ class_Groups_Oab__group__add(X24671) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24670),X24669))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24671),hAPP(hAPP(c_COMBS(tc_Nat_Onat,X24671,X24671),hAPP(hAPP(c_COMBB(X24671,tc_fun(X24671,X24671),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(X24671)),X24668)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24671,tc_Nat_Onat),X24668),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,X24670,X24669)) = c_Groups_Ozero__class_Ozero(X24671)
        | ~ class_Groups_Oab__group__add(X24671) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5392])])]) ).

fof(i_0_6541,plain,
    ! [X27325,X27326,X27327,X27328] :
      ( c_Fun_Oinj__on(X27328,tc_prod(X27327,X27328),esk257_4(X27325,X27326,X27327,X27328),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27327,tc_fun(X27328,tc_HOL_Obool)),X27326),X27325))
      & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27327,X27328),tc_HOL_Obool)),hAPP(c_Set_Oimage(X27328,tc_prod(X27327,X27328),esk257_4(X27325,X27326,X27327,X27328)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27327,tc_fun(X27328,tc_HOL_Obool)),X27326),X27325))),hAPP(hAPP(c_Product__Type_OSigma(X27327,X27328),X27326),X27325))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[fact_Ex__inj__on__UNION__Sigma])]) ).

fof(i_0_6542,plain,
    ! [X18834,X18835,X18836,X18837,X18838] :
      ( ~ class_Groups_Oab__semigroup__mult(X18838)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18838,X18838,c_Groups_Otimes__class_Otimes(X18838),X18837,X18836),X18835))
      | hBOOL(hAPP(hAPP(c_member(X18838),X18837),X18836))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18838,X18838,c_Groups_Otimes__class_Otimes(X18838),X18834,hAPP(hAPP(c_Set_Oinsert(X18838),X18837),X18836)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18838),X18834),X18835))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5393])]) ).

fof(i_0_6543,plain,
    ! [X31522,X31523,X31524,X31525] : hAPP(hAPP(c_List_Omap(tc_prod(X31525,tc_Nat_Onat),X31525),c_Product__Type_Ofst(X31525,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31525,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X31525,tc_Nat_Onat)),X31524),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(X31525,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(X31525,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(X31525,tc_Nat_Onat),X31523),X31522))) = hAPP(hAPP(c_List_Omap(tc_prod(X31525,tc_Nat_Onat),X31525),c_Product__Type_Ofst(X31525,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(X31525,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(X31525,tc_Nat_Onat)),X31524),c_Product__Type_Osnd(X31525,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(X31525,tc_Nat_Onat),X31523),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),X31522)))),
    inference(variable_rename,[status(thm)],[fact_sublist__shift__lemma__Suc]) ).

fof(i_0_6544,plain,
    ! [X27416,X27417,X27418,X27419,X27420,X27421] : hAPP(c_Fun_Ocomp(tc_prod(X27421,X27420),X27421,tc_prod(X27419,X27418),c_Product__Type_Ofst(X27421,X27420)),c_Product__Type_Omap__pair(X27419,X27421,X27418,X27420,X27417,X27416)) = hAPP(c_Fun_Ocomp(X27419,X27421,tc_prod(X27419,X27418),X27417),c_Product__Type_Ofst(X27419,X27418)),
    inference(variable_rename,[status(thm)],[fact_fst__comp__map__pair]) ).

fof(i_0_6545,plain,
    ! [X27422,X27423,X27424,X27425,X27426,X27427] : hAPP(c_Fun_Ocomp(tc_prod(X27427,X27426),X27426,tc_prod(X27425,X27424),c_Product__Type_Osnd(X27427,X27426)),c_Product__Type_Omap__pair(X27425,X27427,X27424,X27426,X27423,X27422)) = hAPP(c_Fun_Ocomp(X27424,X27426,tc_prod(X27425,X27424),X27422),c_Product__Type_Osnd(X27425,X27424)),
    inference(variable_rename,[status(thm)],[fact_snd__comp__map__pair]) ).

fof(i_0_6546,plain,
    ! [X26383,X26384,X26385,X26386,X26387,X26388] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26388,tc_fun(X26387,tc_HOL_Obool)),X26386),hAPP(hAPP(c_COMBC(X26388,tc_fun(X26385,tc_fun(X26387,tc_HOL_Obool)),tc_fun(X26387,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26385,tc_HOL_Obool),tc_fun(tc_fun(X26385,tc_fun(X26387,tc_HOL_Obool)),tc_fun(X26387,tc_HOL_Obool)),X26388),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26385,tc_fun(X26387,tc_HOL_Obool))),X26384)),X26383)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26385,tc_fun(X26387,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26388,tc_fun(X26385,tc_HOL_Obool)),X26386),X26384)),X26383),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I9_J]) ).

fof(i_0_6547,plain,
    ! [X23704,X23705,X23706,X23707,X23708,X23709] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23709,tc_fun(X23708,tc_HOL_Obool)),X23707),hAPP(hAPP(c_COMBC(X23709,tc_fun(X23706,tc_fun(X23708,tc_HOL_Obool)),tc_fun(X23708,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23706,tc_HOL_Obool),tc_fun(tc_fun(X23706,tc_fun(X23708,tc_HOL_Obool)),tc_fun(X23708,tc_HOL_Obool)),X23709),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23706,tc_fun(X23708,tc_HOL_Obool))),X23705)),X23704)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23706,tc_fun(X23708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23709,tc_fun(X23706,tc_HOL_Obool)),X23707),X23705)),X23704),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I9_J]) ).

fof(i_0_6548,plain,
    ! [X26389,X26390,X26391,X26392,X26393,X26394] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26394,tc_fun(X26393,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26392,tc_fun(X26394,tc_HOL_Obool)),X26391),X26390)),X26389) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26392,tc_fun(X26393,tc_HOL_Obool)),X26391),hAPP(hAPP(c_COMBC(X26392,tc_fun(X26394,tc_fun(X26393,tc_HOL_Obool)),tc_fun(X26393,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26394,tc_HOL_Obool),tc_fun(tc_fun(X26394,tc_fun(X26393,tc_HOL_Obool)),tc_fun(X26393,tc_HOL_Obool)),X26392),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26394,tc_fun(X26393,tc_HOL_Obool))),X26390)),X26389)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I9_J]) ).

fof(i_0_6549,plain,
    ! [X23698,X23699,X23700,X23701,X23702,X23703] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23703,tc_fun(X23702,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23701,tc_fun(X23703,tc_HOL_Obool)),X23700),X23699)),X23698) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23701,tc_fun(X23702,tc_HOL_Obool)),X23700),hAPP(hAPP(c_COMBC(X23701,tc_fun(X23703,tc_fun(X23702,tc_HOL_Obool)),tc_fun(X23702,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23703,tc_HOL_Obool),tc_fun(tc_fun(X23703,tc_fun(X23702,tc_HOL_Obool)),tc_fun(X23702,tc_HOL_Obool)),X23701),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23703,tc_fun(X23702,tc_HOL_Obool))),X23699)),X23698)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I9_J]) ).

fof(i_0_6550,plain,
    ! [X23692,X23693,X23694,X23695,X23696,X23697] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23697,tc_fun(X23696,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23695,tc_fun(X23697,tc_HOL_Obool)),X23694),X23693)),X23692) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23695,tc_fun(X23696,tc_HOL_Obool)),X23694),hAPP(hAPP(c_COMBC(X23695,tc_fun(X23697,tc_fun(X23696,tc_HOL_Obool)),tc_fun(X23696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23697,tc_HOL_Obool),tc_fun(tc_fun(X23697,tc_fun(X23696,tc_HOL_Obool)),tc_fun(X23696,tc_HOL_Obool)),X23695),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23697,tc_fun(X23696,tc_HOL_Obool))),X23693)),X23692)),
    inference(variable_rename,[status(thm)],[fact_UN__UN__flatten]) ).

fof(i_0_6551,plain,
    ! [X18134,X18135,X18136,X18137,X18138,X18139,X18140] :
      ( hBOOL(hAPP(hAPP(c_member(X18140),X18139),X18138))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18140,X18137,X18136,X18135,X18138),X18134))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18140,X18137,X18136,X18135,hAPP(hAPP(c_Set_Oinsert(X18140),X18139),X18138)),hAPP(hAPP(X18136,X18139),X18134))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5394])]) ).

fof(i_0_6552,plain,
    ! [X33543,X33544,X33545,X33546] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33546,X33546)),hAPP(hAPP(c_Product__Type_OPair(X33546,X33546),esk554_4(X33543,X33544,X33545,X33546)),esk555_4(X33543,X33544,X33545,X33546))),X33545))
        | c_Equiv__Relations_Ocongruent(X33546,X33543,X33545,X33544) )
      & ( hAPP(X33544,esk554_4(X33543,X33544,X33545,X33546)) != hAPP(X33544,esk555_4(X33543,X33544,X33545,X33546))
        | c_Equiv__Relations_Ocongruent(X33546,X33543,X33545,X33544) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentI])])])]) ).

fof(i_0_6553,plain,
    ! [X29182,X29183] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk373_2(X29182,X29183)),hAPP(X29183,esk373_2(X29182,X29183))))
      | 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)),X29183)),X29182)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__less__ub])])]) ).

fof(i_0_6554,plain,
    ! [X24782,X24783,X24784,X24785,X24786,X24787,X24788,X24789,X24790,X24791] :
      ( ~ c_Equiv__Relations_Ocongruent2(X24791,X24790,X24789,X24788,X24787,X24786)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24791,X24791)),hAPP(hAPP(c_Product__Type_OPair(X24791,X24791),X24785),X24784)),X24788))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24790,X24790)),hAPP(hAPP(c_Product__Type_OPair(X24790,X24790),X24783),X24782)),X24787))
      | hAPP(hAPP(X24786,X24785),X24783) = hAPP(hAPP(X24786,X24784),X24782) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2D])]) ).

fof(i_0_6555,plain,
    ! [X29117,X29118,X29119,X29120,X29121] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29121),esk364_5(X29117,X29118,X29119,X29120,X29121)),X29120))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29121,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29121,tc_HOL_Obool)),X29120),hAPP(c_Set_OCollect(X29121),X29118))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29121,tc_HOL_Obool)),X29119),hAPP(c_Set_OCollect(X29121),X29117))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29121,tc_HOL_Obool)),X29120),X29119)) )
      & ( hBOOL(hAPP(X29118,esk364_5(X29117,X29118,X29119,X29120,X29121)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29121,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29121,tc_HOL_Obool)),X29120),hAPP(c_Set_OCollect(X29121),X29118))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29121,tc_HOL_Obool)),X29119),hAPP(c_Set_OCollect(X29121),X29117))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29121,tc_HOL_Obool)),X29120),X29119)) )
      & ( ~ hBOOL(hAPP(X29117,esk364_5(X29117,X29118,X29119,X29120,X29121)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29121,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29121,tc_HOL_Obool)),X29120),hAPP(c_Set_OCollect(X29121),X29118))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X29121,tc_HOL_Obool)),X29119),hAPP(c_Set_OCollect(X29121),X29117))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29121,tc_HOL_Obool)),X29120),X29119)) ) ),
    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_6556,plain,
    ! [X26617,X26618,X26619] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26619,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26619,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk235_3(X26617,X26618,X26619))),X26618)),X26617))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26619,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26619,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26618)),X26617)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__finite__subset])])]) ).

fof(i_0_6557,plain,
    ! [X27650,X27651,X27652] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27652,tc_HOL_Obool)),X27651),X27650) = hAPP(c_Set_OCollect(X27652),hAPP(hAPP(c_COMBS(X27652,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27652),c_fconj),hAPP(hAPP(c_COMBC(X27652,tc_fun(X27652,tc_HOL_Obool),tc_HOL_Obool),c_member(X27652)),X27651))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27652),c_fNot),hAPP(hAPP(c_COMBC(X27652,tc_fun(X27652,tc_HOL_Obool),tc_HOL_Obool),c_member(X27652)),X27650)))),
    inference(variable_rename,[status(thm)],[fact_set__diff__eq]) ).

fof(i_0_6558,plain,
    ! [X27566,X27567,X27568] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27568),hAPP(c_Set_OCollect(X27568),X27567)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27568),hAPP(c_Set_OCollect(X27568),hAPP(hAPP(c_COMBS(X27568,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27568),c_fconj),X27567)),X27566)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27568),hAPP(c_Set_OCollect(X27568),X27566)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27568),hAPP(c_Set_OCollect(X27568),hAPP(hAPP(c_COMBS(X27568,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27568),c_fconj),X27567)),X27566)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI])])]) ).

fof(i_0_6559,plain,
    ! [X26271,X26272] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26272,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(X26272,tc_HOL_Obool)),tc_fun(X26272,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_fun(X26272,tc_HOL_Obool)),tc_fun(X26272,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26272,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),X26271)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X26272,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),X26271),
    inference(variable_rename,[status(thm)],[fact_UN__UN__finite__eq]) ).

cnf(i_0_6560,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk354_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_5395]) ).

cnf(i_0_6561,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk355_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_5396]) ).

fof(i_0_6562,plain,
    ! [X27391,X27392,X27393,X27394,X27395,X27396,X27397,X27398] : hAPP(c_Product__Type_Omap__pair(X27398,X27397,X27396,X27395,X27394,X27393),hAPP(hAPP(c_Product__Type_OPair(X27398,X27396),X27392),X27391)) = hAPP(hAPP(c_Product__Type_OPair(X27397,X27395),hAPP(X27394,X27392)),hAPP(X27393,X27391)),
    inference(variable_rename,[status(thm)],[fact_map__pair__simp]) ).

cnf(i_0_6563,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_5397]) ).

cnf(i_0_6564,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_5398]) ).

fof(i_0_6565,plain,
    ! [X31232,X31233,X31234,X31235,X31236] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31236,X31235)),esk418_5(X31232,X31233,X31234,X31235,X31236)),hAPP(c_List_Oset(tc_prod(X31236,X31235)),hAPP(hAPP(c_List_Ozip(X31236,X31235),X31234),X31233))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31236)),X31234) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31235)),X31233)
        | c_List_Olist__all2(X31236,X31235,X31232,X31234,X31233) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X31236,X31235,tc_HOL_Obool),X31232),esk418_5(X31232,X31233,X31234,X31235,X31236)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31236)),X31234) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31235)),X31233)
        | c_List_Olist__all2(X31236,X31235,X31232,X31234,X31233) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2I])])])]) ).

fof(i_0_6566,plain,
    ! [X31077,X31078,X31079,X31080,X31081,X31082,X31083,X31084,X31085,X31086,X31087] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31081)),X31078) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31080)),X31077)
        | ~ c_List_Olist__all2(X31081,X31080,X31079,X31078,X31077) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X31081,X31080)),X31082),hAPP(c_List_Oset(tc_prod(X31081,X31080)),hAPP(hAPP(c_List_Ozip(X31081,X31080),X31078),X31077))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X31081,X31080,tc_HOL_Obool),X31079),X31082))
        | ~ c_List_Olist__all2(X31081,X31080,X31079,X31078,X31077) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X31087,X31086)),esk416_5(X31083,X31084,X31085,X31086,X31087)),hAPP(c_List_Oset(tc_prod(X31087,X31086)),hAPP(hAPP(c_List_Ozip(X31087,X31086),X31084),X31083))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31087)),X31084) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31086)),X31083)
        | c_List_Olist__all2(X31087,X31086,X31085,X31084,X31083) )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X31087,X31086,tc_HOL_Obool),X31085),esk416_5(X31083,X31084,X31085,X31086,X31087)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31087)),X31084) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31086)),X31083)
        | c_List_Olist__all2(X31087,X31086,X31085,X31084,X31083) ) ),
    inference(distribute,[status(thm)],[inference(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_6567,plain,
    ! [X27399,X27400,X27401] : hAPP(c_Product__Type_Omap__pair(X27401,X27401,X27400,X27400,c_COMBI(X27401),c_COMBI(X27400)),X27399) = X27399,
    inference(variable_rename,[status(thm)],[fact_map__pair__ident]) ).

fof(i_0_6568,plain,
    ! [X25387,X25388,X25389,X25390,X25391,X25392,X25393,X25394] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X25394,X25393,X25392,X25391,X25390,X25389)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25393),X25388))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25393),X25387))
      | hAPP(hAPP(X25392,hAPP(X25389,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25393,tc_HOL_Obool)),X25388),X25387))),hAPP(X25389,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25393,tc_HOL_Obool)),X25388),X25387))) = hAPP(hAPP(X25392,hAPP(X25389,X25388)),hAPP(X25389,X25387)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__inter])]) ).

fof(i_0_6569,plain,
    ! [X25603,X25604,X25605,X25606,X25607] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25606),esk208_5(X25603,X25604,X25605,X25606,X25607)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25606,tc_HOL_Obool)),X25605),X25604)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25606,X25607),X25603),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25606,tc_HOL_Obool)),X25605),X25604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25607),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25606,X25607),X25603),X25605)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25606,X25607),X25603),X25604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25606),X25604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25606),X25605))
        | ~ class_Groups_Ocomm__monoid__add(X25607) )
      & ( hAPP(X25603,esk208_5(X25603,X25604,X25605,X25606,X25607)) != c_Groups_Ozero__class_Ozero(X25607)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25606,X25607),X25603),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25606,tc_HOL_Obool)),X25605),X25604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25607),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25606,X25607),X25603),X25605)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25606,X25607),X25603),X25604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25606),X25604))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25606),X25605))
        | ~ class_Groups_Ocomm__monoid__add(X25607) ) ),
    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_6570,plain,
    ! [X25597,X25598,X25599,X25600,X25601] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25600),esk207_5(X25597,X25598,X25599,X25600,X25601)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25600,tc_HOL_Obool)),X25599),X25598)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25600,X25601),X25597),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25600,tc_HOL_Obool)),X25599),X25598)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25601),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25600,X25601),X25597),X25599)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25600,X25601),X25597),X25598))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25600),X25598))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25600),X25599))
        | ~ class_Groups_Ocomm__monoid__add(X25601) )
      & ( hAPP(X25597,esk207_5(X25597,X25598,X25599,X25600,X25601)) != c_Groups_Ozero__class_Ozero(X25601)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25600,X25601),X25597),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25600,tc_HOL_Obool)),X25599),X25598)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25601),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25600,X25601),X25597),X25599)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25600,X25601),X25597),X25598))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25600),X25598))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25600),X25599))
        | ~ class_Groups_Ocomm__monoid__add(X25601) ) ),
    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_6571,plain,
    ! [X25591,X25592,X25593,X25594,X25595] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25594),esk206_5(X25591,X25592,X25593,X25594,X25595)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25594,tc_HOL_Obool)),X25593),X25592)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25594,X25595),X25591),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25594,tc_HOL_Obool)),X25593),X25592)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25595),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25594,X25595),X25591),X25593)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25594,X25595),X25591),X25592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25594),X25592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25594),X25593))
        | ~ class_Groups_Ocomm__monoid__mult(X25595) )
      & ( hAPP(X25591,esk206_5(X25591,X25592,X25593,X25594,X25595)) != c_Groups_Oone__class_Oone(X25595)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25594,X25595),X25591),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25594,tc_HOL_Obool)),X25593),X25592)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25595),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25594,X25595),X25591),X25593)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25594,X25595),X25591),X25592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25594),X25592))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25594),X25593))
        | ~ class_Groups_Ocomm__monoid__mult(X25595) ) ),
    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_6572,plain,
    ! [X25579,X25580,X25581,X25582,X25583] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25582),esk205_5(X25579,X25580,X25581,X25582,X25583)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25582,tc_HOL_Obool)),X25581),X25580)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25582,X25583),X25579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25582,tc_HOL_Obool)),X25581),X25580)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25583),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25582,X25583),X25579),X25581)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25582,X25583),X25579),X25580))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25582),X25580))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25582),X25581))
        | ~ class_Groups_Ocomm__monoid__mult(X25583) )
      & ( hAPP(X25579,esk205_5(X25579,X25580,X25581,X25582,X25583)) != c_Groups_Oone__class_Oone(X25583)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25582,X25583),X25579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25582,tc_HOL_Obool)),X25581),X25580)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25583),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25582,X25583),X25579),X25581)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25582,X25583),X25579),X25580))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25582),X25580))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25582),X25581))
        | ~ class_Groups_Ocomm__monoid__mult(X25583) ) ),
    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_6573,plain,
    ! [X27697,X27698,X27699,X27700] : hAPP(c_Relation_OImage(X27700,X27699,X27698),hAPP(hAPP(c_Set_Oinsert(X27700),X27697),c_Orderings_Obot__class_Obot(tc_fun(X27700,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(X27699),hAPP(hAPP(c_COMBC(X27699,tc_fun(tc_prod(X27700,X27699),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(X27700,X27699),tc_fun(tc_fun(tc_prod(X27700,X27699),tc_HOL_Obool),tc_HOL_Obool),X27699),c_member(tc_prod(X27700,X27699))),hAPP(c_Product__Type_OPair(X27700,X27699),X27697))),X27698)),
    inference(variable_rename,[status(thm)],[fact_Image__singleton]) ).

fof(i_0_6574,plain,
    ! [X32348,X32349,X32350,X32351] :
      ( ( ~ hBOOL(hAPP(X32350,X32349))
        | c_List_Olist__all(X32351,hAPP(hAPP(c_COMBS(X32351,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32351),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32351),c_fNot),X32350))),hAPP(c_fequal,X32349)),X32348)
        | ~ c_List_Olist__ex1(X32351,X32350,hAPP(hAPP(c_List_Olist_OCons(X32351),X32349),X32348)) )
      & ( hBOOL(hAPP(X32350,X32349))
        | c_List_Olist__ex1(X32351,X32350,X32348)
        | ~ c_List_Olist__ex1(X32351,X32350,hAPP(hAPP(c_List_Olist_OCons(X32351),X32349),X32348)) )
      & ( ~ hBOOL(hAPP(X32350,X32349))
        | hBOOL(hAPP(X32350,X32349))
        | c_List_Olist__ex1(X32351,X32350,hAPP(hAPP(c_List_Olist_OCons(X32351),X32349),X32348)) )
      & ( ~ c_List_Olist__ex1(X32351,X32350,X32348)
        | hBOOL(hAPP(X32350,X32349))
        | c_List_Olist__ex1(X32351,X32350,hAPP(hAPP(c_List_Olist_OCons(X32351),X32349),X32348)) )
      & ( ~ hBOOL(hAPP(X32350,X32349))
        | ~ c_List_Olist__all(X32351,hAPP(hAPP(c_COMBS(X32351,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32351),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32351),c_fNot),X32350))),hAPP(c_fequal,X32349)),X32348)
        | c_List_Olist__ex1(X32351,X32350,hAPP(hAPP(c_List_Olist_OCons(X32351),X32349),X32348)) )
      & ( ~ c_List_Olist__ex1(X32351,X32350,X32348)
        | ~ c_List_Olist__all(X32351,hAPP(hAPP(c_COMBS(X32351,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X32351),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X32351),c_fNot),X32350))),hAPP(c_fequal,X32349)),X32348)
        | c_List_Olist__ex1(X32351,X32350,hAPP(hAPP(c_List_Olist_OCons(X32351),X32349),X32348)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5399])])]) ).

cnf(i_0_6575,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_5400]) ).

fof(i_0_6576,plain,
    ! [X17437,X17438,X17439,X17440,X17441,X17442,X17443,X17444] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X17444,X17443,X17442,X17441,X17440,X17439)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17443),X17438))
      | ~ hBOOL(hAPP(hAPP(c_member(X17443),X17437),X17438))
      | hAPP(X17439,X17438) = hAPP(hAPP(X17442,hAPP(X17440,X17437)),hAPP(X17439,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17443,tc_HOL_Obool)),X17438),hAPP(hAPP(c_Set_Oinsert(X17443),X17437),c_Orderings_Obot__class_Obot(tc_fun(X17443,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oremove])]) ).

fof(i_0_6577,plain,
    ! [X17061,X17062,X17063,X17064,X17065,X17067,X17068,X17069,X17070,X17071,X17072] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17063,tc_HOL_Obool)),esk6_5(X17061,X17062,X17063,X17064,X17065)),X17061))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17065,tc_HOL_Obool)),X17064),hAPP(c_Set_Oimage(X17063,X17065,X17062),X17061))) )
      & ( X17064 = hAPP(c_Set_Oimage(X17063,X17065,X17062),esk6_5(X17061,X17062,X17063,X17064,X17065))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17065,tc_HOL_Obool)),X17064),hAPP(c_Set_Oimage(X17063,X17065,X17062),X17061))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17069,tc_HOL_Obool)),X17072),X17067))
        | X17070 != hAPP(c_Set_Oimage(X17069,X17071,X17068),X17072)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17071,tc_HOL_Obool)),X17070),hAPP(c_Set_Oimage(X17069,X17071,X17068),X17067))) ) ),
    inference(distribute,[status(thm)],[inference(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_6578,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_5401]) ).

fof(i_0_6579,plain,
    ! [X23754,X23755,X23756,X23757,X23758,X23760,X23761,X23762,X23763,X23764,X23765] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23756),esk133_5(X23754,X23755,X23756,X23757,X23758)),X23755))
        | ~ hBOOL(hAPP(hAPP(c_member(X23758),X23757),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23756,tc_fun(X23758,tc_HOL_Obool)),X23755),X23754))) )
      & ( hBOOL(hAPP(hAPP(c_member(X23758),X23757),hAPP(X23754,esk133_5(X23754,X23755,X23756,X23757,X23758))))
        | ~ hBOOL(hAPP(hAPP(c_member(X23758),X23757),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23756,tc_fun(X23758,tc_HOL_Obool)),X23755),X23754))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23762),X23765),X23761))
        | ~ hBOOL(hAPP(hAPP(c_member(X23764),X23763),hAPP(X23760,X23765)))
        | hBOOL(hAPP(hAPP(c_member(X23764),X23763),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23762,tc_fun(X23764,tc_HOL_Obool)),X23761),X23760))) ) ),
    inference(distribute,[status(thm)],[inference(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_6580,plain,
    ! [X17390,X17391,X17392,X17393,X17394,X17395,X17396,X17397] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X17397,X17396,X17395,X17394,X17393,X17392)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17396),X17391))
      | hAPP(X17392,hAPP(hAPP(c_Set_Oinsert(X17396),X17390),X17391)) = hAPP(hAPP(X17395,hAPP(X17393,X17390)),hAPP(X17392,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17396,tc_HOL_Obool)),X17391),hAPP(hAPP(c_Set_Oinsert(X17396),X17390),c_Orderings_Obot__class_Obot(tc_fun(X17396,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oinsert__remove])]) ).

fof(i_0_6581,plain,
    ! [X33193,X33194,X33195,X33196,X33197,X33198,X33199] :
      ( ~ c_Fun_Oinj__on(X33199,X33198,X33197,hAPP(c_Set_Oimage(X33196,X33199,X33195),X33194))
      | ~ c_Fun_Oinj__on(X33196,X33199,X33195,X33194)
      | ~ hBOOL(hAPP(hAPP(c_member(X33198),X33193),hAPP(c_Set_Oimage(X33199,X33198,X33197),hAPP(c_Set_Oimage(X33196,X33199,X33195),X33194))))
      | hAPP(c_Hilbert__Choice_Oinv__into(X33196,X33198,X33194,hAPP(c_Fun_Ocomp(X33199,X33198,X33196,X33197),X33195)),X33193) = hAPP(hAPP(c_Fun_Ocomp(X33199,X33196,X33198,c_Hilbert__Choice_Oinv__into(X33196,X33199,X33194,X33195)),c_Hilbert__Choice_Oinv__into(X33199,X33198,hAPP(c_Set_Oimage(X33196,X33199,X33195),X33194),X33197)),X33193) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__comp])]) ).

fof(i_0_6582,plain,
    ! [X19633,X19634,X19635,X19636,X19637,X19638,X19639] :
      ( ~ c_Fun_Oinj__on(X19639,X19638,X19637,hAPP(c_Set_Oimage(X19636,X19639,X19635),X19634))
      | ~ c_Fun_Oinj__on(X19636,X19639,X19635,X19634)
      | ~ hBOOL(hAPP(hAPP(c_member(X19638),X19633),hAPP(c_Set_Oimage(X19639,X19638,X19637),hAPP(c_Set_Oimage(X19636,X19639,X19635),X19634))))
      | hAPP(c_Fun_Othe__inv__into(X19636,X19638,X19634,hAPP(c_Fun_Ocomp(X19639,X19638,X19636,X19637),X19635)),X19633) = hAPP(hAPP(c_Fun_Ocomp(X19639,X19636,X19638,c_Fun_Othe__inv__into(X19636,X19639,X19634,X19635)),c_Fun_Othe__inv__into(X19639,X19638,hAPP(c_Set_Oimage(X19636,X19639,X19635),X19634),X19637)),X19633) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__comp])]) ).

cnf(i_0_6583,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_5402]) ).

fof(i_0_6584,plain,
    ! [X25707,X25708,X25709,X25710,X25711] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25710),esk217_5(X25707,X25708,X25709,X25710,X25711)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25710,tc_HOL_Obool)),X25709),X25708)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25710,X25711),X25707),X25709) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25710,X25711),X25707),X25708)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25710,tc_HOL_Obool)),X25708),X25709))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25710),X25709))
        | ~ class_Groups_Ocomm__monoid__add(X25711) )
      & ( hAPP(X25707,esk217_5(X25707,X25708,X25709,X25710,X25711)) != c_Groups_Ozero__class_Ozero(X25711)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25710,X25711),X25707),X25709) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25710,X25711),X25707),X25708)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25710,tc_HOL_Obool)),X25708),X25709))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25710),X25709))
        | ~ class_Groups_Ocomm__monoid__add(X25711) ) ),
    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_6585,plain,
    ! [X25701,X25702,X25703,X25704,X25705] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25704),esk216_5(X25701,X25702,X25703,X25704,X25705)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25704,tc_HOL_Obool)),X25703),X25702)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25704,X25705),X25701),X25702) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25704,X25705),X25701),X25703)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25704,tc_HOL_Obool)),X25702),X25703))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25704),X25703))
        | ~ class_Groups_Ocomm__monoid__add(X25705) )
      & ( hAPP(X25701,esk216_5(X25701,X25702,X25703,X25704,X25705)) != c_Groups_Ozero__class_Ozero(X25705)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25704,X25705),X25701),X25702) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25704,X25705),X25701),X25703)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25704,tc_HOL_Obool)),X25702),X25703))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25704),X25703))
        | ~ class_Groups_Ocomm__monoid__add(X25705) ) ),
    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_6586,plain,
    ! [X23927,X23928,X23929,X23930,X23931] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23930),esk139_5(X23927,X23928,X23929,X23930,X23931)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23930,tc_HOL_Obool)),X23929),X23928)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23930,X23931),X23927),X23928) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23930,X23931),X23927),X23929)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23930,tc_HOL_Obool)),X23928),X23929))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23930),X23929))
        | ~ class_Groups_Ocomm__monoid__mult(X23931) )
      & ( hAPP(X23927,esk139_5(X23927,X23928,X23929,X23930,X23931)) != c_Groups_Oone__class_Oone(X23931)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23930,X23931),X23927),X23928) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23930,X23931),X23927),X23929)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23930,tc_HOL_Obool)),X23928),X23929))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23930),X23929))
        | ~ class_Groups_Ocomm__monoid__mult(X23931) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__left])])])]) ).

fof(i_0_6587,plain,
    ! [X23635,X23636,X23637,X23638,X23639] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23638),esk126_5(X23635,X23636,X23637,X23638,X23639)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23638,tc_HOL_Obool)),X23637),X23636)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23638,X23639),X23635),X23637) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23638,X23639),X23635),X23636)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23638,tc_HOL_Obool)),X23636),X23637))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23638),X23637))
        | ~ class_Groups_Ocomm__monoid__mult(X23639) )
      & ( hAPP(X23635,esk126_5(X23635,X23636,X23637,X23638,X23639)) != c_Groups_Oone__class_Oone(X23639)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23638,X23639),X23635),X23637) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X23638,X23639),X23635),X23636)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23638,tc_HOL_Obool)),X23636),X23637))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23638),X23637))
        | ~ class_Groups_Ocomm__monoid__mult(X23639) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__mono__one__right])])])]) ).

cnf(i_0_6588,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_5385]) ).

cnf(i_0_6589,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_5384]) ).

fof(i_0_6590,plain,
    ! [X23710,X23711,X23712,X23713,X23714,X23716,X23717,X23718,X23719,X23720,X23721] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23714),esk128_5(X23710,X23711,X23712,X23713,X23714)),X23712))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23714,tc_fun(X23713,tc_HOL_Obool)),X23712),X23711),X23710)) )
      & ( hBOOL(hAPP(hAPP(X23711,esk128_5(X23710,X23711,X23712,X23713,X23714)),X23710))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23714,tc_fun(X23713,tc_HOL_Obool)),X23712),X23711),X23710)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23720),X23721),X23718))
        | ~ hBOOL(hAPP(hAPP(X23717,X23721),X23716))
        | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23720,tc_fun(X23719,tc_HOL_Obool)),X23718),X23717),X23716)) ) ),
    inference(distribute,[status(thm)],[inference(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_6591,plain,
    ! [X32207,X32208,X32209,X32210] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32209,X32210)),X32208),X32207))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32209),hAPP(hAPP(c_COMBS(X32209,X32210,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32210,tc_fun(X32210,tc_HOL_Obool),X32209),c_Orderings_Oord__class_Oless__eq(X32210)),X32208)),X32207)))
        | ~ class_Orderings_Oorder(X32210)
        | ~ class_Enum_Oenum(X32209) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32209),hAPP(hAPP(c_COMBS(X32209,X32210,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X32210,tc_fun(X32210,tc_HOL_Obool),X32209),c_Orderings_Oord__class_Oless__eq(X32210)),X32208)),X32207)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X32209,X32210)),X32208),X32207))
        | ~ class_Orderings_Oorder(X32210)
        | ~ class_Enum_Oenum(X32209) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__fun_I1_J])])]) ).

fof(i_0_6592,plain,
    ! [X28930,X28931,X28932] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28932,X28932)),X28931),c_Transitive__Closure_Ortrancl(X28932,X28930)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28932,X28932)),X28931),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X28932,X28932),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(X28932,X28932),tc_HOL_Obool),tc_fun(tc_prod(X28932,X28932),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X28932,X28932),tc_HOL_Obool)),X28930)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__imp__UN__rel__pow])]) ).

fof(i_0_6593,plain,
    ! [X26946,X26947,X26948,X26949,X26950] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26950,tc_fun(X26949,tc_HOL_Obool)),X26948),hAPP(hAPP(c_COMBS(X26950,tc_fun(X26949,tc_HOL_Obool),tc_fun(X26949,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26949,tc_HOL_Obool),tc_fun(tc_fun(X26949,tc_HOL_Obool),tc_fun(X26949,tc_HOL_Obool)),X26950),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26949,tc_HOL_Obool))),X26947)),X26946)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26949,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26949,tc_HOL_Obool),hAPP(c_Set_Oimage(X26950,tc_fun(X26949,tc_HOL_Obool),X26947),X26948))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26949,tc_HOL_Obool),hAPP(c_Set_Oimage(X26950,tc_fun(X26949,tc_HOL_Obool),X26946),X26948))),
    inference(variable_rename,[status(thm)],[fact_Int__Inter__image]) ).

fof(i_0_6594,plain,
    ! [X27077,X27078,X27079,X27080,X27081] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27081,tc_fun(X27080,tc_HOL_Obool)),X27079),hAPP(hAPP(c_COMBS(X27081,tc_fun(X27080,tc_HOL_Obool),tc_fun(X27080,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27080,tc_HOL_Obool),tc_fun(tc_fun(X27080,tc_HOL_Obool),tc_fun(X27080,tc_HOL_Obool)),X27081),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27080,tc_HOL_Obool))),X27078)),X27077)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27080,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27080,tc_HOL_Obool),hAPP(c_Set_Oimage(X27081,tc_fun(X27080,tc_HOL_Obool),X27078),X27079))),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27080,tc_HOL_Obool),hAPP(c_Set_Oimage(X27081,tc_fun(X27080,tc_HOL_Obool),X27077),X27079))),
    inference(variable_rename,[status(thm)],[fact_Un__Union__image]) ).

fof(i_0_6595,plain,
    ! [X30192,X30193,X30194,X30195,X30196,X30197,X30198] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30198,X30198)),hAPP(hAPP(c_Product__Type_OPair(X30198,X30198),X30197),X30196)),X30195))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30198),tc_List_Olist(X30198))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30198),tc_List_Olist(X30198)),hAPP(hAPP(c_List_Oappend(X30198),X30194),hAPP(hAPP(c_List_Olist_OCons(X30198),X30197),X30193))),hAPP(hAPP(c_List_Oappend(X30198),X30194),hAPP(hAPP(c_List_Olist_OCons(X30198),X30196),X30192)))),c_List_Olexord(X30198,X30195))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__left__rightI])]) ).

fof(i_0_6596,plain,
    ! [X23101,X23102,X23103,X23104] :
      ( ( ~ 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),X23104),X23103)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23102),X23101))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23104),X23101) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23102),X23103) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23104),X23101) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X23102),X23103)
        | 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),X23104),X23103)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23102),X23101))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_intrel__iff])]) ).

fof(i_0_6597,plain,
    ! [X22975,X22976,X22977,X22978,X22979,X22980,X22981] :
      ( ~ hBOOL(hAPP(X22981,X22980))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22979,X22979)),hAPP(hAPP(c_Product__Type_OPair(X22979,X22979),X22978),X22977)),hAPP(X22976,X22980)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X22975,X22979),tc_prod(X22975,X22979))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X22975,X22979),tc_prod(X22975,X22979)),hAPP(hAPP(c_Product__Type_OPair(X22975,X22979),X22980),X22978)),hAPP(hAPP(c_Product__Type_OPair(X22975,X22979),X22980),X22977))),c_Recdef_Osame__fst(X22975,X22979,X22981,X22976))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__fstI])]) ).

fof(i_0_6598,plain,
    ! [X23890,X23891,X23892,X23893,X23894,X23896] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23892),esk138_5(X23890,X23891,X23892,X23893,X23894)),X23891))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23894),X23893),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23892,X23894),X23891),X23890)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X23894)
        | ~ class_Orderings_Olinorder(X23894) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23894),X23893),hAPP(X23890,esk138_5(X23890,X23891,X23892,X23893,X23894))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23894),X23893),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23892,X23894),X23891),X23890)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X23894)
        | ~ class_Orderings_Olinorder(X23894) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23892),X23896),X23891))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23894),X23893),hAPP(X23890,X23896)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23894),X23893),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23892,X23894),X23891),X23890)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X23894)
        | ~ class_Orderings_Olinorder(X23894) ) ),
    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_6599,plain,
    ! [X22129,X22130,X22131,X22132,X22133,X22134,X22135,X22136] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22136,X22135,X22134),X22133),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22132,X22131,tc_prod(X22136,X22135)),X22130),X22129)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22132,X22131,X22134),hAPP(hAPP(c_COMBB(tc_fun(X22131,tc_prod(X22136,X22135)),tc_fun(X22131,X22134),X22132),hAPP(c_COMBB(tc_prod(X22136,X22135),X22134,X22131),hAPP(c_Product__Type_Oprod_Oprod__case(X22136,X22135,X22134),X22133))),X22130)),X22129),
    inference(variable_rename,[status(thm)],[fact_split__twice]) ).

cnf(i_0_6600,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_5403]) ).

cnf(i_0_6601,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_5404]) ).

cnf(i_0_6602,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_5405]) ).

fof(i_0_6603,plain,
    ! [X17290,X17291,X17292,X17293] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17293),esk9_4(X17290,X17291,X17292,X17293)))
        | hBOOL(hAPP(X17290,X17292))
        | ~ hBOOL(hAPP(X17290,c_Orderings_Obot__class_Obot(tc_fun(X17293,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17293,tc_HOL_Obool)),X17292),X17291))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17293),X17292)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17293),esk8_4(X17290,X17291,X17292,X17293)),X17291))
        | hBOOL(hAPP(X17290,X17292))
        | ~ hBOOL(hAPP(X17290,c_Orderings_Obot__class_Obot(tc_fun(X17293,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17293,tc_HOL_Obool)),X17292),X17291))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17293),X17292)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17293),esk8_4(X17290,X17291,X17292,X17293)),esk9_4(X17290,X17291,X17292,X17293)))
        | hBOOL(hAPP(X17290,X17292))
        | ~ hBOOL(hAPP(X17290,c_Orderings_Obot__class_Obot(tc_fun(X17293,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17293,tc_HOL_Obool)),X17292),X17291))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17293),X17292)) )
      & ( hBOOL(hAPP(X17290,esk9_4(X17290,X17291,X17292,X17293)))
        | hBOOL(hAPP(X17290,X17292))
        | ~ hBOOL(hAPP(X17290,c_Orderings_Obot__class_Obot(tc_fun(X17293,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17293,tc_HOL_Obool)),X17292),X17291))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17293),X17292)) )
      & ( ~ hBOOL(hAPP(X17290,hAPP(hAPP(c_Set_Oinsert(X17293),esk8_4(X17290,X17291,X17292,X17293)),esk9_4(X17290,X17291,X17292,X17293))))
        | hBOOL(hAPP(X17290,X17292))
        | ~ hBOOL(hAPP(X17290,c_Orderings_Obot__class_Obot(tc_fun(X17293,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17293,tc_HOL_Obool)),X17292),X17291))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17293),X17292)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5406])])])]) ).

fof(i_0_6604,plain,
    ! [X29650,X29651,X29652,X29653] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29653),esk391_4(X29650,X29651,X29652,X29653)),hAPP(c_List_Oset(X29653),X29652)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X29653,X29651,X29652)),c_List_Olist_Olist__size(X29653,X29650,X29652))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X29651,esk391_4(X29650,X29651,X29652,X29653))),hAPP(X29650,esk391_4(X29650,X29651,X29652,X29653))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(X29653,X29651,X29652)),c_List_Olist_Olist__size(X29653,X29650,X29652))) ) ),
    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_6605,plain,
    ! [X27738,X27739] : c_Fun_Oinj__on(tc_fun(X27739,X27738),tc_fun(tc_prod(X27739,X27738),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27739,X27738),tc_HOL_Obool),tc_fun(tc_prod(X27739,X27738),tc_HOL_Obool),tc_fun(X27739,X27738)),c_Set_OCollect(tc_prod(X27739,X27738))),hAPP(hAPP(c_COMBB(tc_fun(X27739,tc_fun(X27738,tc_HOL_Obool)),tc_fun(tc_prod(X27739,X27738),tc_HOL_Obool),tc_fun(X27739,X27738)),c_Product__Type_Oprod_Oprod__case(X27739,X27738,tc_HOL_Obool)),hAPP(c_COMBB(X27738,tc_fun(X27738,tc_HOL_Obool),X27739),hAPP(c_COMBC(X27738,X27738,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X27739,X27738),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__graph]) ).

cnf(i_0_6606,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_6607,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_5407]) ).

cnf(i_0_6608,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_6609,plain,
    ! [X32021,X32022,X32023,X32024,X32025] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32024),esk436_5(X32021,X32022,X32023,X32024,X32025)),hAPP(c_List_Oset(X32024),X32023)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32025),hAPP(hAPP(c_List_Omap(X32024,X32025),X32021),hAPP(c_List_Ofilter(X32024,X32022),X32023))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32025),hAPP(hAPP(c_List_Omap(X32024,X32025),X32021),X32023))
        | ~ class_Groups_Omonoid__add(X32025) )
      & ( ~ hBOOL(hAPP(X32022,esk436_5(X32021,X32022,X32023,X32024,X32025)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32025),hAPP(hAPP(c_List_Omap(X32024,X32025),X32021),hAPP(c_List_Ofilter(X32024,X32022),X32023))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32025),hAPP(hAPP(c_List_Omap(X32024,X32025),X32021),X32023))
        | ~ class_Groups_Omonoid__add(X32025) )
      & ( hAPP(X32021,esk436_5(X32021,X32022,X32023,X32024,X32025)) != c_Groups_Ozero__class_Ozero(X32025)
        | hAPP(c_List_Omonoid__add__class_Olistsum(X32025),hAPP(hAPP(c_List_Omap(X32024,X32025),X32021),hAPP(c_List_Ofilter(X32024,X32022),X32023))) = hAPP(c_List_Omonoid__add__class_Olistsum(X32025),hAPP(hAPP(c_List_Omap(X32024,X32025),X32021),X32023))
        | ~ class_Groups_Omonoid__add(X32025) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5408])])])]) ).

cnf(i_0_6610,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_5409]) ).

cnf(i_0_6611,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_5410]) ).

fof(i_0_6612,plain,
    ! [X32955,X32956,X32957,X32958,X32959,X32961,X32962,X32963,X32964,X32966] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X32958),X32956))
        | ~ c_Wellfounded_Omax__extp(X32958,X32957,X32956,X32955) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X32958),X32955))
        | ~ c_Wellfounded_Omax__extp(X32958,X32957,X32956,X32955) )
      & ( X32955 != c_Orderings_Obot__class_Obot(tc_fun(X32958,tc_HOL_Obool))
        | ~ c_Wellfounded_Omax__extp(X32958,X32957,X32956,X32955) )
      & ( hBOOL(hAPP(hAPP(c_member(X32958),esk509_5(X32955,X32956,X32957,X32958,X32959)),X32955))
        | ~ hBOOL(hAPP(hAPP(c_member(X32958),X32959),X32956))
        | ~ c_Wellfounded_Omax__extp(X32958,X32957,X32956,X32955) )
      & ( hBOOL(hAPP(hAPP(X32957,X32959),esk509_5(X32955,X32956,X32957,X32958,X32959)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32958),X32959),X32956))
        | ~ c_Wellfounded_Omax__extp(X32958,X32957,X32956,X32955) )
      & ( hBOOL(hAPP(hAPP(c_member(X32964),esk510_4(X32961,X32962,X32963,X32964)),X32962))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32964),X32962))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32964),X32961))
        | X32961 = c_Orderings_Obot__class_Obot(tc_fun(X32964,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X32964,X32963,X32962,X32961) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32964),X32966),X32961))
        | ~ hBOOL(hAPP(hAPP(X32963,esk510_4(X32961,X32962,X32963,X32964)),X32966))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32964),X32962))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32964),X32961))
        | X32961 = c_Orderings_Obot__class_Obot(tc_fun(X32964,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X32964,X32963,X32962,X32961) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp_Osimps])])])])])]) ).

fof(i_0_6613,plain,
    ! [X26747,X26748,X26749,X26750,X26751,X26753,X26754,X26755,X26756,X26758] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26750),X26748))
        | ~ c_Wellfounded_Omax__extp(X26750,X26749,X26748,X26747) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26750),X26747))
        | ~ c_Wellfounded_Omax__extp(X26750,X26749,X26748,X26747) )
      & ( X26747 != c_Orderings_Obot__class_Obot(tc_fun(X26750,tc_HOL_Obool))
        | ~ c_Wellfounded_Omax__extp(X26750,X26749,X26748,X26747) )
      & ( hBOOL(hAPP(hAPP(c_member(X26750),esk241_5(X26747,X26748,X26749,X26750,X26751)),X26747))
        | ~ hBOOL(hAPP(hAPP(c_member(X26750),X26751),X26748))
        | ~ c_Wellfounded_Omax__extp(X26750,X26749,X26748,X26747) )
      & ( hBOOL(hAPP(hAPP(X26749,X26751),esk241_5(X26747,X26748,X26749,X26750,X26751)))
        | ~ hBOOL(hAPP(hAPP(c_member(X26750),X26751),X26748))
        | ~ c_Wellfounded_Omax__extp(X26750,X26749,X26748,X26747) )
      & ( hBOOL(hAPP(hAPP(c_member(X26756),esk242_4(X26753,X26754,X26755,X26756)),X26754))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26756),X26754))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26756),X26753))
        | X26753 = c_Orderings_Obot__class_Obot(tc_fun(X26756,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X26756,X26755,X26754,X26753) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26756),X26758),X26753))
        | ~ hBOOL(hAPP(hAPP(X26755,esk242_4(X26753,X26754,X26755,X26756)),X26758))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26756),X26754))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26756),X26753))
        | X26753 = c_Orderings_Obot__class_Obot(tc_fun(X26756,tc_HOL_Obool))
        | c_Wellfounded_Omax__extp(X26756,X26755,X26754,X26753) ) ),
    inference(distribute,[status(thm)],[inference(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_6614,plain,
    ! [X27637,X27638,X27639] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27639,tc_HOL_Obool)),X27638),X27637) = hAPP(c_Set_OCollect(X27639),hAPP(hAPP(c_COMBS(X27639,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27639),c_fconj),hAPP(hAPP(c_COMBC(X27639,tc_fun(X27639,tc_HOL_Obool),tc_HOL_Obool),c_member(X27639)),X27638))),hAPP(hAPP(c_COMBC(X27639,tc_fun(X27639,tc_HOL_Obool),tc_HOL_Obool),c_member(X27639)),X27637))),
    inference(variable_rename,[status(thm)],[fact_Int__def]) ).

fof(i_0_6615,plain,
    ! [X27630,X27631,X27632] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27632,tc_HOL_Obool)),X27631),X27630) = hAPP(c_Set_OCollect(X27632),hAPP(hAPP(c_COMBS(X27632,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27632),c_fdisj),hAPP(hAPP(c_COMBC(X27632,tc_fun(X27632,tc_HOL_Obool),tc_HOL_Obool),c_member(X27632)),X27631))),hAPP(hAPP(c_COMBC(X27632,tc_fun(X27632,tc_HOL_Obool),tc_HOL_Obool),c_member(X27632)),X27630))),
    inference(variable_rename,[status(thm)],[fact_Un__def]) ).

fof(i_0_6616,plain,
    ! [X25450,X25451,X25452,X25453,X25454,X25455,X25456,X25457] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X25457,X25456,X25455,X25454,X25453,X25452)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25456),X25451))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25456),X25450))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25456,tc_HOL_Obool)),X25451),X25450) != c_Orderings_Obot__class_Obot(tc_fun(X25456,tc_HOL_Obool))
      | hAPP(X25452,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25456,tc_HOL_Obool)),X25451),X25450)) = hAPP(hAPP(X25455,hAPP(X25452,X25451)),hAPP(X25452,X25450)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Ounion__disjoint])]) ).

cnf(i_0_6617,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_5411]) ).

fof(i_0_6618,plain,
    ! [X18697,X18698,X18699,X18700,X18701,X18702] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18702),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18702),X18701),X18700)),X18699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18702),X18698),X18700)),X18697)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18702),X18699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18702),X18698),X18701)),X18700)),X18697)))
        | ~ class_Rings_Oordered__ring(X18702) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18702),X18699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18702),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18702),X18698),X18701)),X18700)),X18697)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18702),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18702),X18701),X18700)),X18699)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18702),X18698),X18700)),X18697)))
        | ~ class_Rings_Oordered__ring(X18702) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__iff2])])]) ).

fof(i_0_6619,plain,
    ! [X18685,X18686,X18687,X18688,X18689,X18690] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18690),X18689),X18688)),X18687)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18690),X18686),X18688)),X18685)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18690),X18687),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18690),X18686),X18689)),X18688)),X18685)))
        | ~ class_Rings_Oordered__ring(X18690) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18690),X18687),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18690),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18690),X18686),X18689)),X18688)),X18685)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18690),X18689),X18688)),X18687)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18690),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18690),X18686),X18688)),X18685)))
        | ~ class_Rings_Oordered__ring(X18690) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__iff2])])]) ).

fof(i_0_6620,plain,
    ! [X26578,X26579,X26580,X26581,X26582,X26583] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26583,tc_HOL_Obool)),hAPP(c_Relation_OImage(X26582,X26583,X26581),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26580,tc_fun(X26582,tc_HOL_Obool)),X26579),X26578))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26580,tc_fun(X26583,tc_HOL_Obool)),X26579),hAPP(hAPP(c_COMBB(tc_fun(X26582,tc_HOL_Obool),tc_fun(X26583,tc_HOL_Obool),X26580),c_Relation_OImage(X26582,X26583,X26581)),X26578)))),
    inference(variable_rename,[status(thm)],[fact_Image__INT__subset]) ).

fof(i_0_6621,plain,
    ! [X17316,X17317,X17318,X17319,X17320,X17321,X17322,X17323] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X17323,X17322,X17321,X17320,X17319,X17318)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17322),X17317))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17322,tc_HOL_Obool)),X17316),X17317))
      | hAPP(hAPP(X17321,hAPP(X17318,X17316)),hAPP(X17318,X17317)) = hAPP(X17318,X17317) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Osubset__idem])]) ).

fof(i_0_6622,plain,
    ! [X17228,X17229,X17230,X17231,X17232] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17230,X17231)),X17229),X17228))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17231),hAPP(X17229,X17232)),hAPP(X17228,X17232)))
        | ~ class_Orderings_Oord(X17231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17231),hAPP(X17229,esk7_4(X17228,X17229,X17230,X17231))),hAPP(X17228,esk7_4(X17228,X17229,X17230,X17231))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17230,X17231)),X17229),X17228))
        | ~ class_Orderings_Oord(X17231) ) ),
    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_6623,plain,
    ! [X19359,X19360,X19361,X19362,X19363,X19364,X19365] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X19365,X19364,X19363,X19362,X19361,X19360)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19364),X19359))
      | hAPP(X19360,X19359) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19365,X19364,X19363),X19361),X19362),X19359) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oeq__fold__g])]) ).

fof(i_0_6624,plain,
    ! [X30739,X30740,X30741,X30742,X30743,X30744,X30745,X30746,X30747,X30748,X30749] :
      ( ( hAPP(hAPP(c_List_Omap(X30743,X30742),X30741),X30740) != hAPP(hAPP(c_List_Omap(X30743,X30742),X30739),X30740)
        | ~ hBOOL(hAPP(hAPP(c_member(X30743),X30744),hAPP(c_List_Oset(X30743),X30740)))
        | hAPP(X30741,X30744) = hAPP(X30739,X30744) )
      & ( hBOOL(hAPP(hAPP(c_member(X30749),esk413_5(X30745,X30746,X30747,X30748,X30749)),hAPP(c_List_Oset(X30749),X30746)))
        | hAPP(hAPP(c_List_Omap(X30749,X30748),X30747),X30746) = hAPP(hAPP(c_List_Omap(X30749,X30748),X30745),X30746) )
      & ( hAPP(X30747,esk413_5(X30745,X30746,X30747,X30748,X30749)) != hAPP(X30745,esk413_5(X30745,X30746,X30747,X30748,X30749))
        | hAPP(hAPP(c_List_Omap(X30749,X30748),X30747),X30746) = hAPP(hAPP(c_List_Omap(X30749,X30748),X30745),X30746) ) ),
    inference(distribute,[status(thm)],[inference(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_6625,plain,
    ! [X28009,X28010,X28011,X28012,X28013,X28014,X28015,X28016] :
      ( ~ hBOOL(hAPP(hAPP(X28016,X28015),X28014))
      | ~ hBOOL(hAPP(hAPP(X28013,X28014),X28012))
      | hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X28011,X28010,X28009,X28016,X28013),X28015),X28012)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__comp_Ointros])]) ).

fof(i_0_6626,plain,
    ! [X23411,X23412,X23413,X23414,X23415,X23416,X23417,X23418] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X23418,X23417,X23416,X23415,X23414,X23413)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23417),X23412))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23417),X23411))
      | hAPP(X23413,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23417,tc_HOL_Obool)),X23412),X23411)) = hAPP(hAPP(X23416,hAPP(X23413,X23412)),hAPP(X23413,X23411)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Ounion__idem])]) ).

fof(i_0_6627,plain,
    ! [X24774,X24775,X24776,X24777,X24778,X24779,X24780,X24781] :
      ( ~ c_Equiv__Relations_Oequiv(X24781,X24780,X24779)
      | ~ c_Equiv__Relations_Ocongruent2(X24781,X24778,X24777,X24779,X24776,X24775)
      | ~ hBOOL(hAPP(hAPP(c_member(X24781),X24774),X24780))
      | c_Equiv__Relations_Ocongruent(X24778,X24777,X24776,hAPP(X24775,X24774)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruent2__implies__congruent])]) ).

fof(i_0_6628,plain,
    ! [X30063,X30064,X30065,X30066,X30067,X30070,X30071,X30072,X30073,X30074,X30075,X30076] :
      ( ( hAPP(hAPP(c_List_Oappend(X30067),X30066),esk402_5(X30063,X30064,X30065,X30066,X30067)) = X30064
        | X30066 = hAPP(hAPP(c_List_Oappend(X30067),X30064),esk401_5(X30063,X30064,X30065,X30066,X30067))
        | hAPP(hAPP(c_List_Oappend(X30067),X30066),X30065) != hAPP(hAPP(c_List_Oappend(X30067),X30064),X30063) )
      & ( X30065 = hAPP(hAPP(c_List_Oappend(X30067),esk402_5(X30063,X30064,X30065,X30066,X30067)),X30063)
        | X30066 = hAPP(hAPP(c_List_Oappend(X30067),X30064),esk401_5(X30063,X30064,X30065,X30066,X30067))
        | hAPP(hAPP(c_List_Oappend(X30067),X30066),X30065) != hAPP(hAPP(c_List_Oappend(X30067),X30064),X30063) )
      & ( hAPP(hAPP(c_List_Oappend(X30067),X30066),esk402_5(X30063,X30064,X30065,X30066,X30067)) = X30064
        | hAPP(hAPP(c_List_Oappend(X30067),esk401_5(X30063,X30064,X30065,X30066,X30067)),X30065) = X30063
        | hAPP(hAPP(c_List_Oappend(X30067),X30066),X30065) != hAPP(hAPP(c_List_Oappend(X30067),X30064),X30063) )
      & ( X30065 = hAPP(hAPP(c_List_Oappend(X30067),esk402_5(X30063,X30064,X30065,X30066,X30067)),X30063)
        | hAPP(hAPP(c_List_Oappend(X30067),esk401_5(X30063,X30064,X30065,X30066,X30067)),X30065) = X30063
        | hAPP(hAPP(c_List_Oappend(X30067),X30066),X30065) != hAPP(hAPP(c_List_Oappend(X30067),X30064),X30063) )
      & ( X30073 != hAPP(hAPP(c_List_Oappend(X30074),X30071),X30075)
        | hAPP(hAPP(c_List_Oappend(X30074),X30075),X30072) != X30070
        | hAPP(hAPP(c_List_Oappend(X30074),X30073),X30072) = hAPP(hAPP(c_List_Oappend(X30074),X30071),X30070) )
      & ( hAPP(hAPP(c_List_Oappend(X30074),X30073),X30076) != X30071
        | X30072 != hAPP(hAPP(c_List_Oappend(X30074),X30076),X30070)
        | hAPP(hAPP(c_List_Oappend(X30074),X30073),X30072) = hAPP(hAPP(c_List_Oappend(X30074),X30071),X30070) ) ),
    inference(distribute,[status(thm)],[inference(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_6629,plain,
    ! [X17306,X17307,X17308,X17309,X17310,X17311,X17312,X17313] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X17313,X17312,X17311,X17310,X17309,X17308)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17312),X17307))
      | hBOOL(hAPP(hAPP(c_member(X17312),X17306),X17307))
      | hAPP(X17308,hAPP(hAPP(c_Set_Oinsert(X17312),X17306),X17307)) = hAPP(hAPP(X17311,hAPP(X17309,X17306)),hAPP(X17308,X17307)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5412])]) ).

fof(i_0_6630,plain,
    ! [X18882,X18883,X18884,X18885,X18886] :
      ( ( ~ c_Fun_Oinj__on(X18885,X18883,X18886,X18884)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18883,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18885,X18883,X18886),X18884)),X18882))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18885),X18884)),hAPP(c_Finite__Set_Ocard(X18883),X18882)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18883),X18882))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18885),X18884)) )
      & ( c_Fun_Oinj__on(X18885,X18883,esk28_4(X18882,X18883,X18884,X18885),X18884)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18885),X18884)),hAPP(c_Finite__Set_Ocard(X18883),X18882)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18883),X18882))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18885),X18884)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18883,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18885,X18883,esk28_4(X18882,X18883,X18884,X18885)),X18884)),X18882))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18885),X18884)),hAPP(c_Finite__Set_Ocard(X18883),X18882)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18883),X18882))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18885),X18884)) ) ),
    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_6631,plain,
    ! [X17488,X17489,X17490,X17491,X17492,X17493,X17494,X17495] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X17495,X17494,X17493,X17492,X17491,X17490)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17494),X17489))
      | ~ hBOOL(hAPP(hAPP(c_member(X17494),X17488),X17489))
      | hAPP(hAPP(X17493,hAPP(X17491,X17488)),hAPP(X17490,X17489)) = hAPP(X17490,X17489) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oin__idem])]) ).

fof(i_0_6632,plain,
    ! [X31208,X31209,X31210] : c_Enum_Osublists(X31210,hAPP(hAPP(c_List_Olist_OCons(X31210),X31209),X31208)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(X31210)),tc_List_Olist(tc_List_Olist(X31210))),c_Enum_Osublists(X31210,X31208)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(X31210)),tc_List_Olist(tc_List_Olist(X31210)),tc_List_Olist(tc_List_Olist(X31210))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(X31210)),tc_fun(tc_List_Olist(tc_List_Olist(X31210)),tc_List_Olist(tc_List_Olist(X31210))),tc_List_Olist(tc_List_Olist(X31210))),c_List_Oappend(tc_List_Olist(X31210))),hAPP(c_List_Omap(tc_List_Olist(X31210),tc_List_Olist(X31210)),hAPP(c_List_Olist_OCons(X31210),X31209)))),c_COMBI(tc_List_Olist(tc_List_Olist(X31210))))),
    inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I2_J]) ).

fof(i_0_6633,plain,
    ! [X17324,X17325,X17326,X17327,X17328,X17329,X17330,X17331] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X17331,X17330,X17329,X17328,X17327,X17326)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17330),X17325))
      | hAPP(X17326,hAPP(hAPP(c_Set_Oinsert(X17330),X17324),X17325)) = hAPP(hAPP(X17329,hAPP(X17327,X17324)),hAPP(X17326,X17325)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oinsert__idem])]) ).

fof(i_0_6634,plain,
    ! [X26489,X26490,X26491,X26492,X26493] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26493,tc_fun(X26492,tc_HOL_Obool)),X26491),hAPP(hAPP(c_COMBS(X26493,tc_fun(X26492,tc_HOL_Obool),tc_fun(X26492,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26492,tc_HOL_Obool),tc_fun(tc_fun(X26492,tc_HOL_Obool),tc_fun(X26492,tc_HOL_Obool)),X26493),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26492,tc_HOL_Obool))),X26490)),X26489)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26492,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26493,tc_fun(X26492,tc_HOL_Obool)),X26491),X26490)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26493,tc_fun(X26492,tc_HOL_Obool)),X26491),X26489)),
    inference(variable_rename,[status(thm)],[fact_INT__Int__distrib]) ).

fof(i_0_6635,plain,
    ! [X23828,X23829,X23830,X23831,X23832] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23832,tc_fun(X23831,tc_HOL_Obool)),X23830),hAPP(hAPP(c_COMBS(X23832,tc_fun(X23831,tc_HOL_Obool),tc_fun(X23831,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23831,tc_HOL_Obool),tc_fun(tc_fun(X23831,tc_HOL_Obool),tc_fun(X23831,tc_HOL_Obool)),X23832),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23831,tc_HOL_Obool))),X23829)),X23828)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23831,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23832,tc_fun(X23831,tc_HOL_Obool)),X23830),X23829)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23832,tc_fun(X23831,tc_HOL_Obool)),X23830),X23828)),
    inference(variable_rename,[status(thm)],[fact_UN__Un__distrib]) ).

fof(i_0_6636,plain,
    ! [X17431,X17432,X17433,X17434,X17435,X17436] :
      ( ~ c_Finite__Set_Ofolding__image__simple(X17436,X17435,X17434,X17433,X17432,X17431)
      | hAPP(X17431,c_Orderings_Obot__class_Obot(tc_fun(X17435,tc_HOL_Obool))) = X17433 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple_Oempty])]) ).

fof(i_0_6637,plain,
    ! [X17350,X17351,X17352,X17353,X17354,X17355,X17356] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(X17356,X17355,X17354,X17353,X17352,X17351)
      | hAPP(hAPP(X17354,X17350),X17350) = X17350 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image__simple__idem_Oidem])]) ).

fof(i_0_6638,plain,
    ! [X23083] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23083))
      | X23083 = 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))),X23083)),c_FunDef_Omax__strict)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_smax__emptyI])]) ).

fof(i_0_6639,plain,
    ! [X31492,X31493,X31494] : hAPP(c_List_Oset(X31494),hAPP(c_List_Ofilter(X31494,X31493),X31492)) = hAPP(c_Set_OCollect(X31494),hAPP(hAPP(c_COMBS(X31494,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31494),c_fconj),hAPP(hAPP(c_COMBC(X31494,tc_fun(X31494,tc_HOL_Obool),tc_HOL_Obool),c_member(X31494)),hAPP(c_List_Oset(X31494),X31492)))),X31493)),
    inference(variable_rename,[status(thm)],[fact_set__filter]) ).

fof(i_0_6640,plain,
    ! [X25643,X25644,X25645] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X25645,esk210_3(X25643,X25644,X25645))),hAPP(X25644,esk210_3(X25643,X25644,X25645))))
      | 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),X25644),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X25643))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X25645),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X25643))) = 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)),X25644)),X25645)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X25643)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib])])]) ).

fof(i_0_6641,plain,
    ! [X18898,X18899,X18900,X18901,X18902,X18904] :
      ( ( ~ c_Fun_Oinj__on(X18900,X18899,X18902,X18901)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18899,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18900,X18899,X18902),X18901)),X18898))
        | hAPP(c_Set_Oimage(X18899,X18900,esk29_4(X18898,X18899,X18900,X18901)),X18898) = X18901
        | X18901 = c_Orderings_Obot__class_Obot(tc_fun(X18900,tc_HOL_Obool)) )
      & ( c_Fun_Oinj__on(X18900,X18899,esk30_4(X18898,X18899,X18900,X18901),X18901)
        | hAPP(c_Set_Oimage(X18899,X18900,X18904),X18898) != X18901
        | X18901 = c_Orderings_Obot__class_Obot(tc_fun(X18900,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18899,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18900,X18899,esk30_4(X18898,X18899,X18900,X18901)),X18901)),X18898))
        | hAPP(c_Set_Oimage(X18899,X18900,X18904),X18898) != X18901
        | X18901 = c_Orderings_Obot__class_Obot(tc_fun(X18900,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_6642,plain,
    ! [X27997,X27998,X27999,X28000] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28000),X27999),hAPP(c_Relation_ORange(X27998,X28000),X27997)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27998,X28000)),hAPP(hAPP(c_Product__Type_OPair(X27998,X28000),esk286_4(X27997,X27998,X27999,X28000)),X27999)),X27997)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5413])])]) ).

fof(i_0_6643,plain,
    ! [X27964,X27965,X27966,X27967,X27969,X27970,X27971,X27972,X27973] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27967),X27966),hAPP(c_Relation_ORange(X27965,X27967),X27964)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27965,X27967)),hAPP(hAPP(c_Product__Type_OPair(X27965,X27967),esk285_4(X27964,X27965,X27966,X27967)),X27966)),X27964)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27970,X27972)),hAPP(hAPP(c_Product__Type_OPair(X27970,X27972),X27973),X27971)),X27969))
        | hBOOL(hAPP(hAPP(c_member(X27972),X27971),hAPP(c_Relation_ORange(X27970,X27972),X27969))) ) ),
    inference(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_6644,plain,
    ! [X23097] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),X23097))
      | 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))),X23097)),c_FunDef_Omax__weak)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wmax__emptyI])]) ).

fof(i_0_6645,plain,
    ! [X26543,X26544,X26545,X26546,X26547] :
      ( ( X26547 != c_Orderings_Obot__class_Obot(tc_fun(X26546,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26546,tc_fun(X26545,tc_HOL_Obool)),X26547),hAPP(hAPP(c_COMBC(X26546,tc_fun(X26545,tc_HOL_Obool),tc_fun(X26545,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26545,tc_HOL_Obool),tc_fun(tc_fun(X26545,tc_HOL_Obool),tc_fun(X26545,tc_HOL_Obool)),X26546),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26545,tc_HOL_Obool))),X26544)),X26543)) = c_Orderings_Otop__class_Otop(tc_fun(X26545,tc_HOL_Obool)) )
      & ( X26547 = c_Orderings_Obot__class_Obot(tc_fun(X26546,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26546,tc_fun(X26545,tc_HOL_Obool)),X26547),hAPP(hAPP(c_COMBC(X26546,tc_fun(X26545,tc_HOL_Obool),tc_fun(X26545,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26545,tc_HOL_Obool),tc_fun(tc_fun(X26545,tc_HOL_Obool),tc_fun(X26545,tc_HOL_Obool)),X26546),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26545,tc_HOL_Obool))),X26544)),X26543)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26545,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26546,tc_fun(X26545,tc_HOL_Obool)),X26547),X26544)),X26543) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I1_J])]) ).

fof(i_0_6646,plain,
    ! [X26558,X26559,X26560,X26561,X26562] :
      ( ( X26562 != c_Orderings_Obot__class_Obot(tc_fun(X26561,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26561,tc_fun(X26560,tc_HOL_Obool)),X26562),hAPP(hAPP(c_COMBC(X26561,tc_fun(X26560,tc_HOL_Obool),tc_fun(X26560,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26560,tc_HOL_Obool),tc_fun(tc_fun(X26560,tc_HOL_Obool),tc_fun(X26560,tc_HOL_Obool)),X26561),c_Groups_Ominus__class_Ominus(tc_fun(X26560,tc_HOL_Obool))),X26559)),X26558)) = c_Orderings_Otop__class_Otop(tc_fun(X26560,tc_HOL_Obool)) )
      & ( X26562 = c_Orderings_Obot__class_Obot(tc_fun(X26561,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26561,tc_fun(X26560,tc_HOL_Obool)),X26562),hAPP(hAPP(c_COMBC(X26561,tc_fun(X26560,tc_HOL_Obool),tc_fun(X26560,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26560,tc_HOL_Obool),tc_fun(tc_fun(X26560,tc_HOL_Obool),tc_fun(X26560,tc_HOL_Obool)),X26561),c_Groups_Ominus__class_Ominus(tc_fun(X26560,tc_HOL_Obool))),X26559)),X26558)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26560,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26561,tc_fun(X26560,tc_HOL_Obool)),X26562),X26559)),X26558) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I3_J])]) ).

fof(i_0_6647,plain,
    ! [X23907,X23908,X23909,X23910,X23911] :
      ( ( X23911 != c_Orderings_Obot__class_Obot(tc_fun(X23910,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23910,tc_fun(X23909,tc_HOL_Obool)),X23911),hAPP(hAPP(c_COMBC(X23910,tc_fun(X23909,tc_HOL_Obool),tc_fun(X23909,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23909,tc_HOL_Obool),tc_fun(tc_fun(X23909,tc_HOL_Obool),tc_fun(X23909,tc_HOL_Obool)),X23910),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23909,tc_HOL_Obool))),X23908)),X23907)) = c_Orderings_Obot__class_Obot(tc_fun(X23909,tc_HOL_Obool)) )
      & ( X23911 = c_Orderings_Obot__class_Obot(tc_fun(X23910,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23910,tc_fun(X23909,tc_HOL_Obool)),X23911),hAPP(hAPP(c_COMBC(X23910,tc_fun(X23909,tc_HOL_Obool),tc_fun(X23909,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23909,tc_HOL_Obool),tc_fun(tc_fun(X23909,tc_HOL_Obool),tc_fun(X23909,tc_HOL_Obool)),X23910),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23909,tc_HOL_Obool))),X23908)),X23907)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23909,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23910,tc_fun(X23909,tc_HOL_Obool)),X23911),X23908)),X23907) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I2_J])]) ).

fof(i_0_6648,plain,
    ! [X26528,X26529,X26530,X26531,X26532] :
      ( ( X26532 != c_Orderings_Obot__class_Obot(tc_fun(X26531,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26530,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26531,tc_fun(X26530,tc_HOL_Obool)),X26532),X26529)),X26528) = X26528 )
      & ( X26532 = c_Orderings_Obot__class_Obot(tc_fun(X26531,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26530,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26531,tc_fun(X26530,tc_HOL_Obool)),X26532),X26529)),X26528) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26531,tc_fun(X26530,tc_HOL_Obool)),X26532),hAPP(hAPP(c_COMBC(X26531,tc_fun(X26530,tc_HOL_Obool),tc_fun(X26530,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26530,tc_HOL_Obool),tc_fun(tc_fun(X26530,tc_HOL_Obool),tc_fun(X26530,tc_HOL_Obool)),X26531),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26530,tc_HOL_Obool))),X26529)),X26528)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I1_J])]) ).

fof(i_0_6649,plain,
    ! [X23897,X23898,X23899,X23900,X23901] :
      ( ( X23901 != c_Orderings_Obot__class_Obot(tc_fun(X23900,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23899,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23900,tc_fun(X23899,tc_HOL_Obool)),X23901),X23898)),X23897) = X23897 )
      & ( X23901 = c_Orderings_Obot__class_Obot(tc_fun(X23900,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23899,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23900,tc_fun(X23899,tc_HOL_Obool)),X23901),X23898)),X23897) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23900,tc_fun(X23899,tc_HOL_Obool)),X23901),hAPP(hAPP(c_COMBC(X23900,tc_fun(X23899,tc_HOL_Obool),tc_fun(X23899,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23899,tc_HOL_Obool),tc_fun(tc_fun(X23899,tc_HOL_Obool),tc_fun(X23899,tc_HOL_Obool)),X23900),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23899,tc_HOL_Obool))),X23898)),X23897)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I2_J])]) ).

fof(i_0_6650,plain,
    ! [X26553,X26554,X26555,X26556,X26557] :
      ( ( X26557 != c_Orderings_Obot__class_Obot(tc_fun(X26556,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26555,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26556,tc_fun(X26555,tc_HOL_Obool)),X26557),X26554)),X26553) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26555,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26555,tc_HOL_Obool))),X26553) )
      & ( X26557 = c_Orderings_Obot__class_Obot(tc_fun(X26556,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26555,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26556,tc_fun(X26555,tc_HOL_Obool)),X26557),X26554)),X26553) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26556,tc_fun(X26555,tc_HOL_Obool)),X26557),hAPP(hAPP(c_COMBC(X26556,tc_fun(X26555,tc_HOL_Obool),tc_fun(X26555,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26555,tc_HOL_Obool),tc_fun(tc_fun(X26555,tc_HOL_Obool),tc_fun(X26555,tc_HOL_Obool)),X26556),c_Groups_Ominus__class_Ominus(tc_fun(X26555,tc_HOL_Obool))),X26554)),X26553)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I3_J])]) ).

fof(i_0_6651,plain,
    ! [X26424,X26425,X26426,X26427,X26428] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26428,tc_fun(X26427,tc_HOL_Obool)),X26426),hAPP(hAPP(c_COMBC(X26428,tc_fun(X26427,tc_HOL_Obool),tc_fun(X26427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26427,tc_HOL_Obool),tc_fun(tc_fun(X26427,tc_HOL_Obool),tc_fun(X26427,tc_HOL_Obool)),X26428),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26427,tc_HOL_Obool))),X26425)),X26424)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26427,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26428,tc_fun(X26427,tc_HOL_Obool)),X26426),X26425)),X26424),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I6_J]) ).

fof(i_0_6652,plain,
    ! [X25173,X25174,X25175,X25176,X25177] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25177,tc_fun(X25176,tc_HOL_Obool)),X25175),hAPP(hAPP(c_COMBC(X25177,tc_fun(X25176,tc_HOL_Obool),tc_fun(X25176,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25176,tc_HOL_Obool),tc_fun(tc_fun(X25176,tc_HOL_Obool),tc_fun(X25176,tc_HOL_Obool)),X25177),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25176,tc_HOL_Obool))),X25174)),X25173)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25176,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25177,tc_fun(X25176,tc_HOL_Obool)),X25175),X25174)),X25173),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I4_J]) ).

fof(i_0_6653,plain,
    ! [X23850,X23851,X23852,X23853,X23854] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23854,tc_fun(X23853,tc_HOL_Obool)),X23852),hAPP(hAPP(c_COMBC(X23854,tc_fun(X23853,tc_HOL_Obool),tc_fun(X23853,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23853,tc_HOL_Obool),tc_fun(tc_fun(X23853,tc_HOL_Obool),tc_fun(X23853,tc_HOL_Obool)),X23854),c_Groups_Ominus__class_Ominus(tc_fun(X23853,tc_HOL_Obool))),X23851)),X23850)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23853,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23854,tc_fun(X23853,tc_HOL_Obool)),X23852),X23851)),X23850),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I6_J]) ).

fof(i_0_6654,plain,
    ! [X25188,X25189,X25190,X25191,X25192] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25192,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25191,tc_fun(X25192,tc_HOL_Obool)),X25190),X25189)),X25188) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25191,tc_fun(X25192,tc_HOL_Obool)),X25190),hAPP(hAPP(c_COMBC(X25191,tc_fun(X25192,tc_HOL_Obool),tc_fun(X25192,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X25192,tc_HOL_Obool),tc_fun(tc_fun(X25192,tc_HOL_Obool),tc_fun(X25192,tc_HOL_Obool)),X25191),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25192,tc_HOL_Obool))),X25189)),X25188)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I4_J]) ).

fof(i_0_6655,plain,
    ! [X26439,X26440,X26441,X26442,X26443] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26443,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26442,tc_fun(X26443,tc_HOL_Obool)),X26441),X26440)),X26439) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26442,tc_fun(X26443,tc_HOL_Obool)),X26441),hAPP(hAPP(c_COMBC(X26442,tc_fun(X26443,tc_HOL_Obool),tc_fun(X26443,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X26443,tc_HOL_Obool),tc_fun(tc_fun(X26443,tc_HOL_Obool),tc_fun(X26443,tc_HOL_Obool)),X26442),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26443,tc_HOL_Obool))),X26440)),X26439)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I6_J]) ).

fof(i_0_6656,plain,
    ! [X23845,X23846,X23847,X23848,X23849] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23849,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23848,tc_fun(X23849,tc_HOL_Obool)),X23847),X23846)),X23845) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23848,tc_fun(X23849,tc_HOL_Obool)),X23847),hAPP(hAPP(c_COMBC(X23848,tc_fun(X23849,tc_HOL_Obool),tc_fun(X23849,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X23849,tc_HOL_Obool),tc_fun(tc_fun(X23849,tc_HOL_Obool),tc_fun(X23849,tc_HOL_Obool)),X23848),c_Groups_Ominus__class_Ominus(tc_fun(X23849,tc_HOL_Obool))),X23846)),X23845)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I6_J]) ).

fof(i_0_6657,plain,
    ! [X27946,X27947,X27948,X27949,X27950,X27951,X27952,X27953] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27953,X27952),tc_HOL_Obool)),X27951),hAPP(hAPP(c_Product__Type_OSigma(X27953,X27952),X27950),hAPP(c_COMBK(tc_fun(X27952,tc_HOL_Obool),X27953),X27949))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27952,X27948),tc_HOL_Obool)),X27947),hAPP(hAPP(c_Product__Type_OSigma(X27952,X27948),X27949),hAPP(c_COMBK(tc_fun(X27948,tc_HOL_Obool),X27952),X27946))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27953,X27948),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27953,X27952,X27948),X27951),X27947)),hAPP(hAPP(c_Product__Type_OSigma(X27953,X27948),X27950),hAPP(c_COMBK(tc_fun(X27948,tc_HOL_Obool),X27953),X27946)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__subset__Sigma])]) ).

fof(i_0_6658,plain,
    ! [X29290,X29291,X29292,X29293,X29294,X29295] :
      ( ( X29294 = X29292
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29295,X29295)),hAPP(hAPP(c_Product__Type_OPair(X29295,X29295),X29294),X29292)),X29290))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29294),X29293)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29292),X29291))),c_List_Olistrel1(X29295,X29290))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),X29293),X29291)),c_List_Olistrel1(X29295,X29290)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29295,X29295)),hAPP(hAPP(c_Product__Type_OPair(X29295,X29295),X29294),X29292)),X29290))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29294),X29293)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29292),X29291))),c_List_Olistrel1(X29295,X29290))) )
      & ( X29294 = X29292
        | X29293 = X29291
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29294),X29293)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29292),X29291))),c_List_Olistrel1(X29295,X29290))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),X29293),X29291)),c_List_Olistrel1(X29295,X29290)))
        | X29293 = X29291
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29294),X29293)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29292),X29291))),c_List_Olistrel1(X29295,X29290))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29295,X29295)),hAPP(hAPP(c_Product__Type_OPair(X29295,X29295),X29294),X29292)),X29290))
        | X29293 != X29291
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29294),X29293)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29292),X29291))),c_List_Olistrel1(X29295,X29290))) )
      & ( X29294 != X29292
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),X29293),X29291)),c_List_Olistrel1(X29295,X29290)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29295),tc_List_Olist(X29295))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29295),tc_List_Olist(X29295)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29294),X29293)),hAPP(hAPP(c_List_Olist_OCons(X29295),X29292),X29291))),c_List_Olistrel1(X29295,X29290))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__listrel1__Cons])])]) ).

fof(i_0_6659,plain,
    ! [X29237,X29238,X29239,X29240,X29241,X29242] :
      ( ( X29241 = X29239
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29242,X29242)),hAPP(hAPP(c_Product__Type_OPair(X29242,X29242),X29241),X29239)),X29237))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29242),tc_List_Olist(X29242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29242),tc_List_Olist(X29242)),hAPP(hAPP(c_List_Olist_OCons(X29242),X29241),X29240)),hAPP(hAPP(c_List_Olist_OCons(X29242),X29239),X29238))),c_List_Olexord(X29242,X29237))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29242),tc_List_Olist(X29242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29242),tc_List_Olist(X29242)),X29240),X29238)),c_List_Olexord(X29242,X29237)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29242,X29242)),hAPP(hAPP(c_Product__Type_OPair(X29242,X29242),X29241),X29239)),X29237))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29242),tc_List_Olist(X29242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29242),tc_List_Olist(X29242)),hAPP(hAPP(c_List_Olist_OCons(X29242),X29241),X29240)),hAPP(hAPP(c_List_Olist_OCons(X29242),X29239),X29238))),c_List_Olexord(X29242,X29237))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29242,X29242)),hAPP(hAPP(c_Product__Type_OPair(X29242,X29242),X29241),X29239)),X29237))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29242),tc_List_Olist(X29242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29242),tc_List_Olist(X29242)),hAPP(hAPP(c_List_Olist_OCons(X29242),X29241),X29240)),hAPP(hAPP(c_List_Olist_OCons(X29242),X29239),X29238))),c_List_Olexord(X29242,X29237))) )
      & ( X29241 != X29239
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29242),tc_List_Olist(X29242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29242),tc_List_Olist(X29242)),X29240),X29238)),c_List_Olexord(X29242,X29237)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29242),tc_List_Olist(X29242))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29242),tc_List_Olist(X29242)),hAPP(hAPP(c_List_Olist_OCons(X29242),X29241),X29240)),hAPP(hAPP(c_List_Olist_OCons(X29242),X29239),X29238))),c_List_Olexord(X29242,X29237))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__cons__cons])])]) ).

fof(i_0_6660,plain,
    ! [X29221,X29222,X29223,X29224,X29225,X29226] :
      ( ( X29225 = X29223
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29226,X29226)),hAPP(hAPP(c_Product__Type_OPair(X29226,X29226),X29225),X29223)),X29221))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29225),X29224)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29223),X29222))),c_List_Olex(X29226,X29221))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),X29224),X29222)),c_List_Olex(X29226,X29221)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29226,X29226)),hAPP(hAPP(c_Product__Type_OPair(X29226,X29226),X29225),X29223)),X29221))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29225),X29224)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29223),X29222))),c_List_Olex(X29226,X29221))) )
      & ( X29225 = X29223
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29226)),X29224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29226)),X29222)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29225),X29224)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29223),X29222))),c_List_Olex(X29226,X29221))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),X29224),X29222)),c_List_Olex(X29226,X29221)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29226)),X29224) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29226)),X29222)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29225),X29224)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29223),X29222))),c_List_Olex(X29226,X29221))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29226,X29226)),hAPP(hAPP(c_Product__Type_OPair(X29226,X29226),X29225),X29223)),X29221))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29226)),X29224) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29226)),X29222)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29225),X29224)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29223),X29222))),c_List_Olex(X29226,X29221))) )
      & ( X29225 != X29223
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),X29224),X29222)),c_List_Olex(X29226,X29221)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29226),tc_List_Olist(X29226))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29226),tc_List_Olist(X29226)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29225),X29224)),hAPP(hAPP(c_List_Olist_OCons(X29226),X29223),X29222))),c_List_Olex(X29226,X29221))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lex])])]) ).

fof(i_0_6661,plain,
    ! [X27219,X27220,X27221,X27222,X27223] : hAPP(hAPP(c_Product__Type_OSigma(X27223,X27222),X27221),hAPP(hAPP(c_COMBS(X27223,tc_fun(X27222,tc_HOL_Obool),tc_fun(X27222,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27222,tc_HOL_Obool),tc_fun(tc_fun(X27222,tc_HOL_Obool),tc_fun(X27222,tc_HOL_Obool)),X27223),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27222,tc_HOL_Obool))),X27220)),X27219)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27223,X27222),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27223,X27222),X27221),X27220)),hAPP(hAPP(c_Product__Type_OSigma(X27223,X27222),X27221),X27219)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib2]) ).

fof(i_0_6662,plain,
    ! [X27193,X27194,X27195,X27196,X27197] : hAPP(hAPP(c_Product__Type_OSigma(X27197,X27196),X27195),hAPP(hAPP(c_COMBS(X27197,tc_fun(X27196,tc_HOL_Obool),tc_fun(X27196,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27196,tc_HOL_Obool),tc_fun(tc_fun(X27196,tc_HOL_Obool),tc_fun(X27196,tc_HOL_Obool)),X27197),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27196,tc_HOL_Obool))),X27194)),X27193)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27197,X27196),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27197,X27196),X27195),X27194)),hAPP(hAPP(c_Product__Type_OSigma(X27197,X27196),X27195),X27193)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib2]) ).

fof(i_0_6663,plain,
    ! [X27136,X27137,X27138,X27139,X27140] : hAPP(hAPP(c_Product__Type_OSigma(X27140,X27139),X27138),hAPP(hAPP(c_COMBS(X27140,tc_fun(X27139,tc_HOL_Obool),tc_fun(X27139,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X27139,tc_HOL_Obool),tc_fun(tc_fun(X27139,tc_HOL_Obool),tc_fun(X27139,tc_HOL_Obool)),X27140),c_Groups_Ominus__class_Ominus(tc_fun(X27139,tc_HOL_Obool))),X27137)),X27136)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27140,X27139),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27140,X27139),X27138),X27137)),hAPP(hAPP(c_Product__Type_OSigma(X27140,X27139),X27138),X27136)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib2]) ).

fof(i_0_6664,plain,
    ! [X25948,X25949,X25950,X25951,X25952] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25952)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25952),hAPP(c_Groups_Oabs__class_Oabs(X25952),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25952),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25952),X25951),X25950)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25952),X25949),X25948)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25952),hAPP(c_Groups_Oabs__class_Oabs(X25952),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25952),X25951),X25949))),hAPP(c_Groups_Oabs__class_Oabs(X25952),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25952),X25950),X25948))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__diff__triangle__ineq])]) ).

fof(i_0_6665,plain,
    ! [X18888,X18889,X18890,X18891,X18892] :
      ( ( ~ 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),X18892),X18890)),X18889)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18891),X18890)),X18888)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18889),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),X18891),X18892)),X18890)),X18888)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18892),X18891)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18889),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),X18891),X18892)),X18890)),X18888)))
        | 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),X18892),X18890)),X18889)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18891),X18890)),X18888)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18892),X18891)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__add__iff2])])]) ).

fof(i_0_6666,plain,
    ! [X18916,X18917,X18918,X18919,X18920] :
      ( ( ~ 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),X18920),X18918)),X18917)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18919),X18918)),X18916)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18917),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),X18919),X18920)),X18918)),X18916)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18920),X18919)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18917),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),X18919),X18920)),X18918)),X18916)))
        | 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),X18920),X18918)),X18917)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18919),X18918)),X18916)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18920),X18919)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2])])]) ).

fof(i_0_6667,plain,
    ! [X19902,X19903,X19904,X19905,X19906,X19907,X19908,X19909] :
      ( ~ c_Finite__Set_Ofolding__image(X19909,X19908,X19907,X19906,X19905)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19908),X19904))
      | hAPP(hAPP(X19905,hAPP(hAPP(c_COMBS(X19908,X19909,X19909),hAPP(hAPP(c_COMBB(X19909,tc_fun(X19909,X19909),X19908),X19907),X19903)),X19902)),X19904) = hAPP(hAPP(X19907,hAPP(hAPP(X19905,X19903),X19904)),hAPP(hAPP(X19905,X19902),X19904)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Odistrib])]) ).

cnf(i_0_6668,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_5414]) ).

fof(i_0_6669,plain,
    ! [X25499,X25500,X25501,X25502,X25503] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25503)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25502),X25501))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25502),X25500))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25503),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25503,X25502,c_Groups_Otimes__class_Otimes(X25503)),X25499),c_Groups_Oone__class_Oone(X25503)),X25501)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25503,X25502,c_Groups_Otimes__class_Otimes(X25503)),X25499),c_Groups_Oone__class_Oone(X25503)),X25500)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25503),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25503,X25502,c_Groups_Otimes__class_Otimes(X25503)),X25499),c_Groups_Oone__class_Oone(X25503)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25502,tc_HOL_Obool)),X25501),X25500))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25503,X25502,c_Groups_Otimes__class_Otimes(X25503)),X25499),c_Groups_Oone__class_Oone(X25503)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25502,tc_HOL_Obool)),X25501),X25500))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__Un__Int])]) ).

fof(i_0_6670,plain,
    ! [X24390,X24391,X24392] : 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),X24392)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),X24391))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24390))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24392),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24390),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X24391)))),
    inference(variable_rename,[status(thm)],[fact_arith__series__nat]) ).

fof(i_0_6671,plain,
    ! [X24925,X24926,X24927,X24928] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24928,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24928,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24928,tc_HOL_Obool)),X24927),X24926)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24928,tc_HOL_Obool)),X24926),X24925))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24928,tc_HOL_Obool)),X24925),X24927)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24928,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24928,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24928,tc_HOL_Obool)),X24927),X24926)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24928,tc_HOL_Obool)),X24926),X24925))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24928,tc_HOL_Obool)),X24925),X24927)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__crazy]) ).

fof(i_0_6672,plain,
    ! [X29247,X29248,X29249,X29250,X29251,X29252] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29252,X29252)),hAPP(hAPP(c_Product__Type_OPair(X29252,X29252),X29251),X29250)),c_Transitive__Closure_Ortrancl(X29252,X29249)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29252),tc_List_Olist(X29252))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29252),tc_List_Olist(X29252)),X29248),X29247)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29252),c_List_Olistrel1(X29252,X29249))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29252),tc_List_Olist(X29252))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29252),tc_List_Olist(X29252)),hAPP(hAPP(c_List_Olist_OCons(X29252),X29251),X29248)),hAPP(hAPP(c_List_Olist_OCons(X29252),X29250),X29247))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29252),c_List_Olistrel1(X29252,X29249)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI2])]) ).

fof(i_0_6673,plain,
    ! [X17426,X17427,X17428,X17429,X17430] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17430,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17430,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17429,X17430,X17428),X17427)),hAPP(c_Set_Oimage(X17429,X17430,X17428),X17426))),hAPP(c_Set_Oimage(X17429,X17430,X17428),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17429,tc_HOL_Obool)),X17427),X17426)))),
    inference(variable_rename,[status(thm)],[fact_image__diff__subset]) ).

cnf(i_0_6674,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_5415]) ).

cnf(i_0_6675,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_5416]) ).

fof(i_0_6676,plain,
    ! [X27747] : hAPP(c_Set_OCollect(tc_Nat_Onat),X27747) = 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),X27747),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(i_0_6677,plain,
    ! [X29185,X29186] : c_List_Olenlex(X29186,X29185) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(X29186)),tc_List_Olist(X29186)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(X29186),c_Wellfounded_Oless__than,c_List_Olex(X29186,X29185))),hAPP(hAPP(c_COMBS(tc_List_Olist(X29186),tc_List_Olist(X29186),tc_prod(tc_Nat_Onat,tc_List_Olist(X29186))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(X29186),tc_prod(tc_Nat_Onat,tc_List_Olist(X29186))),tc_List_Olist(X29186)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(X29186))),c_Nat_Osize__class_Osize(tc_List_Olist(X29186)))),c_COMBI(tc_List_Olist(X29186)))),
    inference(variable_rename,[status(thm)],[fact_lenlex__def]) ).

fof(i_0_6678,plain,
    ! [X33280,X33281,X33282,X33283,X33284,X33285,X33286,X33287] :
      ( ( ~ c_Fun_Obij__betw(X33282,X33287,X33281,X33280,X33284)
        | c_Fun_Obij__betw(X33282,X33286,hAPP(c_Fun_Ocomp(X33287,X33286,X33282,X33285),X33281),X33280,X33283)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33287,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33282,X33287,X33281),X33280)),X33284))
        | ~ c_Fun_Obij__betw(X33287,X33286,X33285,X33284,X33283) )
      & ( ~ c_Fun_Obij__betw(X33282,X33286,hAPP(c_Fun_Ocomp(X33287,X33286,X33282,X33285),X33281),X33280,X33283)
        | c_Fun_Obij__betw(X33282,X33287,X33281,X33280,X33284)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33287,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33282,X33287,X33281),X33280)),X33284))
        | ~ c_Fun_Obij__betw(X33287,X33286,X33285,X33284,X33283) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__comp__iff2])])]) ).

fof(i_0_6679,plain,
    ! [X27525,X27526,X27527] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27527),esk270_3(X27525,X27526,X27527)),X27525))
        | c_Relation_Orefl__on(X27527,X27525,X27526)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27527,X27527),tc_HOL_Obool)),X27526),hAPP(hAPP(c_Product__Type_OSigma(X27527,X27527),X27525),hAPP(c_COMBK(tc_fun(X27527,tc_HOL_Obool),X27527),X27525)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27527,X27527)),hAPP(hAPP(c_Product__Type_OPair(X27527,X27527),esk270_3(X27525,X27526,X27527)),esk270_3(X27525,X27526,X27527))),X27526))
        | c_Relation_Orefl__on(X27527,X27525,X27526)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27527,X27527),tc_HOL_Obool)),X27526),hAPP(hAPP(c_Product__Type_OSigma(X27527,X27527),X27525),hAPP(c_COMBK(tc_fun(X27527,tc_HOL_Obool),X27527),X27525)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onI])])])]) ).

fof(i_0_6680,plain,
    ! [X27485,X27486,X27487,X27488,X27489,X27490,X27491] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27487,X27487),tc_HOL_Obool)),X27485),hAPP(hAPP(c_Product__Type_OSigma(X27487,X27487),X27486),hAPP(c_COMBK(tc_fun(X27487,tc_HOL_Obool),X27487),X27486))))
        | ~ c_Relation_Orefl__on(X27487,X27486,X27485) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27487),X27488),X27486))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27487,X27487)),hAPP(hAPP(c_Product__Type_OPair(X27487,X27487),X27488),X27488)),X27485))
        | ~ c_Relation_Orefl__on(X27487,X27486,X27485) )
      & ( hBOOL(hAPP(hAPP(c_member(X27491),esk267_3(X27489,X27490,X27491)),X27490))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27491,X27491),tc_HOL_Obool)),X27489),hAPP(hAPP(c_Product__Type_OSigma(X27491,X27491),X27490),hAPP(c_COMBK(tc_fun(X27491,tc_HOL_Obool),X27491),X27490))))
        | c_Relation_Orefl__on(X27491,X27490,X27489) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27491,X27491)),hAPP(hAPP(c_Product__Type_OPair(X27491,X27491),esk267_3(X27489,X27490,X27491)),esk267_3(X27489,X27490,X27491))),X27489))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27491,X27491),tc_HOL_Obool)),X27489),hAPP(hAPP(c_Product__Type_OSigma(X27491,X27491),X27490),hAPP(c_COMBK(tc_fun(X27491,tc_HOL_Obool),X27491),X27490))))
        | c_Relation_Orefl__on(X27491,X27490,X27489) ) ),
    inference(distribute,[status(thm)],[inference(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_6681,plain,
    ! [X27627,X27628,X27629] : hAPP(hAPP(c_Set_Oinsert(X27629),X27628),X27627) = hAPP(c_Set_OCollect(X27629),hAPP(hAPP(c_COMBS(X27629,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27629),c_fdisj),hAPP(hAPP(c_COMBC(X27629,X27629,tc_HOL_Obool),c_fequal),X27628))),hAPP(hAPP(c_COMBC(X27629,tc_fun(X27629,tc_HOL_Obool),tc_HOL_Obool),c_member(X27629)),X27627))),
    inference(variable_rename,[status(thm)],[fact_insert__compr__raw]) ).

fof(i_0_6682,plain,
    ! [X27624,X27625,X27626] : hAPP(hAPP(c_Set_Oinsert(X27626),X27625),X27624) = hAPP(c_Set_OCollect(X27626),hAPP(hAPP(c_COMBS(X27626,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27626),c_fdisj),hAPP(hAPP(c_COMBC(X27626,X27626,tc_HOL_Obool),c_fequal),X27625))),hAPP(hAPP(c_COMBC(X27626,tc_fun(X27626,tc_HOL_Obool),tc_HOL_Obool),c_member(X27626)),X27624))),
    inference(variable_rename,[status(thm)],[fact_insert__compr]) ).

cnf(i_0_6683,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk355_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_5396]) ).

fof(i_0_6684,plain,
    ! [X29341,X29342,X29343,X29344,X29345,X29346] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29346,X29346)),hAPP(hAPP(c_Product__Type_OPair(X29346,X29346),X29345),X29344)),X29343))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29346),tc_List_Olist(X29346))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29346),tc_List_Olist(X29346)),X29342),X29341)),c_List_Olistrel(X29346,X29343)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29346),tc_List_Olist(X29346))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29346),tc_List_Olist(X29346)),hAPP(hAPP(c_List_Olist_OCons(X29346),X29345),X29342)),hAPP(hAPP(c_List_Olist_OCons(X29346),X29344),X29341))),c_List_Olistrel(X29346,X29343))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel_OCons])]) ).

cnf(i_0_6685,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk354_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_5395]) ).

fof(i_0_6686,plain,
    ! [X18155,X18156,X18157,X18158,X18159] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18159,X18159,X18158,X18157,X18156),X18155))
      | hBOOL(hAPP(hAPP(c_member(X18159),X18157),X18156))
      | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18159,X18158,hAPP(hAPP(c_Set_Oinsert(X18159),X18157),X18156)),X18155)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5417])]) ).

cnf(i_0_6687,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_5418]) ).

cnf(i_0_6688,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_5419]) ).

cnf(i_0_6689,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_5420]) ).

fof(i_0_6690,plain,
    ! [X23084] :
      ( X23084 = 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)),X23084),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_6691,plain,
    ! [X24224,X24225] : 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),X24225),X24224)),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),X24224),X24225)),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_6692,plain,
    ! [X23098] : 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)),X23098),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_6693,plain,
    ! [X19807,X19808,X19809,X19810,X19811,X19812] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19812,X19811,X19810)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19812,X19811,X19810,X19809,X19808),X19807))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19812,X19811,X19810),X19809),X19808) = X19807 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__equality])]) ).

fof(i_0_6694,plain,
    ! [X18056,X18057,X18058,X18059,X18060] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18060,X18059,X18058,X18057,c_Orderings_Obot__class_Obot(tc_fun(X18060,tc_HOL_Obool))),X18056))
      | X18056 = X18057 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__fold__graphE])]) ).

fof(i_0_6695,plain,
    ! [X24682,X24683,X24684,X24685,X24686] :
      ( ~ c_Equiv__Relations_Oequiv(X24686,X24685,X24684)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24686,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24686,X24686,X24684),hAPP(hAPP(c_Set_Oinsert(X24686),X24683),c_Orderings_Obot__class_Obot(tc_fun(X24686,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X24686,X24686,X24684),hAPP(hAPP(c_Set_Oinsert(X24686),X24682),c_Orderings_Obot__class_Obot(tc_fun(X24686,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(X24686),X24683),X24685))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X24686,X24686)),hAPP(hAPP(c_Product__Type_OPair(X24686,X24686),X24682),X24683)),X24684)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__equiv__class])]) ).

fof(i_0_6696,plain,
    ! [X19005,X19006,X19007,X19008,X19009,X19010] :
      ( ( hBOOL(hAPP(hAPP(X19008,X19006),X19009))
        | ~ hBOOL(hAPP(hAPP(c_member(X19010),X19009),c_SetInterval_Oord_OatLeastLessThan(X19010,X19008,X19007,X19006,X19005))) )
      & ( hBOOL(hAPP(hAPP(X19007,X19009),X19005))
        | ~ hBOOL(hAPP(hAPP(c_member(X19010),X19009),c_SetInterval_Oord_OatLeastLessThan(X19010,X19008,X19007,X19006,X19005))) )
      & ( ~ hBOOL(hAPP(hAPP(X19008,X19006),X19009))
        | ~ hBOOL(hAPP(hAPP(X19007,X19009),X19005))
        | hBOOL(hAPP(hAPP(c_member(X19010),X19009),c_SetInterval_Oord_OatLeastLessThan(X19010,X19008,X19007,X19006,X19005))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastLessThan__iff])])]) ).

fof(i_0_6697,plain,
    ! [X18999,X19000,X19001,X19002,X19003,X19004] :
      ( ( hBOOL(hAPP(hAPP(X19001,X19000),X19003))
        | ~ hBOOL(hAPP(hAPP(c_member(X19004),X19003),c_SetInterval_Oord_OgreaterThanAtMost(X19004,X19002,X19001,X19000,X18999))) )
      & ( hBOOL(hAPP(hAPP(X19002,X19003),X18999))
        | ~ hBOOL(hAPP(hAPP(c_member(X19004),X19003),c_SetInterval_Oord_OgreaterThanAtMost(X19004,X19002,X19001,X19000,X18999))) )
      & ( ~ hBOOL(hAPP(hAPP(X19001,X19000),X19003))
        | ~ hBOOL(hAPP(hAPP(X19002,X19003),X18999))
        | hBOOL(hAPP(hAPP(c_member(X19004),X19003),c_SetInterval_Oord_OgreaterThanAtMost(X19004,X19002,X19001,X19000,X18999))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanAtMost__iff])])]) ).

fof(i_0_6698,plain,
    ! [X26092,X26093,X26094,X26095,X26096] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk223_5(X26092,X26093,X26094,X26095,X26096)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26096),X26093),X26095) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26096),X26092),X26094)
        | ~ c_Nat__Transfer_Onat__set(X26094)
        | X26095 != X26094
        | ~ class_Groups_Ocomm__monoid__add(X26096)
        | ~ class_Groups_Ocomm__monoid__mult(X26096) )
      & ( hAPP(X26093,esk223_5(X26092,X26093,X26094,X26095,X26096)) != hAPP(X26092,esk223_5(X26092,X26093,X26094,X26095,X26096))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26096),X26093),X26095) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X26096),X26092),X26094)
        | ~ c_Nat__Transfer_Onat__set(X26094)
        | X26095 != X26094
        | ~ class_Groups_Ocomm__monoid__add(X26096)
        | ~ class_Groups_Ocomm__monoid__mult(X26096) ) ),
    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_6699,plain,
    ! [X25725,X25726,X25727,X25728,X25729] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk220_5(X25725,X25726,X25727,X25728,X25729)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X25729),X25726),X25728) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X25729),X25725),X25727)
        | ~ c_Nat__Transfer_Onat__set(X25727)
        | X25728 != X25727
        | ~ class_Groups_Ocomm__monoid__add(X25729)
        | ~ class_Groups_Ocomm__monoid__mult(X25729) )
      & ( hAPP(X25726,esk220_5(X25725,X25726,X25727,X25728,X25729)) != hAPP(X25725,esk220_5(X25725,X25726,X25727,X25728,X25729))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X25729),X25726),X25728) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X25729),X25725),X25727)
        | ~ c_Nat__Transfer_Onat__set(X25727)
        | X25728 != X25727
        | ~ class_Groups_Ocomm__monoid__add(X25729)
        | ~ class_Groups_Ocomm__monoid__mult(X25729) ) ),
    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_6700,plain,
    ! [X31526,X31527] : c_Random_Oselect__weight(X31527,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X31527),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X31527,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X31527,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X31527)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X31526)) = c_Random_Oselect__weight(X31527,X31526),
    inference(variable_rename,[status(thm)],[fact_select__weigth__drop__zero]) ).

fof(i_0_6701,plain,
    ! [X31528,X31529] : c_Random_Opick(X31529,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,X31529),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,X31529,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(X31529,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,X31529)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),X31528)) = c_Random_Opick(X31529,X31528),
    inference(variable_rename,[status(thm)],[fact_pick__drop__zero]) ).

cnf(i_0_6702,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_6703,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(split_conjunct,[status(thm)],[fact_transfer__nat__int__numerals_I3_J]) ).

fof(i_0_6704,plain,
    ! [X33275,X33276,X33277,X33278,X33279] :
      ( ~ c_Fun_Obij__betw(X33279,X33278,X33277,c_Orderings_Otop__class_Otop(tc_fun(X33279,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33278,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(X33276,X33279,X33275,c_Orderings_Otop__class_Otop(tc_fun(X33276,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33279,tc_HOL_Obool)))
      | c_Hilbert__Choice_Oinv__into(X33276,X33278,c_Orderings_Otop__class_Otop(tc_fun(X33276,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X33279,X33278,X33276,X33277),X33275)) = hAPP(c_Fun_Ocomp(X33279,X33276,X33278,c_Hilbert__Choice_Oinv__into(X33276,X33279,c_Orderings_Otop__class_Otop(tc_fun(X33276,tc_HOL_Obool)),X33275)),c_Hilbert__Choice_Oinv__into(X33279,X33278,c_Orderings_Otop__class_Otop(tc_fun(X33279,tc_HOL_Obool)),X33277)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__inv__distrib])]) ).

cnf(i_0_6705,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_5421]) ).

cnf(i_0_6706,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_5422]) ).

fof(i_0_6707,plain,
    ! [X28184,X28185,X28186,X28187] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28187,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X28187,X28186),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28187,X28186),tc_HOL_Obool)),X28185),X28184))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28187,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X28187,X28186),X28185)),hAPP(c_Relation_ODomain(X28187,X28186),X28184)))),
    inference(variable_rename,[status(thm)],[fact_Domain__Int__subset]) ).

fof(i_0_6708,plain,
    ! [X27979,X27980,X27981,X27982] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27982,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27981,X27982),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27981,X27982),tc_HOL_Obool)),X27980),X27979))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27982,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27981,X27982),X27980)),hAPP(c_Relation_ORange(X27981,X27982),X27979)))),
    inference(variable_rename,[status(thm)],[fact_Range__Int__subset]) ).

fof(i_0_6709,plain,
    ! [X24486,X24487,X24488,X24489,X24490] :
      ( ~ class_Groups_Ocomm__monoid__add(X24490)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24489),X24488))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24489,X24490),hAPP(hAPP(c_COMBS(X24489,X24490,X24490),hAPP(hAPP(c_COMBB(X24490,tc_fun(X24490,X24490),X24489),c_Groups_Oplus__class_Oplus(X24490)),X24487)),X24486)),X24488) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24490),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24489,X24490),X24487),X24488)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24489,X24490),X24486),X24488)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Odistrib])]) ).

fof(i_0_6710,plain,
    ! [X22666,X22667,X22668,X22669,X22670] :
      ( ~ class_Fields_Ofield__inverse__zero(X22670)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22669),X22668))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22669,X22670),hAPP(hAPP(c_COMBS(X22669,X22670,X22670),hAPP(hAPP(c_COMBB(X22670,tc_fun(X22670,X22670),X22669),c_Rings_Oinverse__class_Odivide(X22670)),X22667)),X22666)),X22668) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22670),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22669,X22670),X22667),X22668)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22669,X22670),X22666),X22668)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dividef])]) ).

fof(i_0_6711,plain,
    ! [X21918,X21919,X21920,X21921,X21922] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21922)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21921),X21920))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21921,X21922),hAPP(hAPP(c_COMBS(X21921,X21922,X21922),hAPP(hAPP(c_COMBB(X21922,tc_fun(X21922,X21922),X21921),c_Groups_Otimes__class_Otimes(X21922)),X21919)),X21918)),X21920) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21922),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21921,X21922),X21919),X21920)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21921,X21922),X21918),X21920)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Odistrib])]) ).

fof(i_0_6712,plain,
    ! [X18069,X18070,X18071,X18072,X18073,X18074] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18074,X18073,X18072,X18071,X18070),X18069))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X18074),X18070)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__graph__imp__finite])]) ).

fof(i_0_6713,plain,
    ! [X30222,X30223] : hAPP(c_List_Orotate1(X30223),X30222) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X30223),X30223,c_List_Olist_ONil(X30223),hAPP(hAPP(c_COMBB(tc_List_Olist(X30223),tc_fun(tc_List_Olist(X30223),tc_List_Olist(X30223)),X30223),hAPP(c_COMBC(tc_List_Olist(X30223),tc_List_Olist(X30223),tc_List_Olist(X30223)),c_List_Oappend(X30223))),hAPP(hAPP(c_COMBC(X30223,tc_List_Olist(X30223),tc_List_Olist(X30223)),c_List_Olist_OCons(X30223)),c_List_Olist_ONil(X30223)))),X30222),
    inference(variable_rename,[status(thm)],[fact_rotate1__def]) ).

fof(i_0_6714,plain,
    ! [X24449,X24450,X24451,X24452,X24453] :
      ( ~ class_Groups_Ocomm__monoid__add(X24453)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24452,X24453),hAPP(hAPP(c_COMBS(X24452,X24453,X24453),hAPP(hAPP(c_COMBB(X24453,tc_fun(X24453,X24453),X24452),c_Groups_Oplus__class_Oplus(X24453)),X24451)),X24450)),X24449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24453),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24452,X24453),X24451),X24449)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24452,X24453),X24450),X24449)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__addf])]) ).

fof(i_0_6715,plain,
    ! [X24427,X24428,X24429,X24430,X24431] :
      ( ~ class_Groups_Oab__group__add(X24431)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24430,X24431),hAPP(hAPP(c_COMBS(X24430,X24431,X24431),hAPP(hAPP(c_COMBB(X24431,tc_fun(X24431,X24431),X24430),c_Groups_Ominus__class_Ominus(X24431)),X24429)),X24428)),X24427) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24431),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24430,X24431),X24429),X24427)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24430,X24431),X24428),X24427)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__subtractf])]) ).

fof(i_0_6716,plain,
    ! [X21874,X21875,X21876,X21877,X21878] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21878)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21877,X21878),hAPP(hAPP(c_COMBS(X21877,X21878,X21878),hAPP(hAPP(c_COMBB(X21878,tc_fun(X21878,X21878),X21877),c_Groups_Otimes__class_Otimes(X21878)),X21876)),X21875)),X21874) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21878),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21877,X21878),X21876),X21874)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21877,X21878),X21875),X21874)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__timesf])]) ).

fof(i_0_6717,plain,
    ! [X22263,X22264,X22265,X22266,X22267] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22267,X22266),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22265),X22264)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22266))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22263))
      | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22267,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22266),X22263)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22265),X22263)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X22266),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22265,X22263))),X22264)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__mult2__eq])]) ).

fof(i_0_6718,plain,
    ! [X31015,X31016,X31017] : c_List_Olistsp(X31017,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31017,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X31017,tc_fun(X31017,tc_HOL_Obool),tc_HOL_Obool),c_member(X31017)),X31016)),hAPP(hAPP(c_COMBC(X31017,tc_fun(X31017,tc_HOL_Obool),tc_HOL_Obool),c_member(X31017)),X31015))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X31017),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(X31017),tc_fun(tc_List_Olist(X31017),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X31017))),c_List_Olists(X31017,X31016))),hAPP(hAPP(c_COMBC(tc_List_Olist(X31017),tc_fun(tc_List_Olist(X31017),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(X31017))),c_List_Olists(X31017,X31015))),
    inference(variable_rename,[status(thm)],[fact_lists__Int__eq]) ).

fof(i_0_6719,plain,
    ! [X30965,X30966] : c_Random_Oselect__weight(X30966,X30965) = 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(X30966,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,X30966),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30966)),X30965)))),hAPP(hAPP(c_COMBB(X30966,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X30966,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X30966,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(X30966,X30965))),
    inference(variable_rename,[status(thm)],[fact_select__weight__def]) ).

fof(i_0_6720,plain,
    ! [X27294,X27295,X27296,X27297,X27298,X27299] : hAPP(hAPP(c_Product__Type_OSigma(X27299,X27298),hAPP(hAPP(c_Set_Oinsert(X27299),X27297),X27296)),hAPP(c_COMBK(tc_fun(X27298,tc_HOL_Obool),X27299),hAPP(hAPP(c_Set_Oinsert(X27298),X27295),X27294))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(X27299,X27298)),hAPP(hAPP(c_Product__Type_OPair(X27299,X27298),X27297),X27295)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27299,X27298),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27299,X27298),X27296),hAPP(c_COMBK(tc_fun(X27298,tc_HOL_Obool),X27299),hAPP(hAPP(c_Set_Oinsert(X27298),X27295),X27294)))),hAPP(hAPP(c_Product__Type_OSigma(X27299,X27298),hAPP(hAPP(c_Set_Oinsert(X27299),X27297),X27296)),hAPP(c_COMBK(tc_fun(X27298,tc_HOL_Obool),X27299),X27294)))),
    inference(variable_rename,[status(thm)],[fact_insert__times__insert]) ).

fof(i_0_6721,plain,
    ! [X24454,X24455,X24456,X24457,X24458] :
      ( ~ class_Fields_Ofield(X24458)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24458),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24457,X24458),X24456),X24455)),X24454) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24457,X24458),hAPP(hAPP(c_COMBC(X24457,X24458,X24458),hAPP(hAPP(c_COMBB(X24458,tc_fun(X24458,X24458),X24457),c_Rings_Oinverse__class_Odivide(X24458)),X24456)),X24454)),X24455) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__divide__distrib])]) ).

fof(i_0_6722,plain,
    ! [X24437,X24438,X24439,X24440,X24441] :
      ( ~ class_Rings_Osemiring__0(X24441)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24441),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24440,X24441),X24439),X24438)),X24437) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24440,X24441),hAPP(hAPP(c_COMBC(X24440,X24441,X24441),hAPP(hAPP(c_COMBB(X24441,tc_fun(X24441,X24441),X24440),c_Groups_Otimes__class_Otimes(X24441)),X24439)),X24437)),X24438) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__left__distrib])]) ).

fof(i_0_6723,plain,
    ! [X21834,X21835,X21836,X21837,X21838] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21838,X21837),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21836),X21835)))
      | X21837 = 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)),X21834))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21838,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21837),X21834)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21836),X21834)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21837),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21836,X21834))),X21835)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma])]) ).

fof(i_0_6724,plain,
    ! [X29323,X29324,X29325,X29326,X29327] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29327),tc_List_Olist(X29327))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29327),tc_List_Olist(X29327)),X29326),X29325)),c_List_Olistrel(X29327,c_Transitive__Closure_Ortrancl(X29327,X29324))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29327),tc_List_Olist(X29327))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29327),tc_List_Olist(X29327)),X29325),X29323)),c_List_Olistrel(X29327,c_Transitive__Closure_Ortrancl(X29327,X29324))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29327),tc_List_Olist(X29327))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29327),tc_List_Olist(X29327)),X29326),X29323)),c_List_Olistrel(X29327,c_Transitive__Closure_Ortrancl(X29327,X29324)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__rtrancl__trans])]) ).

cnf(i_0_6725,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_5423]) ).

cnf(i_0_6726,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_5424]) ).

fof(i_0_6727,plain,
    ! [X17134,X17135,X17136] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17136,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X17136,tc_fun(X17136,tc_HOL_Obool),tc_HOL_Obool),c_member(X17136)),X17135)),hAPP(hAPP(c_COMBC(X17136,tc_fun(X17136,tc_HOL_Obool),tc_HOL_Obool),c_member(X17136)),X17134)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17136,tc_HOL_Obool)),X17135),X17134)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17136,tc_HOL_Obool)),X17135),X17134))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17136,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X17136,tc_fun(X17136,tc_HOL_Obool),tc_HOL_Obool),c_member(X17136)),X17135)),hAPP(hAPP(c_COMBC(X17136,tc_fun(X17136,tc_HOL_Obool),tc_HOL_Obool),c_member(X17136)),X17134))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__subset__eq])]) ).

cnf(i_0_6728,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_5425]) ).

cnf(i_0_6729,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_5426]) ).

fof(i_0_6730,plain,
    ! [X28180,X28181,X28182,X28183] :
      ( ~ c_FunDef_Oreduction__pair(X28183,X28182)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28183,X28183),tc_HOL_Obool)),X28181),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(X28183,X28183),tc_HOL_Obool),tc_fun(tc_prod(X28183,X28183),tc_HOL_Obool)),X28182)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28183,X28183),tc_HOL_Obool)),X28180),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(X28183,X28183),tc_HOL_Obool),tc_fun(tc_prod(X28183,X28183),tc_HOL_Obool)),X28182)))
      | ~ c_Wellfounded_Owf(X28183,X28180)
      | c_Wellfounded_Owf(X28183,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28183,X28183),tc_HOL_Obool)),X28181),X28180)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma])]) ).

fof(i_0_6731,plain,
    ! [X27082,X27083,X27084] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27084,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27084,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X27084,tc_HOL_Obool),tc_HOL_Obool)),X27083),X27082))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27084,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27084,tc_HOL_Obool),X27083)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27084,tc_HOL_Obool),X27082)))),
    inference(variable_rename,[status(thm)],[fact_Union__Int__subset]) ).

fof(i_0_6732,plain,
    ! [X19163,X19164,X19165,X19166,X19167,X19168,X19169] :
      ( X19169 = X19168
      | c_Fun_Ofun__upd(X19167,X19166,c_Fun_Ofun__upd(X19167,X19166,X19165,X19169,X19164),X19168,X19163) = c_Fun_Ofun__upd(X19167,X19166,c_Fun_Ofun__upd(X19167,X19166,X19165,X19168,X19163),X19169,X19164) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__twist])]) ).

fof(i_0_6733,plain,
    ! [X28859,X28860,X28861,X28862,X28863] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28863,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28862,X28863,X28861),X28860)),X28859))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28862,tc_HOL_Obool)),X28860),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28862,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28863,X28862,hAPP(c_Relation_Oconverse(X28862,X28863),X28861)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28863,tc_HOL_Obool)),X28859))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28862,tc_HOL_Obool)),X28860),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28862,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28863,X28862,hAPP(c_Relation_Oconverse(X28862,X28863),X28861)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X28863,tc_HOL_Obool)),X28859)))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28863,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28862,X28863,X28861),X28860)),X28859)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset__eq])]) ).

cnf(i_0_6734,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),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_5427]) ).

cnf(i_0_6735,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X5)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Otrancl(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5428]) ).

fof(i_0_6736,plain,
    ! [X23672,X23673,X23674,X23675] : hAPP(c_Set_Oimage(X23675,X23674,X23673),X23672) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23675,tc_fun(X23674,tc_HOL_Obool)),X23672),hAPP(hAPP(c_COMBC(X23675,tc_fun(X23674,tc_HOL_Obool),tc_fun(X23674,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(X23674,tc_fun(tc_fun(X23674,tc_HOL_Obool),tc_fun(X23674,tc_HOL_Obool)),X23675),c_Set_Oinsert(X23674)),X23673)),c_Orderings_Obot__class_Obot(tc_fun(X23674,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_image__eq__UN]) ).

fof(i_0_6737,plain,
    ! [X27647,X27648,X27649] :
      ( ( ~ hBOOL(hAPP(X27649,X27648))
        | hAPP(c_Set_OCollect(X27647),hAPP(hAPP(c_COMBS(X27647,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27647),c_fconj),hAPP(hAPP(c_COMBC(X27647,X27647,tc_HOL_Obool),c_fequal),X27648))),X27649)) = hAPP(hAPP(c_Set_Oinsert(X27647),X27648),c_Orderings_Obot__class_Obot(tc_fun(X27647,tc_HOL_Obool))) )
      & ( hBOOL(hAPP(X27649,X27648))
        | hAPP(c_Set_OCollect(X27647),hAPP(hAPP(c_COMBS(X27647,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27647),c_fconj),hAPP(hAPP(c_COMBC(X27647,X27647,tc_HOL_Obool),c_fequal),X27648))),X27649)) = c_Orderings_Obot__class_Obot(tc_fun(X27647,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5429])]) ).

fof(i_0_6738,plain,
    ! [X29273,X29274,X29275,X29276,X29277] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29277),tc_List_Olist(X29277))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29277),tc_List_Olist(X29277)),X29276),X29275)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29277),c_List_Olistrel1(X29277,X29274))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29277),tc_List_Olist(X29277))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29277),tc_List_Olist(X29277)),hAPP(hAPP(c_List_Olist_OCons(X29277),X29273),X29276)),hAPP(hAPP(c_List_Olist_OCons(X29277),X29273),X29275))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29277),c_List_Olistrel1(X29277,X29274)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__ConsI1])]) ).

fof(i_0_6739,plain,
    ! [X23063,X23064,X23065,X23066] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23066),X23065))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X23064),X23063))
      | 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),X23066),X23064)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23065),X23063))),c_FunDef_Opair__leq)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI2])]) ).

fof(i_0_6740,plain,
    ! [X22990,X22991,X22992,X22993] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22993),X22992))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22991),X22990))
      | 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),X22993),X22991)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22992),X22990))),c_FunDef_Opair__less)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI2])]) ).

fof(i_0_6741,plain,
    ! [X28646,X28647,X28648] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28648,X28648),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28648,X28648),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28648,X28647)),c_Transitive__Closure_Ortrancl(X28648,X28646))),c_Transitive__Closure_Ortrancl(X28648,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28648,X28648),tc_HOL_Obool)),X28647),X28646)))),
    inference(variable_rename,[status(thm)],[fact_rtrancl__Un__subset]) ).

fof(i_0_6742,plain,
    ! [X32821,X32822,X32823,X32824,X32825] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32825),tc_List_Olist(X32825))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32825),tc_List_Olist(X32825)),X32824),X32823)),c_List_Olexord(X32825,X32822)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32825),tc_List_Olist(X32825))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32825),tc_List_Olist(X32825)),X32823),X32821)),c_List_Olexord(X32825,X32822)))
      | ~ c_Relation_Otrans(X32825,X32822)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X32825),tc_List_Olist(X32825))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X32825),tc_List_Olist(X32825)),X32824),X32821)),c_List_Olexord(X32825,X32822))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__trans])]) ).

fof(i_0_6743,plain,
    ! [X25281,X25282,X25283,X25284,X25285] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25285,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25284,X25285,X25283),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25284,tc_HOL_Obool)),X25282),X25281))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25285,tc_HOL_Obool)),hAPP(c_Relation_OImage(X25284,X25285,X25283),X25282)),hAPP(c_Relation_OImage(X25284,X25285,X25283),X25281)))),
    inference(variable_rename,[status(thm)],[fact_Image__Int__subset]) ).

fof(i_0_6744,plain,
    ! [X25245,X25246,X25247,X25248,X25249] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25249,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25248,X25249,X25247),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25248,tc_HOL_Obool)),X25246),X25245))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25249,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25248,X25249,X25247),X25246)),hAPP(c_Set_Oimage(X25248,X25249,X25247),X25245)))),
    inference(variable_rename,[status(thm)],[fact_image__Int__subset]) ).

fof(i_0_6745,plain,
    ! [X29114,X29115] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk363_2(X29114,X29115)))
        | 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)))),X29115)) = 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)))),X29114)) )
      & ( ~ hBOOL(hAPP(X29115,esk363_2(X29114,X29115)))
        | ~ hBOOL(hAPP(X29114,esk363_2(X29114,X29115)))
        | 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)))),X29115)) = 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)))),X29114)) )
      & ( hBOOL(hAPP(X29115,esk363_2(X29114,X29115)))
        | hBOOL(hAPP(X29114,esk363_2(X29114,X29115)))
        | 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)))),X29115)) = 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)))),X29114)) ) ),
    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_6746,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_5430]) ).

fof(i_0_6747,plain,
    ! [X23075,X23076,X23077,X23078] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23078),X23077))
      | 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),X23078),X23076)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23077),X23075))),c_FunDef_Opair__leq)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__leqI1])]) ).

fof(i_0_6748,plain,
    ! [X23022,X23023,X23024,X23025] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23025),X23024))
      | 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),X23025),X23023)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X23024),X23022))),c_FunDef_Opair__less)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__lessI1])]) ).

fof(i_0_6749,plain,
    ! [X29554,X29555] : c_List_Olists(X29555,X29554) = hAPP(c_Set_OCollect(tc_List_Olist(X29555)),hAPP(hAPP(c_COMBC(tc_List_Olist(X29555),tc_fun(X29555,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X29555,tc_HOL_Obool),tc_fun(tc_fun(X29555,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X29555)),c_Orderings_Oord__class_Oless__eq(tc_fun(X29555,tc_HOL_Obool))),c_List_Oset(X29555))),X29554)),
    inference(variable_rename,[status(thm)],[fact_lists__eq__set]) ).

fof(i_0_6750,plain,
    ! [X19136,X19137,X19138,X19139,X19140,X19141] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19141),X19140),X19139))
        | hAPP(c_Set_Oimage(X19141,X19138,c_Fun_Ofun__upd(X19141,X19138,X19137,X19140,X19136)),X19139) = hAPP(hAPP(c_Set_Oinsert(X19138),X19136),hAPP(c_Set_Oimage(X19141,X19138,X19137),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19141,tc_HOL_Obool)),X19139),hAPP(hAPP(c_Set_Oinsert(X19141),X19140),c_Orderings_Obot__class_Obot(tc_fun(X19141,tc_HOL_Obool)))))) )
      & ( hBOOL(hAPP(hAPP(c_member(X19141),X19140),X19139))
        | hAPP(c_Set_Oimage(X19141,X19138,c_Fun_Ofun__upd(X19141,X19138,X19137,X19140,X19136)),X19139) = hAPP(c_Set_Oimage(X19141,X19138,X19137),X19139) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5431])]) ).

fof(i_0_6751,plain,
    ! [X30157,X30158,X30159,X30160,X30161,X30162] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30162),tc_List_Olist(X30162))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30162),tc_List_Olist(X30162)),X30161),X30160)),c_List_Olistrel1(X30162,X30159)))
        | X30158 != X30157
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30162),tc_List_Olist(X30162))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30162),tc_List_Olist(X30162)),hAPP(hAPP(c_List_Oappend(X30162),X30161),X30158)),hAPP(hAPP(c_List_Oappend(X30162),X30160),X30157))),c_List_Olistrel1(X30162,X30159))) )
      & ( X30161 != X30160
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30162),tc_List_Olist(X30162))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30162),tc_List_Olist(X30162)),X30158),X30157)),c_List_Olistrel1(X30162,X30159)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30162),tc_List_Olist(X30162))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30162),tc_List_Olist(X30162)),hAPP(hAPP(c_List_Oappend(X30162),X30161),X30158)),hAPP(hAPP(c_List_Oappend(X30162),X30160),X30157))),c_List_Olistrel1(X30162,X30159))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__listrel1I])])]) ).

fof(i_0_6752,plain,
    ! [X30163,X30164,X30165,X30166,X30167] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30167),tc_List_Olist(X30167))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30167),tc_List_Olist(X30167)),X30166),X30165)),c_List_Olexord(X30167,X30164)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30167),tc_List_Olist(X30167))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30167),tc_List_Olist(X30167)),hAPP(hAPP(c_List_Oappend(X30167),X30163),X30166)),hAPP(hAPP(c_List_Oappend(X30167),X30163),X30165))),c_List_Olexord(X30167,X30164))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__leftI])]) ).

fof(i_0_6753,plain,
    ! [X29268,X29269,X29270,X29271,X29272] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29272),tc_List_Olist(X29272))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29272),tc_List_Olist(X29272)),X29271),X29270)),c_List_Olistrel1(X29272,X29269)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29272),tc_List_Olist(X29272))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29272),tc_List_Olist(X29272)),hAPP(hAPP(c_List_Olist_OCons(X29272),X29268),X29271)),hAPP(hAPP(c_List_Olist_OCons(X29272),X29268),X29270))),c_List_Olistrel1(X29272,X29269))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I2])]) ).

cnf(i_0_6754,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_5432]) ).

fof(i_0_6755,plain,
    ! [X27740] : 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)))),X27740))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(i_0_6756,plain,
    ! [X33293,X33294,X33295,X33296,X33297,X33298,X33299,X33300] :
      ( ( ~ c_Fun_Obij__betw(X33299,X33295,X33294,X33296,X33293)
        | c_Fun_Obij__betw(X33300,X33295,hAPP(c_Fun_Ocomp(X33299,X33295,X33300,X33294),X33298),X33297,X33293)
        | ~ c_Fun_Obij__betw(X33300,X33299,X33298,X33297,X33296) )
      & ( ~ c_Fun_Obij__betw(X33300,X33295,hAPP(c_Fun_Ocomp(X33299,X33295,X33300,X33294),X33298),X33297,X33293)
        | c_Fun_Obij__betw(X33299,X33295,X33294,X33296,X33293)
        | ~ c_Fun_Obij__betw(X33300,X33299,X33298,X33297,X33296) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__comp__iff])])]) ).

fof(i_0_6757,plain,
    ! [X30694,X30695,X30696,X30697,X30698,X30699] : hAPP(hAPP(c_List_Ozip(X30699,X30698),hAPP(hAPP(c_List_Omap(X30697,X30699),X30696),X30695)),X30694) = hAPP(hAPP(c_List_Omap(tc_prod(X30697,X30698),tc_prod(X30699,X30698)),hAPP(c_Product__Type_Oprod_Oprod__case(X30697,X30698,tc_prod(X30699,X30698)),hAPP(hAPP(c_COMBB(X30699,tc_fun(X30698,tc_prod(X30699,X30698)),X30697),c_Product__Type_OPair(X30699,X30698)),X30696))),hAPP(hAPP(c_List_Ozip(X30697,X30698),X30695),X30694)),
    inference(variable_rename,[status(thm)],[fact_zip__map1]) ).

fof(i_0_6758,plain,
    ! [X23105,X23106,X23107] : c_Wellfounded_Omlex__prod(X23107,X23106,X23105) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X23107),X23107),c_Wellfounded_Olex__prod(tc_Nat_Onat,X23107,c_Wellfounded_Oless__than,X23105)),hAPP(hAPP(c_COMBS(X23107,X23107,tc_prod(tc_Nat_Onat,X23107)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X23107,tc_prod(tc_Nat_Onat,X23107)),X23107),c_Product__Type_OPair(tc_Nat_Onat,X23107)),X23106)),c_COMBI(X23107))),
    inference(variable_rename,[status(thm)],[fact_mlex__prod__def]) ).

fof(i_0_6759,plain,
    ! [X17538,X17539,X17540] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17540),esk13_3(X17538,X17539,X17540)))
        | hBOOL(hAPP(X17538,c_Orderings_Obot__class_Obot(tc_fun(X17540,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X17538,X17539))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17540),X17539)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17540),esk12_3(X17538,X17539,X17540)),esk13_3(X17538,X17539,X17540)))
        | hBOOL(hAPP(X17538,c_Orderings_Obot__class_Obot(tc_fun(X17540,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X17538,X17539))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17540),X17539)) )
      & ( hBOOL(hAPP(X17538,esk13_3(X17538,X17539,X17540)))
        | hBOOL(hAPP(X17538,c_Orderings_Obot__class_Obot(tc_fun(X17540,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X17538,X17539))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17540),X17539)) )
      & ( ~ hBOOL(hAPP(X17538,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17540,tc_HOL_Obool)),esk13_3(X17538,X17539,X17540)),hAPP(hAPP(c_Set_Oinsert(X17540),esk12_3(X17538,X17539,X17540)),c_Orderings_Obot__class_Obot(tc_fun(X17540,tc_HOL_Obool))))))
        | hBOOL(hAPP(X17538,c_Orderings_Obot__class_Obot(tc_fun(X17540,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X17538,X17539))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17540),X17539)) ) ),
    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_6760,plain,
    ! [X27266,X27267,X27268,X27269,X27270,X27271] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27268,X27271),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27268,X27271),X27267),hAPP(c_COMBK(tc_fun(X27271,tc_HOL_Obool),X27268),X27269))),hAPP(hAPP(c_Product__Type_OSigma(X27268,X27271),X27266),hAPP(c_COMBK(tc_fun(X27271,tc_HOL_Obool),X27268),X27269))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27268,tc_HOL_Obool)),X27267),X27266))
        | ~ hBOOL(hAPP(hAPP(c_member(X27271),X27270),X27269)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27268,tc_HOL_Obool)),X27267),X27266))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27268,X27271),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27268,X27271),X27267),hAPP(c_COMBK(tc_fun(X27271,tc_HOL_Obool),X27268),X27269))),hAPP(hAPP(c_Product__Type_OSigma(X27268,X27271),X27266),hAPP(c_COMBK(tc_fun(X27271,tc_HOL_Obool),X27268),X27269))))
        | ~ hBOOL(hAPP(hAPP(c_member(X27271),X27270),X27269)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__subset__cancel2])])]) ).

cnf(i_0_6761,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_5433]) ).

fof(i_0_6762,plain,
    ! [X28989,X28990,X28991,X28992,X28993,X28994] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28994,X28994)),hAPP(hAPP(c_Product__Type_OPair(X28994,X28994),X28993),X28992)),X28991))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28994,X28994)),hAPP(hAPP(c_Product__Type_OPair(X28994,X28994),X28992),X28990)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28994,X28994),tc_HOL_Obool),X28989),X28991)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28994,X28994)),hAPP(hAPP(c_Product__Type_OPair(X28994,X28994),X28993),X28990)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28994,X28994),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28989)),X28991))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I2])]) ).

fof(i_0_6763,plain,
    ! [X28995,X28996,X28997,X28998,X28999,X29000] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29000,X29000)),hAPP(hAPP(c_Product__Type_OPair(X29000,X29000),X28999),X28998)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29000,X29000),tc_HOL_Obool),X28997),X28996)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29000,X29000)),hAPP(hAPP(c_Product__Type_OPair(X29000,X29000),X28998),X28995)),X28996))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X29000,X29000)),hAPP(hAPP(c_Product__Type_OPair(X29000,X29000),X28999),X28995)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X29000,X29000),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28997)),X28996))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__Suc__I])]) ).

fof(i_0_6764,plain,
    ! [X33288,X33289,X33290,X33291,X33292] :
      ( ~ c_Fun_Obij__betw(X33292,X33291,X33290,c_Orderings_Otop__class_Otop(tc_fun(X33292,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33291,tc_HOL_Obool)))
      | ~ c_Fun_Obij__betw(X33291,X33289,X33288,c_Orderings_Otop__class_Otop(tc_fun(X33291,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33289,tc_HOL_Obool)))
      | c_Fun_Obij__betw(X33292,X33289,hAPP(c_Fun_Ocomp(X33291,X33289,X33292,X33288),X33290),c_Orderings_Otop__class_Otop(tc_fun(X33292,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33289,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__comp])]) ).

fof(i_0_6765,plain,
    ! [X23978,X23979,X23980,X23981,X23982] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23982,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23981,X23982,X23980),X23979)),X23978))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X23982,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(X23981,tc_HOL_Obool),tc_fun(X23982,tc_HOL_Obool),c_Set_Oimage(X23981,X23982,X23980)),hAPP(c_Set_OPow(X23981),X23979))),hAPP(c_Set_OPow(X23982),X23978))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__mono])]) ).

fof(i_0_6766,plain,
    ! [X22246,X22247] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22246),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Onorm__frac(X22247,X22246) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22247),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22246))
        | ~ 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),X22247),X22246))) )
      & ( X22247 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22247,X22246) = 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),X22246),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),X22247),X22246))) )
      & ( X22246 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22247,X22246) = 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),X22246),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),X22247),X22246))) )
      & ( X22247 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X22246 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22247,X22246) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X22247),X22246)),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),X22247))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22246)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22246),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),X22247),X22246))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5434])])]) ).

cnf(i_0_6767,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_5435]) ).

fof(i_0_6768,plain,
    ! [X30962,X30963,X30964] :
      ( ~ 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,X30964),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30964)),X30963))))
      | hBOOL(hAPP(hAPP(c_member(X30964),hAPP(c_Product__Type_Ofst(X30964,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(X30964,X30963),X30962))),hAPP(c_List_Oset(X30964),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30964),X30964),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X30964)),X30963)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weight__member])]) ).

fof(i_0_6769,plain,
    ! [X25835,X25836,X25837,X25838] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25838)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25838),hAPP(c_Groups_Oabs__class_Oabs(X25838),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25837,X25838),X25836),X25835))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25837,X25838),hAPP(hAPP(c_COMBB(X25838,X25838,X25837),c_Groups_Oabs__class_Oabs(X25838)),X25836)),X25835))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs])]) ).

fof(i_0_6770,plain,
    ! [X31499,X31500,X31501] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X31501,tc_HOL_Obool)),hAPP(c_List_Oset(X31501),X31500)),hAPP(hAPP(c_Set_Oinsert(X31501),X31499),c_Orderings_Obot__class_Obot(tc_fun(X31501,tc_HOL_Obool)))) = hAPP(c_List_Oset(X31501),hAPP(c_List_Ofilter(X31501,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31501),c_fNot),hAPP(hAPP(c_COMBC(X31501,X31501,tc_HOL_Obool),c_fequal),X31499))),X31500)),
    inference(variable_rename,[status(thm)],[fact_set__minus__filter__out]) ).

fof(i_0_6771,plain,
    ! [X31427,X31428,X31429,X31430] : hAPP(c_List_Ofilter(X31430,X31429),hAPP(c_List_Ofilter(X31430,X31428),X31427)) = hAPP(c_List_Ofilter(X31430,hAPP(hAPP(c_COMBS(X31430,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X31430),c_fconj),X31428)),X31429)),X31427),
    inference(variable_rename,[status(thm)],[fact_filter__filter]) ).

fof(i_0_6772,plain,
    ! [X28188,X28189,X28190,X28191] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28191,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X28191,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X28191,X28190),X28189)),hAPP(c_Relation_ODomain(X28191,X28190),X28188))),hAPP(c_Relation_ODomain(X28191,X28190),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X28191,X28190),tc_HOL_Obool)),X28189),X28188)))),
    inference(variable_rename,[status(thm)],[fact_Domain__Diff__subset]) ).

fof(i_0_6773,plain,
    ! [X27983,X27984,X27985,X27986] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27986,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27986,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27985,X27986),X27984)),hAPP(c_Relation_ORange(X27985,X27986),X27983))),hAPP(c_Relation_ORange(X27985,X27986),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27985,X27986),tc_HOL_Obool)),X27984),X27983)))),
    inference(variable_rename,[status(thm)],[fact_Range__Diff__subset]) ).

fof(i_0_6774,plain,
    ! [X17789,X17790,X17791,X17792] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),c_Orderings_Obot__class_Obot(tc_fun(X17792,tc_HOL_Obool))))),X17789))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),c_Orderings_Obot__class_Obot(tc_fun(X17792,tc_HOL_Obool))))),X17789))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),c_Orderings_Obot__class_Obot(tc_fun(X17792,tc_HOL_Obool))))),X17789))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17792),X17790),X17791))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),c_Orderings_Obot__class_Obot(tc_fun(X17792,tc_HOL_Obool))))),X17789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),c_Orderings_Obot__class_Obot(tc_fun(X17792,tc_HOL_Obool))))),X17789))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),X17789))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17792,tc_HOL_Obool)),X17791),hAPP(hAPP(c_Set_Oinsert(X17792),X17790),X17789))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5436])])]) ).

fof(i_0_6775,plain,
    ! [X29410,X29411,X29412] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29412,X29412)),hAPP(hAPP(c_Product__Type_OPair(X29412,X29412),esk381_3(X29410,X29411,X29412)),esk381_3(X29410,X29411,X29412))),X29411))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29412),tc_List_Olist(X29412))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29412),tc_List_Olist(X29412)),X29410),X29410)),c_List_Olexord(X29412,X29411))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5437])])]) ).

fof(i_0_6776,plain,
    ! [X17781] : c_Finite__Set_Ofun__left__comm__idem(X17781,tc_fun(X17781,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X17781,tc_HOL_Obool),tc_fun(tc_fun(X17781,tc_HOL_Obool),tc_fun(X17781,tc_HOL_Obool)),X17781),hAPP(c_COMBC(tc_fun(X17781,tc_HOL_Obool),tc_fun(X17781,tc_HOL_Obool),tc_fun(X17781,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(X17781,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(X17781,tc_fun(X17781,tc_HOL_Obool),tc_fun(X17781,tc_HOL_Obool)),c_Set_Oinsert(X17781)),c_Orderings_Obot__class_Obot(tc_fun(X17781,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__remove]) ).

cnf(i_0_6777,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_5438]) ).

fof(i_0_6778,plain,
    ! [X17535,X17536,X17537] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17537),X17536))
      | ~ hBOOL(hAPP(hAPP(c_member(X17537),X17535),X17536))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17537),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17537,tc_HOL_Obool)),X17536),hAPP(hAPP(c_Set_Oinsert(X17537),X17535),c_Orderings_Obot__class_Obot(tc_fun(X17537,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X17537),X17536))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__less])]) ).

fof(i_0_6779,plain,
    ! [X22326,X22327,X22328,X22329,X22330,X22331] : hAPP(hAPP(c_COMBS(tc_prod(X22331,X22330),X22330,X22329),hAPP(hAPP(c_COMBB(X22328,tc_fun(X22330,X22329),tc_prod(X22331,X22330)),X22327),hAPP(hAPP(c_COMBB(X22331,X22328,tc_prod(X22331,X22330)),X22326),c_Product__Type_Ofst(X22331,X22330)))),c_Product__Type_Osnd(X22331,X22330)) = hAPP(c_Product__Type_Oprod_Oprod__case(X22331,X22330,X22329),hAPP(hAPP(c_COMBB(X22328,tc_fun(X22330,X22329),X22331),X22327),X22326)),
    inference(variable_rename,[status(thm)],[fact_split__comp__eq]) ).

fof(i_0_6780,plain,
    ! [X31651,X31652,X31653,X31654,X31655] :
      ( ~ class_Orderings_Olinorder(X31655)
      | ~ hBOOL(hAPP(hAPP(c_member(X31654),X31653),hAPP(c_List_Oset(X31654),X31652)))
      | ~ c_List_Olinorder__class_Osorted(X31655,hAPP(hAPP(c_List_Omap(X31654,X31655),X31651),X31652))
      | hAPP(c_List_Ohd(X31654),hAPP(c_List_Ofilter(X31654,hAPP(hAPP(c_COMBB(X31655,tc_HOL_Obool,X31654),hAPP(c_fequal,hAPP(X31651,X31653))),X31651)),X31652)) != X31653
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31654,X31655,X31651),X31653),c_List_Oremove1(X31654,X31653,X31652)) = X31652 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__remove1])]) ).

fof(i_0_6781,plain,
    ! [X33340,X33341,X33342,X33343,X33344,X33345,X33346] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33346,tc_HOL_Obool)),X33345),X33344) != c_Orderings_Obot__class_Obot(tc_fun(X33346,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33343,tc_HOL_Obool)),X33342),X33341) != c_Orderings_Obot__class_Obot(tc_fun(X33343,tc_HOL_Obool))
      | ~ c_Fun_Obij__betw(X33346,X33343,X33340,X33345,X33342)
      | ~ c_Fun_Obij__betw(X33346,X33343,X33340,X33344,X33341)
      | c_Fun_Obij__betw(X33346,X33343,X33340,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33346,tc_HOL_Obool)),X33345),X33344),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33343,tc_HOL_Obool)),X33342),X33341)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__Disj__Un])]) ).

fof(i_0_6782,plain,
    ! [X23990,X23991] :
      ( ( 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)),X23991),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)),X23990),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)),X23991),X23990)),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)),X23991),X23990)),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)),X23991),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)),X23990),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_6783,plain,
    ! [X32719,X32720,X32721,X32722] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk489_4(X32719,X32720,X32721,X32722)),X32720))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk488_4(X32719,X32720,X32721,X32722)),X32720))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk490_4(X32719,X32720,X32721,X32722)),X32720))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk488_4(X32719,X32720,X32721,X32722)),X32720))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( esk489_4(X32719,X32720,X32721,X32722) != esk490_4(X32719,X32720,X32721,X32722)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk488_4(X32719,X32720,X32721,X32722)),X32720))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hBOOL(hAPP(hAPP(c_member(X32721),esk491_4(X32719,X32720,X32721,X32722)),esk489_4(X32719,X32720,X32721,X32722)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk488_4(X32719,X32720,X32721,X32722)),X32720))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hBOOL(hAPP(hAPP(c_member(X32721),esk491_4(X32719,X32720,X32721,X32722)),esk490_4(X32719,X32720,X32721,X32722)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk488_4(X32719,X32720,X32721,X32722)),X32720))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hAPP(X32719,esk491_4(X32719,X32720,X32721,X32722)) != c_Groups_Ozero__class_Ozero(X32722)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk488_4(X32719,X32720,X32721,X32722)),X32720))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk489_4(X32719,X32720,X32721,X32722)),X32720))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32721),esk488_4(X32719,X32720,X32721,X32722)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X32721,tc_HOL_Obool)),esk490_4(X32719,X32720,X32721,X32722)),X32720))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32721),esk488_4(X32719,X32720,X32721,X32722)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( esk489_4(X32719,X32720,X32721,X32722) != esk490_4(X32719,X32720,X32721,X32722)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32721),esk488_4(X32719,X32720,X32721,X32722)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hBOOL(hAPP(hAPP(c_member(X32721),esk491_4(X32719,X32720,X32721,X32722)),esk489_4(X32719,X32720,X32721,X32722)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32721),esk488_4(X32719,X32720,X32721,X32722)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hBOOL(hAPP(hAPP(c_member(X32721),esk491_4(X32719,X32720,X32721,X32722)),esk490_4(X32719,X32720,X32721,X32722)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32721),esk488_4(X32719,X32720,X32721,X32722)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) )
      & ( hAPP(X32719,esk491_4(X32719,X32720,X32721,X32722)) != c_Groups_Ozero__class_Ozero(X32722)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719),c_Complete__Lattice_OSup__class_OSup(tc_fun(X32721,tc_HOL_Obool),X32720)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(X32721,tc_HOL_Obool),X32722),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X32721,X32722),X32719)),X32720)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32721),esk488_4(X32719,X32720,X32721,X32722)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X32721,tc_HOL_Obool)),X32720))
        | ~ class_Groups_Ocomm__monoid__add(X32722) ) ),
    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_6784,plain,
    ! [X17880,X17881,X17882,X17883] : c_Nitpick_Ofold__graph_H(X17883,X17882,X17881,X17880,c_Orderings_Obot__class_Obot(tc_fun(X17883,tc_HOL_Obool)),X17880),
    inference(variable_rename,[status(thm)],[fact_fold__graph_H_Oequations_I1_J]) ).

fof(i_0_6785,plain,
    ! [X17876,X17877,X17878,X17879] : c_Nitpick_Ofold__graph_H(X17879,X17878,X17877,X17876,c_Orderings_Obot__class_Obot(tc_fun(X17879,tc_HOL_Obool)),X17876),
    inference(variable_rename,[status(thm)],[fact_fold__graph_H_Ointros_I1_J]) ).

fof(i_0_6786,plain,
    ! [X18842,X18843,X18844,X18845,X18846] :
      ( ( c_Fun_Oinj__on(X18846,X18845,X18844,X18842)
        | ~ c_Fun_Oinj__on(X18846,X18845,X18844,hAPP(hAPP(c_Set_Oinsert(X18846),X18843),X18842)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18845),hAPP(X18844,X18843)),hAPP(c_Set_Oimage(X18846,X18845,X18844),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18846,tc_HOL_Obool)),X18842),hAPP(hAPP(c_Set_Oinsert(X18846),X18843),c_Orderings_Obot__class_Obot(tc_fun(X18846,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(X18846,X18845,X18844,hAPP(hAPP(c_Set_Oinsert(X18846),X18843),X18842)) )
      & ( ~ c_Fun_Oinj__on(X18846,X18845,X18844,X18842)
        | hBOOL(hAPP(hAPP(c_member(X18845),hAPP(X18844,X18843)),hAPP(c_Set_Oimage(X18846,X18845,X18844),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18846,tc_HOL_Obool)),X18842),hAPP(hAPP(c_Set_Oinsert(X18846),X18843),c_Orderings_Obot__class_Obot(tc_fun(X18846,tc_HOL_Obool)))))))
        | c_Fun_Oinj__on(X18846,X18845,X18844,hAPP(hAPP(c_Set_Oinsert(X18846),X18843),X18842)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5439])])]) ).

cnf(i_0_6787,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_5440]) ).

fof(i_0_6788,plain,
    ! [X27796,X27797] : c_Product__Type_Omap__pair(X27797,X27797,X27796,X27796,c_Fun_Oid(X27797),c_Fun_Oid(X27796)) = c_Fun_Oid(tc_prod(X27797,X27796)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Oid]) ).

fof(i_0_6789,plain,
    ! [X27798,X27799] : c_Product__Type_Omap__pair(X27799,X27799,X27798,X27798,c_COMBI(X27799),c_COMBI(X27798)) = c_Fun_Oid(tc_prod(X27799,X27798)),
    inference(variable_rename,[status(thm)],[fact_map__pair_Oidentity]) ).

cnf(i_0_6790,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_5441]) ).

fof(i_0_6791,plain,
    ! [X19813,X19814,X19815,X19816,X19817] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19817,X19816,X19815)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19817),X19814))
      | hBOOL(hAPP(c_Finite__Set_Ofold__graph(X19817,X19816,X19815,X19813,X19814),hAPP(hAPP(c_Finite__Set_Ofold(X19817,X19816,X19815),X19813),X19814))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__graph__fold])]) ).

fof(i_0_6792,plain,
    ! [X33301,X33302,X33303,X33304,X33305,X33306,X33307,X33308] :
      ( ~ c_Fun_Obij__betw(X33308,X33307,X33306,X33305,X33304)
      | ~ c_Fun_Obij__betw(X33307,X33303,X33302,X33304,X33301)
      | c_Fun_Obij__betw(X33308,X33303,hAPP(c_Fun_Ocomp(X33307,X33303,X33308,X33302),X33306),X33305,X33301) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__trans])]) ).

cnf(i_0_6793,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_6794,plain,
    ! [X17499,X17500,X17501] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17501),X17500))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17501),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17501,tc_HOL_Obool)),X17500),hAPP(hAPP(c_Set_Oinsert(X17501),X17499),c_Orderings_Obot__class_Obot(tc_fun(X17501,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X17501),X17500))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff1__le])]) ).

fof(i_0_6795,plain,
    ! [X27897,X27898,X27899,X27900,X27901,X27902,X27903] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27903,X27902),tc_HOL_Obool)),X27901),X27900))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27902,X27899),tc_HOL_Obool)),X27898),X27897))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27903,X27899),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27903,X27902,X27899),X27901),X27898)),hAPP(hAPP(c_Relation_Orel__comp(X27903,X27902,X27899),X27900),X27897))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__comp__mono])]) ).

fof(i_0_6796,plain,
    ! [X24736,X24737,X24738,X24739,X24740] :
      ( ~ c_Equiv__Relations_Oequiv(X24740,X24739,X24738)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24740,X24740)),hAPP(hAPP(c_Product__Type_OPair(X24740,X24740),X24737),X24736)),X24738))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24740,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24740,X24740,X24738),hAPP(hAPP(c_Set_Oinsert(X24740),X24737),c_Orderings_Obot__class_Obot(tc_fun(X24740,tc_HOL_Obool))))),hAPP(c_Relation_OImage(X24740,X24740,X24738),hAPP(hAPP(c_Set_Oinsert(X24740),X24736),c_Orderings_Obot__class_Obot(tc_fun(X24740,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__subset])]) ).

fof(i_0_6797,plain,
    ! [X19142,X19143,X19144,X19145,X19146,X19147] :
      ( ~ c_Fun_Oinj__on(X19147,X19146,X19145,X19144)
      | ~ hBOOL(hAPP(hAPP(c_member(X19146),X19143),hAPP(c_Set_Oimage(X19147,X19146,X19145),X19144)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19147,tc_HOL_Obool)),X19144),X19142))
      | hBOOL(hAPP(hAPP(c_member(X19147),hAPP(c_Fun_Othe__inv__into(X19147,X19146,X19144,X19145),X19143)),X19142)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__into])]) ).

fof(i_0_6798,plain,
    ! [X26198,X26199,X26200,X26201,X26202] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26202),hAPP(c_Set_Oimage(X26201,X26202,X26200),c_Orderings_Otop__class_Otop(tc_fun(X26201,tc_HOL_Obool)))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26199),hAPP(c_Set_Oimage(X26201,X26199,hAPP(hAPP(c_COMBB(X26202,X26199,X26201),X26198),X26200)),c_Orderings_Otop__class_Otop(tc_fun(X26201,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__range__imageI])]) ).

fof(i_0_6799,plain,
    ! [X26951,X26952,X26953] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26953,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26953,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26953,tc_HOL_Obool),X26952)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26953,tc_HOL_Obool),X26951))),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26953,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X26953,tc_HOL_Obool),tc_HOL_Obool)),X26952),X26951)))),
    inference(variable_rename,[status(thm)],[fact_Inter__Un__subset]) ).

fof(i_0_6800,plain,
    ! [X29377,X29378,X29379] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29379,X29379),tc_HOL_Obool)),X29378),hAPP(hAPP(c_Product__Type_OSigma(X29379,X29379),X29377),hAPP(c_COMBK(tc_fun(X29379,tc_HOL_Obool),X29379),X29377))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29379),tc_List_Olist(X29379)),tc_HOL_Obool)),c_List_Olistrel(X29379,X29378)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(X29379),tc_List_Olist(X29379)),c_List_Olists(X29379,X29377)),hAPP(c_COMBK(tc_fun(tc_List_Olist(X29379),tc_HOL_Obool),tc_List_Olist(X29379)),c_List_Olists(X29379,X29377))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__subset])]) ).

fof(i_0_6801,plain,
    ! [X19419,X19420,X19421,X19422,X19423,X19424,X19425] :
      ( ~ class_Groups_Oab__semigroup__mult(X19425)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19424),X19423))
      | ~ c_Fun_Oinj__on(X19424,X19422,X19421,X19423)
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19425,X19422,c_Groups_Otimes__class_Otimes(X19425)),X19420),X19419),hAPP(c_Set_Oimage(X19424,X19422,X19421),X19423)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19425,X19424,c_Groups_Otimes__class_Otimes(X19425)),hAPP(c_Fun_Ocomp(X19422,X19425,X19424,X19420),X19421)),X19419),X19423) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__image__reindex])]) ).

fof(i_0_6802,plain,
    ! [X21017,X21018,X21019,X21020] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21020))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21019))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21019),X21018))
      | 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),X21018),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21017,X21020))),X21019)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21018),X21020))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux4])]) ).

fof(i_0_6803,plain,
    ! [X28459,X28460,X28461,X28462] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28462),esk329_4(X28459,X28460,X28461,X28462)),X28461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28462),hAPP(hAPP(c_Finite__Set_Ofold(X28462,X28462,c_Lattices_Osemilattice__sup__class_Osup(X28462)),X28459),X28461)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X28462),X28460),X28459)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28462),X28461))
        | ~ class_Lattices_Osemilattice__sup(X28462) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28462),esk329_4(X28459,X28460,X28461,X28462)),X28460))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28462),hAPP(hAPP(c_Finite__Set_Ofold(X28462,X28462,c_Lattices_Osemilattice__sup__class_Osup(X28462)),X28459),X28461)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X28462),X28460),X28459)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28462),X28461))
        | ~ class_Lattices_Osemilattice__sup(X28462) ) ),
    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_6804,plain,
    ! [X28428,X28429,X28430,X28431] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28431),esk322_4(X28428,X28429,X28430,X28431)),X28430))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28431),hAPP(hAPP(c_Finite__Set_Ofold(X28431,X28431,c_Orderings_Oord__class_Omax(X28431)),X28428),X28430)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X28431),X28429),X28428)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28431),X28430))
        | ~ class_Orderings_Olinorder(X28431) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28431),esk322_4(X28428,X28429,X28430,X28431)),X28429))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28431),hAPP(hAPP(c_Finite__Set_Ofold(X28431,X28431,c_Orderings_Oord__class_Omax(X28431)),X28428),X28430)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X28431),X28429),X28428)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28431),X28430))
        | ~ class_Orderings_Olinorder(X28431) ) ),
    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_6805,plain,
    ! [X33333,X33334,X33335,X33336,X33337,X33338,X33339] :
      ( ~ c_Fun_Obij__betw(X33339,X33338,X33337,X33336,X33335)
      | ~ c_Fun_Obij__betw(X33339,X33338,X33337,X33334,X33333)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X33338,tc_HOL_Obool)),X33335),X33333) != c_Orderings_Obot__class_Obot(tc_fun(X33338,tc_HOL_Obool))
      | c_Fun_Obij__betw(X33339,X33338,X33337,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33339,tc_HOL_Obool)),X33336),X33334),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X33338,tc_HOL_Obool)),X33335),X33333)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__combine])]) ).

cnf(i_0_6806,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_5442]) ).

fof(i_0_6807,plain,
    ! [X17473,X17474,X17475,X17476] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17476),X17474),X17475))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),c_Orderings_Obot__class_Obot(tc_fun(X17476,tc_HOL_Obool))))),X17473))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),X17473))) )
      & ( hBOOL(hAPP(hAPP(c_member(X17476),X17474),X17475))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),X17473))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),X17473))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17476),X17474),X17475))
        | hBOOL(hAPP(hAPP(c_member(X17476),X17474),X17475))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),X17473))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),X17473))
        | hBOOL(hAPP(hAPP(c_member(X17476),X17474),X17475))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),X17473))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17476),X17474),X17475))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),c_Orderings_Obot__class_Obot(tc_fun(X17476,tc_HOL_Obool))))),X17473))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),X17473))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),X17473))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),c_Orderings_Obot__class_Obot(tc_fun(X17476,tc_HOL_Obool))))),X17473))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17476,tc_HOL_Obool)),X17475),hAPP(hAPP(c_Set_Oinsert(X17476),X17474),X17473))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5443])])]) ).

fof(i_0_6808,plain,
    ! [X29296,X29297,X29298,X29299,X29300] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29300,X29300)),hAPP(hAPP(c_Product__Type_OPair(X29300,X29300),X29299),X29298)),X29297))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29300),tc_List_Olist(X29300))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29300),tc_List_Olist(X29300)),hAPP(hAPP(c_List_Olist_OCons(X29300),X29299),X29296)),hAPP(hAPP(c_List_Olist_OCons(X29300),X29298),X29296))),c_List_Olistrel1(X29300,X29297))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I1])]) ).

cnf(i_0_6809,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_5444]) ).

cnf(i_0_6810,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_5445]) ).

fof(i_0_6811,plain,
    ! [X31773,X31774,X31775] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31775),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31775))),X31774)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31773),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31775))),X31774)))
      | hAPP(hAPP(c_List_Omap(tc_List_Olist(X31775),X31775),hAPP(hAPP(c_COMBC(tc_List_Olist(X31775),tc_Nat_Onat,X31775),c_List_Onth(X31775)),X31773)),hAPP(c_List_Ofilter(tc_List_Olist(X31775),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31775)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31773)),c_Nat_Osize__class_Osize(tc_List_Olist(X31775)))),c_List_Otranspose(X31775,X31774))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(X31775)),X31774),X31773) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column])]) ).

fof(i_0_6812,plain,
    ! [X28395,X28396,X28397] : c_Hilbert__Choice_OEps(tc_prod(X28397,X28396),X28395) = c_Hilbert__Choice_OEps(tc_prod(X28397,X28396),hAPP(c_Product__Type_Oprod_Oprod__case(X28397,X28396,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X28396,tc_prod(X28397,X28396)),tc_fun(X28396,tc_HOL_Obool),X28397),hAPP(c_COMBB(tc_prod(X28397,X28396),tc_HOL_Obool,X28396),X28395)),c_Product__Type_OPair(X28397,X28396)))),
    inference(variable_rename,[status(thm)],[fact_split__paired__Eps]) ).

fof(i_0_6813,plain,
    ! [X22165,X22166,X22167] : c_HOL_OThe(tc_prod(X22167,X22166),X22165) = c_HOL_OThe(tc_prod(X22167,X22166),hAPP(c_Product__Type_Oprod_Oprod__case(X22167,X22166,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X22166,tc_prod(X22167,X22166)),tc_fun(X22166,tc_HOL_Obool),X22167),hAPP(c_COMBB(tc_prod(X22167,X22166),tc_HOL_Obool,X22166),X22165)),c_Product__Type_OPair(X22167,X22166)))),
    inference(variable_rename,[status(thm)],[fact_split__paired__The]) ).

fof(i_0_6814,plain,
    ! [X29018,X29019,X29020,X29021,X29022,X29023,X29024,X29025] :
      ( ( ~ c_Relation_Ototal__on(X29020,X29019,X29018)
        | ~ hBOOL(hAPP(hAPP(c_member(X29020),X29021),X29019))
        | ~ hBOOL(hAPP(hAPP(c_member(X29020),X29022),X29019))
        | X29021 = X29022
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29020,X29020)),hAPP(hAPP(c_Product__Type_OPair(X29020,X29020),X29021),X29022)),X29018))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29020,X29020)),hAPP(hAPP(c_Product__Type_OPair(X29020,X29020),X29022),X29021)),X29018)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29025),esk340_3(X29023,X29024,X29025)),X29024))
        | c_Relation_Ototal__on(X29025,X29024,X29023) )
      & ( hBOOL(hAPP(hAPP(c_member(X29025),esk341_3(X29023,X29024,X29025)),X29024))
        | c_Relation_Ototal__on(X29025,X29024,X29023) )
      & ( esk340_3(X29023,X29024,X29025) != esk341_3(X29023,X29024,X29025)
        | c_Relation_Ototal__on(X29025,X29024,X29023) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29025,X29025)),hAPP(hAPP(c_Product__Type_OPair(X29025,X29025),esk340_3(X29023,X29024,X29025)),esk341_3(X29023,X29024,X29025))),X29023))
        | c_Relation_Ototal__on(X29025,X29024,X29023) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29025,X29025)),hAPP(hAPP(c_Product__Type_OPair(X29025,X29025),esk341_3(X29023,X29024,X29025)),esk340_3(X29023,X29024,X29025))),X29023))
        | c_Relation_Ototal__on(X29025,X29024,X29023) ) ),
    inference(distribute,[status(thm)],[inference(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_6815,plain,
    ! [X21368,X21369,X21370,X21371] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21371))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21370),X21369))
      | 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),X21369),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21368,X21371))),X21370)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21369),X21371))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__lemma])]) ).

fof(i_0_6816,plain,
    ! [X28917,X28918,X28919,X28920,X28921] :
      ( ~ c_Relation_Osingle__valued(X28921,X28921,X28920)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28921,X28921)),hAPP(hAPP(c_Product__Type_OPair(X28921,X28921),X28919),X28918)),c_Transitive__Closure_Ortrancl(X28921,X28920)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28921,X28921)),hAPP(hAPP(c_Product__Type_OPair(X28921,X28921),X28919),X28917)),c_Transitive__Closure_Ortrancl(X28921,X28920)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28921,X28921)),hAPP(hAPP(c_Product__Type_OPair(X28921,X28921),X28918),X28917)),c_Transitive__Closure_Ortrancl(X28921,X28920)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28921,X28921)),hAPP(hAPP(c_Product__Type_OPair(X28921,X28921),X28917),X28918)),c_Transitive__Closure_Ortrancl(X28921,X28920))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__confluent])]) ).

fof(i_0_6817,plain,
    ! [X28048,X28049,X28050] :
      ( ~ c_Wellfounded_Owf(X28050,X28049)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28050,X28050),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28050,X28050,X28050),X28049),X28048)),X28049))
      | c_FunDef_Oreduction__pair(X28050,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(X28050,X28050),tc_HOL_Obool),tc_fun(tc_prod(X28050,X28050),tc_HOL_Obool)),X28049),X28048)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reduction__pairI])]) ).

fof(i_0_6818,plain,
    ! [X21009,X21010,X21011,X21012] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21012))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21011),X21010))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21010),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),X21011),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21009,X21012))),X21010)),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_6819,plain,
    ! [X30967,X30968] : c_Random_Oselect(X30968,X30967) = 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(X30968,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(X30968)),X30967)))),hAPP(hAPP(c_COMBB(X30968,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(X30968,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(X30968,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X30968,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(X30968),X30967)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[fact_select__def]) ).

fof(i_0_6820,plain,
    ! [X22048,X22049] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22049),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | c_Nitpick_Onorm__frac(X22048,X22049) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22048),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22049)) )
      & ( X22048 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22048,X22049) = 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),X22049),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X22049 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22048,X22049) = 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),X22049),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X22048 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X22049 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Nitpick_Onorm__frac(X22048,X22049) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X22048),X22049)),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),X22048))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22049)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22049),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5446])])]) ).

fof(i_0_6821,plain,
    ! [X24212,X24213,X24214] :
      ( ~ class_Rings_Oring__1(X24214)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24214),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),X24213),X24212)),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(X24214),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24214),X24213)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24214),X24212)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int])]) ).

cnf(i_0_6822,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk439_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_5447]) ).

cnf(i_0_6823,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_5448]) ).

cnf(i_0_6824,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_5449]) ).

fof(i_0_6825,plain,
    ! [X17469,X17470,X17471,X17472] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17472,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17472,tc_HOL_Obool)),X17471),hAPP(hAPP(c_Set_Oinsert(X17472),X17470),c_Orderings_Obot__class_Obot(tc_fun(X17472,tc_HOL_Obool))))),X17469))
      | ~ hBOOL(hAPP(hAPP(c_member(X17472),X17470),X17471))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17472,tc_HOL_Obool)),X17471),hAPP(hAPP(c_Set_Oinsert(X17472),X17470),X17469))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__single__insert])]) ).

fof(i_0_6826,plain,
    ! [X24231,X24232] : 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),X24232),X24231)),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),X24232),X24231),
    inference(variable_rename,[status(thm)],[fact_nat]) ).

cnf(i_0_6827,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_5450]) ).

cnf(i_0_6828,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_5451]) ).

cnf(i_0_6829,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_5452]) ).

fof(i_0_6830,plain,
    ! [X25494,X25495,X25496,X25497,X25498] :
      ( ( c_Fun_Oinj__on(X25498,X25497,X25496,X25495)
        | ~ c_Fun_Oinj__on(X25498,X25497,X25496,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25498,tc_HOL_Obool)),X25495),X25494)) )
      & ( c_Fun_Oinj__on(X25498,X25497,X25496,X25494)
        | ~ c_Fun_Oinj__on(X25498,X25497,X25496,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25498,tc_HOL_Obool)),X25495),X25494)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25497,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25498,X25497,X25496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25498,tc_HOL_Obool)),X25495),X25494))),hAPP(c_Set_Oimage(X25498,X25497,X25496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25498,tc_HOL_Obool)),X25494),X25495))) = c_Orderings_Obot__class_Obot(tc_fun(X25497,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(X25498,X25497,X25496,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25498,tc_HOL_Obool)),X25495),X25494)) )
      & ( ~ c_Fun_Oinj__on(X25498,X25497,X25496,X25495)
        | ~ c_Fun_Oinj__on(X25498,X25497,X25496,X25494)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25497,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25498,X25497,X25496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25498,tc_HOL_Obool)),X25495),X25494))),hAPP(c_Set_Oimage(X25498,X25497,X25496),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25498,tc_HOL_Obool)),X25494),X25495))) != c_Orderings_Obot__class_Obot(tc_fun(X25497,tc_HOL_Obool))
        | c_Fun_Oinj__on(X25498,X25497,X25496,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25498,tc_HOL_Obool)),X25495),X25494)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un])])]) ).

fof(i_0_6831,plain,
    ! [X22445,X22446,X22447] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22447,tc_HOL_Obool)),X22446),X22445))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22447,tc_HOL_Obool),tc_fun(X22447,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22447,tc_HOL_Obool),tc_fun(X22447,tc_HOL_Obool)),X22446),X22445)),c_Wellfounded_Ofinite__psubset(X22447))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22447),X22445))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22447,tc_HOL_Obool),tc_fun(X22447,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22447,tc_HOL_Obool),tc_fun(X22447,tc_HOL_Obool)),X22446),X22445)),c_Wellfounded_Ofinite__psubset(X22447))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X22447,tc_HOL_Obool)),X22446),X22445))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22447),X22445))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X22447,tc_HOL_Obool),tc_fun(X22447,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X22447,tc_HOL_Obool),tc_fun(X22447,tc_HOL_Obool)),X22446),X22445)),c_Wellfounded_Ofinite__psubset(X22447))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__finite__psubset])])]) ).

fof(i_0_6832,plain,
    ! [X28207,X28208,X28209,X28210] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28210),X28209),hAPP(c_Relation_ODomain(X28210,X28208),X28207)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28210,X28208)),hAPP(hAPP(c_Product__Type_OPair(X28210,X28208),X28209),esk294_4(X28207,X28208,X28209,X28210))),X28207)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5453])])]) ).

fof(i_0_6833,plain,
    ! [X28162,X28163,X28164,X28165,X28167,X28168,X28169,X28170,X28171] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X28165),X28164),hAPP(c_Relation_ODomain(X28165,X28163),X28162)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28165,X28163)),hAPP(hAPP(c_Product__Type_OPair(X28165,X28163),X28164),esk293_4(X28162,X28163,X28164,X28165))),X28162)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28170,X28168)),hAPP(hAPP(c_Product__Type_OPair(X28170,X28168),X28169),X28171)),X28167))
        | hBOOL(hAPP(hAPP(c_member(X28170),X28169),hAPP(c_Relation_ODomain(X28170,X28168),X28167))) ) ),
    inference(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_6834,plain,
    ! [X23971,X23972,X23973] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X23973,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X23973,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X23973),X23972)),hAPP(c_Set_OPow(X23973),X23971))),hAPP(c_Set_OPow(X23973),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23973,tc_HOL_Obool)),X23972),X23971)))),
    inference(variable_rename,[status(thm)],[fact_Un__Pow__subset]) ).

fof(i_0_6835,plain,
    ! [X33188,X33189,X33190,X33191,X33192] :
      ( ~ c_Fun_Oinj__on(X33192,X33191,X33190,c_Orderings_Otop__class_Otop(tc_fun(X33192,tc_HOL_Obool)))
      | hAPP(c_Fun_Ocomp(X33191,X33189,X33192,hAPP(c_Fun_Ocomp(X33192,X33189,X33191,X33188),c_Hilbert__Choice_Oinv__into(X33192,X33191,c_Orderings_Otop__class_Otop(tc_fun(X33192,tc_HOL_Obool)),X33190))),X33190) = X33188 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__inv__o__cancel])]) ).

fof(i_0_6836,plain,
    ! [X18926,X18927,X18928,X18929,X18930] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18930),X18929))
      | 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),X18929),X18928)),X18927)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18930),X18928)),X18926)) = 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),X18929),X18930)),X18928)),X18927)),X18926) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1])]) ).

cnf(i_0_6837,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_5454]) ).

fof(i_0_6838,plain,
    ! [X30942,X30943,X30944] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30944),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30943),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X30943)),X30942))))
      | hBOOL(hAPP(hAPP(c_member(X30943),hAPP(c_Random_Opick(X30943,X30942),X30944)),hAPP(c_List_Oset(X30943),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,X30943),X30943),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X30943)),X30942)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__member])]) ).

fof(i_0_6839,plain,
    ! [X33649,X33650,X33651,X33652] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33650),X33652))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33652),X33651))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33652,X33651)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33650,X33649))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33651),X33649))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33652),X33651))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33652,X33651)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33650,X33649))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33652),X33651))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33652,X33651)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33650,X33649))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33650),X33652))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33651),X33649))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33652,X33651)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33650,X33649))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5455])])]) ).

fof(i_0_6840,plain,
    ! [X27867,X27868,X27869,X27870,X27871,X27872,X27873,X27874] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27874,X27873)),hAPP(hAPP(c_Product__Type_OPair(X27874,X27873),X27872),X27871)),X27870))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27873,X27869)),hAPP(hAPP(c_Product__Type_OPair(X27873,X27869),X27871),X27868)),X27867))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27874,X27869)),hAPP(hAPP(c_Product__Type_OPair(X27874,X27869),X27872),X27868)),hAPP(hAPP(c_Relation_Orel__comp(X27874,X27873,X27869),X27870),X27867))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__compI])]) ).

fof(i_0_6841,plain,
    ! [X31702,X31703,X31704,X31705,X31706] :
      ( ~ class_Orderings_Olinorder(X31706)
      | ~ c_List_Olinorder__class_Osorted(X31706,hAPP(hAPP(c_List_Omap(X31705,X31706),X31704),X31703))
      | c_List_Olinorder__class_Osorted(X31706,hAPP(hAPP(c_List_Omap(X31705,X31706),X31704),c_List_Olinorder__class_Oinsort__insert__key(X31705,X31706,X31704,X31702,X31703))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert__key])]) ).

fof(i_0_6842,plain,
    ! [X31116,X31117,X31118,X31119,X31120,X31121,X31122] :
      ( ( c_List_Olist__all2(X31122,X31120,X31118,X31121,X31119)
        | ~ c_List_Olist__all2(X31122,X31120,X31118,hAPP(hAPP(c_List_Oappend(X31122),X31121),X31117),hAPP(hAPP(c_List_Oappend(X31120),X31119),X31116))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31122)),X31121) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31120)),X31119) )
      & ( c_List_Olist__all2(X31122,X31120,X31118,X31117,X31116)
        | ~ c_List_Olist__all2(X31122,X31120,X31118,hAPP(hAPP(c_List_Oappend(X31122),X31121),X31117),hAPP(hAPP(c_List_Oappend(X31120),X31119),X31116))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31122)),X31121) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31120)),X31119) )
      & ( ~ c_List_Olist__all2(X31122,X31120,X31118,X31121,X31119)
        | ~ c_List_Olist__all2(X31122,X31120,X31118,X31117,X31116)
        | c_List_Olist__all2(X31122,X31120,X31118,hAPP(hAPP(c_List_Oappend(X31122),X31121),X31117),hAPP(hAPP(c_List_Oappend(X31120),X31119),X31116))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31122)),X31121) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31120)),X31119) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__append])])]) ).

fof(i_0_6843,plain,
    ! [X23252,X23253,X23254,X23255,X23256,X23259,X23260,X23261,X23262,X23263,X23264] :
      ( ( hBOOL(hAPP(hAPP(c_member(X23255),esk111_4(X23252,X23253,X23254,X23255)),X23253))
        | hBOOL(hAPP(hAPP(c_member(X23255),esk110_4(X23252,X23253,X23254,X23255)),X23254))
        | ~ hBOOL(hAPP(hAPP(c_member(X23255),X23256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23255,tc_HOL_Obool)),X23254),X23253)))
        | ~ hBOOL(hAPP(X23252,X23256)) )
      & ( hBOOL(hAPP(X23252,esk111_4(X23252,X23253,X23254,X23255)))
        | hBOOL(hAPP(hAPP(c_member(X23255),esk110_4(X23252,X23253,X23254,X23255)),X23254))
        | ~ hBOOL(hAPP(hAPP(c_member(X23255),X23256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23255,tc_HOL_Obool)),X23254),X23253)))
        | ~ hBOOL(hAPP(X23252,X23256)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23255),esk111_4(X23252,X23253,X23254,X23255)),X23253))
        | hBOOL(hAPP(X23252,esk110_4(X23252,X23253,X23254,X23255)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23255),X23256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23255,tc_HOL_Obool)),X23254),X23253)))
        | ~ hBOOL(hAPP(X23252,X23256)) )
      & ( hBOOL(hAPP(X23252,esk111_4(X23252,X23253,X23254,X23255)))
        | hBOOL(hAPP(X23252,esk110_4(X23252,X23253,X23254,X23255)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23255),X23256),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23255,tc_HOL_Obool)),X23254),X23253)))
        | ~ hBOOL(hAPP(X23252,X23256)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23262),esk112_4(X23259,X23260,X23261,X23262)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23262,tc_HOL_Obool)),X23261),X23260)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23262),X23263),X23261))
        | ~ hBOOL(hAPP(X23259,X23263)) )
      & ( hBOOL(hAPP(X23259,esk112_4(X23259,X23260,X23261,X23262)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23262),X23263),X23261))
        | ~ hBOOL(hAPP(X23259,X23263)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23262),esk112_4(X23259,X23260,X23261,X23262)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23262,tc_HOL_Obool)),X23261),X23260)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23262),X23264),X23260))
        | ~ hBOOL(hAPP(X23259,X23264)) )
      & ( hBOOL(hAPP(X23259,esk112_4(X23259,X23260,X23261,X23262)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23262),X23264),X23260))
        | ~ hBOOL(hAPP(X23259,X23264)) ) ),
    inference(distribute,[status(thm)],[inference(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_6844,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_5456]) ).

fof(i_0_6845,plain,
    ! [X23238,X23239,X23240,X23241,X23243,X23244,X23245,X23246,X23247,X23248,X23251] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23241),X23243),X23240))
        | hBOOL(hAPP(X23238,X23243))
        | hBOOL(hAPP(hAPP(c_member(X23241),esk107_4(X23238,X23239,X23240,X23241)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23241,tc_HOL_Obool)),X23240),X23239))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23241),X23244),X23239))
        | hBOOL(hAPP(X23238,X23244))
        | hBOOL(hAPP(hAPP(c_member(X23241),esk107_4(X23238,X23239,X23240,X23241)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23241,tc_HOL_Obool)),X23240),X23239))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23241),X23243),X23240))
        | hBOOL(hAPP(X23238,X23243))
        | ~ hBOOL(hAPP(X23238,esk107_4(X23238,X23239,X23240,X23241))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23241),X23244),X23239))
        | hBOOL(hAPP(X23238,X23244))
        | ~ hBOOL(hAPP(X23238,esk107_4(X23238,X23239,X23240,X23241))) )
      & ( hBOOL(hAPP(hAPP(c_member(X23248),esk109_4(X23245,X23246,X23247,X23248)),X23246))
        | hBOOL(hAPP(hAPP(c_member(X23248),esk108_4(X23245,X23246,X23247,X23248)),X23247))
        | ~ hBOOL(hAPP(hAPP(c_member(X23248),X23251),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23248,tc_HOL_Obool)),X23247),X23246)))
        | hBOOL(hAPP(X23245,X23251)) )
      & ( ~ hBOOL(hAPP(X23245,esk109_4(X23245,X23246,X23247,X23248)))
        | hBOOL(hAPP(hAPP(c_member(X23248),esk108_4(X23245,X23246,X23247,X23248)),X23247))
        | ~ hBOOL(hAPP(hAPP(c_member(X23248),X23251),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23248,tc_HOL_Obool)),X23247),X23246)))
        | hBOOL(hAPP(X23245,X23251)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23248),esk109_4(X23245,X23246,X23247,X23248)),X23246))
        | ~ hBOOL(hAPP(X23245,esk108_4(X23245,X23246,X23247,X23248)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23248),X23251),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23248,tc_HOL_Obool)),X23247),X23246)))
        | hBOOL(hAPP(X23245,X23251)) )
      & ( ~ hBOOL(hAPP(X23245,esk109_4(X23245,X23246,X23247,X23248)))
        | ~ hBOOL(hAPP(X23245,esk108_4(X23245,X23246,X23247,X23248)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23248),X23251),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23248,tc_HOL_Obool)),X23247),X23246)))
        | hBOOL(hAPP(X23245,X23251)) ) ),
    inference(distribute,[status(thm)],[inference(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_6846,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_5457]) ).

cnf(i_0_6847,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_5458]) ).

cnf(i_0_6848,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_5419]) ).

fof(i_0_6849,plain,
    ! [X26333,X26334,X26335,X26336,X26337,X26338,X26339,X26340] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26340,tc_fun(X26339,tc_fun(X26338,tc_HOL_Obool))),X26337),X26336),X26335),X26334))
      | ~ hBOOL(hAPP(hAPP(c_member(X26340),X26333),X26337))
      | hBOOL(hAPP(hAPP(hAPP(X26336,X26333),X26335),X26334)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF2__D])]) ).

fof(i_0_6850,plain,
    ! [X26325,X26326,X26327,X26328,X26329,X26330,X26331,X26332] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26332,tc_fun(X26331,tc_fun(X26330,tc_HOL_Obool))),X26329),X26328),X26327),X26326))
      | hBOOL(hAPP(hAPP(hAPP(X26328,X26325),X26327),X26326))
      | ~ hBOOL(hAPP(hAPP(c_member(X26332),X26325),X26329)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5459])]) ).

cnf(i_0_6851,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_5460]) ).

cnf(i_0_6852,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_5461]) ).

cnf(i_0_6853,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_5462]) ).

cnf(i_0_6854,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_5463]) ).

cnf(i_0_6855,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_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_5420]) ).

cnf(i_0_6856,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_5419]) ).

fof(i_0_6857,plain,
    ! [X31109,X31110,X31111,X31112,X31113,X31114,X31115] :
      ( ~ c_List_Olist__all2(X31115,X31114,X31113,X31112,X31111)
      | ~ c_List_Olist__all2(X31115,X31114,X31113,X31110,X31109)
      | c_List_Olist__all2(X31115,X31114,X31113,hAPP(hAPP(c_List_Oappend(X31115),X31112),X31110),hAPP(hAPP(c_List_Oappend(X31114),X31111),X31109)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__appendI])]) ).

cnf(i_0_6858,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_6859,plain,
    ! [X30873,X30874,X30875,X30876,X30877,X30878] :
      ( hBOOL(hAPP(hAPP(c_member(X30878),X30877),hAPP(c_List_Oset(X30878),X30876)))
      | hAPP(hAPP(c_List_Omap(X30878,X30875),c_Fun_Ofun__upd(X30878,X30875,X30874,X30877,X30873)),X30876) = hAPP(hAPP(c_List_Omap(X30878,X30875),X30874),X30876) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5464])]) ).

fof(i_0_6860,plain,
    ! [X19578,X19579,X19580,X19581,X19582,X19583,X19584] : hAPP(c_Fun_Ocomp(X19584,X19583,X19582,X19581),c_Fun_Ofun__upd(X19582,X19584,X19580,X19579,X19578)) = c_Fun_Ofun__upd(X19582,X19583,hAPP(c_Fun_Ocomp(X19584,X19583,X19582,X19581),X19580),X19579,hAPP(X19581,X19578)),
    inference(variable_rename,[status(thm)],[fact_fun__upd__comp]) ).

cnf(i_0_6861,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_6862,plain,
    ! [X27660,X27661,X27662,X27663] : hAPP(c_Set_Ovimage(X27663,X27662,X27661),X27660) = hAPP(c_Set_OCollect(X27663),hAPP(hAPP(c_COMBC(X27663,tc_fun(X27662,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(X27662,tc_fun(tc_fun(X27662,tc_HOL_Obool),tc_HOL_Obool),X27663),c_member(X27662)),X27661)),X27660)),
    inference(variable_rename,[status(thm)],[fact_vimage__def]) ).

fof(i_0_6863,plain,
    ! [X30348,X30349,X30350,X30351,X30352] : hAPP(hAPP(c_List_Ozip(X30352,X30351),X30350),hAPP(hAPP(c_List_Oappend(X30351),X30349),X30348)) = hAPP(hAPP(c_List_Oappend(tc_prod(X30352,X30351)),hAPP(hAPP(c_List_Ozip(X30352,X30351),hAPP(hAPP(c_List_Otake(X30352),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30351)),X30349)),X30350)),X30349)),hAPP(hAPP(c_List_Ozip(X30352,X30351),hAPP(hAPP(c_List_Odrop(X30352),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30351)),X30349)),X30350)),X30348)),
    inference(variable_rename,[status(thm)],[fact_zip__append2]) ).

fof(i_0_6864,plain,
    ! [X29286,X29287,X29288,X29289] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29289),tc_List_Olist(X29289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29289),tc_List_Olist(X29289)),X29288),X29287)),c_List_Olistrel1(X29289,hAPP(c_Relation_Oconverse(X29289,X29289),X29286))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29289),tc_List_Olist(X29289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29289),tc_List_Olist(X29289)),X29288),X29287)),hAPP(c_Relation_Oconverse(tc_List_Olist(X29289),tc_List_Olist(X29289)),c_List_Olistrel1(X29289,X29286)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29289),tc_List_Olist(X29289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29289),tc_List_Olist(X29289)),X29288),X29287)),hAPP(c_Relation_Oconverse(tc_List_Olist(X29289),tc_List_Olist(X29289)),c_List_Olistrel1(X29289,X29286))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29289),tc_List_Olist(X29289))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29289),tc_List_Olist(X29289)),X29288),X29287)),c_List_Olistrel1(X29289,hAPP(c_Relation_Oconverse(X29289,X29289),X29286)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__listrel1__converse])]) ).

fof(i_0_6865,plain,
    ! [X30018,X30019,X30020,X30021,X30022,X30024,X30025,X30026,X30027,X30028,X30029] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(X30022),X30021),esk400_5(X30018,X30019,X30020,X30021,X30022)) = X30019
        | X30019 = c_List_Olist_ONil(X30022)
        | hAPP(hAPP(c_List_Olist_OCons(X30022),X30021),X30020) != hAPP(hAPP(c_List_Oappend(X30022),X30019),X30018) )
      & ( X30020 = hAPP(hAPP(c_List_Oappend(X30022),esk400_5(X30018,X30019,X30020,X30021,X30022)),X30018)
        | X30019 = c_List_Olist_ONil(X30022)
        | hAPP(hAPP(c_List_Olist_OCons(X30022),X30021),X30020) != hAPP(hAPP(c_List_Oappend(X30022),X30019),X30018) )
      & ( hAPP(hAPP(c_List_Olist_OCons(X30022),X30021),esk400_5(X30018,X30019,X30020,X30021,X30022)) = X30019
        | hAPP(hAPP(c_List_Olist_OCons(X30022),X30021),X30020) = X30018
        | hAPP(hAPP(c_List_Olist_OCons(X30022),X30021),X30020) != hAPP(hAPP(c_List_Oappend(X30022),X30019),X30018) )
      & ( X30020 = hAPP(hAPP(c_List_Oappend(X30022),esk400_5(X30018,X30019,X30020,X30021,X30022)),X30018)
        | hAPP(hAPP(c_List_Olist_OCons(X30022),X30021),X30020) = X30018
        | hAPP(hAPP(c_List_Olist_OCons(X30022),X30021),X30020) != hAPP(hAPP(c_List_Oappend(X30022),X30019),X30018) )
      & ( X30025 != c_List_Olist_ONil(X30028)
        | hAPP(hAPP(c_List_Olist_OCons(X30028),X30027),X30026) != X30024
        | hAPP(hAPP(c_List_Olist_OCons(X30028),X30027),X30026) = hAPP(hAPP(c_List_Oappend(X30028),X30025),X30024) )
      & ( hAPP(hAPP(c_List_Olist_OCons(X30028),X30027),X30029) != X30025
        | X30026 != hAPP(hAPP(c_List_Oappend(X30028),X30029),X30024)
        | hAPP(hAPP(c_List_Olist_OCons(X30028),X30027),X30026) = hAPP(hAPP(c_List_Oappend(X30028),X30025),X30024) ) ),
    inference(distribute,[status(thm)],[inference(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_6866,plain,
    ! [X30006,X30007,X30008,X30009,X30010,X30012,X30013,X30014,X30015,X30016,X30017] :
      ( ( X30009 = hAPP(hAPP(c_List_Olist_OCons(X30010),X30007),esk399_5(X30006,X30007,X30008,X30009,X30010))
        | X30009 = c_List_Olist_ONil(X30010)
        | hAPP(hAPP(c_List_Oappend(X30010),X30009),X30008) != hAPP(hAPP(c_List_Olist_OCons(X30010),X30007),X30006) )
      & ( hAPP(hAPP(c_List_Oappend(X30010),esk399_5(X30006,X30007,X30008,X30009,X30010)),X30008) = X30006
        | X30009 = c_List_Olist_ONil(X30010)
        | hAPP(hAPP(c_List_Oappend(X30010),X30009),X30008) != hAPP(hAPP(c_List_Olist_OCons(X30010),X30007),X30006) )
      & ( X30009 = hAPP(hAPP(c_List_Olist_OCons(X30010),X30007),esk399_5(X30006,X30007,X30008,X30009,X30010))
        | X30008 = hAPP(hAPP(c_List_Olist_OCons(X30010),X30007),X30006)
        | hAPP(hAPP(c_List_Oappend(X30010),X30009),X30008) != hAPP(hAPP(c_List_Olist_OCons(X30010),X30007),X30006) )
      & ( hAPP(hAPP(c_List_Oappend(X30010),esk399_5(X30006,X30007,X30008,X30009,X30010)),X30008) = X30006
        | X30008 = hAPP(hAPP(c_List_Olist_OCons(X30010),X30007),X30006)
        | hAPP(hAPP(c_List_Oappend(X30010),X30009),X30008) != hAPP(hAPP(c_List_Olist_OCons(X30010),X30007),X30006) )
      & ( X30015 != c_List_Olist_ONil(X30016)
        | X30014 != hAPP(hAPP(c_List_Olist_OCons(X30016),X30013),X30012)
        | hAPP(hAPP(c_List_Oappend(X30016),X30015),X30014) = hAPP(hAPP(c_List_Olist_OCons(X30016),X30013),X30012) )
      & ( X30015 != hAPP(hAPP(c_List_Olist_OCons(X30016),X30013),X30017)
        | hAPP(hAPP(c_List_Oappend(X30016),X30017),X30014) != X30012
        | hAPP(hAPP(c_List_Oappend(X30016),X30015),X30014) = hAPP(hAPP(c_List_Olist_OCons(X30016),X30013),X30012) ) ),
    inference(distribute,[status(thm)],[inference(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_6867,plain,
    ! [X33148,X33149,X33150,X33151,X33152] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33152),X33151),hAPP(c_Set_Oimage(X33150,X33152,X33149),X33148)))
      | hBOOL(hAPP(hAPP(c_member(X33150),hAPP(c_Hilbert__Choice_Oinv__into(X33150,X33152,X33148,X33149),X33151)),X33148)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__into])]) ).

fof(i_0_6868,plain,
    ! [X23079,X23080] :
      ( ~ class_Orderings_Olinorder(X23080)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23080),X23079))
      | X23079 = c_Orderings_Obot__class_Obot(tc_fun(X23080,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X23080),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23080),esk99_2(X23079,X23080)),esk100_2(X23079,X23080))),hAPP(hAPP(c_Set_Oinsert(X23080),esk99_2(X23079,X23080)),hAPP(hAPP(c_Set_Oinsert(X23080),esk100_2(X23079,X23080)),c_Orderings_Obot__class_Obot(tc_fun(X23080,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X23080),c_Big__Operators_Olattice_OSup__fin(X23080,c_Orderings_Oord__class_Omax(X23080),X23079)),X23079)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oclosed])])]) ).

fof(i_0_6869,plain,
    ! [X21826,X21827] :
      ( ~ class_Orderings_Olinorder(X21827)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21827),X21826))
      | X21826 = c_Orderings_Obot__class_Obot(tc_fun(X21827,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X21827),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21827),esk79_2(X21826,X21827)),esk80_2(X21826,X21827))),hAPP(hAPP(c_Set_Oinsert(X21827),esk79_2(X21826,X21827)),hAPP(hAPP(c_Set_Oinsert(X21827),esk80_2(X21826,X21827)),c_Orderings_Obot__class_Obot(tc_fun(X21827,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X21827),c_Big__Operators_Olattice_OInf__fin(X21827,c_Orderings_Oord__class_Omin(X21827),X21826)),X21826)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oclosed])])]) ).

fof(i_0_6870,plain,
    ! [X27356,X27357,X27358,X27359] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27359),esk262_4(X27356,X27357,X27358,X27359)),X27358))
        | hAPP(c_Finite__Set_Ocard(tc_prod(X27359,X27357)),hAPP(hAPP(c_Product__Type_OSigma(X27359,X27357),X27358),X27356)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27359,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27357,tc_HOL_Obool),tc_Nat_Onat,X27359),c_Finite__Set_Ocard(X27357)),X27356)),X27358)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27359),X27358)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27357),hAPP(X27356,esk262_4(X27356,X27357,X27358,X27359))))
        | hAPP(c_Finite__Set_Ocard(tc_prod(X27359,X27357)),hAPP(hAPP(c_Product__Type_OSigma(X27359,X27357),X27358),X27356)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27359,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(X27357,tc_HOL_Obool),tc_Nat_Onat,X27359),c_Finite__Set_Ocard(X27357)),X27356)),X27358)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27359),X27358)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__SigmaI])])])]) ).

fof(i_0_6871,plain,
    ! [X18065,X18066,X18067,X18068] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18068,X18067,X18066,X18065,c_Orderings_Obot__class_Obot(tc_fun(X18068,tc_HOL_Obool))),X18065)),
    inference(variable_rename,[status(thm)],[fact_fold__graph_Oequations_I1_J]) ).

fof(i_0_6872,plain,
    ! [X18061,X18062,X18063,X18064] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X18064,X18063,X18062,X18061,c_Orderings_Obot__class_Obot(tc_fun(X18064,tc_HOL_Obool))),X18061)),
    inference(variable_rename,[status(thm)],[fact_fold__graph_OemptyI]) ).

fof(i_0_6873,plain,
    ! [X28159,X28160,X28161] :
      ( ~ c_Wellfounded_Owf(X28161,X28160)
      | ~ c_Wellfounded_Owf(X28161,X28159)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28161,X28161),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X28161,X28161,X28161),X28160),X28159)),X28160))
      | c_Wellfounded_Owf(X28161,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28161,X28161),tc_HOL_Obool)),X28160),X28159)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__union__compatible])]) ).

fof(i_0_6874,plain,
    ! [X19387,X19388] :
      ( ~ class_Groups_Oab__semigroup__mult(X19388)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19388),X19387))
      | X19387 = c_Orderings_Obot__class_Obot(tc_fun(X19388,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X19388),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19388),esk44_2(X19387,X19388)),esk45_2(X19387,X19388))),hAPP(hAPP(c_Set_Oinsert(X19388),esk44_2(X19387,X19388)),hAPP(hAPP(c_Set_Oinsert(X19388),esk45_2(X19387,X19388)),c_Orderings_Obot__class_Obot(tc_fun(X19388,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X19388),hAPP(c_Finite__Set_Ofold1(X19388,c_Groups_Otimes__class_Otimes(X19388)),X19387)),X19387)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__in])])]) ).

cnf(i_0_6875,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_5465]) ).

fof(i_0_6876,plain,
    ! [X19668,X19669,X19670,X19671,X19672] :
      ( ~ 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),X19672),X19671)),X19670)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19672),X19669)),X19668)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19670),X19672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19668),X19672))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19671),X19669)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma])]) ).

fof(i_0_6877,plain,
    ! [X19657,X19658,X19659,X19660,X19661] :
      ( ~ 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),X19661),X19660)),X19659)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19661),X19658)),X19657)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19657),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19661),X19657))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19661),X19659))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19658),X19660)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg])]) ).

fof(i_0_6878,plain,
    ! [X30595,X30596,X30597,X30598,X30599] :
      ( ~ class_Orderings_Olinorder(X30599)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30598),X30597))
      | hBOOL(hAPP(c_List_Odistinct(X30598),c_List_Olinorder__class_Oinsort__insert__key(X30598,X30599,X30596,X30595,X30597))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insort__insert])]) ).

fof(i_0_6879,plain,
    ! [X31485,X31486,X31487] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31487),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31486))),c_List_Otranspose(X31486,X31485))))
      | hAPP(hAPP(c_List_Onth(tc_List_Olist(X31486)),c_List_Otranspose(X31486,X31485)),X31487) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31486),X31486),hAPP(hAPP(c_COMBC(tc_List_Olist(X31486),tc_Nat_Onat,X31486),c_List_Onth(X31486)),X31487)),hAPP(c_List_Ofilter(tc_List_Olist(X31486),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31486)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31487)),c_Nat_Osize__class_Osize(tc_List_Olist(X31486)))),X31485)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__transpose])]) ).

fof(i_0_6880,plain,
    ! [X23983,X23984,X23985] :
      ( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X23985,hAPP(hAPP(c_COMBC(X23985,tc_fun(X23985,tc_HOL_Obool),tc_HOL_Obool),c_member(X23985)),X23984)),X23983))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X23985,tc_HOL_Obool)),X23983),hAPP(c_Set_OPow(X23985),X23984))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X23985,tc_HOL_Obool)),X23983),hAPP(c_Set_OPow(X23985),X23984)))
        | hBOOL(hAPP(c_Predicate_OPowp(X23985,hAPP(hAPP(c_COMBC(X23985,tc_fun(X23985,tc_HOL_Obool),tc_HOL_Obool),c_member(X23985)),X23984)),X23983)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__Pow__eq])]) ).

fof(i_0_6881,plain,
    ! [X18870,X18871,X18872,X18873,X18874,X18875] :
      ( ~ c_Fun_Oinj__on(X18875,X18874,X18873,X18872)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18874,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18875,X18874,X18873),X18872)),X18871))
      | ~ c_Fun_Oinj__on(X18874,X18875,X18870,X18871)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18875,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18874,X18875,X18870),X18871)),X18872))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18875),X18872))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18874),X18871))
      | hAPP(c_Finite__Set_Ocard(X18875),X18872) = hAPP(c_Finite__Set_Ocard(X18874),X18871) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__bij__eq])]) ).

fof(i_0_6882,plain,
    ! [X28361,X28362,X28363] : c_Hilbert__Choice_OEps(tc_prod(X28363,X28362),hAPP(c_Product__Type_Oprod_Oprod__case(X28363,X28362,tc_HOL_Obool),X28361)) = c_Hilbert__Choice_OEps(tc_prod(X28363,X28362),hAPP(hAPP(c_COMBS(tc_prod(X28363,X28362),X28362,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X28363,tc_fun(X28362,tc_HOL_Obool),tc_prod(X28363,X28362)),X28361),c_Product__Type_Ofst(X28363,X28362))),c_Product__Type_Osnd(X28363,X28362))),
    inference(variable_rename,[status(thm)],[fact_Eps__split]) ).

fof(i_0_6883,plain,
    ! [X22369,X22370,X22371] : c_HOL_OThe(tc_prod(X22371,X22370),hAPP(c_Product__Type_Oprod_Oprod__case(X22371,X22370,tc_HOL_Obool),X22369)) = c_HOL_OThe(tc_prod(X22371,X22370),hAPP(hAPP(c_COMBS(tc_prod(X22371,X22370),X22370,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X22371,tc_fun(X22370,tc_HOL_Obool),tc_prod(X22371,X22370)),X22369),c_Product__Type_Ofst(X22371,X22370))),c_Product__Type_Osnd(X22371,X22370))),
    inference(variable_rename,[status(thm)],[fact_The__split]) ).

fof(i_0_6884,plain,
    ! [X32111,X32112,X32113,X32114,X32115] :
      ( ( hAPP(X32112,X32114) = hAPP(X32112,X32113)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32112,X32114)),hAPP(X32112,X32113)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32115,X32115)),hAPP(hAPP(c_Product__Type_OPair(X32115,X32115),X32114),X32113)),c_List_Omeasures(X32115,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32115,tc_Nat_Onat)),X32112),X32111)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32115,X32115)),hAPP(hAPP(c_Product__Type_OPair(X32115,X32115),X32114),X32113)),c_List_Omeasures(X32115,X32111)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32112,X32114)),hAPP(X32112,X32113)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32115,X32115)),hAPP(hAPP(c_Product__Type_OPair(X32115,X32115),X32114),X32113)),c_List_Omeasures(X32115,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32115,tc_Nat_Onat)),X32112),X32111)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32112,X32114)),hAPP(X32112,X32113)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32115,X32115)),hAPP(hAPP(c_Product__Type_OPair(X32115,X32115),X32114),X32113)),c_List_Omeasures(X32115,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32115,tc_Nat_Onat)),X32112),X32111)))) )
      & ( hAPP(X32112,X32114) != hAPP(X32112,X32113)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32115,X32115)),hAPP(hAPP(c_Product__Type_OPair(X32115,X32115),X32114),X32113)),c_List_Omeasures(X32115,X32111)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32115,X32115)),hAPP(hAPP(c_Product__Type_OPair(X32115,X32115),X32114),X32113)),c_List_Omeasures(X32115,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32115,tc_Nat_Onat)),X32112),X32111)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__measures_I2_J])])]) ).

fof(i_0_6885,plain,
    ! [X33849,X33850,X33851,X33852,X33853,X33854] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33852),X33851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33852),X33853),X33849)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33852),X33851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33852),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X33852),X33853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33852),X33854),X33850))),X33849)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33852),X33851),X33850))
        | ~ class_Rings_Ocomm__ring(X33852)
        | ~ class_Rings_Odvd(X33852) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33852),X33851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33852),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X33852),X33853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33852),X33854),X33850))),X33849)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33852),X33851),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33852),X33853),X33849)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33852),X33851),X33850))
        | ~ class_Rings_Ocomm__ring(X33852)
        | ~ class_Rings_Odvd(X33852) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J])])])]) ).

fof(i_0_6886,plain,
    ! [X33843,X33844,X33845,X33846,X33847,X33848] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33846),X33845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33846),X33847),X33843)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33846),X33845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33846),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X33846),X33847),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33846),X33848),X33844))),X33843)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33846),X33845),X33844))
        | ~ class_Rings_Ocomm__ring(X33846)
        | ~ class_Rings_Odvd(X33846) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33846),X33845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33846),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X33846),X33847),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33846),X33848),X33844))),X33843)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33846),X33845),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33846),X33847),X33843)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33846),X33845),X33844))
        | ~ class_Rings_Ocomm__ring(X33846)
        | ~ class_Rings_Odvd(X33846) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J])])])]) ).

fof(i_0_6887,plain,
    ! [X20846,X20847,X20848,X20849] :
      ( ~ class_Divides_Osemiring__div(X20849)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20849),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20849),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20849),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20849),X20848),X20847)),X20847)),c_Divides_Odiv__class_Omod(X20849,X20848,X20847))),X20846) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20849),X20848),X20846) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality])]) ).

fof(i_0_6888,plain,
    ! [X19181,X19182,X19183,X19184,X19185,X19186] : c_Fun_Ofun__upd(X19186,X19185,c_Fun_Ofun__upd(X19186,X19185,X19184,X19183,X19182),X19183,X19181) = c_Fun_Ofun__upd(X19186,X19185,X19184,X19183,X19181),
    inference(variable_rename,[status(thm)],[fact_fun__upd__upd]) ).

fof(i_0_6889,plain,
    ! [X25552,X25553,X25554,X25555,X25556] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25556)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25555),X25554))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25555),X25553))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25555,tc_HOL_Obool)),X25554),X25553) != c_Orderings_Obot__class_Obot(tc_fun(X25555,tc_HOL_Obool))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25556,X25555,c_Groups_Otimes__class_Otimes(X25556)),X25552),c_Groups_Oone__class_Oone(X25556)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25555,tc_HOL_Obool)),X25554),X25553)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25556),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25556,X25555,c_Groups_Otimes__class_Otimes(X25556)),X25552),c_Groups_Oone__class_Oone(X25556)),X25554)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X25556,X25555,c_Groups_Otimes__class_Otimes(X25556)),X25552),c_Groups_Oone__class_Oone(X25556)),X25553)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__Un__disjoint])]) ).

fof(i_0_6890,plain,
    ! [X33431,X33432,X33433,X33434,X33435] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33435,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X33435,X33434,X33433),X33432)),X33431))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33434,tc_HOL_Obool)),X33432),hAPP(c_Set_Oimage(X33435,X33434,X33433),X33431)))
        | ~ c_Fun_Obij__betw(X33435,X33434,X33433,c_Orderings_Otop__class_Otop(tc_fun(X33435,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33434,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33434,tc_HOL_Obool)),X33432),hAPP(c_Set_Oimage(X33435,X33434,X33433),X33431)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33435,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X33435,X33434,X33433),X33432)),X33431))
        | ~ c_Fun_Obij__betw(X33435,X33434,X33433,c_Orderings_Otop__class_Otop(tc_fun(X33435,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33434,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subset__eq])])]) ).

cnf(i_0_6891,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_5466]) ).

fof(i_0_6892,plain,
    ! [X30885,X30886,X30887,X30888] :
      ( ~ class_Groups_Oab__group__add(X30888)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X30888),hAPP(c_List_Omonoid__add__class_Olistsum(X30888),hAPP(hAPP(c_List_Omap(X30887,X30888),X30886),X30885))) = hAPP(c_List_Omonoid__add__class_Olistsum(X30888),hAPP(hAPP(c_List_Omap(X30887,X30888),hAPP(c_Fun_Ocomp(X30888,X30888,X30887,c_Groups_Ouminus__class_Ouminus(X30888)),X30886)),X30885)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__listsum__map])]) ).

fof(i_0_6893,plain,
    ! [X32411,X32412,X32413,X32414] : c_New__Random__Sequence_Oneg__map(X32414,X32413,X32412,X32411) = c_New__Random__Sequence_Oneg__bind(X32414,X32413,X32411,hAPP(c_Fun_Ocomp(X32413,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(X32413)))))),X32414,c_New__Random__Sequence_Oneg__single(X32413)),X32412)),
    inference(variable_rename,[status(thm)],[fact_neg__map__def]) ).

fof(i_0_6894,plain,
    ! [X31061,X31062,X31063] :
      ( ( ~ hBOOL(hAPP(c_List_Olistsp(X31063,hAPP(hAPP(c_COMBC(X31063,tc_fun(X31063,tc_HOL_Obool),tc_HOL_Obool),c_member(X31063)),X31062)),X31061))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31063)),X31061),c_List_Olists(X31063,X31062))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31063)),X31061),c_List_Olists(X31063,X31062)))
        | hBOOL(hAPP(c_List_Olistsp(X31063,hAPP(hAPP(c_COMBC(X31063,tc_fun(X31063,tc_HOL_Obool),tc_HOL_Obool),c_member(X31063)),X31062)),X31061)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__lists__eq])]) ).

fof(i_0_6895,plain,
    ! [X25839,X25840,X25841,X25842] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25842)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25842),c_Groups_Ozero__class_Ozero(X25842)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25841,X25842),hAPP(hAPP(c_COMBB(X25842,X25842,X25841),c_Groups_Oabs__class_Oabs(X25842)),X25840)),X25839))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__abs__ge__zero])]) ).

fof(i_0_6896,plain,
    ! [X27722,X27723] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27723),X27722))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27723,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(X27723,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X27723,tc_HOL_Obool),tc_fun(X27723,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X27723,tc_HOL_Obool))),X27722)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__subsets])]) ).

fof(i_0_6897,plain,
    ! [X18493,X18494,X18495] :
      ( ( X18494 = c_Groups_Ozero__class_Ozero(X18495)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18495),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18495),X18494),X18494)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18495),X18493),X18493))),c_Groups_Ozero__class_Ozero(X18495)))
        | ~ class_Rings_Olinordered__ring__strict(X18495) )
      & ( X18493 = c_Groups_Ozero__class_Ozero(X18495)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18495),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18495),X18494),X18494)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18495),X18493),X18493))),c_Groups_Ozero__class_Ozero(X18495)))
        | ~ class_Rings_Olinordered__ring__strict(X18495) )
      & ( X18494 != c_Groups_Ozero__class_Ozero(X18495)
        | X18493 != c_Groups_Ozero__class_Ozero(X18495)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18495),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18495),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18495),X18494),X18494)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18495),X18493),X18493))),c_Groups_Ozero__class_Ozero(X18495)))
        | ~ class_Rings_Olinordered__ring__strict(X18495) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff])])]) ).

fof(i_0_6898,plain,
    ! [X25686,X25687] :
      ( ~ class_Lattices_Olattice(X25687)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25687),X25686))
      | X25686 = c_Orderings_Obot__class_Obot(tc_fun(X25687,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X25687),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25687),esk211_2(X25686,X25687)),esk212_2(X25686,X25687))),hAPP(hAPP(c_Set_Oinsert(X25687),esk211_2(X25686,X25687)),hAPP(hAPP(c_Set_Oinsert(X25687),esk212_2(X25686,X25687)),c_Orderings_Obot__class_Obot(tc_fun(X25687,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X25687),c_Big__Operators_Olattice__class_OInf__fin(X25687,X25686)),X25686)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oclosed])])]) ).

fof(i_0_6899,plain,
    ! [X23563,X23564] :
      ( ~ class_Lattices_Olattice(X23564)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23564),X23563))
      | X23563 = c_Orderings_Obot__class_Obot(tc_fun(X23564,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X23564),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23564),esk116_2(X23563,X23564)),esk117_2(X23563,X23564))),hAPP(hAPP(c_Set_Oinsert(X23564),esk116_2(X23563,X23564)),hAPP(hAPP(c_Set_Oinsert(X23564),esk117_2(X23563,X23564)),c_Orderings_Obot__class_Obot(tc_fun(X23564,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X23564),c_Big__Operators_Olattice__class_OSup__fin(X23564,X23563)),X23563)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oclosed])])]) ).

fof(i_0_6900,plain,
    ! [X23093,X23094] :
      ( ~ class_Orderings_Olinorder(X23094)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23094),X23093))
      | X23093 = c_Orderings_Obot__class_Obot(tc_fun(X23094,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X23094),hAPP(hAPP(c_Orderings_Oord__class_Omax(X23094),esk101_2(X23093,X23094)),esk102_2(X23093,X23094))),hAPP(hAPP(c_Set_Oinsert(X23094),esk101_2(X23093,X23094)),hAPP(hAPP(c_Set_Oinsert(X23094),esk102_2(X23093,X23094)),c_Orderings_Obot__class_Obot(tc_fun(X23094,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X23094),c_Big__Operators_Olinorder__class_OMax(X23094,X23093)),X23093)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oclosed])])]) ).

fof(i_0_6901,plain,
    ! [X21830,X21831] :
      ( ~ class_Orderings_Olinorder(X21831)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21831),X21830))
      | X21830 = c_Orderings_Obot__class_Obot(tc_fun(X21831,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X21831),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21831),esk81_2(X21830,X21831)),esk82_2(X21830,X21831))),hAPP(hAPP(c_Set_Oinsert(X21831),esk81_2(X21830,X21831)),hAPP(hAPP(c_Set_Oinsert(X21831),esk82_2(X21830,X21831)),c_Orderings_Obot__class_Obot(tc_fun(X21831,tc_HOL_Obool))))))
      | hBOOL(hAPP(hAPP(c_member(X21831),c_Big__Operators_Olinorder__class_OMin(X21831,X21830)),X21830)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oclosed])])]) ).

fof(i_0_6902,plain,
    ! [X18499,X18500,X18501] :
      ( ~ class_Rings_Olinordered__ring(X18501)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18501),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18501),X18500),X18500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18501),X18499),X18499))),c_Groups_Ozero__class_Ozero(X18501))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5467])]) ).

fof(i_0_6903,plain,
    ! [X19856,X19857,X19858,X19859,X19860,X19861,X19862,X19863] :
      ( ~ c_Finite__Set_Ofolding__image(X19863,X19862,X19861,X19860,X19859)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19862),X19858))
      | ~ c_Fun_Oinj__on(X19862,X19862,X19857,X19858)
      | hAPP(hAPP(X19859,X19856),hAPP(c_Set_Oimage(X19862,X19862,X19857),X19858)) = hAPP(hAPP(X19859,hAPP(c_Fun_Ocomp(X19862,X19863,X19862,X19856),X19857)),X19858) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oreindex])]) ).

fof(i_0_6904,plain,
    ! [X31885,X31886,X31887] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31887),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31887))),X31886)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31885),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31887))),X31886)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31887))),hAPP(c_List_Ofilter(tc_List_Olist(X31887),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(X31887)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31885)),c_Nat_Osize__class_Osize(tc_List_Olist(X31887)))),c_List_Otranspose(X31887,X31886))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31887)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31887)),X31886),X31885)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__column__length])]) ).

fof(i_0_6905,plain,
    ! [X22041,X22042,X22043,X22044,X22045,X22046,X22047] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22047,X22046)),hAPP(hAPP(c_Product__Type_OPair(X22047,X22046),X22045),X22044)),X22043))
      | hBOOL(hAPP(hAPP(c_member(X22042),hAPP(hAPP(X22041,X22045),X22044)),hAPP(c_Set_Oimage(tc_prod(X22047,X22046),X22042,hAPP(c_Product__Type_Oprod_Oprod__case(X22047,X22046,X22042),X22041)),X22043))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__imageI])]) ).

fof(i_0_6906,plain,
    ! [X31469,X31470,X31471,X31472,X31473] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31473)),hAPP(c_List_Ofilter(X31473,X31472),hAPP(hAPP(c_List_Omap(X31471,X31473),X31470),X31469))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31471)),hAPP(c_List_Ofilter(X31471,hAPP(c_Fun_Ocomp(X31473,tc_HOL_Obool,X31471,X31472),X31470)),X31469)),
    inference(variable_rename,[status(thm)],[fact_length__filter__map]) ).

cnf(i_0_6907,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_5468]) ).

fof(i_0_6908,plain,
    ! [X28750,X28751,X28752,X28753,X28754] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28754,X28754)),hAPP(hAPP(c_Product__Type_OPair(X28754,X28754),X28753),X28752)),c_Transitive__Closure_Ortrancl(X28754,X28751)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28754,X28754),tc_HOL_Obool)),X28751),hAPP(hAPP(c_Product__Type_OSigma(X28754,X28754),X28750),hAPP(c_COMBK(tc_fun(X28754,tc_HOL_Obool),X28754),X28750))))
      | X28753 = X28752
      | hBOOL(hAPP(hAPP(c_member(X28754),X28753),X28750)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__subset__Sigma__aux])]) ).

fof(i_0_6909,plain,
    ! [X23573,X23574,X23575,X23576,X23577,X23578] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23578,tc_fun(X23577,tc_HOL_Obool))),X23576),X23575),X23574),X23573))
      | hBOOL(hAPP(hAPP(X23576,X23574),X23573))
      | hBOOL(hAPP(hAPP(X23575,X23574),X23573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5469])]) ).

fof(i_0_6910,plain,
    ! [X31401,X31402,X31403] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31403)),hAPP(c_List_Ofilter(X31403,X31402),X31401))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31403)),hAPP(c_List_Ofilter(X31403,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31403),c_fNot),X31402)),X31401))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31403)),X31401),
    inference(variable_rename,[status(thm)],[fact_sum__length__filter__compl]) ).

fof(i_0_6911,plain,
    ! [X28658,X28659,X28660,X28661,X28662] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28662,X28662)),hAPP(hAPP(c_Product__Type_OPair(X28662,X28662),X28661),X28660)),c_Transitive__Closure_Ortrancl(X28662,X28659)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28662,X28662)),hAPP(hAPP(c_Product__Type_OPair(X28662,X28662),X28660),X28658)),c_Transitive__Closure_Ortrancl(X28662,X28659)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28662,X28662)),hAPP(hAPP(c_Product__Type_OPair(X28662,X28662),X28661),X28658)),c_Transitive__Closure_Ortrancl(X28662,X28659))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__trans])]) ).

cnf(i_0_6912,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_5470]) ).

cnf(i_0_6913,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_5471]) ).

fof(i_0_6914,plain,
    ! [X20832,X20833,X20834] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20834),X20833)),X20832) = 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),X20834),X20832)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20833),X20832))),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,X20834,X20832)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20833,X20832))),X20832)),
    inference(variable_rename,[status(thm)],[fact_zdiv__zadd1__eq]) ).

fof(i_0_6915,plain,
    ! [X21199,X21200,X21201] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X21201),X21200)),X21199) = 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),X21201),X21199)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21200),X21199))),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,X21201,X21199)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21200,X21199))),X21199)),
    inference(variable_rename,[status(thm)],[fact_div__add1__eq]) ).

fof(i_0_6916,plain,
    ! [X25609,X25610,X25611,X25612,X25613,X25614] :
      ( ( hBOOL(hAPP(hAPP(X25612,X25610),X25609))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25614,tc_fun(X25613,tc_HOL_Obool))),X25612),X25611),X25610),X25609)) )
      & ( hBOOL(hAPP(hAPP(X25611,X25610),X25609))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25614,tc_fun(X25613,tc_HOL_Obool))),X25612),X25611),X25610),X25609)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5472])])]) ).

fof(i_0_6917,plain,
    ! [X25627,X25628,X25629,X25630,X25631,X25632] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25632,tc_fun(X25631,tc_HOL_Obool))),X25630),X25629),X25628),X25627))
      | hBOOL(hAPP(hAPP(X25630,X25628),X25627)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D1])]) ).

fof(i_0_6918,plain,
    ! [X25621,X25622,X25623,X25624,X25625,X25626] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25626,tc_fun(X25625,tc_HOL_Obool))),X25624),X25623),X25622),X25621))
      | hBOOL(hAPP(hAPP(X25623,X25622),X25621)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2D2])]) ).

cnf(i_0_6919,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk423_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_5268]) ).

cnf(i_0_6920,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk422_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_5269]) ).

fof(i_0_6921,plain,
    ! [X32040,X32041,X32042,X32043] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk441_4(X32040,X32041,X32042,X32043)),X32043))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32043),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32041)),X32040)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32043),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32041)),c_List_OtakeWhile(X32041,X32042,X32040)))) )
      & ( ~ hBOOL(hAPP(X32042,hAPP(hAPP(c_List_Onth(X32041),X32040),esk441_4(X32040,X32041,X32042,X32043))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32043),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32041)),X32040)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X32043),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32041)),c_List_OtakeWhile(X32041,X32042,X32040)))) ) ),
    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_6922,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_5473]) ).

cnf(i_0_6923,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_5474]) ).

cnf(i_0_6924,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_5475]) ).

cnf(i_0_6925,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_5476]) ).

fof(i_0_6926,plain,
    ! [X28668,X28669,X28670,X28671,X28672] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28672,X28672)),hAPP(hAPP(c_Product__Type_OPair(X28672,X28672),X28671),X28670)),X28669))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28672,X28672)),hAPP(hAPP(c_Product__Type_OPair(X28672,X28672),X28670),X28668)),c_Transitive__Closure_Ortrancl(X28672,X28669)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28672,X28672)),hAPP(hAPP(c_Product__Type_OPair(X28672,X28672),X28671),X28668)),c_Transitive__Closure_Ortrancl(X28672,X28669))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__rtrancl__into__rtrancl])]) ).

fof(i_0_6927,plain,
    ! [X28663,X28664,X28665,X28666,X28667] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28667,X28667)),hAPP(hAPP(c_Product__Type_OPair(X28667,X28667),X28666),X28665)),c_Transitive__Closure_Ortrancl(X28667,X28664)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28667,X28667)),hAPP(hAPP(c_Product__Type_OPair(X28667,X28667),X28665),X28663)),X28664))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28667,X28667)),hAPP(hAPP(c_Product__Type_OPair(X28667,X28667),X28666),X28663)),c_Transitive__Closure_Ortrancl(X28667,X28664))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl_Ortrancl__into__rtrancl])]) ).

fof(i_0_6928,plain,
    ! [X29337,X29338,X29339,X29340] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29340),tc_List_Olist(X29340))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29340),tc_List_Olist(X29340)),X29339),X29338)),c_List_Olistrel(X29340,X29337)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29340),tc_List_Olist(X29340))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29340),tc_List_Olist(X29340)),X29339),X29338)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29340),c_List_Olistrel1(X29340,X29337)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__if__listrel])]) ).

fof(i_0_6929,plain,
    ! [X19744,X19745,X19746,X19747,X19748,X19749,X19750,X19751,X19752,X19753,X19754] :
      ( ~ c_Finite__Set_Ofolding(X19754,X19753,X19752,X19751)
      | hAPP(c_Fun_Ocomp(X19750,X19749,X19748,X19747),hAPP(c_Fun_Ocomp(X19746,X19750,X19748,X19745),X19744)) = hAPP(c_Fun_Ocomp(X19746,X19749,X19748,hAPP(c_Fun_Ocomp(X19750,X19749,X19746,X19747),X19745)),X19744) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comps_I1_J])]) ).

cnf(i_0_6930,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_5477]) ).

fof(i_0_6931,plain,
    ! [X19651,X19652,X19653,X19654,X19655,X19656] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19656),X19655)),X19654) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19653),X19652)),X19651)
      | ~ 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),X19653),X19652)),X19651)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19654),X19656))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19651))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19653))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19653),X19656))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19652),X19655)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma])]) ).

fof(i_0_6932,plain,
    ! [X27746] : 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)))),X27746)) = 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),X27746),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_6933,plain,
    ! [X29330,X29331,X29332,X29333] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29333),tc_List_Olist(X29333))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29333),tc_List_Olist(X29333)),X29332),X29331)),c_List_Olistrel1(X29333,X29330)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29333),tc_List_Olist(X29333))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29333),tc_List_Olist(X29333)),X29332),X29331)),c_List_Olistrel(X29333,c_Transitive__Closure_Ortrancl(X29333,X29330)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__reflcl__if__listrel1])]) ).

fof(i_0_6934,plain,
    ! [X29243,X29244,X29245,X29246] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29246),tc_List_Olist(X29246))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29246),tc_List_Olist(X29246)),X29245),X29244)),c_List_Olexord(X29246,X29243)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29246),tc_List_Olist(X29246))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29246),tc_List_Olist(X29246)),X29245),X29244)),c_List_Olex(X29246,X29243))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29246)),X29245) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29246)),X29244)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29246),tc_List_Olist(X29246))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29246),tc_List_Olist(X29246)),X29245),X29244)),c_List_Olex(X29246,X29243))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29246),tc_List_Olist(X29246))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29246),tc_List_Olist(X29246)),X29245),X29244)),c_List_Olexord(X29246,X29243)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29246)),X29245) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29246)),X29244)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29246),tc_List_Olist(X29246))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29246),tc_List_Olist(X29246)),X29245),X29244)),c_List_Olex(X29246,X29243))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__lex])])]) ).

fof(i_0_6935,plain,
    ! [X31445,X31446,X31447,X31448,X31449] : hAPP(c_List_Ofilter(X31449,X31448),hAPP(hAPP(c_List_Omap(X31447,X31449),X31446),X31445)) = hAPP(hAPP(c_List_Omap(X31447,X31449),X31446),hAPP(c_List_Ofilter(X31447,hAPP(c_Fun_Ocomp(X31449,tc_HOL_Obool,X31447,X31448),X31446)),X31445)),
    inference(variable_rename,[status(thm)],[fact_filter__map]) ).

fof(i_0_6936,plain,
    ! [X28334,X28335,X28336] :
      ( ( hAPP(X28335,esk307_3(X28334,X28335,X28336)) != hAPP(X28335,esk308_3(X28334,X28335,X28336))
        | c_Wellfounded_OwfP(X28336,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28334,tc_fun(X28336,tc_fun(X28336,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28334,tc_HOL_Obool))),X28335))
        | ~ c_Wellfounded_OwfP(X28336,hAPP(X28335,esk306_3(X28334,X28335,X28336))) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28336,tc_HOL_Obool)),c_Predicate_ODomainP(X28336,X28336,hAPP(X28335,esk307_3(X28334,X28335,X28336)))),c_Predicate_ORangeP(X28336,X28336,hAPP(X28335,esk308_3(X28334,X28335,X28336)))) != c_Orderings_Obot__class_Obot(tc_fun(X28336,tc_HOL_Obool))
        | c_Wellfounded_OwfP(X28336,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28334,tc_fun(X28336,tc_fun(X28336,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X28334,tc_HOL_Obool))),X28335))
        | ~ c_Wellfounded_OwfP(X28336,hAPP(X28335,esk306_3(X28334,X28335,X28336))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__SUP])])])]) ).

fof(i_0_6937,plain,
    ! [X31418,X31419,X31420] : c_List_Opartition(X31420,X31419,X31418) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31420),tc_List_Olist(X31420)),hAPP(c_List_Ofilter(X31420,X31419),X31418)),hAPP(c_List_Ofilter(X31420,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X31420,c_fNot),X31419)),X31418)),
    inference(variable_rename,[status(thm)],[fact_partition__filter__conv]) ).

cnf(i_0_6938,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_5478]) ).

fof(i_0_6939,plain,
    ! [X29991,X29992,X29993] :
      ( ( 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),esk397_3(X29991,X29992,X29993)),esk398_3(X29991,X29992,X29993))))
        | hBOOL(hAPP(hAPP(X29991,X29993),X29992))
        | ~ 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),X29993),X29992))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk397_3(X29991,X29992,X29993)),esk398_3(X29991,X29992,X29993)))
        | hBOOL(hAPP(hAPP(X29991,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk397_3(X29991,X29992,X29993)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk398_3(X29991,X29992,X29993)))
        | hBOOL(hAPP(hAPP(X29991,X29993),X29992))
        | ~ 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),X29993),X29992))) )
      & ( ~ hBOOL(hAPP(hAPP(X29991,esk397_3(X29991,X29992,X29993)),esk398_3(X29991,X29992,X29993)))
        | hBOOL(hAPP(hAPP(X29991,X29993),X29992))
        | ~ 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),X29993),X29992))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto_Opinduct])])])]) ).

fof(i_0_6940,plain,
    ! [X31089,X31090,X31091,X31092,X31093,X31094,X31095] :
      ( ( ~ c_List_Olist__all2(X31095,X31094,X31093,hAPP(hAPP(c_List_Omap(X31092,X31095),X31091),X31090),X31089)
        | c_List_Olist__all2(X31092,X31094,hAPP(hAPP(c_COMBB(X31095,tc_fun(X31094,tc_HOL_Obool),X31092),X31093),X31091),X31090,X31089) )
      & ( ~ c_List_Olist__all2(X31092,X31094,hAPP(hAPP(c_COMBB(X31095,tc_fun(X31094,tc_HOL_Obool),X31092),X31093),X31091),X31090,X31089)
        | c_List_Olist__all2(X31095,X31094,X31093,hAPP(hAPP(c_List_Omap(X31092,X31095),X31091),X31090),X31089) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__map1])]) ).

cnf(i_0_6941,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_5479]) ).

fof(i_0_6942,plain,
    ! [X32094,X32095,X32096,X32097,X32098] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X32098,X32097)),hAPP(X32098,X32096)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32095,X32095)),hAPP(hAPP(c_Product__Type_OPair(X32095,X32095),X32097),X32096)),c_List_Omeasures(X32095,X32094)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32095,X32095)),hAPP(hAPP(c_Product__Type_OPair(X32095,X32095),X32097),X32096)),c_List_Omeasures(X32095,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32095,tc_Nat_Onat)),X32098),X32094)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__lesseq])]) ).

fof(i_0_6943,plain,
    ! [X32840,X32841,X32842,X32843,X32844] :
      ( ~ c_Relation_Otrans(X32844,X32843)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32844,X32844)),hAPP(hAPP(c_Product__Type_OPair(X32844,X32844),X32842),X32841)),X32843))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32844,X32844)),hAPP(hAPP(c_Product__Type_OPair(X32844,X32844),X32841),X32840)),X32843))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32844,X32844)),hAPP(hAPP(c_Product__Type_OPair(X32844,X32844),X32842),X32840)),X32843)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transD])]) ).

fof(i_0_6944,plain,
    ! [X32830,X32831,X32832,X32833,X32834,X32835,X32836] :
      ( ( ~ c_Relation_Otrans(X32831,X32830)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32831,X32831)),hAPP(hAPP(c_Product__Type_OPair(X32831,X32831),X32832),X32833)),X32830))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32831,X32831)),hAPP(hAPP(c_Product__Type_OPair(X32831,X32831),X32833),X32834)),X32830))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X32831,X32831)),hAPP(hAPP(c_Product__Type_OPair(X32831,X32831),X32832),X32834)),X32830)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32836,X32836)),hAPP(hAPP(c_Product__Type_OPair(X32836,X32836),esk500_2(X32835,X32836)),esk501_2(X32835,X32836))),X32835))
        | c_Relation_Otrans(X32836,X32835) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32836,X32836)),hAPP(hAPP(c_Product__Type_OPair(X32836,X32836),esk501_2(X32835,X32836)),esk502_2(X32835,X32836))),X32835))
        | c_Relation_Otrans(X32836,X32835) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32836,X32836)),hAPP(hAPP(c_Product__Type_OPair(X32836,X32836),esk500_2(X32835,X32836)),esk502_2(X32835,X32836))),X32835))
        | c_Relation_Otrans(X32836,X32835) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__def])])])])])]) ).

fof(i_0_6945,plain,
    ! [X19134,X19135] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19135),c_Groups_Oone__class_Oone(X19135)),X19134)),X19134)),c_Groups_Ozero__class_Ozero(X19135)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19135),X19134),c_Groups_Ozero__class_Ozero(X19135)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19135),X19134),c_Int_Oring__1__class_OInts(X19135)))
        | ~ class_Rings_Olinordered__idom(X19135) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19135),X19134),c_Groups_Ozero__class_Ozero(X19135)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19135),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19135),c_Groups_Oone__class_Oone(X19135)),X19134)),X19134)),c_Groups_Ozero__class_Ozero(X19135)))
        | ~ hBOOL(hAPP(hAPP(c_member(X19135),X19134),c_Int_Oring__1__class_OInts(X19135)))
        | ~ class_Rings_Olinordered__idom(X19135) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__less__0])])]) ).

cnf(i_0_6946,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_5480]) ).

fof(i_0_6947,plain,
    ! [X20903,X20904,X20905] : 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),X20905),X20904)),X20904)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20905,X20904))),X20903) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20905),X20903),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality2]) ).

cnf(i_0_6948,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk451_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_5481]) ).

cnf(i_0_6949,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_5482]) ).

fof(i_0_6950,plain,
    ! [X31946,X31947,X31948] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31948)),c_List_OtakeWhile(X31948,X31947,X31946))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31948)),X31946)))
      | ~ hBOOL(hAPP(X31947,hAPP(hAPP(c_List_Onth(X31948),X31946),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31948)),c_List_OtakeWhile(X31948,X31947,X31946))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5483])]) ).

cnf(i_0_6951,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_5484]) ).

cnf(i_0_6952,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk339_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_5485]) ).

fof(i_0_6953,plain,
    ! [X30524,X30525,X30526,X30527] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30527)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X30526,X30527),hAPP(c_List_Oset(X30526),X30525)),X30524) = hAPP(c_List_Ofoldl(X30527,X30526,hAPP(c_COMBC(X30526,X30527,X30527),hAPP(hAPP(c_COMBB(X30527,tc_fun(X30527,X30527),X30526),c_Lattices_Osemilattice__inf__class_Oinf(X30527)),X30524)),c_Orderings_Otop__class_Otop(X30527)),X30525) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__set__fold])]) ).

fof(i_0_6954,plain,
    ! [X30520,X30521,X30522,X30523] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30523)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X30522,X30523),hAPP(c_List_Oset(X30522),X30521)),X30520) = hAPP(c_List_Ofoldl(X30523,X30522,hAPP(c_COMBC(X30522,X30523,X30523),hAPP(hAPP(c_COMBB(X30523,tc_fun(X30523,X30523),X30522),c_Lattices_Osemilattice__sup__class_Osup(X30523)),X30520)),c_Orderings_Obot__class_Obot(X30523)),X30521) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__set__fold])]) ).

cnf(i_0_6955,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_5486]) ).

fof(i_0_6956,plain,
    ! [X28327,X28328,X28329,X28330] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28330),esk305_4(X28327,X28328,X28329,X28330)),X28329))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X28328),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28330,tc_fun(X28328,tc_HOL_Obool)),X28329),X28327)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28330),X28329)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28328),hAPP(X28327,esk305_4(X28327,X28328,X28329,X28330))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X28328),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28330,tc_fun(X28328,tc_HOL_Obool)),X28329),X28327)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28330),X28329)) ) ),
    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_6957,plain,
    ! [X23655,X23656,X23657,X23658,X23659] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23656),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23658,tc_fun(X23656,tc_HOL_Obool)),X23657),X23655)))
        | ~ hBOOL(hAPP(hAPP(c_member(X23658),X23659),X23657))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23656),hAPP(X23655,X23659)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23658),X23657)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23658),esk127_4(X23655,X23656,X23657,X23658)),X23657))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23656),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23658,tc_fun(X23656,tc_HOL_Obool)),X23657),X23655)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23658),X23657)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23656),hAPP(X23655,esk127_4(X23655,X23656,X23657,X23658))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23656),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23658,tc_fun(X23656,tc_HOL_Obool)),X23657),X23655)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23658),X23657)) ) ),
    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_6958,plain,
    ! [X27916,X27917,X27918,X27919,X27920,X27921,X27922] : hAPP(hAPP(c_Relation_Orel__comp(X27922,X27921,X27920),X27919),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27918,tc_fun(tc_prod(X27921,X27920),tc_HOL_Obool)),X27917),X27916)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27918,tc_fun(tc_prod(X27922,X27920),tc_HOL_Obool)),X27917),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X27921,X27920),tc_HOL_Obool),tc_fun(tc_prod(X27922,X27920),tc_HOL_Obool),X27918),hAPP(c_Relation_Orel__comp(X27922,X27921,X27920),X27919)),X27916)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__UNION__distrib]) ).

fof(i_0_6959,plain,
    ! [X19532,X19533,X19534,X19535,X19536,X19537,X19538] : hAPP(c_Fun_Ocomp(X19538,X19537,X19536,X19535),hAPP(c_Fun_Ocomp(X19534,X19538,X19536,X19533),X19532)) = hAPP(c_Fun_Ocomp(X19534,X19537,X19536,hAPP(c_Fun_Ocomp(X19538,X19537,X19534,X19535),X19533)),X19532),
    inference(variable_rename,[status(thm)],[fact_o__assoc]) ).

fof(i_0_6960,plain,
    ! [X26255,X26256,X26257,X26258] :
      ( hAPP(c_Set_Oimage(X26258,X26257,X26256),c_Orderings_Otop__class_Otop(tc_fun(X26258,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26257,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26257,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26257,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26258,X26257,X26256),X26255))),hAPP(c_Set_Oimage(X26258,X26257,X26256),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26258,tc_HOL_Obool)),X26255)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__Compl__image__subset])]) ).

fof(i_0_6961,plain,
    ! [X33425,X33426,X33427,X33428,X33429,X33430] :
      ( ~ c_Fun_Obij__betw(X33430,X33429,X33428,c_Orderings_Otop__class_Otop(tc_fun(X33430,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33429,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33430,X33429,X33428),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33427,tc_fun(X33430,tc_HOL_Obool)),X33426),X33425)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X33427,tc_fun(X33429,tc_HOL_Obool)),X33426),hAPP(hAPP(c_COMBB(tc_fun(X33430,tc_HOL_Obool),tc_fun(X33429,tc_HOL_Obool),X33427),c_Set_Oimage(X33430,X33429,X33428)),X33425)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__image__INT])]) ).

fof(i_0_6962,plain,
    ! [X23460,X23461,X23462,X23463,X23464,X23465] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23465,X23465)),hAPP(hAPP(c_Product__Type_OPair(X23465,X23465),X23464),X23463)),hAPP(hAPP(c_Relation_Oinv__image(X23462,X23465),X23461),X23460)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23462,X23462)),hAPP(hAPP(c_Product__Type_OPair(X23462,X23462),hAPP(X23460,X23464)),hAPP(X23460,X23463))),X23461)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23462,X23462)),hAPP(hAPP(c_Product__Type_OPair(X23462,X23462),hAPP(X23460,X23464)),hAPP(X23460,X23463))),X23461))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X23465,X23465)),hAPP(hAPP(c_Product__Type_OPair(X23465,X23465),X23464),X23463)),hAPP(hAPP(c_Relation_Oinv__image(X23462,X23465),X23461),X23460))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__inv__image])]) ).

fof(i_0_6963,plain,
    ! [X33000,X33001] :
      ( ~ c_Relation_Osym(X33001,X33000)
      | ~ c_Relation_Otrans(X33001,X33000)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X33001,X33001),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X33001,X33001,X33001),hAPP(c_Relation_Oconverse(X33001,X33001),X33000)),X33000)),X33000)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__trans__comp__subset])]) ).

fof(i_0_6964,plain,
    ! [X19712,X19713,X19714,X19715,X19716,X19717] :
      ( ~ c_Finite__Set_Ofolding(X19717,X19716,X19715,X19714)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19717),X19713))
      | ~ hBOOL(hAPP(hAPP(c_member(X19717),X19712),X19713))
      | hAPP(X19714,X19713) = hAPP(c_Fun_Ocomp(X19716,X19716,X19716,hAPP(X19714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19717,tc_HOL_Obool)),X19713),hAPP(hAPP(c_Set_Oinsert(X19717),X19712),c_Orderings_Obot__class_Obot(tc_fun(X19717,tc_HOL_Obool)))))),hAPP(X19715,X19712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oremove])]) ).

fof(i_0_6965,plain,
    ! [X27272,X27273,X27274,X27275,X27276,X27277] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27277,X27276),tc_HOL_Obool)),X27275),hAPP(hAPP(c_Product__Type_OSigma(X27277,X27276),X27274),hAPP(c_COMBK(tc_fun(X27276,tc_HOL_Obool),X27277),X27273))))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27276,tc_HOL_Obool)),hAPP(c_Relation_OImage(X27277,X27276,X27275),X27272)),X27273)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__subset])]) ).

fof(i_0_6966,plain,
    ! [X30432,X30433,X30434] : hAPP(c_List_Otl(X30434),hAPP(hAPP(c_List_Oappend(X30434),X30433),X30432)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(X30434),X30434,hAPP(c_List_Otl(X30434),X30432),hAPP(c_COMBK(tc_fun(tc_List_Olist(X30434),tc_List_Olist(X30434)),X30434),hAPP(hAPP(c_COMBC(tc_List_Olist(X30434),tc_List_Olist(X30434),tc_List_Olist(X30434)),c_List_Oappend(X30434)),X30432))),X30433),
    inference(variable_rename,[status(thm)],[fact_tl__append]) ).

fof(i_0_6967,plain,
    ! [X32430,X32431,X32432,X32433] : c_New__Random__Sequence_Opos__map(X32433,X32432,X32431,X32430) = c_New__Random__Sequence_Opos__bind(X32433,X32432,X32430,hAPP(c_Fun_Ocomp(X32432,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(X32432))))),X32433,c_New__Random__Sequence_Opos__single(X32432)),X32431)),
    inference(variable_rename,[status(thm)],[fact_pos__map__def]) ).

fof(i_0_6968,plain,
    ! [X26275,X26276,X26277,X26278] :
      ( ~ c_Fun_Oinj__on(X26278,X26277,X26276,c_Orderings_Otop__class_Otop(tc_fun(X26278,tc_HOL_Obool)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26277,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26278,X26277,X26276),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26278,tc_HOL_Obool)),X26275))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26277,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26278,X26277,X26276),X26275)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__Compl__subset])]) ).

fof(i_0_6969,plain,
    ! [X33258,X33259,X33260] :
      ( ~ c_Fun_Obij__betw(X33260,X33259,X33258,c_Orderings_Otop__class_Otop(tc_fun(X33260,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33259,tc_HOL_Obool)))
      | c_Fun_Obij__betw(X33259,X33260,c_Hilbert__Choice_Oinv__into(X33260,X33259,c_Orderings_Otop__class_Otop(tc_fun(X33260,tc_HOL_Obool)),X33258),c_Orderings_Otop__class_Otop(tc_fun(X33259,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33260,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__imp__bij__inv])]) ).

fof(i_0_6970,plain,
    ! [X19836,X19837,X19838,X19839,X19840,X19841] :
      ( ~ c_Finite__Set_Ofolding(X19841,X19840,X19839,X19838)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19841),X19837))
      | hAPP(X19838,hAPP(hAPP(c_Set_Oinsert(X19841),X19836),X19837)) = hAPP(c_Fun_Ocomp(X19840,X19840,X19840,hAPP(X19838,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19841,tc_HOL_Obool)),X19837),hAPP(hAPP(c_Set_Oinsert(X19841),X19836),c_Orderings_Obot__class_Obot(tc_fun(X19841,tc_HOL_Obool)))))),hAPP(X19839,X19836)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oinsert__remove])]) ).

fof(i_0_6971,plain,
    ! [X31179,X31180,X31181,X31182,X31183,X31184,X31185,X31186] :
      ( ~ c_List_Olist__all2(X31186,X31185,X31184,X31183,X31182)
      | ~ hBOOL(hAPP(hAPP(X31184,X31181),X31180))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31179),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31185)),X31182)))
      | c_List_Olist__all2(X31186,X31185,X31184,hAPP(hAPP(c_List_Olist__update(X31186,X31183),X31179),X31181),hAPP(hAPP(c_List_Olist__update(X31185,X31182),X31179),X31180)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong2])]) ).

fof(i_0_6972,plain,
    ! [X31187,X31188,X31189,X31190,X31191,X31192,X31193,X31194] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31194),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31193)),X31192)))
      | ~ c_List_Olist__all2(X31193,X31191,X31190,X31192,X31189)
      | ~ hBOOL(hAPP(hAPP(X31190,X31188),X31187))
      | c_List_Olist__all2(X31193,X31191,X31190,hAPP(hAPP(c_List_Olist__update(X31193,X31192),X31194),X31188),hAPP(hAPP(c_List_Olist__update(X31191,X31189),X31194),X31187)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__update__cong])]) ).

fof(i_0_6973,plain,
    ! [X33241,X33242,X33243,X33244] :
      ( ~ c_Fun_Obij__betw(X33244,X33243,X33242,c_Orderings_Otop__class_Otop(tc_fun(X33244,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33243,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33244,X33243,X33242),hAPP(c_Set_OCollect(X33244),X33241)) = hAPP(c_Set_OCollect(X33243),hAPP(hAPP(c_COMBB(X33244,tc_HOL_Obool,X33243),X33241),c_Hilbert__Choice_Oinv__into(X33244,X33243,c_Orderings_Otop__class_Otop(tc_fun(X33244,tc_HOL_Obool)),X33242))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__image__Collect__eq])]) ).

fof(i_0_6974,plain,
    ! [X29767,X29768,X29769,X29770] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29770),X29769))
      | hBOOL(hAPP(hAPP(c_member(X29770),X29768),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29770,tc_HOL_Obool)),hAPP(c_List_Oset(X29770),X29769)),hAPP(hAPP(c_Set_Oinsert(X29770),hAPP(hAPP(c_List_Onth(X29770),X29769),X29767)),c_Orderings_Obot__class_Obot(tc_fun(X29770,tc_HOL_Obool))))))
      | hBOOL(hAPP(c_List_Odistinct(X29770),hAPP(hAPP(c_List_Olist__update(X29770,X29769),X29767),X29768))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5487])]) ).

fof(i_0_6975,plain,
    ! [X18810,X18811,X18812,X18813] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18813),hAPP(c_Set_Oimage(X18812,X18813,X18811),X18810))),hAPP(c_Finite__Set_Ocard(X18812),X18810)))
      | ~ c_Fun_Oinj__on(X18812,X18813,X18811,X18810) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5488])]) ).

fof(i_0_6976,plain,
    ! [X29145,X29146,X29147,X29148] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29147),esk371_4(X29145,X29146,X29147,X29148)),X29146))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29148),c_Groups_Ozero__class_Ozero(X29148)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29147,X29148),X29145),X29146)))
        | ~ class_Rings_Olinordered__semidom(X29148) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29148),c_Groups_Ozero__class_Ozero(X29148)),hAPP(X29145,esk371_4(X29145,X29146,X29147,X29148))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X29148),c_Groups_Ozero__class_Ozero(X29148)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29147,X29148),X29145),X29146)))
        | ~ class_Rings_Olinordered__semidom(X29148) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__pos])])])]) ).

fof(i_0_6977,plain,
    ! [X29171,X29172,X29173,X29174] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29173),esk372_4(X29171,X29172,X29173,X29174)),X29172))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29174),c_Groups_Ozero__class_Ozero(X29174)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29173,X29174),X29171),X29172)))
        | ~ class_Rings_Olinordered__semidom(X29174) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29174),c_Groups_Ozero__class_Ozero(X29174)),hAPP(X29171,esk372_4(X29171,X29172,X29173,X29174))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X29174),c_Groups_Ozero__class_Ozero(X29174)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X29173,X29174),X29171),X29172)))
        | ~ class_Rings_Olinordered__semidom(X29174) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__nonneg])])])]) ).

fof(i_0_6978,plain,
    ! [X32494,X32495,X32496,X32497,X32498] : c_Predicate_Oconversep(X32498,X32497,c_Predicate_Opred__comp(X32498,X32496,X32497,X32495,X32494)) = c_Predicate_Opred__comp(X32497,X32496,X32498,c_Predicate_Oconversep(X32496,X32497,X32494),c_Predicate_Oconversep(X32498,X32496,X32495)),
    inference(variable_rename,[status(thm)],[fact_converse__pred__comp]) ).

cnf(i_0_6979,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_5470]) ).

cnf(i_0_6980,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_5489]) ).

fof(i_0_6981,plain,
    ! [X19787,X19788,X19789,X19790,X19791,X19792,X19793,X19794] :
      ( ~ c_Finite__Set_Ofolding(X19794,X19793,X19792,X19791)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19794),X19790))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19794),X19789))
      | hAPP(c_Fun_Ocomp(X19793,X19793,X19788,hAPP(X19791,X19789)),hAPP(c_Fun_Ocomp(X19793,X19793,X19788,hAPP(X19791,X19790)),X19787)) = hAPP(c_Fun_Ocomp(X19793,X19793,X19788,hAPP(X19791,X19790)),hAPP(c_Fun_Ocomp(X19793,X19793,X19788,hAPP(X19791,X19789)),X19787)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H_H])]) ).

fof(i_0_6982,plain,
    ! [X33184,X33185,X33186,X33187] : hAPP(c_Hilbert__Choice_Oinv__into(X33187,X33186,c_Orderings_Otop__class_Otop(tc_fun(X33187,tc_HOL_Obool)),X33185),X33184) = c_Hilbert__Choice_OEps(X33187,hAPP(hAPP(c_COMBC(X33187,X33186,tc_HOL_Obool),hAPP(hAPP(c_COMBB(X33186,tc_fun(X33186,tc_HOL_Obool),X33187),c_fequal),X33185)),X33184)),
    inference(variable_rename,[status(thm)],[fact_inv__def]) ).

fof(i_0_6983,plain,
    ! [X27337,X27338,X27339,X27340] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27340),esk259_4(X27337,X27338,X27339,X27340)),X27339))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27340,X27338)),hAPP(hAPP(c_Product__Type_OSigma(X27340,X27338),X27339),X27337)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27340),X27339)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27338),hAPP(X27337,esk259_4(X27337,X27338,X27339,X27340))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27340,X27338)),hAPP(hAPP(c_Product__Type_OSigma(X27340,X27338),X27339),X27337)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27340),X27339)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__SigmaI])])])]) ).

fof(i_0_6984,plain,
    ! [X18640,X18641,X18642,X18643,X18644,X18645] :
      ( ~ class_Rings_Olinordered__semiring__1__strict(X18645)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18645),X18644),X18643))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18645),X18642),X18643))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18645),c_Groups_Ozero__class_Ozero(X18645)),X18641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18645),c_Groups_Ozero__class_Ozero(X18645)),X18640))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18645),X18641),X18640) != c_Groups_Oone__class_Oone(X18645)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18645),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18645),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18645),X18641),X18644)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18645),X18640),X18642))),X18643)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__lt])]) ).

fof(i_0_6985,plain,
    ! [X18517,X18518,X18519,X18520,X18521,X18522] :
      ( ~ class_Rings_Olinordered__semiring__1(X18522)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18522),X18521),X18520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18522),X18519),X18520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18522),c_Groups_Ozero__class_Ozero(X18522)),X18518))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18522),c_Groups_Ozero__class_Ozero(X18522)),X18517))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18522),X18518),X18517) != c_Groups_Oone__class_Oone(X18522)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18522),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18522),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18522),X18518),X18521)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18522),X18517),X18519))),X18520)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_convex__bound__le])]) ).

fof(i_0_6986,plain,
    ! [X24276,X24277,X24278,X24279] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk152_4(X24276,X24277,X24278,X24279)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24278)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24279),X24277))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24279),X24278)),X24277))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24277),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24276))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24278)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk153_4(X24276,X24277,X24278,X24279)),X24276))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24279),X24277))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24279),X24278)),X24277))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24277),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24276))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24278)) )
      & ( X24279 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk153_4(X24276,X24277,X24278,X24279)),esk152_4(X24276,X24277,X24278,X24279))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24279),X24277))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24279),X24278)),X24277))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24277),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24276))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24278)) ) ),
    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_6987,plain,
    ! [X32035,X32036,X32037,X32038] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32037)),X32036)))
        | c_List_OtakeWhile(X32037,X32035,X32036) = hAPP(hAPP(c_List_Otake(X32037),X32038),X32036)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk440_4(X32035,X32036,X32037,X32038)),X32038)) )
      & ( hBOOL(hAPP(X32035,hAPP(hAPP(c_List_Onth(X32037),X32036),X32038)))
        | c_List_OtakeWhile(X32037,X32035,X32036) = hAPP(hAPP(c_List_Otake(X32037),X32038),X32036)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk440_4(X32035,X32036,X32037,X32038)),X32038)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32037)),X32036)))
        | c_List_OtakeWhile(X32037,X32035,X32036) = hAPP(hAPP(c_List_Otake(X32037),X32038),X32036)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk440_4(X32035,X32036,X32037,X32038)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32037)),X32036))) )
      & ( hBOOL(hAPP(X32035,hAPP(hAPP(c_List_Onth(X32037),X32036),X32038)))
        | c_List_OtakeWhile(X32037,X32035,X32036) = hAPP(hAPP(c_List_Otake(X32037),X32038),X32036)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk440_4(X32035,X32036,X32037,X32038)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32037)),X32036))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32037)),X32036)))
        | c_List_OtakeWhile(X32037,X32035,X32036) = hAPP(hAPP(c_List_Otake(X32037),X32038),X32036)
        | ~ hBOOL(hAPP(X32035,hAPP(hAPP(c_List_Onth(X32037),X32036),esk440_4(X32035,X32036,X32037,X32038)))) )
      & ( hBOOL(hAPP(X32035,hAPP(hAPP(c_List_Onth(X32037),X32036),X32038)))
        | c_List_OtakeWhile(X32037,X32035,X32036) = hAPP(hAPP(c_List_Otake(X32037),X32038),X32036)
        | ~ hBOOL(hAPP(X32035,hAPP(hAPP(c_List_Onth(X32037),X32036),esk440_4(X32035,X32036,X32037,X32038)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5490])])])]) ).

fof(i_0_6988,plain,
    ! [X33235,X33236,X33237,X33238,X33239,X33240] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X33240,X33239,X33238,X33237,c_Lazy__Sequence_Olazy__sequence_OInsert(X33239,X33236,X33235)) = hAPP(hAPP(hAPP(X33237,X33236),X33235),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X33240,X33239,X33238,X33237,X33235)),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Orecs_I2_J]) ).

fof(i_0_6989,plain,
    ! [X32932,X32933,X32934,X32935,X32937] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32935),esk508_4(X32932,X32933,X32934,X32935)),X32934))
        | c_Wellfounded_Omax__extp(X32935,X32932,X32934,X32933)
        | X32933 = c_Orderings_Obot__class_Obot(tc_fun(X32935,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32935),X32933))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32935),X32934)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32935),X32937),X32933))
        | ~ hBOOL(hAPP(hAPP(X32932,esk508_4(X32932,X32933,X32934,X32935)),X32937))
        | c_Wellfounded_Omax__extp(X32935,X32932,X32934,X32933)
        | X32933 = c_Orderings_Obot__class_Obot(tc_fun(X32935,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32935),X32933))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32935),X32934)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__extp_Ointros])])])])]) ).

fof(i_0_6990,plain,
    ! [X19773,X19774,X19775,X19776,X19777,X19778,X19779,X19780] :
      ( ~ c_Finite__Set_Ofolding(X19780,X19779,X19778,X19777)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19780),X19776))
      | hAPP(c_Fun_Ocomp(X19779,X19779,X19775,hAPP(X19778,X19774)),hAPP(c_Fun_Ocomp(X19779,X19779,X19775,hAPP(X19777,X19776)),X19773)) = hAPP(c_Fun_Ocomp(X19779,X19779,X19775,hAPP(X19777,X19776)),hAPP(c_Fun_Ocomp(X19779,X19779,X19775,hAPP(X19778,X19774)),X19773)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp_H])]) ).

fof(i_0_6991,plain,
    ! [X30184,X30185,X30186,X30187,X30188,X30189,X30190,X30191] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X30191,X30191)),hAPP(hAPP(c_Product__Type_OPair(X30191,X30191),X30190),X30189)),X30188))
      | X30187 != hAPP(hAPP(c_List_Oappend(X30191),X30186),hAPP(hAPP(c_List_Olist_OCons(X30191),X30190),X30185))
      | X30184 != hAPP(hAPP(c_List_Oappend(X30191),X30186),hAPP(hAPP(c_List_Olist_OCons(X30191),X30189),X30185))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30191),tc_List_Olist(X30191))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30191),tc_List_Olist(X30191)),X30187),X30184)),c_List_Olistrel1(X30191,X30188))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1I])]) ).

fof(i_0_6992,plain,
    ! [X33475,X33476,X33477,X33478,X33480] :
      ( ( hBOOL(hAPP(hAPP(c_member(X33478),esk539_4(X33475,X33476,X33477,X33478)),c_Quotient_ORespects(X33478,X33477)))
        | ~ hBOOL(hAPP(X33476,X33480))
        | hBOOL(hAPP(X33476,esk538_4(X33475,X33476,X33477,X33478)))
        | ~ c_Equiv__Relations_Oequivp(X33478,X33477) )
      & ( hBOOL(hAPP(X33475,esk539_4(X33475,X33476,X33477,X33478)))
        | ~ hBOOL(hAPP(X33476,X33480))
        | hBOOL(hAPP(X33476,esk538_4(X33475,X33476,X33477,X33478)))
        | ~ c_Equiv__Relations_Oequivp(X33478,X33477) )
      & ( hBOOL(hAPP(hAPP(c_member(X33478),esk539_4(X33475,X33476,X33477,X33478)),c_Quotient_ORespects(X33478,X33477)))
        | ~ hBOOL(hAPP(X33476,X33480))
        | ~ hBOOL(hAPP(X33475,esk538_4(X33475,X33476,X33477,X33478)))
        | ~ c_Equiv__Relations_Oequivp(X33478,X33477) )
      & ( hBOOL(hAPP(X33475,esk539_4(X33475,X33476,X33477,X33478)))
        | ~ hBOOL(hAPP(X33476,X33480))
        | ~ hBOOL(hAPP(X33475,esk538_4(X33475,X33476,X33477,X33478)))
        | ~ c_Equiv__Relations_Oequivp(X33478,X33477) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__reg__right])])])])]) ).

cnf(i_0_6993,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_5491]) ).

fof(i_0_6994,plain,
    ! [X31238,X31239,X31240,X31241] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk419_4(X31238,X31239,X31240,X31241)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31241)),X31240)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31241),X31238),hAPP(c_List_Oset(X31241),X31240)))
        | hBOOL(hAPP(X31239,X31238)) )
      & ( ~ hBOOL(hAPP(X31239,hAPP(hAPP(c_List_Onth(X31241),X31240),esk419_4(X31238,X31239,X31240,X31241))))
        | ~ hBOOL(hAPP(hAPP(c_member(X31241),X31238),hAPP(c_List_Oset(X31241),X31240)))
        | hBOOL(hAPP(X31239,X31238)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__nth__imp__all__set])])])]) ).

cnf(i_0_6995,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]) ).

cnf(i_0_6996,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]) ).

fof(i_0_6997,plain,
    ! [X28454,X28455,X28456,X28457] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28457),esk328_4(X28454,X28455,X28456,X28457)),X28456))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X28457),X28455),X28454)),hAPP(hAPP(c_Finite__Set_Ofold(X28457,X28457,c_Lattices_Osemilattice__inf__class_Oinf(X28457)),X28454),X28456)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28457),X28456))
        | ~ class_Lattices_Osemilattice__inf(X28457) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28457),X28455),esk328_4(X28454,X28455,X28456,X28457)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28457),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X28457),X28455),X28454)),hAPP(hAPP(c_Finite__Set_Ofold(X28457,X28457,c_Lattices_Osemilattice__inf__class_Oinf(X28457)),X28454),X28456)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28457),X28456))
        | ~ class_Lattices_Osemilattice__inf(X28457) ) ),
    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_6998,plain,
    ! [X28433,X28434,X28435,X28436] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28436),esk323_4(X28433,X28434,X28435,X28436)),X28435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28436),hAPP(hAPP(c_Orderings_Oord__class_Omin(X28436),X28434),X28433)),hAPP(hAPP(c_Finite__Set_Ofold(X28436,X28436,c_Orderings_Oord__class_Omin(X28436)),X28433),X28435)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28436),X28435))
        | ~ class_Orderings_Olinorder(X28436) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28436),X28434),esk323_4(X28433,X28434,X28435,X28436)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28436),hAPP(hAPP(c_Orderings_Oord__class_Omin(X28436),X28434),X28433)),hAPP(hAPP(c_Finite__Set_Ofold(X28436,X28436,c_Orderings_Oord__class_Omin(X28436)),X28433),X28435)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28436),X28435))
        | ~ class_Orderings_Olinorder(X28436) ) ),
    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_6999,plain,
    ! [X24497,X24498,X24499,X24500,X24501] :
      ( ~ class_Groups_Ocomm__monoid__add(X24501)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24501),X24500),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24499),X24498)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24497),X24498))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24501),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24501,tc_Nat_Onat),X24500),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X24498))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24499),X24497)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__nat__ivl])]) ).

fof(i_0_7000,plain,
    ! [X33404,X33405,X33406,X33407,X33408,X33409,X33410] :
      ( ~ c_Fun_Obij__betw(X33410,X33409,X33408,X33407,X33406)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33410,tc_HOL_Obool)),X33405),X33407))
      | hAPP(c_Set_Oimage(X33410,X33409,X33408),X33405) != X33404
      | c_Fun_Obij__betw(X33410,X33409,X33408,X33405,X33404) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__subset])]) ).

fof(i_0_7001,plain,
    ! [X28652,X28653,X28654,X28655] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28655,X28655)),X28654),c_Transitive__Closure_Ortrancl(X28655,X28653)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28655,X28655)),X28654),c_Transitive__Closure_Ortrancl(X28655,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28655,X28655),tc_HOL_Obool)),X28653),X28652)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28655,X28655)),X28654),c_Transitive__Closure_Ortrancl(X28655,X28652)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28655,X28655)),X28654),c_Transitive__Closure_Ortrancl(X28655,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28655,X28655),tc_HOL_Obool)),X28653),X28652)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rtrancl__UnI])])]) ).

fof(i_0_7002,plain,
    ! [X19730,X19731,X19732,X19733,X19734,X19735,X19736,X19737] :
      ( ~ c_Finite__Set_Ofolding(X19737,X19736,X19735,X19734)
      | hAPP(c_Fun_Ocomp(X19736,X19736,X19733,hAPP(X19735,X19732)),hAPP(c_Fun_Ocomp(X19736,X19736,X19733,hAPP(X19735,X19731)),X19730)) = hAPP(c_Fun_Ocomp(X19736,X19736,X19733,hAPP(X19735,X19731)),hAPP(c_Fun_Ocomp(X19736,X19736,X19733,hAPP(X19735,X19732)),X19730)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__left__comp])]) ).

cnf(i_0_7003,plain,
    ( c_List_OdropWhile(X4,X1,hAPP(hAPP(c_List_Oappend(X4),X3),X2)) = c_List_OdropWhile(X4,X1,X2)
    | ~ hBOOL(hAPP(X1,esk451_4(X2,X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5481]) ).

fof(i_0_7004,plain,
    ! [X26223,X26224,X26225,X26226,X26228,X26229] :
      ( ( X26223 = hAPP(X26224,esk224_4(X26223,X26224,X26225,X26226))
        | ~ hBOOL(hAPP(hAPP(c_member(X26225),X26223),hAPP(c_Set_Oimage(X26226,X26225,X26224),c_Orderings_Otop__class_Otop(tc_fun(X26226,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X26226,X26225,X26224,c_Orderings_Otop__class_Otop(tc_fun(X26226,tc_HOL_Obool))) )
      & ( X26223 != hAPP(X26224,X26228)
        | X26228 = esk224_4(X26223,X26224,X26225,X26226)
        | ~ hBOOL(hAPP(hAPP(c_member(X26225),X26223),hAPP(c_Set_Oimage(X26226,X26225,X26224),c_Orderings_Otop__class_Otop(tc_fun(X26226,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X26226,X26225,X26224,c_Orderings_Otop__class_Otop(tc_fun(X26226,tc_HOL_Obool))) )
      & ( X26223 = hAPP(X26224,esk225_5(X26223,X26224,X26225,X26226,X26229))
        | X26223 != hAPP(X26224,X26229)
        | hBOOL(hAPP(hAPP(c_member(X26225),X26223),hAPP(c_Set_Oimage(X26226,X26225,X26224),c_Orderings_Otop__class_Otop(tc_fun(X26226,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X26226,X26225,X26224,c_Orderings_Otop__class_Otop(tc_fun(X26226,tc_HOL_Obool))) )
      & ( esk225_5(X26223,X26224,X26225,X26226,X26229) != X26229
        | X26223 != hAPP(X26224,X26229)
        | hBOOL(hAPP(hAPP(c_member(X26225),X26223),hAPP(c_Set_Oimage(X26226,X26225,X26224),c_Orderings_Otop__class_Otop(tc_fun(X26226,tc_HOL_Obool)))))
        | ~ c_Fun_Oinj__on(X26226,X26225,X26224,c_Orderings_Otop__class_Otop(tc_fun(X26226,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_7005,plain,
    ! [X25476,X25477,X25478,X25479,X25480] :
      ( ~ class_Groups_Oab__group__add(X25480)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25479),X25478))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25479),X25477))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25479,X25480),X25476),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25479,tc_HOL_Obool)),X25478),X25477)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25480),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25479,X25480),X25476),X25478)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25479,X25480),X25476),X25477))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25479,X25480),X25476),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25479,tc_HOL_Obool)),X25478),X25477))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un])]) ).

fof(i_0_7006,plain,
    ! [X31872,X31873,X31874,X31875] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31875),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31874)),X31873)))
      | hAPP(c_List_Orev(X31874),hAPP(hAPP(c_List_Olist__update(X31874,X31873),X31875),X31872)) = hAPP(hAPP(c_List_Olist__update(X31874,hAPP(c_List_Orev(X31874),X31873)),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(X31874)),X31873)),X31875)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X31872) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__update])]) ).

fof(i_0_7007,plain,
    ! [X33939,X33940,X33941,X33942] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X33942,tc_HOL_Obool)),esk564_4(X33939,X33940,X33941,X33942)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X33942),X33941),X33940)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33939),hAPP(c_Finite__Set_Ocard(X33942),X33941)))
        | ~ c_Equiv__Relations_Oequiv(X33942,X33941,X33940)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33942),X33941)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33939),hAPP(c_Finite__Set_Ocard(X33942),esk564_4(X33939,X33940,X33941,X33942))))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33939),hAPP(c_Finite__Set_Ocard(X33942),X33941)))
        | ~ c_Equiv__Relations_Oequiv(X33942,X33941,X33940)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33942),X33941)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__imp__dvd__card])])])]) ).

cnf(i_0_7008,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_5445]) ).

cnf(i_0_7009,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_5444]) ).

fof(i_0_7010,plain,
    ! [X27664,X27665,X27666] : hAPP(c_Set_OCollect(X27666),hAPP(hAPP(c_COMBS(X27666,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27666),c_fimplies),X27665)),X27664)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27666,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27666,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27666),X27665))),hAPP(c_Set_OCollect(X27666),X27664)),
    inference(variable_rename,[status(thm)],[fact_Collect__imp__eq]) ).

fof(i_0_7011,plain,
    ! [X22713,X22714,X22715,X22716] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)),X22715))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)),X22715))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)),X22715))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),X22714))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22714),c_Groups_Ozero__class_Ozero(X22716)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)),X22715))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),c_Groups_Ozero__class_Ozero(X22716)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)),X22715))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),X22715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22716),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)),X22714)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22716),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22716),X22715),X22714)),hAPP(c_Int_Onumber__class_Onumber__of(X22716),X22713)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22716)
        | ~ class_Int_Onumber(X22716) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5493])])]) ).

fof(i_0_7012,plain,
    ! [X22738,X22739,X22740,X22741] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),X22740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)),X22740))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),c_Groups_Ozero__class_Ozero(X22741)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),c_Groups_Ozero__class_Ozero(X22741)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)),X22740))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),c_Groups_Ozero__class_Ozero(X22741)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)),X22740))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),c_Groups_Ozero__class_Ozero(X22741)),X22739))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),X22740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),X22740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),c_Groups_Ozero__class_Ozero(X22741)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),X22740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22741),X22739),c_Groups_Ozero__class_Ozero(X22741)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)),X22740))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),X22740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),c_Groups_Ozero__class_Ozero(X22741)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)),X22740))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),X22740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22741),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)),X22739)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22741),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22741),X22740),X22739)),hAPP(c_Int_Onumber__class_Onumber__of(X22741),X22738)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22741)
        | ~ class_Int_Onumber(X22741) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5494])])]) ).

fof(i_0_7013,plain,
    ! [X28899,X28900,X28901,X28902,X28903,X28904,X28905,X28906,X28907] :
      ( ( ~ c_Relation_Osingle__valued(X28901,X28900,X28899)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28901,X28900)),hAPP(hAPP(c_Product__Type_OPair(X28901,X28900),X28902),X28903)),X28899))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28901,X28900)),hAPP(hAPP(c_Product__Type_OPair(X28901,X28900),X28902),X28904)),X28899))
        | X28903 = X28904 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28907,X28906)),hAPP(hAPP(c_Product__Type_OPair(X28907,X28906),esk335_3(X28905,X28906,X28907)),esk336_3(X28905,X28906,X28907))),X28905))
        | c_Relation_Osingle__valued(X28907,X28906,X28905) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28907,X28906)),hAPP(hAPP(c_Product__Type_OPair(X28907,X28906),esk335_3(X28905,X28906,X28907)),esk337_3(X28905,X28906,X28907))),X28905))
        | c_Relation_Osingle__valued(X28907,X28906,X28905) )
      & ( esk336_3(X28905,X28906,X28907) != esk337_3(X28905,X28906,X28907)
        | c_Relation_Osingle__valued(X28907,X28906,X28905) ) ),
    inference(distribute,[status(thm)],[inference(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_7014,plain,
    ! [X22709,X22710,X22711,X22712] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)),X22710))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),c_Groups_Ozero__class_Ozero(X22712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),c_Groups_Ozero__class_Ozero(X22712)),X22709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)),X22710))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)),X22710))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),c_Groups_Ozero__class_Ozero(X22712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)),X22710))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22709),c_Groups_Ozero__class_Ozero(X22712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)),X22710))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),c_Groups_Ozero__class_Ozero(X22712)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),X22710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),X22709)),X22710))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22712),hAPP(c_Int_Onumber__class_Onumber__of(X22712),X22711)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22712),X22710),X22709)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22712)
        | ~ class_Int_Onumber(X22712) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5495])])]) ).

fof(i_0_7015,plain,
    ! [X22742,X22743,X22744,X22745] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)),X22743))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),X22743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),X22743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),c_Groups_Ozero__class_Ozero(X22745)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),X22743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),c_Groups_Ozero__class_Ozero(X22745)),X22742))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)),X22743))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)),X22743))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),c_Groups_Ozero__class_Ozero(X22745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)),X22743))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22745),X22742),c_Groups_Ozero__class_Ozero(X22745)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),X22743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)),X22743))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),c_Groups_Ozero__class_Ozero(X22745)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),X22743),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),X22742)),X22743))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22745),hAPP(c_Int_Onumber__class_Onumber__of(X22745),X22744)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22745),X22743),X22742)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22745)
        | ~ class_Int_Onumber(X22745) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5496])])]) ).

fof(i_0_7016,plain,
    ! [X22398,X22399,X22400,X22401,X22402] : c_Product__Type_Oprod_Oprod__size(X22402,X22401,X22400,X22399,X22398) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X22400,hAPP(c_Product__Type_Ofst(X22402,X22401),X22398))),hAPP(X22399,hAPP(c_Product__Type_Osnd(X22402,X22401),X22398)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_prod__size__simp]) ).

fof(i_0_7017,plain,
    ! [X24506,X24507,X24508,X24509,X24510] :
      ( ~ class_Groups_Ocomm__monoid__add(X24510)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24510),X24509),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24508),X24507),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24506),X24507))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24510),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24510,tc_Nat_Onat),X24509),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X24507))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24508,X24506)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__nat__ivl])]) ).

fof(i_0_7018,plain,
    ! [X24270,X24271,X24272,X24273] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk150_4(X24270,X24271,X24272,X24273)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24272)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24271),X24273))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24273),X24272)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24271),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24270))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24272)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk151_4(X24270,X24271,X24272,X24273)),X24270))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24271),X24273))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24273),X24272)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24271),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24270))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24272)) )
      & ( X24273 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk151_4(X24270,X24271,X24272,X24273)),esk150_4(X24270,X24271,X24272,X24273))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24271),X24273))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24271),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24273),X24272)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24271),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24270))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24272)) ) ),
    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_7019,plain,
    ! [X27300,X27301,X27302,X27303] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27303),X27302))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27303,X27303),tc_HOL_Obool)),X27301),hAPP(hAPP(c_Product__Type_OSigma(X27303,X27303),X27302),hAPP(c_COMBK(tc_fun(X27303,tc_HOL_Obool),X27303),X27302))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27303,tc_HOL_Obool)),X27300),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27303),X27302),X27301)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27303),X27300)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__equiv__class])]) ).

fof(i_0_7020,plain,
    ! [X19228,X19229,X19230,X19231,X19232,X19233] :
      ( ~ c_Fun_Oinj__on(X19233,X19232,X19231,X19230)
      | hBOOL(hAPP(hAPP(c_member(X19232),X19229),hAPP(c_Set_Oimage(X19233,X19232,X19231),X19230)))
      | c_Fun_Oinj__on(X19233,X19232,c_Fun_Ofun__upd(X19233,X19232,X19231,X19228,X19229),X19230) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5497])]) ).

fof(i_0_7021,plain,
    ! [X24707,X24708,X24709,X24710,X24711,X24712,X24713] :
      ( ~ c_Equiv__Relations_Oequiv(X24713,X24712,X24711)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24713,tc_HOL_Obool)),X24710),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24713),X24712),X24711)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24713,tc_HOL_Obool)),X24709),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24713),X24712),X24711)))
      | ~ hBOOL(hAPP(hAPP(c_member(X24713),X24708),X24710))
      | ~ hBOOL(hAPP(hAPP(c_member(X24713),X24707),X24709))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24713,X24713)),hAPP(hAPP(c_Product__Type_OPair(X24713,X24713),X24708),X24707)),X24711))
      | X24710 = X24709 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eqI])]) ).

fof(i_0_7022,plain,
    ! [X24714,X24715,X24716,X24717,X24718,X24719,X24720] :
      ( ( X24717 != X24716
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24720,X24720)),hAPP(hAPP(c_Product__Type_OPair(X24720,X24720),X24715),X24714)),X24718))
        | ~ hBOOL(hAPP(hAPP(c_member(X24720),X24714),X24716))
        | ~ hBOOL(hAPP(hAPP(c_member(X24720),X24715),X24717))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24720,tc_HOL_Obool)),X24716),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24720),X24719),X24718)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24720,tc_HOL_Obool)),X24717),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24720),X24719),X24718)))
        | ~ c_Equiv__Relations_Oequiv(X24720,X24719,X24718) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24720,X24720)),hAPP(hAPP(c_Product__Type_OPair(X24720,X24720),X24715),X24714)),X24718))
        | X24717 = X24716
        | ~ hBOOL(hAPP(hAPP(c_member(X24720),X24714),X24716))
        | ~ hBOOL(hAPP(hAPP(c_member(X24720),X24715),X24717))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24720,tc_HOL_Obool)),X24716),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24720),X24719),X24718)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24720,tc_HOL_Obool)),X24717),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24720),X24719),X24718)))
        | ~ c_Equiv__Relations_Oequiv(X24720,X24719,X24718) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__eq__iff])])]) ).

fof(i_0_7023,plain,
    ! [X25721,X25722,X25723] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25723),c_Groups_Ozero__class_Ozero(X25723)),esk219_3(X25721,X25722,X25723)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25723),X25722),X25721))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25723) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25723),esk219_3(X25721,X25722,X25723)),c_Groups_Oone__class_Oone(X25723)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25723),X25722),X25721))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25723) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25723),esk219_3(X25721,X25722,X25723)),X25722)),X25721))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25723),X25722),X25721))
        | ~ class_Fields_Olinordered__field__inverse__zero(X25723) ) ),
    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_7024,plain,
    ! [X32628,X32629] : c_Predicate_Opred__comp(X32629,X32629,X32629,c_fequal,c_Predicate_Opred__comp(X32629,X32629,X32629,X32628,c_fequal)) = X32628,
    inference(variable_rename,[status(thm)],[fact_eq__comp__r]) ).

fof(i_0_7025,plain,
    ! [X33314,X33315,X33316,X33317,X33318] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X33318,X33317,tc_HOL_Obool,X33316),X33315),X33314))
      | hBOOL(hAPP(X33316,hAPP(hAPP(c_Product__Type_OPair(X33318,X33317),X33315),X33314))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryE])]) ).

fof(i_0_7026,plain,
    ! [X33309,X33310,X33311,X33312,X33313] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X33313,X33312,tc_HOL_Obool,X33311),X33310),X33309))
      | hBOOL(hAPP(X33311,hAPP(hAPP(c_Product__Type_OPair(X33313,X33312),X33310),X33309))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryD])]) ).

fof(i_0_7027,plain,
    ! [X26934,X26935,X26936,X26937] : hAPP(c_Set_Ovimage(X26937,X26936,X26935),X26934) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26936,tc_fun(X26937,tc_HOL_Obool)),X26934),hAPP(hAPP(c_COMBB(tc_fun(X26936,tc_HOL_Obool),tc_fun(X26937,tc_HOL_Obool),X26936),c_Set_Ovimage(X26937,X26936,X26935)),hAPP(hAPP(c_COMBC(X26936,tc_fun(X26936,tc_HOL_Obool),tc_fun(X26936,tc_HOL_Obool)),c_Set_Oinsert(X26936)),c_Orderings_Obot__class_Obot(tc_fun(X26936,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_vimage__eq__UN]) ).

fof(i_0_7028,plain,
    ! [X24158,X24159,X24160,X24161] : hAPP(c_Relation_OImage(X24161,X24160,X24159),X24158) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24161,tc_fun(X24160,tc_HOL_Obool)),X24158),hAPP(hAPP(c_COMBB(tc_fun(X24161,tc_HOL_Obool),tc_fun(X24160,tc_HOL_Obool),X24161),c_Relation_OImage(X24161,X24160,X24159)),hAPP(hAPP(c_COMBC(X24161,tc_fun(X24161,tc_HOL_Obool),tc_fun(X24161,tc_HOL_Obool)),c_Set_Oinsert(X24161)),c_Orderings_Obot__class_Obot(tc_fun(X24161,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Image__eq__UN]) ).

fof(i_0_7029,plain,
    ! [X25200,X25201,X25202,X25203] :
      ( ~ class_Lattices_Olattice(X25203)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25203),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25203),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25203),X25202),X25201)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25203),X25202),X25200))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25203),X25202),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25203),X25201),X25200)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__inf__le])]) ).

fof(i_0_7030,plain,
    ! [X22651,X22652,X22653,X22654] :
      ( ~ class_Orderings_Olinorder(X22654)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22654),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22654),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22654),X22653),X22652)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22654),X22653),X22651))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22654),X22653),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22654),X22652),X22651)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__inf__le])]) ).

fof(i_0_7031,plain,
    ! [X33270,X33271,X33272,X33273,X33274] :
      ( ~ c_Fun_Obij__betw(X33274,X33273,X33272,X33271,X33270)
      | c_Fun_Obij__betw(X33273,X33274,c_Hilbert__Choice_Oinv__into(X33274,X33273,X33271,X33272),X33270,X33271) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__inv__into])]) ).

fof(i_0_7032,plain,
    ! [X33375,X33376,X33377,X33378,X33379] :
      ( ~ c_Fun_Obij__betw(X33379,X33378,X33377,X33376,X33375)
      | c_Fun_Obij__betw(X33378,X33379,c_Fun_Othe__inv__into(X33379,X33378,X33376,X33377),X33375,X33376) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__the__inv__into])]) ).

fof(i_0_7033,plain,
    ! [X33264,X33265,X33266,X33267,X33268,X33269] :
      ( ~ c_Fun_Obij__betw(X33269,X33268,X33267,X33266,X33265)
      | ~ hBOOL(hAPP(hAPP(c_member(X33269),X33264),X33266))
      | hAPP(c_Hilbert__Choice_Oinv__into(X33268,X33269,X33265,c_Hilbert__Choice_Oinv__into(X33269,X33268,X33266,X33267)),X33264) = hAPP(X33267,X33264) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__inv__into__eq])]) ).

fof(i_0_7034,plain,
    ! [X23647,X23648,X23649,X23650,X23651,X23652,X23653,X23654] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23654),X23653),X23652))
      | ~ hBOOL(hAPP(hAPP(hAPP(X23651,X23653),X23650),X23649))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23654,tc_fun(X23648,tc_fun(X23647,tc_HOL_Obool))),X23652),X23651),X23650),X23649)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP2__I])]) ).

fof(i_0_7035,plain,
    ! [X22075,X22076,X22077,X22078,X22079,X22080,X22081] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22081,X22080,tc_fun(X22079,tc_HOL_Obool)),X22078),hAPP(hAPP(c_Product__Type_OPair(X22081,X22080),X22077),X22076)),X22075))
      | hBOOL(hAPP(hAPP(hAPP(X22078,X22077),X22076),X22075)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD_H])]) ).

fof(i_0_7036,plain,
    ! [X27904,X27905,X27906,X27907,X27908,X27909] : hAPP(hAPP(c_Relation_Orel__comp(X27909,X27908,X27907),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27909,X27908),tc_HOL_Obool)),X27906),X27905)),X27904) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27909,X27907),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27909,X27908,X27907),X27906),X27904)),hAPP(hAPP(c_Relation_Orel__comp(X27909,X27908,X27907),X27905),X27904)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__distrib2]) ).

fof(i_0_7037,plain,
    ! [X26612,X26613,X26614,X26615,X26616] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26616)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26615),X26614))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26616),X26613),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26615,X26616),X26614),X26612)) = hAPP(hAPP(c_Finite__Set_Ofold(X26615,X26616,hAPP(hAPP(c_COMBB(X26616,tc_fun(X26616,X26616),X26615),c_Lattices_Osemilattice__inf__class_Oinf(X26616)),X26612)),X26613),X26614) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__INFI__fold__inf])]) ).

fof(i_0_7038,plain,
    ! [X23667,X23668,X23669,X23670,X23671] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X23671)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23670),X23669))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23671),X23668),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23670,X23671),X23669),X23667)) = hAPP(hAPP(c_Finite__Set_Ofold(X23670,X23671,hAPP(hAPP(c_COMBB(X23671,tc_fun(X23671,X23671),X23670),c_Lattices_Osemilattice__sup__class_Osup(X23671)),X23667)),X23668),X23669) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__SUPR__fold__sup])]) ).

fof(i_0_7039,plain,
    ! [X25537,X25538,X25539,X25540] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25540),X25539))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25540),X25538))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25540,tc_Nat_Onat),X25537),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25540,tc_HOL_Obool)),X25539),X25538)) = 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(X25540,tc_Nat_Onat),X25537),X25539)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25540,tc_Nat_Onat),X25537),X25538))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25540,tc_Nat_Onat),X25537),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25540,tc_HOL_Obool)),X25539),X25538))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__nat])]) ).

fof(i_0_7040,plain,
    ! [X27653,X27654] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27654),hAPP(c_Set_OCollect(X27654),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27654),c_fNot),X27653))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27654),c_Orderings_Otop__class_Otop(tc_fun(X27654,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27654),hAPP(c_Set_OCollect(X27654),X27653))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27654),c_Orderings_Otop__class_Otop(tc_fun(X27654,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27654),hAPP(c_Set_OCollect(X27654),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27654),c_fNot),X27653))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27654),hAPP(c_Set_OCollect(X27654),X27653))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Collect__not])])]) ).

fof(i_0_7041,plain,
    ! [X33436,X33437,X33438,X33439] :
      ( ~ c_Fun_Obij__betw(X33439,X33438,X33437,c_Orderings_Otop__class_Otop(tc_fun(X33439,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33438,tc_HOL_Obool)))
      | hAPP(c_Set_Ovimage(X33439,X33438,X33437),X33436) = hAPP(c_Set_Oimage(X33438,X33439,c_Hilbert__Choice_Oinv__into(X33439,X33438,c_Orderings_Otop__class_Otop(tc_fun(X33439,tc_HOL_Obool)),X33437)),X33436) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__vimage__eq__inv__image])]) ).

fof(i_0_7042,plain,
    ! [X21013,X21014,X21015,X21016] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21016))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21015),X21014))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21014),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),X21015),X21016)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21015),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21013,X21016))),X21014))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux1])]) ).

fof(i_0_7043,plain,
    ! [X18911,X18912,X18913,X18914,X18915] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18915),X18914))
      | 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),X18915),X18913)),X18912)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18914),X18913)),X18911)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18912),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),X18914),X18915)),X18913)),X18911)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2])]) ).

fof(i_0_7044,plain,
    ! [X25843,X25844,X25845,X25846] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25846)
      | hAPP(c_Groups_Oabs__class_Oabs(X25846),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25845,X25846),hAPP(hAPP(c_COMBB(X25846,X25846,X25845),c_Groups_Oabs__class_Oabs(X25846)),X25844)),X25843)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25845,X25846),hAPP(hAPP(c_COMBB(X25846,X25846,X25845),c_Groups_Oabs__class_Oabs(X25846)),X25844)),X25843) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setsum__abs])]) ).

fof(i_0_7045,plain,
    ! [X26240,X26241,X26242,X26243,X26244] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26243,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26244,X26243,X26242),X26241)),hAPP(c_Set_Oimage(X26244,X26243,X26242),X26240)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26244,tc_HOL_Obool)),X26241),X26240))
        | ~ c_Fun_Oinj__on(X26244,X26243,X26242,c_Orderings_Otop__class_Otop(tc_fun(X26244,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26244,tc_HOL_Obool)),X26241),X26240))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26243,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26244,X26243,X26242),X26241)),hAPP(c_Set_Oimage(X26244,X26243,X26242),X26240)))
        | ~ c_Fun_Oinj__on(X26244,X26243,X26242,c_Orderings_Otop__class_Otop(tc_fun(X26244,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__image__subset__iff])])]) ).

cnf(i_0_7046,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oconcat(X1,X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk445_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),esk446_2(X2,X1))),hAPP(c_List_Oset(X1),esk447_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_5498]) ).

fof(i_0_7047,plain,
    ! [X22949,X22950,X22951] :
      ( ~ class_Fields_Olinordered__field(X22951)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22951),X22950),X22949))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22951),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22951),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22951),X22950),X22949)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22951),c_Groups_Oone__class_Oone(X22951)),c_Groups_Oone__class_Oone(X22951)))),X22949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gt__half__sum])]) ).

fof(i_0_7048,plain,
    ! [X33142,X33143,X33144,X33145,X33146,X33147] :
      ( hAPP(c_Hilbert__Choice_Oinv__into(X33147,X33146,X33145,X33144),X33143) != hAPP(c_Hilbert__Choice_Oinv__into(X33147,X33146,X33145,X33144),X33142)
      | ~ hBOOL(hAPP(hAPP(c_member(X33146),X33143),hAPP(c_Set_Oimage(X33147,X33146,X33144),X33145)))
      | ~ hBOOL(hAPP(hAPP(c_member(X33146),X33142),hAPP(c_Set_Oimage(X33147,X33146,X33144),X33145)))
      | X33143 = X33142 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__injective])]) ).

fof(i_0_7049,plain,
    ! [X31123,X31124,X31125,X31126,X31127,X31128,X31129] :
      ( ( hBOOL(hAPP(hAPP(X31127,X31126),X31124))
        | ~ c_List_Olist__all2(X31129,X31128,X31127,hAPP(hAPP(c_List_Olist_OCons(X31129),X31126),X31125),hAPP(hAPP(c_List_Olist_OCons(X31128),X31124),X31123)) )
      & ( c_List_Olist__all2(X31129,X31128,X31127,X31125,X31123)
        | ~ c_List_Olist__all2(X31129,X31128,X31127,hAPP(hAPP(c_List_Olist_OCons(X31129),X31126),X31125),hAPP(hAPP(c_List_Olist_OCons(X31128),X31124),X31123)) )
      & ( ~ hBOOL(hAPP(hAPP(X31127,X31126),X31124))
        | ~ c_List_Olist__all2(X31129,X31128,X31127,X31125,X31123)
        | c_List_Olist__all2(X31129,X31128,X31127,hAPP(hAPP(c_List_Olist_OCons(X31129),X31126),X31125),hAPP(hAPP(c_List_Olist_OCons(X31128),X31124),X31123)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Cons])])]) ).

fof(i_0_7050,plain,
    ! [X19673,X19674,X19675] :
      ( ~ 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),X19675),X19674)),X19673)),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)),X19673))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19675))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19674),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_7051,plain,
    ! [X27644,X27645,X27646] :
      ( ( ~ hBOOL(hAPP(X27646,X27645))
        | hAPP(c_Set_OCollect(X27644),hAPP(hAPP(c_COMBS(X27644,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27644),c_fconj),hAPP(c_fequal,X27645))),X27646)) = hAPP(hAPP(c_Set_Oinsert(X27644),X27645),c_Orderings_Obot__class_Obot(tc_fun(X27644,tc_HOL_Obool))) )
      & ( hBOOL(hAPP(X27646,X27645))
        | hAPP(c_Set_OCollect(X27644),hAPP(hAPP(c_COMBS(X27644,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27644),c_fconj),hAPP(c_fequal,X27645))),X27646)) = c_Orderings_Obot__class_Obot(tc_fun(X27644,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5499])]) ).

cnf(i_0_7052,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_5500]) ).

cnf(i_0_7053,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_5501]) ).

fof(i_0_7054,plain,
    ! [X29619,X29620,X29621,X29622] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29622),X29621),hAPP(c_List_Oset(X29622),X29619)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29622,X29622)),hAPP(hAPP(c_Product__Type_OPair(X29622,X29622),X29621),X29620)),hAPP(c_List_Oset(tc_prod(X29622,X29622)),hAPP(hAPP(c_List_Ozip(X29622,X29622),X29619),X29619)))) )
      & ( X29621 = X29620
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29622,X29622)),hAPP(hAPP(c_Product__Type_OPair(X29622,X29622),X29621),X29620)),hAPP(c_List_Oset(tc_prod(X29622,X29622)),hAPP(hAPP(c_List_Ozip(X29622,X29622),X29619),X29619)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29622),X29621),hAPP(c_List_Oset(X29622),X29619)))
        | X29621 != X29620
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X29622,X29622)),hAPP(hAPP(c_Product__Type_OPair(X29622,X29622),X29621),X29620)),hAPP(c_List_Oset(tc_prod(X29622,X29622)),hAPP(hAPP(c_List_Ozip(X29622,X29622),X29619),X29619)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__same])])]) ).

fof(i_0_7055,plain,
    ! [X29601,X29602,X29603,X29604,X29605,X29606] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29606),X29604),hAPP(c_List_Oset(X29606),X29602)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29606,X29605)),hAPP(hAPP(c_Product__Type_OPair(X29606,X29605),X29604),X29603)),hAPP(c_List_Oset(tc_prod(X29606,X29605)),hAPP(hAPP(c_List_Ozip(X29606,X29605),X29602),X29601)))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29605),X29603),hAPP(c_List_Oset(X29605),X29601)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29606,X29605)),hAPP(hAPP(c_Product__Type_OPair(X29606,X29605),X29604),X29603)),hAPP(c_List_Oset(tc_prod(X29606,X29605)),hAPP(hAPP(c_List_Ozip(X29606,X29605),X29602),X29601)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5502])])]) ).

fof(i_0_7056,plain,
    ! [X29613,X29614,X29615,X29616,X29617,X29618] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29618,X29617)),hAPP(hAPP(c_Product__Type_OPair(X29618,X29617),X29616),X29615)),hAPP(c_List_Oset(tc_prod(X29618,X29617)),hAPP(hAPP(c_List_Ozip(X29618,X29617),X29614),X29613))))
      | hBOOL(hAPP(hAPP(c_member(X29618),X29616),hAPP(c_List_Oset(X29618),X29614))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__leftD])]) ).

fof(i_0_7057,plain,
    ! [X29607,X29608,X29609,X29610,X29611,X29612] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29612,X29611)),hAPP(hAPP(c_Product__Type_OPair(X29612,X29611),X29610),X29609)),hAPP(c_List_Oset(tc_prod(X29612,X29611)),hAPP(hAPP(c_List_Ozip(X29612,X29611),X29608),X29607))))
      | hBOOL(hAPP(hAPP(c_member(X29611),X29609),hAPP(c_List_Oset(X29611),X29607))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__zip__rightD])]) ).

fof(i_0_7058,plain,
    ! [X25439,X25440,X25441,X25442,X25443,X25444] :
      ( ~ c_Finite__Set_Ofolding(X25444,X25443,X25442,X25441)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25444),X25440))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25444),X25439))
      | hAPP(c_Fun_Ocomp(X25443,X25443,X25443,hAPP(X25441,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25444,tc_HOL_Obool)),X25440),X25439))),hAPP(X25441,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25444,tc_HOL_Obool)),X25440),X25439))) = hAPP(c_Fun_Ocomp(X25443,X25443,X25443,hAPP(X25441,X25440)),hAPP(X25441,X25439)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion__inter])]) ).

fof(i_0_7059,plain,
    ! [X25904,X25905,X25906] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25906)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25906),hAPP(c_Groups_Oabs__class_Oabs(X25906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25906),hAPP(c_Groups_Oabs__class_Oabs(X25906),X25905)),hAPP(c_Groups_Oabs__class_Oabs(X25906),X25904)))),hAPP(c_Groups_Oabs__class_Oabs(X25906),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25906),X25905),X25904)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq3])]) ).

cnf(i_0_7060,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_5503]) ).

fof(i_0_7061,plain,
    ! [X19444] :
      ( ( ~ 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)),X19444)),X19444)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19444),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19444),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)),X19444)),X19444)),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_7062,plain,
    ! [X26290,X26291,X26292,X26293] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26293)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26292),X26291))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26292,X26293),X26291),X26290) = hAPP(hAPP(c_Finite__Set_Ofold(X26292,X26293,hAPP(hAPP(c_COMBB(X26293,tc_fun(X26293,X26293),X26292),c_Lattices_Osemilattice__inf__class_Oinf(X26293)),X26290)),c_Orderings_Otop__class_Otop(X26293)),X26291) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__fold__inf])]) ).

fof(i_0_7063,plain,
    ! [X23617,X23618,X23619,X23620] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X23620)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23619),X23618))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23619,X23620),X23618),X23617) = hAPP(hAPP(c_Finite__Set_Ofold(X23619,X23620,hAPP(hAPP(c_COMBB(X23620,tc_fun(X23620,X23620),X23619),c_Lattices_Osemilattice__sup__class_Osup(X23620)),X23617)),c_Orderings_Obot__class_Obot(X23620)),X23618) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__fold__sup])]) ).

fof(i_0_7064,plain,
    ! [X28739,X28740,X28741,X28742] :
      ( ( c_Wellfounded_Oacyclic(X28742,X28739)
        | ~ c_Wellfounded_Oacyclic(X28742,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28742,X28742)),hAPP(hAPP(c_Product__Type_OPair(X28742,X28742),X28741),X28740)),X28739)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28742,X28742)),hAPP(hAPP(c_Product__Type_OPair(X28742,X28742),X28740),X28741)),c_Transitive__Closure_Ortrancl(X28742,X28739)))
        | ~ c_Wellfounded_Oacyclic(X28742,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28742,X28742)),hAPP(hAPP(c_Product__Type_OPair(X28742,X28742),X28741),X28740)),X28739)) )
      & ( ~ c_Wellfounded_Oacyclic(X28742,X28739)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28742,X28742)),hAPP(hAPP(c_Product__Type_OPair(X28742,X28742),X28740),X28741)),c_Transitive__Closure_Ortrancl(X28742,X28739)))
        | c_Wellfounded_Oacyclic(X28742,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28742,X28742)),hAPP(hAPP(c_Product__Type_OPair(X28742,X28742),X28741),X28740)),X28739)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5504])])]) ).

fof(i_0_7065,plain,
    ! [X28735,X28736,X28737,X28738] :
      ( ( c_Wellfounded_Owf(X28738,X28735)
        | ~ c_Wellfounded_Owf(X28738,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28738,X28738)),hAPP(hAPP(c_Product__Type_OPair(X28738,X28738),X28737),X28736)),X28735)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28738,X28738)),hAPP(hAPP(c_Product__Type_OPair(X28738,X28738),X28736),X28737)),c_Transitive__Closure_Ortrancl(X28738,X28735)))
        | ~ c_Wellfounded_Owf(X28738,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28738,X28738)),hAPP(hAPP(c_Product__Type_OPair(X28738,X28738),X28737),X28736)),X28735)) )
      & ( ~ c_Wellfounded_Owf(X28738,X28735)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28738,X28738)),hAPP(hAPP(c_Product__Type_OPair(X28738,X28738),X28736),X28737)),c_Transitive__Closure_Ortrancl(X28738,X28735)))
        | c_Wellfounded_Owf(X28738,hAPP(hAPP(c_Set_Oinsert(tc_prod(X28738,X28738)),hAPP(hAPP(c_Product__Type_OPair(X28738,X28738),X28737),X28736)),X28735)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5505])])]) ).

cnf(i_0_7066,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_5506]) ).

fof(i_0_7067,plain,
    ! [X28911,X28912,X28913,X28914,X28915,X28916] :
      ( ~ c_Relation_Osingle__valued(X28916,X28915,X28914)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28916,X28915)),hAPP(hAPP(c_Product__Type_OPair(X28916,X28915),X28913),X28912)),X28914))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28916,X28915)),hAPP(hAPP(c_Product__Type_OPair(X28916,X28915),X28913),X28911)),X28914))
      | X28912 = X28911 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valuedD])]) ).

fof(i_0_7068,plain,
    ! [X27592,X27593,X27594] : hAPP(c_Set_OCollect(X27594),hAPP(hAPP(c_COMBS(X27594,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27594),c_fdisj),X27593)),X27592)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27594,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27594),X27593)),hAPP(c_Set_OCollect(X27594),X27592)),
    inference(variable_rename,[status(thm)],[fact_Collect__disj__eq]) ).

fof(i_0_7069,plain,
    ! [X27586,X27587,X27588] : hAPP(c_Set_OCollect(X27588),hAPP(hAPP(c_COMBS(X27588,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X27588),c_fconj),X27587)),X27586)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27588,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27588),X27587)),hAPP(c_Set_OCollect(X27588),X27586)),
    inference(variable_rename,[status(thm)],[fact_Collect__conj__eq]) ).

fof(i_0_7070,plain,
    ! [X29102,X29103,X29104,X29105,X29107,X29108,X29109,X29112] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29103),esk359_3(X29102,X29103,X29104)),X29104))
        | ~ hBOOL(hAPP(hAPP(c_member(X29103),X29105),X29104))
        | ~ c_Wellfounded_Owf(X29103,X29102) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29103,X29103)),hAPP(hAPP(c_Product__Type_OPair(X29103,X29103),X29107),esk359_3(X29102,X29103,X29104))),X29102))
        | ~ hBOOL(hAPP(hAPP(c_member(X29103),X29107),X29104))
        | ~ hBOOL(hAPP(hAPP(c_member(X29103),X29105),X29104))
        | ~ c_Wellfounded_Owf(X29103,X29102) )
      & ( hBOOL(hAPP(hAPP(c_member(X29109),esk361_2(X29108,X29109)),esk360_2(X29108,X29109)))
        | c_Wellfounded_Owf(X29109,X29108) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29109,X29109)),hAPP(hAPP(c_Product__Type_OPair(X29109,X29109),esk362_3(X29108,X29109,X29112)),X29112)),X29108))
        | ~ hBOOL(hAPP(hAPP(c_member(X29109),X29112),esk360_2(X29108,X29109)))
        | c_Wellfounded_Owf(X29109,X29108) )
      & ( hBOOL(hAPP(hAPP(c_member(X29109),esk362_3(X29108,X29109,X29112)),esk360_2(X29108,X29109)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29109),X29112),esk360_2(X29108,X29109)))
        | c_Wellfounded_Owf(X29109,X29108) ) ),
    inference(distribute,[status(thm)],[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_5507])])])])])]) ).

cnf(i_0_7071,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_5508]) ).

cnf(i_0_7072,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_5509]) ).

cnf(i_0_7073,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_5510]) ).

cnf(i_0_7074,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_5511]) ).

cnf(i_0_7075,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_5512]) ).

cnf(i_0_7076,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_5513]) ).

cnf(i_0_7077,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_5514]) ).

fof(i_0_7078,plain,
    ! [X31103,X31104,X31105,X31106,X31107,X31108] :
      ( ~ c_List_Olist__all2(X31108,X31107,X31106,X31105,X31104)
      | c_List_Olist__all2(X31108,X31107,X31106,hAPP(hAPP(c_List_Odrop(X31108),X31103),X31105),hAPP(hAPP(c_List_Odrop(X31107),X31103),X31104)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__dropI])]) ).

fof(i_0_7079,plain,
    ! [X31130,X31131,X31132,X31133,X31134,X31135] :
      ( ~ c_List_Olist__all2(X31135,X31134,X31133,X31132,X31131)
      | c_List_Olist__all2(X31135,X31134,X31133,hAPP(hAPP(c_List_Otake(X31135),X31130),X31132),hAPP(hAPP(c_List_Otake(X31134),X31130),X31131)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__takeI])]) ).

fof(i_0_7080,plain,
    ! [X28843,X28844,X28845,X28846] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28846,X28846)),hAPP(hAPP(c_Product__Type_OPair(X28846,X28846),X28845),X28844)),c_Transitive__Closure_Ortrancl(X28846,hAPP(c_Relation_Oconverse(X28846,X28846),X28843))))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28846,X28846)),hAPP(hAPP(c_Product__Type_OPair(X28846,X28846),X28844),X28845)),c_Transitive__Closure_Ortrancl(X28846,X28843))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseD])]) ).

fof(i_0_7081,plain,
    ! [X32986,X32987,X32988,X32989] :
      ( ~ c_Relation_Oantisym(X32989,X32988)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32989,X32989)),hAPP(hAPP(c_Product__Type_OPair(X32989,X32989),X32987),X32986)),X32988))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32989,X32989)),hAPP(hAPP(c_Product__Type_OPair(X32989,X32989),X32986),X32987)),X32988))
      | X32987 = X32986 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisymD])]) ).

fof(i_0_7082,plain,
    ! [X32978,X32979,X32980,X32981,X32982,X32983] :
      ( ( ~ c_Relation_Oantisym(X32979,X32978)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32979,X32979)),hAPP(hAPP(c_Product__Type_OPair(X32979,X32979),X32980),X32981)),X32978))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32979,X32979)),hAPP(hAPP(c_Product__Type_OPair(X32979,X32979),X32981),X32980)),X32978))
        | X32980 = X32981 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32983,X32983)),hAPP(hAPP(c_Product__Type_OPair(X32983,X32983),esk511_2(X32982,X32983)),esk512_2(X32982,X32983))),X32982))
        | c_Relation_Oantisym(X32983,X32982) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X32983,X32983)),hAPP(hAPP(c_Product__Type_OPair(X32983,X32983),esk512_2(X32982,X32983)),esk511_2(X32982,X32983))),X32982))
        | c_Relation_Oantisym(X32983,X32982) )
      & ( esk511_2(X32982,X32983) != esk512_2(X32982,X32983)
        | c_Relation_Oantisym(X32983,X32982) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__def])])])])])]) ).

fof(i_0_7083,plain,
    ! [X28103,X28104,X28105,X28106] :
      ( ~ c_Wellfounded_Owf(X28106,X28105)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28106,X28106)),hAPP(hAPP(c_Product__Type_OPair(X28106,X28106),X28104),X28103)),X28105))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28106,X28106)),hAPP(hAPP(c_Product__Type_OPair(X28106,X28106),X28103),X28104)),X28105)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5515])]) ).

fof(i_0_7084,plain,
    ! [X28099,X28100,X28101,X28102] :
      ( ~ c_Wellfounded_Owf(X28102,X28101)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28102,X28102)),hAPP(hAPP(c_Product__Type_OPair(X28102,X28102),X28100),X28099)),X28101))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28102,X28102)),hAPP(hAPP(c_Product__Type_OPair(X28102,X28102),X28099),X28100)),X28101)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5516])]) ).

fof(i_0_7085,plain,
    ! [X30765,X30766,X30767,X30768,X30769] :
      ( ~ class_Rings_Osemiring__0(X30769)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30769),hAPP(hAPP(c_List_Omap(X30768,X30769),hAPP(hAPP(c_COMBB(X30769,X30769,X30768),hAPP(c_Groups_Otimes__class_Otimes(X30769),X30767)),X30766)),X30765)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X30769),X30767),hAPP(c_List_Omonoid__add__class_Olistsum(X30769),hAPP(hAPP(c_List_Omap(X30768,X30769),X30766),X30765))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__const__mult])]) ).

fof(i_0_7086,plain,
    ! [X24060,X24061,X24062,X24063,X24064,X24065] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X24065,X24064),tc_HOL_Obool)),X24063),X24062))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24065,tc_HOL_Obool)),X24061),X24060))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24064,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24065,X24064,X24063),X24061)),hAPP(c_Relation_OImage(X24065,X24064,X24062),X24060))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__mono])]) ).

fof(i_0_7087,plain,
    ! [X22428,X22429,X22430] :
      ( ( X22430 = 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( X22429 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22428) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( 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),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),X22429))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22429),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),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)),X22429))
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( X22429 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22429),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),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)),X22429))
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | ~ 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),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),X22429))
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22429),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),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),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),X22429))
        | X22429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( X22429 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22428) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22428) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22429),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),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)),X22429))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22428) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22429))
        | ~ 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),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),X22429))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22428) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X22429),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),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),X22428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428)),X22429))
        | hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X22428) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X22430 != 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),X22428)),X22429)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X22428))
        | hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22430,X22429),X22428)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5517])])]) ).

fof(i_0_7088,plain,
    ! [X22414,X22415,X22416,X22417,X22418] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(X22418,X22417)),hAPP(X22418,X22416)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22415,X22415)),hAPP(hAPP(c_Product__Type_OPair(X22415,X22415),X22417),X22416)),X22414))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X22415,X22415)),hAPP(hAPP(c_Product__Type_OPair(X22415,X22415),X22417),X22416)),c_Wellfounded_Omlex__prod(X22415,X22418,X22414))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__leq])]) ).

fof(i_0_7089,plain,
    ! [X22717,X22718,X22719,X22720] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),X22719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22719))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),X22717))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),X22717))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22719))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),X22717))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22719))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),X22719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),X22719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),X22717))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),X22719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718)),c_Groups_Ozero__class_Ozero(X22720)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22719))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),X22719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),c_Groups_Ozero__class_Ozero(X22720)),X22717))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22719))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),X22719),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22720),X22717),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22720),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22720),X22719),hAPP(c_Int_Onumber__class_Onumber__of(X22720),X22718))),X22717))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22720)
        | ~ class_Int_Onumber(X22720) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5518])])]) ).

fof(i_0_7090,plain,
    ! [X22734,X22735,X22736,X22737] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),X22736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22736))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),c_Groups_Ozero__class_Ozero(X22737)),X22734))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),c_Groups_Ozero__class_Ozero(X22737)),X22734))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22736))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),c_Groups_Ozero__class_Ozero(X22737)),X22734))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22736))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),c_Groups_Ozero__class_Ozero(X22737)),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),X22736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),X22736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),c_Groups_Ozero__class_Ozero(X22737)),X22734))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),X22736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22737),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735)),c_Groups_Ozero__class_Ozero(X22737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22736))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),X22736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),c_Groups_Ozero__class_Ozero(X22737)),X22734))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22736))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),X22736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22737),X22734),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22737),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22737),X22736),hAPP(c_Int_Onumber__class_Onumber__of(X22737),X22735))),X22734))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22737)
        | ~ class_Int_Onumber(X22737) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5519])])]) ).

cnf(i_0_7091,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_5485]) ).

fof(i_0_7092,plain,
    ! [X27208,X27209,X27210,X27211] : hAPP(c_Set_Oimage(tc_prod(X27211,X27210),tc_prod(X27210,X27211),hAPP(c_Product__Type_Oprod_Oprod__case(X27211,X27210,tc_prod(X27210,X27211)),hAPP(c_COMBC(X27210,X27211,tc_prod(X27210,X27211)),c_Product__Type_OPair(X27210,X27211)))),hAPP(hAPP(c_Product__Type_OSigma(X27211,X27210),X27209),hAPP(c_COMBK(tc_fun(X27210,tc_HOL_Obool),X27211),X27208))) = hAPP(hAPP(c_Product__Type_OSigma(X27210,X27211),X27208),hAPP(c_COMBK(tc_fun(X27211,tc_HOL_Obool),X27210),X27209)),
    inference(variable_rename,[status(thm)],[fact_swap__product]) ).

cnf(i_0_7093,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_5520]) ).

fof(i_0_7094,plain,
    ! [X24607,X24608,X24609,X24610] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X24610),X24609),X24608))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X24610,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24610,X24610,X24607),hAPP(hAPP(c_Set_Oinsert(X24610),X24609),c_Orderings_Obot__class_Obot(tc_fun(X24610,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24610),X24608),X24607))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotientI])]) ).

fof(i_0_7095,plain,
    ! [X24199,X24200,X24201,X24202,X24203] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24203),X24202),hAPP(c_Relation_OImage(X24201,X24203,X24200),hAPP(hAPP(c_Set_Oinsert(X24201),X24199),c_Orderings_Obot__class_Obot(tc_fun(X24201,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24201,X24203)),hAPP(hAPP(c_Product__Type_OPair(X24201,X24203),X24199),X24202)),X24200)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24201,X24203)),hAPP(hAPP(c_Product__Type_OPair(X24201,X24203),X24199),X24202)),X24200))
        | hBOOL(hAPP(hAPP(c_member(X24203),X24202),hAPP(c_Relation_OImage(X24201,X24203,X24200),hAPP(hAPP(c_Set_Oinsert(X24201),X24199),c_Orderings_Obot__class_Obot(tc_fun(X24201,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__singleton__iff])]) ).

fof(i_0_7096,plain,
    ! [X31813,X31814,X31815,X31816,X31817] :
      ( ( ~ c_List_Olist__all2(X31817,X31816,X31815,hAPP(c_List_Orev(X31817),X31814),hAPP(c_List_Orev(X31816),X31813))
        | c_List_Olist__all2(X31817,X31816,X31815,X31814,X31813) )
      & ( ~ c_List_Olist__all2(X31817,X31816,X31815,X31814,X31813)
        | c_List_Olist__all2(X31817,X31816,X31815,hAPP(c_List_Orev(X31817),X31814),hAPP(c_List_Orev(X31816),X31813)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev])]) ).

cnf(i_0_7097,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),esk446_2(X2,X1))),hAPP(c_List_Oset(X1),esk447_2(X2,X1))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),esk445_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5498]) ).

fof(i_0_7098,plain,
    ! [X22301,X22302,X22303] :
      ( ( 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),esk97_3(X22301,X22302,X22303)),esk98_3(X22301,X22302,X22303))))
        | hBOOL(hAPP(hAPP(X22301,X22303),X22302))
        | ~ 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),X22303),X22302))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk98_3(X22301,X22302,X22303)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X22301,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk97_3(X22301,X22302,X22303))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk98_3(X22301,X22302,X22303))))
        | hBOOL(hAPP(hAPP(X22301,X22303),X22302))
        | ~ 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),X22303),X22302))) )
      & ( ~ hBOOL(hAPP(hAPP(X22301,esk97_3(X22301,X22302,X22303)),esk98_3(X22301,X22302,X22303)))
        | hBOOL(hAPP(hAPP(X22301,X22303),X22302))
        | ~ 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),X22303),X22302))) ) ),
    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_7099,plain,
    ! [X24310,X24311,X24312,X24313] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk164_4(X24310,X24311,X24312,X24313)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24312)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24313),X24311))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24313),X24312)),X24311))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24311),X24310))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24312)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk165_4(X24310,X24311,X24312,X24313)),X24310))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24313),X24311))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24313),X24312)),X24311))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24311),X24310))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24312)) )
      & ( X24313 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk165_4(X24310,X24311,X24312,X24313)),esk164_4(X24310,X24311,X24312,X24313))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24313),X24311))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24313),X24312)),X24311))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24311),X24310))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24312)) ) ),
    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_7100,plain,
    ! [X20850,X20851,X20852,X20853] :
      ( ~ class_Divides_Osemiring__div(X20853)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20853),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20853),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20853),X20852),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20853),X20851),X20852))),c_Divides_Odiv__class_Omod(X20853,X20851,X20852))),X20850) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20853),X20851),X20850) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mod__equality2])]) ).

fof(i_0_7101,plain,
    ! [X31818,X31819,X31820,X31821,X31822] :
      ( ( ~ c_List_Olist__all2(X31822,X31821,X31820,hAPP(c_List_Orev(X31822),X31819),X31818)
        | c_List_Olist__all2(X31822,X31821,X31820,X31819,hAPP(c_List_Orev(X31821),X31818)) )
      & ( ~ c_List_Olist__all2(X31822,X31821,X31820,X31819,hAPP(c_List_Orev(X31821),X31818))
        | c_List_Olist__all2(X31822,X31821,X31820,hAPP(c_List_Orev(X31822),X31819),X31818) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__rev1])]) ).

fof(i_0_7102,plain,
    ! [X30533,X30534,X30535,X30538,X30539,X30540,X30541,X30542] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30535),tc_List_Olist(X30535))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30535),tc_List_Olist(X30535)),c_List_Olist_ONil(X30535)),X30534)),c_List_Olexord(X30535,X30533)))
        | X30534 = hAPP(hAPP(c_List_Olist_OCons(X30535),esk409_3(X30533,X30534,X30535)),esk410_3(X30533,X30534,X30535)) )
      & ( X30539 != hAPP(hAPP(c_List_Olist_OCons(X30540),X30541),X30542)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30540),tc_List_Olist(X30540))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30540),tc_List_Olist(X30540)),c_List_Olist_ONil(X30540)),X30539)),c_List_Olexord(X30540,X30538))) ) ),
    inference(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_7103,plain,
    ! [X26859,X26860,X26861,X26862] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26862,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26861,X26862,X26860),hAPP(c_Set_Ovimage(X26861,X26862,X26860),X26859))),X26859)),
    inference(variable_rename,[status(thm)],[fact_image__vimage__subset]) ).

fof(i_0_7104,plain,
    ! [X31768,X31769,X31770,X31771,X31772] :
      ( ~ class_Orderings_Olinorder(X31772)
      | ~ c_Fun_Oinj__on(X31771,X31772,X31770,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31771,tc_HOL_Obool)),hAPP(c_List_Oset(X31771),X31769)),hAPP(c_List_Oset(X31771),X31768)))
      | ~ c_List_Olinorder__class_Osorted(X31772,hAPP(hAPP(c_List_Omap(X31771,X31772),X31770),X31769))
      | ~ hBOOL(hAPP(c_List_Odistinct(X31772),hAPP(hAPP(c_List_Omap(X31771,X31772),X31770),X31769)))
      | ~ c_List_Olinorder__class_Osorted(X31772,hAPP(hAPP(c_List_Omap(X31771,X31772),X31770),X31768))
      | ~ hBOOL(hAPP(c_List_Odistinct(X31772),hAPP(hAPP(c_List_Omap(X31771,X31772),X31770),X31768)))
      | hAPP(c_List_Oset(X31771),X31769) != hAPP(c_List_Oset(X31771),X31768)
      | X31769 = X31768 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__sorted__distinct__set__unique])]) ).

fof(i_0_7105,plain,
    ! [X21021,X21022,X21023,X21024] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21023))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21023),X21022))
      | 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),X21022),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21021,X21024))),X21023))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult2__lemma__aux3])]) ).

fof(i_0_7106,plain,
    ! [X27322,X27323,X27324] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27324),X27323))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27324,X27324),tc_HOL_Obool)),X27322),hAPP(hAPP(c_Product__Type_OSigma(X27324,X27324),X27323),hAPP(c_COMBK(tc_fun(X27324,tc_HOL_Obool),X27324),X27323))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27324,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27324),X27323),X27322))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__quotient])]) ).

fof(i_0_7107,plain,
    ! [X30480,X30481,X30482,X30483,X30484,X30485] : hAPP(c_List_Ofoldl(X30485,X30484,X30483,X30482),hAPP(hAPP(c_List_Oappend(X30484),X30481),X30480)) = hAPP(c_List_Ofoldl(X30485,X30484,X30483,hAPP(c_List_Ofoldl(X30485,X30484,X30483,X30482),X30481)),X30480),
    inference(variable_rename,[status(thm)],[fact_foldl__append]) ).

cnf(i_0_7108,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk447_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)),esk445_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_5498]) ).

cnf(i_0_7109,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk446_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)),esk445_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_5498]) ).

fof(i_0_7110,plain,
    ! [X28847,X28848,X28849,X28850] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28850,X28850)),hAPP(hAPP(c_Product__Type_OPair(X28850,X28850),X28849),X28848)),c_Transitive__Closure_Ortrancl(X28850,X28847)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28850,X28850)),hAPP(hAPP(c_Product__Type_OPair(X28850,X28850),X28848),X28849)),c_Transitive__Closure_Ortrancl(X28850,hAPP(c_Relation_Oconverse(X28850,X28850),X28847)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__converseI])]) ).

fof(i_0_7111,plain,
    ! [X32668,X32669,X32670] :
      ( ( 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),esk483_3(X32668,X32669,X32670)),esk484_3(X32668,X32669,X32670))))
        | hBOOL(hAPP(hAPP(X32668,X32670),X32669))
        | ~ 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),X32670),X32669))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk483_3(X32668,X32669,X32670)),esk484_3(X32668,X32669,X32670)))
        | hBOOL(hAPP(hAPP(X32668,esk483_3(X32668,X32669,X32670)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk484_3(X32668,X32669,X32670)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(X32668,X32670),X32669))
        | ~ 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),X32670),X32669))) )
      & ( ~ hBOOL(hAPP(hAPP(X32668,esk483_3(X32668,X32669,X32670)),esk484_3(X32668,X32669,X32670)))
        | hBOOL(hAPP(hAPP(X32668,X32670),X32669))
        | ~ 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),X32670),X32669))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5521])])])]) ).

fof(i_0_7112,plain,
    ! [X30343,X30344,X30345,X30346,X30347] : hAPP(hAPP(c_List_Ozip(X30347,X30346),hAPP(hAPP(c_List_Oappend(X30347),X30345),X30344)),X30343) = hAPP(hAPP(c_List_Oappend(tc_prod(X30347,X30346)),hAPP(hAPP(c_List_Ozip(X30347,X30346),X30345),hAPP(hAPP(c_List_Otake(X30346),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30347)),X30345)),X30343))),hAPP(hAPP(c_List_Ozip(X30347,X30346),X30344),hAPP(hAPP(c_List_Odrop(X30346),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30347)),X30345)),X30343))),
    inference(variable_rename,[status(thm)],[fact_zip__append1]) ).

fof(i_0_7113,plain,
    ! [X23394,X23395,X23396,X23397] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23397,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23397,tc_HOL_Obool)),X23396),X23395)),X23394))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23397,tc_HOL_Obool)),X23396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23397,tc_HOL_Obool)),X23395),X23394))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23397,tc_HOL_Obool)),X23396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23397,tc_HOL_Obool)),X23395),X23394)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23397,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23397,tc_HOL_Obool)),X23396),X23395)),X23394)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__subset__conv])]) ).

cnf(i_0_7114,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_5522]) ).

fof(i_0_7115,plain,
    ! [X24687,X24688,X24689,X24690] :
      ( ( X24689 = hAPP(c_Relation_OImage(X24690,X24690,X24687),hAPP(hAPP(c_Set_Oinsert(X24690),esk187_4(X24687,X24688,X24689,X24690)),c_Orderings_Obot__class_Obot(tc_fun(X24690,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24690,tc_HOL_Obool)),X24689),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24690),X24688),X24687))) )
      & ( hBOOL(hAPP(hAPP(c_member(X24690),esk187_4(X24687,X24688,X24689,X24690)),X24688))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X24690,tc_HOL_Obool)),X24689),hAPP(hAPP(c_Equiv__Relations_Oquotient(X24690),X24688),X24687))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5523])])])]) ).

cnf(i_0_7116,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_5524]) ).

cnf(i_0_7117,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_5525]) ).

cnf(i_0_7118,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_5526]) ).

fof(i_0_7119,plain,
    ! [X33138,X33139,X33140,X33141] :
      ( hAPP(c_Set_Oimage(X33141,X33140,X33139),c_Orderings_Otop__class_Otop(tc_fun(X33141,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33140,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X33141,X33140,X33139),hAPP(c_Set_Oimage(X33140,X33141,c_Hilbert__Choice_Oinv__into(X33141,X33140,c_Orderings_Otop__class_Otop(tc_fun(X33141,tc_HOL_Obool)),X33139)),X33138)) = X33138 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__surj__f__inv__f])]) ).

fof(i_0_7120,plain,
    ! [X24339,X24340,X24341,X24342] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk176_4(X24339,X24340,X24341,X24342)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24341)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24342),X24339))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24342),X24341)),X24339))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24341)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk177_4(X24339,X24340,X24341,X24342)),X24340))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24342),X24339))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24342),X24341)),X24339))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24341)) )
      & ( X24342 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk177_4(X24339,X24340,X24341,X24342)),esk176_4(X24339,X24340,X24341,X24342))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24342),X24339))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24342),X24341)),X24339))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24341)) ) ),
    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_7121,plain,
    ! [X24322,X24323,X24324,X24325] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk168_4(X24322,X24323,X24324,X24325)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24324)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24325),X24322))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24325),X24324)),X24322))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24324)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk169_4(X24322,X24323,X24324,X24325)),X24323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24325),X24322))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24325),X24324)),X24322))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24324)) )
      & ( X24325 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk169_4(X24322,X24323,X24324,X24325)),esk168_4(X24322,X24323,X24324,X24325))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24325),X24322))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24325),X24324)),X24322))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24324)) ) ),
    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_7122,plain,
    ! [X30321,X30322,X30323,X30324,X30325] :
      ( ( X30324 = hAPP(hAPP(c_List_Otake(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),X30322)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)))
        | hAPP(hAPP(c_List_Oappend(X30325),X30324),X30323) != hAPP(hAPP(c_List_Oappend(X30325),X30322),X30321) )
      & ( X30323 = hAPP(hAPP(c_List_Oappend(X30325),hAPP(hAPP(c_List_Odrop(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),X30322)),X30321)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)))
        | hAPP(hAPP(c_List_Oappend(X30325),X30324),X30323) != hAPP(hAPP(c_List_Oappend(X30325),X30322),X30321) )
      & ( hAPP(hAPP(c_List_Otake(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)),X30324) = X30322
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)))
        | hAPP(hAPP(c_List_Oappend(X30325),X30324),X30323) != hAPP(hAPP(c_List_Oappend(X30325),X30322),X30321) )
      & ( hAPP(hAPP(c_List_Oappend(X30325),hAPP(hAPP(c_List_Odrop(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)),X30324)),X30323) = X30321
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)))
        | hAPP(hAPP(c_List_Oappend(X30325),X30324),X30323) != hAPP(hAPP(c_List_Oappend(X30325),X30322),X30321) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)))
        | hAPP(hAPP(c_List_Oappend(X30325),X30324),X30323) = hAPP(hAPP(c_List_Oappend(X30325),X30322),X30321) )
      & ( hAPP(hAPP(c_List_Otake(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)),X30324) != X30322
        | hAPP(hAPP(c_List_Oappend(X30325),hAPP(hAPP(c_List_Odrop(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)),X30324)),X30323) != X30321
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)))
        | hAPP(hAPP(c_List_Oappend(X30325),X30324),X30323) = hAPP(hAPP(c_List_Oappend(X30325),X30322),X30321) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)))
        | X30324 != hAPP(hAPP(c_List_Otake(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),X30322)
        | X30323 != hAPP(hAPP(c_List_Oappend(X30325),hAPP(hAPP(c_List_Odrop(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),X30322)),X30321)
        | hAPP(hAPP(c_List_Oappend(X30325),X30324),X30323) = hAPP(hAPP(c_List_Oappend(X30325),X30322),X30321) )
      & ( hAPP(hAPP(c_List_Otake(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)),X30324) != X30322
        | hAPP(hAPP(c_List_Oappend(X30325),hAPP(hAPP(c_List_Odrop(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30322)),X30324)),X30323) != X30321
        | X30324 != hAPP(hAPP(c_List_Otake(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),X30322)
        | X30323 != hAPP(hAPP(c_List_Oappend(X30325),hAPP(hAPP(c_List_Odrop(X30325),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30325)),X30324)),X30322)),X30321)
        | hAPP(hAPP(c_List_Oappend(X30325),X30324),X30323) = hAPP(hAPP(c_List_Oappend(X30325),X30322),X30321) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5527])])]) ).

fof(i_0_7123,plain,
    ! [X25417,X25418,X25419,X25420,X25421] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25421)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25420),X25419))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25420),X25418))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25421),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25420,X25421),X25417),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25420,tc_HOL_Obool)),X25419),X25418))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25420,X25421),X25417),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25420,tc_HOL_Obool)),X25419),X25418))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25421),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25420,X25421),X25417),X25419)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25420,X25421),X25417),X25418)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__Int])]) ).

fof(i_0_7124,plain,
    ! [X25412,X25413,X25414,X25415,X25416] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25416)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25415),X25414))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25415),X25413))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25416),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25415,X25416),X25412),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25415,tc_HOL_Obool)),X25414),X25413))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25415,X25416),X25412),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25415,tc_HOL_Obool)),X25414),X25413))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25416),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25415,X25416),X25412),X25414)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25415,X25416),X25412),X25413)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__inter])]) ).

fof(i_0_7125,plain,
    ! [X25407,X25408,X25409,X25410,X25411] :
      ( ~ class_Groups_Ocomm__monoid__add(X25411)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25410),X25409))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25410),X25408))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25411),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25410,X25411),X25407),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25410,tc_HOL_Obool)),X25409),X25408))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25410,X25411),X25407),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25410,tc_HOL_Obool)),X25409),X25408))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25411),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25410,X25411),X25407),X25409)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25410,X25411),X25407),X25408)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__Int])]) ).

cnf(i_0_7126,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_5528]) ).

cnf(i_0_7127,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_5529]) ).

cnf(i_0_7128,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_5530]) ).

cnf(i_0_7129,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_5531]) ).

cnf(i_0_7130,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_5532]) ).

fof(i_0_7131,plain,
    ! [X25615,X25616,X25617,X25618,X25619,X25620] :
      ( ~ hBOOL(hAPP(hAPP(X25620,X25619),X25618))
      | ~ hBOOL(hAPP(hAPP(X25617,X25619),X25618))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25616,tc_fun(X25615,tc_HOL_Obool))),X25620),X25617),X25619),X25618)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf2I])]) ).

fof(i_0_7132,plain,
    ! [X26913,X26914,X26915,X26916,X26917] :
      ( hAPP(c_Set_Oimage(X26917,X26916,X26915),c_Orderings_Otop__class_Otop(tc_fun(X26917,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26916,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26917,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26917,X26916,X26915),X26914)),X26913))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26916,tc_HOL_Obool)),X26914),hAPP(c_Set_Oimage(X26917,X26916,X26915),X26913))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetD])]) ).

fof(i_0_7133,plain,
    ! [X24304,X24305,X24306,X24307] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk162_4(X24304,X24305,X24306,X24307)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24306)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24305),X24307))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24307),X24306)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24305),X24304))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24306)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk163_4(X24304,X24305,X24306,X24307)),X24304))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24305),X24307))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24307),X24306)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24305),X24304))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24306)) )
      & ( X24307 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk163_4(X24304,X24305,X24306,X24307)),esk162_4(X24304,X24305,X24306,X24307))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24305),X24307))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24305),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24307),X24306)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24305),X24304))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24306)) ) ),
    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_7134,plain,
    ! [X19662,X19663,X19664,X19665,X19666,X19667] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19667),X19666)),X19665) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19664),X19663)),X19662)
      | ~ 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),X19664),X19663)),X19662)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19662),X19664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19665))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19664))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19664),X19667))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19666),X19663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma])]) ).

fof(i_0_7135,plain,
    ! [X28824,X28825,X28826,X28827,X28828] : hAPP(c_Relation_Oconverse(X28828,X28827),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28826,tc_fun(tc_prod(X28828,X28827),tc_HOL_Obool)),X28825),X28824)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28826,tc_fun(tc_prod(X28827,X28828),tc_HOL_Obool)),X28825),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28828,X28827),tc_HOL_Obool),tc_fun(tc_prod(X28827,X28828),tc_HOL_Obool),X28826),c_Relation_Oconverse(X28828,X28827)),X28824)),
    inference(variable_rename,[status(thm)],[fact_converse__INTER]) ).

fof(i_0_7136,plain,
    ! [X28819,X28820,X28821,X28822,X28823] : hAPP(c_Relation_Oconverse(X28823,X28822),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28821,tc_fun(tc_prod(X28823,X28822),tc_HOL_Obool)),X28820),X28819)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X28821,tc_fun(tc_prod(X28822,X28823),tc_HOL_Obool)),X28820),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(X28823,X28822),tc_HOL_Obool),tc_fun(tc_prod(X28822,X28823),tc_HOL_Obool),X28821),c_Relation_Oconverse(X28823,X28822)),X28819)),
    inference(variable_rename,[status(thm)],[fact_converse__UNION]) ).

fof(i_0_7137,plain,
    ! [X24328] : X24328 = 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),esk170_1(X24328)),esk171_1(X24328))),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_7138,plain,
    ! [X16991,X16992,X16993,X16994,X16995,X16997,X16998,X16999,X17000,X17001,X17002] :
      ( ( hBOOL(hAPP(hAPP(c_member(X16993),esk5_4(X16991,X16992,X16993,X16994)),X16991))
        | ~ hBOOL(hAPP(hAPP(c_member(X16995),X16994),hAPP(c_Set_Oimage(X16993,X16995,X16992),X16991))) )
      & ( X16994 = hAPP(X16992,esk5_4(X16991,X16992,X16993,X16994))
        | ~ hBOOL(hAPP(hAPP(c_member(X16995),X16994),hAPP(c_Set_Oimage(X16993,X16995,X16992),X16991))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X16999),X17001),X16997))
        | X17000 != hAPP(X16998,X17001)
        | hBOOL(hAPP(hAPP(c_member(X17002),X17000),hAPP(c_Set_Oimage(X16999,X17002,X16998),X16997))) ) ),
    inference(distribute,[status(thm)],[inference(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_7139,plain,
    ! [X24741,X24742,X24743,X24744,X24745] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X24745),hAPP(hAPP(c_Set_Oinsert(X24745),X24742),c_Orderings_Obot__class_Obot(tc_fun(X24745,tc_HOL_Obool)))),X24743) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X24745),hAPP(hAPP(c_Set_Oinsert(X24745),X24741),c_Orderings_Obot__class_Obot(tc_fun(X24745,tc_HOL_Obool)))),X24743)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24745,X24745)),hAPP(hAPP(c_Product__Type_OPair(X24745,X24745),X24742),X24741)),X24743))
        | ~ hBOOL(hAPP(hAPP(c_member(X24745),X24741),X24744))
        | ~ hBOOL(hAPP(hAPP(c_member(X24745),X24742),X24744))
        | ~ c_Equiv__Relations_Oequiv(X24745,X24744,X24743) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24745,X24745)),hAPP(hAPP(c_Product__Type_OPair(X24745,X24745),X24742),X24741)),X24743))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(X24745),hAPP(hAPP(c_Set_Oinsert(X24745),X24742),c_Orderings_Obot__class_Obot(tc_fun(X24745,tc_HOL_Obool)))),X24743) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X24745),hAPP(hAPP(c_Set_Oinsert(X24745),X24741),c_Orderings_Obot__class_Obot(tc_fun(X24745,tc_HOL_Obool)))),X24743)
        | ~ hBOOL(hAPP(hAPP(c_member(X24745),X24741),X24744))
        | ~ hBOOL(hAPP(hAPP(c_member(X24745),X24742),X24744))
        | ~ c_Equiv__Relations_Oequiv(X24745,X24744,X24743) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff2])])]) ).

fof(i_0_7140,plain,
    ! [X33120,X33121,X33122,X33123,X33124,X33125] :
      ( hAPP(c_Set_Oimage(X33125,X33124,X33123),X33122) != X33121
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33124,tc_HOL_Obool)),X33120),X33121))
      | hAPP(c_Set_Oimage(X33125,X33124,X33123),hAPP(c_Set_Oimage(X33124,X33125,c_Hilbert__Choice_Oinv__into(X33125,X33124,X33122,X33123)),X33120)) = X33120 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__into__cancel])]) ).

fof(i_0_7141,plain,
    ! [X33090,X33091,X33092] :
      ( ( ~ c_Fun_Oinj__on(X33092,X33091,X33090,c_Orderings_Otop__class_Otop(tc_fun(X33092,tc_HOL_Obool)))
        | hAPP(c_Fun_Ocomp(X33091,X33092,X33092,c_Hilbert__Choice_Oinv__into(X33092,X33091,c_Orderings_Otop__class_Otop(tc_fun(X33092,tc_HOL_Obool)),X33090)),X33090) = c_Fun_Oid(X33092) )
      & ( hAPP(c_Fun_Ocomp(X33091,X33092,X33092,c_Hilbert__Choice_Oinv__into(X33092,X33091,c_Orderings_Otop__class_Otop(tc_fun(X33092,tc_HOL_Obool)),X33090)),X33090) != c_Fun_Oid(X33092)
        | c_Fun_Oinj__on(X33092,X33091,X33090,c_Orderings_Otop__class_Otop(tc_fun(X33092,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__iff])]) ).

cnf(i_0_7142,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_5533]) ).

fof(i_0_7143,plain,
    ! [X22309,X22310,X22311,X22312,X22313,X22314,X22315] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22315,X22314,X22313),hAPP(c_Fun_Ocomp(X22312,tc_fun(X22314,X22313),X22315,X22311),X22310)),X22309) = hAPP(hAPP(X22311,hAPP(X22310,hAPP(c_Product__Type_Ofst(X22315,X22314),X22309))),hAPP(c_Product__Type_Osnd(X22315,X22314),X22309)),
    inference(variable_rename,[status(thm)],[fact_split__comp]) ).

fof(i_0_7144,plain,
    ! [X33261,X33262,X33263] :
      ( ~ c_Fun_Obij__betw(X33263,X33262,X33261,c_Orderings_Otop__class_Otop(tc_fun(X33263,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33262,tc_HOL_Obool)))
      | c_Hilbert__Choice_Oinv__into(X33262,X33263,c_Orderings_Otop__class_Otop(tc_fun(X33262,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X33263,X33262,c_Orderings_Otop__class_Otop(tc_fun(X33263,tc_HOL_Obool)),X33261)) = X33261 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__inv__eq])]) ).

cnf(i_0_7145,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_5534]) ).

cnf(i_0_7146,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_5535]) ).

fof(i_0_7147,plain,
    ! [X20146,X20147] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X20147),X20146))
        | 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)),X20147)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20146))) )
      & ( ~ 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)),X20147)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20146)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X20147),X20146)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I4_J])]) ).

fof(i_0_7148,plain,
    ! [X20148,X20149] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X20149),X20148))
        | 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)),X20149)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20148))) )
      & ( ~ 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)),X20149)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20148)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X20149),X20148)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I5_J])]) ).

fof(i_0_7149,plain,
    ! [X23112,X23113,X23114] :
      ( ~ class_Orderings_Olinorder(X23114)
      | hAPP(X23113,hAPP(hAPP(c_Orderings_Oord__class_Omax(X23114),esk103_3(X23112,X23113,X23114)),esk104_3(X23112,X23113,X23114))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X23114),hAPP(X23113,esk103_3(X23112,X23113,X23114))),hAPP(X23113,esk104_3(X23112,X23113,X23114)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23114),X23112))
      | X23112 = c_Orderings_Obot__class_Obot(tc_fun(X23114,tc_HOL_Obool))
      | hAPP(X23113,c_Big__Operators_Olattice_OSup__fin(X23114,c_Orderings_Oord__class_Omax(X23114),X23112)) = c_Big__Operators_Olattice_OSup__fin(X23114,c_Orderings_Oord__class_Omax(X23114),hAPP(c_Set_Oimage(X23114,X23114,X23113),X23112)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ohom__commute])])]) ).

fof(i_0_7150,plain,
    ! [X23117,X23118,X23119] :
      ( ~ class_Orderings_Olinorder(X23119)
      | hAPP(X23118,hAPP(hAPP(c_Orderings_Oord__class_Omin(X23119),esk105_3(X23117,X23118,X23119)),esk106_3(X23117,X23118,X23119))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X23119),hAPP(X23118,esk105_3(X23117,X23118,X23119))),hAPP(X23118,esk106_3(X23117,X23118,X23119)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23119),X23117))
      | X23117 = c_Orderings_Obot__class_Obot(tc_fun(X23119,tc_HOL_Obool))
      | hAPP(X23118,c_Big__Operators_Olattice_OInf__fin(X23119,c_Orderings_Oord__class_Omin(X23119),X23117)) = c_Big__Operators_Olattice_OInf__fin(X23119,c_Orderings_Oord__class_Omin(X23119),hAPP(c_Set_Oimage(X23119,X23119,X23118),X23117)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ohom__commute])])]) ).

fof(i_0_7151,plain,
    ! [X31161,X31162,X31163,X31164,X31165,X31166] :
      ( ~ c_List_Olist__all2(X31166,X31165,X31164,X31163,X31162)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31161),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31166)),X31163)))
      | hBOOL(hAPP(hAPP(X31164,hAPP(hAPP(c_List_Onth(X31166),X31163),X31161)),hAPP(hAPP(c_List_Onth(X31165),X31162),X31161))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD])]) ).

fof(i_0_7152,plain,
    ! [X31155,X31156,X31157,X31158,X31159,X31160] :
      ( ~ c_List_Olist__all2(X31160,X31159,X31158,X31157,X31156)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31155),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31159)),X31156)))
      | hBOOL(hAPP(hAPP(X31158,hAPP(hAPP(c_List_Onth(X31160),X31157),X31155)),hAPP(hAPP(c_List_Onth(X31159),X31156),X31155))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__nthD2])]) ).

fof(i_0_7153,plain,
    ! [X26941,X26942,X26943,X26944,X26945] :
      ( ~ c_Fun_Oinj__on(X26945,X26944,X26943,c_Orderings_Otop__class_Otop(tc_fun(X26945,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26944,tc_HOL_Obool)),X26942),hAPP(c_Set_Oimage(X26945,X26944,X26943),X26941)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26945,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26945,X26944,X26943),X26942)),X26941)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__subsetI])]) ).

cnf(i_0_7154,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_5473]) ).

cnf(i_0_7155,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_5474]) ).

cnf(i_0_7156,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_5475]) ).

cnf(i_0_7157,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_5476]) ).

fof(i_0_7158,plain,
    ! [X22705,X22706,X22707,X22708] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))),X22706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),c_Groups_Ozero__class_Ozero(X22708)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),c_Groups_Ozero__class_Ozero(X22708)),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))),X22706))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))),X22706))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),c_Groups_Ozero__class_Ozero(X22708)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))),X22706))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705)),c_Groups_Ozero__class_Ozero(X22708)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))),X22706))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),c_Groups_Ozero__class_Ozero(X22708)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22708),X22707),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))),X22706))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22708),X22707),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22708),X22706),hAPP(c_Int_Onumber__class_Onumber__of(X22708),X22705))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22708)
        | ~ class_Int_Onumber(X22708) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5536])])]) ).

fof(i_0_7159,plain,
    ! [X22746,X22747,X22748,X22749] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))),X22747))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),c_Groups_Ozero__class_Ozero(X22749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),c_Groups_Ozero__class_Ozero(X22749)),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))),X22747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))),X22747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),c_Groups_Ozero__class_Ozero(X22749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))),X22747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22749),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746)),c_Groups_Ozero__class_Ozero(X22749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))),X22747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),c_Groups_Ozero__class_Ozero(X22749)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22747),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22749),X22748),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))),X22747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22749),X22748),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22749),X22747),hAPP(c_Int_Onumber__class_Onumber__of(X22749),X22746))))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22749)
        | ~ class_Int_Onumber(X22749) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5537])])]) ).

fof(i_0_7160,plain,
    ! [X28814,X28815,X28816,X28817,X28818] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28818,X28817)),hAPP(hAPP(c_Product__Type_OPair(X28818,X28817),X28816),X28815)),hAPP(c_Relation_Oconverse(X28817,X28818),X28814)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28817,X28818)),hAPP(hAPP(c_Product__Type_OPair(X28817,X28818),X28815),X28816)),X28814)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseD])]) ).

fof(i_0_7161,plain,
    ! [X28804,X28805,X28806,X28807,X28808] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28808,X28807)),hAPP(hAPP(c_Product__Type_OPair(X28808,X28807),X28806),X28805)),hAPP(c_Relation_Oconverse(X28807,X28808),X28804)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28807,X28808)),hAPP(hAPP(c_Product__Type_OPair(X28807,X28808),X28805),X28806)),X28804)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28807,X28808)),hAPP(hAPP(c_Product__Type_OPair(X28807,X28808),X28805),X28806)),X28804))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28808,X28807)),hAPP(hAPP(c_Product__Type_OPair(X28808,X28807),X28806),X28805)),hAPP(c_Relation_Oconverse(X28807,X28808),X28804))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converse__iff])]) ).

fof(i_0_7162,plain,
    ! [X33329,X33330,X33331,X33332] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33332),hAPP(c_Set_Ovimage(X33332,X33331,X33330),X33329)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33331),X33329))
        | ~ c_Fun_Obij__betw(X33332,X33331,X33330,c_Orderings_Otop__class_Otop(tc_fun(X33332,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33331,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33331),X33329))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33332),hAPP(c_Set_Ovimage(X33332,X33331,X33330),X33329)))
        | ~ c_Fun_Obij__betw(X33332,X33331,X33330,c_Orderings_Otop__class_Otop(tc_fun(X33332,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33331,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimage__iff])])]) ).

fof(i_0_7163,plain,
    ! [X23585,X23586,X23587,X23588,X23589,X23590] :
      ( ~ hBOOL(hAPP(hAPP(X23590,X23589),X23588))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23587,tc_fun(X23586,tc_HOL_Obool))),X23590),X23585),X23589),X23588)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I1])]) ).

fof(i_0_7164,plain,
    ! [X23567,X23568,X23569,X23570,X23571,X23572] :
      ( ( ~ hBOOL(hAPP(hAPP(X23572,X23571),X23570))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23568,tc_fun(X23567,tc_HOL_Obool))),X23569),X23572),X23571),X23570)) )
      & ( ~ hBOOL(hAPP(hAPP(X23569,X23571),X23570))
        | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23568,tc_fun(X23567,tc_HOL_Obool))),X23569),X23572),X23571),X23570)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5538])])]) ).

fof(i_0_7165,plain,
    ! [X23579,X23580,X23581,X23582,X23583,X23584] :
      ( ~ hBOOL(hAPP(hAPP(X23584,X23583),X23582))
      | hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23581,tc_fun(X23580,tc_HOL_Obool))),X23579),X23584),X23583),X23582)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup2I2])]) ).

fof(i_0_7166,plain,
    ! [X25019,X25020,X25021,X25022,X25023] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25023,tc_HOL_Obool)),X25022),X25021))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25023,tc_HOL_Obool)),X25020),X25019))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25023,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25023,tc_HOL_Obool)),X25022),X25020)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25023,tc_HOL_Obool)),X25021),X25019))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__mono])]) ).

fof(i_0_7167,plain,
    ! [X23361,X23362,X23363,X23364,X23365] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23365,tc_HOL_Obool)),X23364),X23363))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23365,tc_HOL_Obool)),X23362),X23361))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23365,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23365,tc_HOL_Obool)),X23364),X23362)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23365,tc_HOL_Obool)),X23363),X23361))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__mono])]) ).

fof(i_0_7168,plain,
    ! [X17382,X17383,X17384,X17385,X17386] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17386,tc_HOL_Obool)),X17385),X17384))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17386,tc_HOL_Obool)),X17383),X17382))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17386,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17386,tc_HOL_Obool)),X17385),X17382)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17386,tc_HOL_Obool)),X17384),X17383))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__mono])]) ).

fof(i_0_7169,plain,
    ! [X19391,X19392,X19393] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19393)
      | hAPP(X19392,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19393),esk46_3(X19391,X19392,X19393)),esk47_3(X19391,X19392,X19393))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19393),hAPP(X19392,esk46_3(X19391,X19392,X19393))),hAPP(X19392,esk47_3(X19391,X19392,X19393)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19393),X19391))
      | X19391 = c_Orderings_Obot__class_Obot(tc_fun(X19393,tc_HOL_Obool))
      | hAPP(X19392,hAPP(c_Finite__Set_Ofold1(X19393,c_Groups_Otimes__class_Otimes(X19393)),X19391)) = hAPP(c_Finite__Set_Ofold1(X19393,c_Groups_Otimes__class_Otimes(X19393)),hAPP(c_Set_Oimage(X19393,X19393,X19392),X19391)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hom__fold1__commute])])]) ).

fof(i_0_7170,plain,
    ! [X24575,X24576,X24577,X24578,X24579] :
      ( ~ class_Groups_Ocomm__monoid__add(X24579)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24578),X24577))
      | ~ c_Fun_Oinj__on(X24578,X24578,X24576,X24577)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24578,X24579),X24575),hAPP(c_Set_Oimage(X24578,X24578,X24576),X24577)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24578,X24579),hAPP(c_Fun_Ocomp(X24578,X24579,X24578,X24575),X24576)),X24577) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oreindex])]) ).

fof(i_0_7171,plain,
    ! [X21993,X21994,X21995,X21996,X21997] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21997)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21996),X21995))
      | ~ c_Fun_Oinj__on(X21996,X21996,X21994,X21995)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21996,X21997),X21993),hAPP(c_Set_Oimage(X21996,X21996,X21994),X21995)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21996,X21997),hAPP(c_Fun_Ocomp(X21996,X21997,X21996,X21993),X21994)),X21995) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oreindex])]) ).

fof(i_0_7172,plain,
    ! [X28412,X28413,X28414] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28414,X28414)),hAPP(hAPP(c_Product__Type_OPair(X28414,X28414),esk319_3(X28412,X28413,X28414)),X28413)),X28412))
        | hBOOL(hAPP(hAPP(c_member(X28414),X28413),c_Wellfounded_Oacc(X28414,X28412))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28414),esk319_3(X28412,X28413,X28414)),c_Wellfounded_Oacc(X28414,X28412)))
        | hBOOL(hAPP(hAPP(c_member(X28414),X28413),c_Wellfounded_Oacc(X28414,X28412))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc_OaccI])])])]) ).

fof(i_0_7173,plain,
    ! [X28408,X28409,X28410] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X28410,X28410)),hAPP(hAPP(c_Product__Type_OPair(X28410,X28410),esk318_3(X28408,X28409,X28410)),X28409)),X28408))
        | hBOOL(hAPP(hAPP(c_member(X28410),X28409),c_Wellfounded_Oacc(X28410,X28408))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28410),esk318_3(X28408,X28409,X28410)),c_Wellfounded_Oacc(X28410,X28408)))
        | hBOOL(hAPP(hAPP(c_member(X28410),X28409),c_Wellfounded_Oacc(X28410,X28408))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5539])])])]) ).

fof(i_0_7174,plain,
    ! [X26259,X26260,X26261,X26262,X26263,X26264,X26265] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26261),X26260),c_Wellfounded_Oacc(X26261,X26259)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26261,X26261)),hAPP(hAPP(c_Product__Type_OPair(X26261,X26261),X26262),X26260)),X26259))
        | hBOOL(hAPP(hAPP(c_member(X26261),X26262),c_Wellfounded_Oacc(X26261,X26259))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X26265,X26265)),hAPP(hAPP(c_Product__Type_OPair(X26265,X26265),esk226_3(X26263,X26264,X26265)),X26264)),X26263))
        | hBOOL(hAPP(hAPP(c_member(X26265),X26264),c_Wellfounded_Oacc(X26265,X26263))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26265),esk226_3(X26263,X26264,X26265)),c_Wellfounded_Oacc(X26265,X26263)))
        | hBOOL(hAPP(hAPP(c_member(X26265),X26264),c_Wellfounded_Oacc(X26265,X26263))) ) ),
    inference(distribute,[status(thm)],[inference(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_7175,plain,
    ! [X29282,X29283,X29284,X29285] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29285),tc_List_Olist(X29285))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29285),tc_List_Olist(X29285)),X29284),X29283)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29285),c_List_Olistrel1(X29285,X29282))))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29285)),X29284) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29285)),X29283) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__listrel1__eq__len])]) ).

fof(i_0_7176,hypothesis,
    ! [X34054,X34055] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X34054),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
      | hAPP(c_Finite__Set_Ocard(t_a),X34054) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n)
      | ~ v_wt(X34055)
      | v_P(X34054,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X34055)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_1])])]) ).

cnf(i_0_7177,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk447_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),esk445_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5498]) ).

cnf(i_0_7178,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk446_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),esk445_2(X2,X1)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5498]) ).

fof(i_0_7179,plain,
    ! [X29714,X29715,X29716,X29717,X29718] : hAPP(hAPP(c_List_Olist__update(X29718,hAPP(hAPP(c_List_Olist_OCons(X29718),X29717),X29716)),X29715),X29714) = c_Nat_Onat_Onat__case(tc_List_Olist(X29718),hAPP(hAPP(c_List_Olist_OCons(X29718),X29714),X29716),hAPP(hAPP(c_COMBB(tc_List_Olist(X29718),tc_List_Olist(X29718),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X29718),X29717)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,X29718,tc_List_Olist(X29718)),c_List_Olist__update(X29718,X29716)),X29714)),X29715),
    inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I2_J]) ).

fof(i_0_7180,plain,
    ! [X22157,X22158,X22159,X22160] : hAPP(c_Product__Type_Oprod_Oprod__case(X22160,X22159,X22158),hAPP(hAPP(c_COMBB(tc_fun(X22159,tc_prod(X22160,X22159)),tc_fun(X22159,X22158),X22160),hAPP(c_COMBB(tc_prod(X22160,X22159),X22158,X22159),X22157)),c_Product__Type_OPair(X22160,X22159))) = X22157,
    inference(variable_rename,[status(thm)],[fact_split__eta]) ).

fof(i_0_7181,plain,
    ! [X24345,X24346,X24347,X24348] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk178_4(X24345,X24346,X24347,X24348)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24345),X24348))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24345),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24348),X24347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24347)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk179_4(X24345,X24346,X24347,X24348)),X24346))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24345),X24348))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24345),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24348),X24347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24347)) )
      & ( X24348 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk179_4(X24345,X24346,X24347,X24348)),esk178_4(X24345,X24346,X24347,X24348))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24345),X24348))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24345),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24348),X24347)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24347)) ) ),
    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_7182,plain,
    ! [X24316,X24317,X24318,X24319] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk166_4(X24316,X24317,X24318,X24319)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24318)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24316),X24319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24319),X24318)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24318)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk167_4(X24316,X24317,X24318,X24319)),X24317))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24316),X24319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24319),X24318)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24318)) )
      & ( X24319 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk167_4(X24316,X24317,X24318,X24319)),esk166_4(X24316,X24317,X24318,X24319))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24316),X24319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X24316),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24319),X24318)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24318)) ) ),
    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_7183,plain,
    ! [X17507,X17508,X17509] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17509,tc_HOL_Obool)),X17508),hAPP(hAPP(c_Set_Oinsert(X17509),X17507),c_Orderings_Obot__class_Obot(tc_fun(X17509,tc_HOL_Obool)))))
        | c_Partial__Function_Oflat__lub(X17509,X17507,X17508) = X17507 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17509,tc_HOL_Obool)),X17508),hAPP(hAPP(c_Set_Oinsert(X17509),X17507),c_Orderings_Obot__class_Obot(tc_fun(X17509,tc_HOL_Obool)))))
        | c_Partial__Function_Oflat__lub(X17509,X17507,X17508) = c_HOL_OThe(X17509,hAPP(hAPP(c_COMBC(X17509,tc_fun(X17509,tc_HOL_Obool),tc_HOL_Obool),c_member(X17509)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17509,tc_HOL_Obool)),X17508),hAPP(hAPP(c_Set_Oinsert(X17509),X17507),c_Orderings_Obot__class_Obot(tc_fun(X17509,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5540])]) ).

fof(i_0_7184,plain,
    ! [X29810,X29811,X29812,X29813] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk396_4(X29810,X29811,X29812,X29813)),X29813))
        | hAPP(hAPP(c_List_Otake(X29812),X29813),X29811) = hAPP(hAPP(c_List_Otake(X29812),X29813),X29810)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29813),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29812)),X29810)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29813),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29812)),X29811))) )
      & ( hAPP(hAPP(c_List_Onth(X29812),X29811),esk396_4(X29810,X29811,X29812,X29813)) != hAPP(hAPP(c_List_Onth(X29812),X29810),esk396_4(X29810,X29811,X29812,X29813))
        | hAPP(hAPP(c_List_Otake(X29812),X29813),X29811) = hAPP(hAPP(c_List_Otake(X29812),X29813),X29810)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29813),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29812)),X29810)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29813),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29812)),X29811))) ) ),
    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_7185,plain,
    ! [X28982,X28983,X28984,X28985] :
      ( ~ 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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28982)))
      | X28984 = X28983 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__0__E])]) ).

fof(i_0_7186,plain,
    ! [X22409,X22410,X22411,X22412,X22413] :
      ( ~ hBOOL(hAPP(hAPP(X22413,X22412),X22411))
      | hBOOL(hAPP(hAPP(X22413,hAPP(c_Product__Type_Osnd(X22410,X22409),hAPP(hAPP(c_Product__Type_OPair(X22410,X22409),X22411),X22412))),hAPP(c_Product__Type_Ofst(X22410,X22409),hAPP(hAPP(c_Product__Type_OPair(X22410,X22409),X22411),X22412)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exI__realizer])]) ).

fof(i_0_7187,plain,
    ! [X19605,X19606,X19607,X19608,X19609,X19610] :
      ( ( ~ c_Fun_Oinj__on(X19609,X19606,X19605,hAPP(c_Set_Oimage(X19610,X19609,X19608),X19607))
        | c_Fun_Oinj__on(X19610,X19606,hAPP(c_Fun_Ocomp(X19609,X19606,X19610,X19605),X19608),X19607)
        | ~ c_Fun_Oinj__on(X19610,X19609,X19608,X19607) )
      & ( ~ c_Fun_Oinj__on(X19610,X19606,hAPP(c_Fun_Ocomp(X19609,X19606,X19610,X19605),X19608),X19607)
        | c_Fun_Oinj__on(X19609,X19606,X19605,hAPP(c_Set_Oimage(X19610,X19609,X19608),X19607))
        | ~ c_Fun_Oinj__on(X19610,X19609,X19608,X19607) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on__iff])])]) ).

fof(i_0_7188,plain,
    ! [X26167,X26168,X26169,X26170,X26171] :
      ( hAPP(c_Set_Oimage(X26171,X26170,X26169),c_Orderings_Otop__class_Otop(tc_fun(X26171,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26170,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X26170,X26168,X26167),c_Orderings_Otop__class_Otop(tc_fun(X26170,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26168,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X26171,X26168,hAPP(c_Fun_Ocomp(X26170,X26168,X26171,X26167),X26169)),c_Orderings_Otop__class_Otop(tc_fun(X26171,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26168,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__surj])]) ).

fof(i_0_7189,plain,
    ! [X20906,X20907,X20908] : 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),X20908),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20907),X20908))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20907,X20908))),X20906) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20907),X20906),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmod__equality]) ).

fof(i_0_7190,plain,
    ! [X24518,X24519,X24520,X24521,X24522,X24523] :
      ( ~ class_Groups_Ocomm__monoid__add(X24523)
      | ~ c_Fun_Oinj__on(X24522,X24521,X24520,X24519)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24521,X24523),X24518),hAPP(c_Set_Oimage(X24522,X24521,X24520),X24519)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24522,X24523),hAPP(c_Fun_Ocomp(X24521,X24523,X24522,X24518),X24520)),X24519) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex])]) ).

fof(i_0_7191,plain,
    ! [X21952,X21953,X21954,X21955,X21956,X21957] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21957)
      | ~ c_Fun_Oinj__on(X21956,X21955,X21954,X21953)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21955,X21957),X21952),hAPP(c_Set_Oimage(X21956,X21955,X21954),X21953)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21956,X21957),hAPP(c_Fun_Ocomp(X21955,X21957,X21956,X21952),X21954)),X21953) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex])]) ).

fof(i_0_7192,plain,
    ! [X25531,X25532,X25533] :
      ( ~ class_Orderings_Olinorder(X25533)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25533),X25532))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25533),X25531))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25533,tc_HOL_Obool)),X25532),X25531) = c_Orderings_Obot__class_Obot(tc_fun(X25533,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25533),c_Big__Operators_Olattice_OSup__fin(X25533,c_Orderings_Oord__class_Omax(X25533),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25533,tc_HOL_Obool)),X25532),X25531))),c_Big__Operators_Olattice_OSup__fin(X25533,c_Orderings_Oord__class_Omax(X25533),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25533,tc_HOL_Obool)),X25532),X25531))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25533),c_Big__Operators_Olattice_OSup__fin(X25533,c_Orderings_Oord__class_Omax(X25533),X25532)),c_Big__Operators_Olattice_OSup__fin(X25533,c_Orderings_Oord__class_Omax(X25533),X25531)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__inter])]) ).

fof(i_0_7193,plain,
    ! [X25525,X25526,X25527] :
      ( ~ class_Orderings_Olinorder(X25527)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25527),X25526))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25527),X25525))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25527,tc_HOL_Obool)),X25526),X25525) = c_Orderings_Obot__class_Obot(tc_fun(X25527,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25527),c_Big__Operators_Olattice_OInf__fin(X25527,c_Orderings_Oord__class_Omin(X25527),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25527,tc_HOL_Obool)),X25526),X25525))),c_Big__Operators_Olattice_OInf__fin(X25527,c_Orderings_Oord__class_Omin(X25527),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25527,tc_HOL_Obool)),X25526),X25525))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25527),c_Big__Operators_Olattice_OInf__fin(X25527,c_Orderings_Oord__class_Omin(X25527),X25526)),c_Big__Operators_Olattice_OInf__fin(X25527,c_Orderings_Oord__class_Omin(X25527),X25525)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__inter])]) ).

fof(i_0_7194,plain,
    ! [X29187,X29188,X29189,X29190,X29191] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29191)),X29190) = X29187
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29191),tc_List_Olist(X29191))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29191),tc_List_Olist(X29191)),X29190),X29189)),hAPP(c_List_Olexn(X29191,X29188),X29187))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29191)),X29189) = X29187
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29191),tc_List_Olist(X29191))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29191),tc_List_Olist(X29191)),X29190),X29189)),hAPP(c_List_Olexn(X29191,X29188),X29187))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexn__length])])]) ).

fof(i_0_7195,plain,
    ! [X28809,X28810,X28811,X28812,X28813] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28813,X28812)),hAPP(hAPP(c_Product__Type_OPair(X28813,X28812),X28811),X28810)),X28809))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28812,X28813)),hAPP(hAPP(c_Product__Type_OPair(X28812,X28813),X28810),X28811)),hAPP(c_Relation_Oconverse(X28813,X28812),X28809))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_converseI])]) ).

fof(i_0_7196,plain,
    ! [X27910,X27911,X27912,X27913,X27914,X27915] : hAPP(hAPP(c_Relation_Orel__comp(X27915,X27914,X27913),X27912),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27914,X27913),tc_HOL_Obool)),X27911),X27910)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27915,X27913),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X27915,X27914,X27913),X27912),X27911)),hAPP(hAPP(c_Relation_Orel__comp(X27915,X27914,X27913),X27912),X27910)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__distrib]) ).

cnf(i_0_7197,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_5541]) ).

fof(i_0_7198,plain,
    ! [X21855,X21856,X21857,X21858] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X21858,tc_fun(X21857,tc_HOL_Obool))),X21856),X21855))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X21858,X21857)),hAPP(hAPP(c_Product__Type_OPair(X21858,X21857),X21856),X21855)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X21858,X21857),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X21858,X21857)),hAPP(hAPP(c_Product__Type_OPair(X21858,X21857),X21856),X21855)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X21858,X21857),tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X21858,tc_fun(X21857,tc_HOL_Obool))),X21856),X21855)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq2])]) ).

fof(i_0_7199,plain,
    ! [X31888,X31889] :
      ( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31889),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31889))),X31888)))
      | c_List_Otranspose(X31889,c_List_Otranspose(X31889,X31888)) = c_List_OtakeWhile(tc_List_Olist(X31889),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(X31889)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(X31889),tc_List_Olist(X31889),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(X31889))),X31888) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose__transpose])]) ).

fof(i_0_7200,plain,
    ! [X25690,X25691,X25692] :
      ( ~ class_Lattices_Olattice(X25692)
      | hAPP(X25691,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25692),esk213_3(X25690,X25691,X25692)),esk214_3(X25690,X25691,X25692))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25692),hAPP(X25691,esk213_3(X25690,X25691,X25692))),hAPP(X25691,esk214_3(X25690,X25691,X25692)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25692),X25690))
      | X25690 = c_Orderings_Obot__class_Obot(tc_fun(X25692,tc_HOL_Obool))
      | hAPP(X25691,c_Big__Operators_Olattice__class_OInf__fin(X25692,X25690)) = c_Big__Operators_Olattice__class_OInf__fin(X25692,hAPP(c_Set_Oimage(X25692,X25692,X25691),X25690)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ohom__commute])])]) ).

fof(i_0_7201,plain,
    ! [X23610,X23611,X23612] :
      ( ~ class_Lattices_Olattice(X23612)
      | hAPP(X23611,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23612),esk121_3(X23610,X23611,X23612)),esk122_3(X23610,X23611,X23612))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23612),hAPP(X23611,esk121_3(X23610,X23611,X23612))),hAPP(X23611,esk122_3(X23610,X23611,X23612)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23612),X23610))
      | X23610 = c_Orderings_Obot__class_Obot(tc_fun(X23612,tc_HOL_Obool))
      | hAPP(X23611,c_Big__Operators_Olattice__class_OSup__fin(X23612,X23610)) = c_Big__Operators_Olattice__class_OSup__fin(X23612,hAPP(c_Set_Oimage(X23612,X23612,X23611),X23610)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ohom__commute])])]) ).

fof(i_0_7202,plain,
    ! [X23472,X23473,X23474] :
      ( ~ class_Orderings_Olinorder(X23474)
      | hAPP(X23473,hAPP(hAPP(c_Orderings_Oord__class_Omax(X23474),esk113_3(X23472,X23473,X23474)),esk114_3(X23472,X23473,X23474))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X23474),hAPP(X23473,esk113_3(X23472,X23473,X23474))),hAPP(X23473,esk114_3(X23472,X23473,X23474)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23474),X23472))
      | X23472 = c_Orderings_Obot__class_Obot(tc_fun(X23474,tc_HOL_Obool))
      | hAPP(X23473,c_Big__Operators_Olinorder__class_OMax(X23474,X23472)) = c_Big__Operators_Olinorder__class_OMax(X23474,hAPP(c_Set_Oimage(X23474,X23474,X23473),X23472)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ohom__commute])])]) ).

fof(i_0_7203,plain,
    ! [X23600,X23601,X23602] :
      ( ~ class_Orderings_Olinorder(X23602)
      | hAPP(X23601,hAPP(hAPP(c_Orderings_Oord__class_Omin(X23602),esk118_3(X23600,X23601,X23602)),esk119_3(X23600,X23601,X23602))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X23602),hAPP(X23601,esk118_3(X23600,X23601,X23602))),hAPP(X23601,esk119_3(X23600,X23601,X23602)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23602),X23600))
      | X23600 = c_Orderings_Obot__class_Obot(tc_fun(X23602,tc_HOL_Obool))
      | hAPP(X23601,c_Big__Operators_Olinorder__class_OMin(X23602,X23600)) = c_Big__Operators_Olinorder__class_OMin(X23602,hAPP(c_Set_Oimage(X23602,X23602,X23601),X23600)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ohom__commute])])]) ).

fof(i_0_7204,plain,
    ! [X24331,X24332,X24335,X24337] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk174_2(X24331,X24332)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24332)))
        | ~ hBOOL(hAPP(X24331,X24335))
        | ~ hBOOL(hAPP(X24331,esk172_2(X24331,X24332)))
        | ~ hBOOL(hAPP(X24331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X24331,X24332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_2(X24331,X24332)),X24332))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24332)) )
      & ( hBOOL(hAPP(X24331,esk174_2(X24331,X24332)))
        | ~ hBOOL(hAPP(X24331,X24335))
        | ~ hBOOL(hAPP(X24331,esk172_2(X24331,X24332)))
        | ~ hBOOL(hAPP(X24331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X24331,X24332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_2(X24331,X24332)),X24332))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24332)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24337),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24332)))
        | ~ hBOOL(hAPP(X24331,X24337))
        | hBOOL(hAPP(X24331,esk175_2(X24331,X24332)))
        | ~ hBOOL(hAPP(X24331,esk172_2(X24331,X24332)))
        | ~ hBOOL(hAPP(X24331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X24331,X24332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_2(X24331,X24332)),X24332))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24332)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk174_2(X24331,X24332)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24332)))
        | ~ hBOOL(hAPP(X24331,X24335))
        | hBOOL(hAPP(X24331,esk172_2(X24331,X24332)))
        | hBOOL(hAPP(X24331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X24331,X24332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_2(X24331,X24332)),X24332))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24332)) )
      & ( hBOOL(hAPP(X24331,esk174_2(X24331,X24332)))
        | ~ hBOOL(hAPP(X24331,X24335))
        | hBOOL(hAPP(X24331,esk172_2(X24331,X24332)))
        | hBOOL(hAPP(X24331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X24331,X24332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_2(X24331,X24332)),X24332))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24332)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24337),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24332)))
        | ~ hBOOL(hAPP(X24331,X24337))
        | hBOOL(hAPP(X24331,esk175_2(X24331,X24332)))
        | hBOOL(hAPP(X24331,esk172_2(X24331,X24332)))
        | hBOOL(hAPP(X24331,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X24331,X24332)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_2(X24331,X24332)),X24332))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24332)) ) ),
    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_7205,plain,
    ! [X29827,X29828,X29829] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29829),tc_List_Olist(X29829))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29829),tc_List_Olist(X29829)),c_List_Olist_ONil(X29829)),X29828)),c_List_Olistrel(X29829,X29827)))
      | X29828 = c_List_Olist_ONil(X29829) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil1])]) ).

cnf(i_0_7206,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk445_2(X1,X2)),hAPP(c_List_Oset(tc_List_Olist(X2)),X1)))
    | esk446_2(X1,X2) != esk447_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5498]) ).

fof(i_0_7207,plain,
    ! [X17304,X17305] : c_Set_Othe__elem(X17305,X17304) = c_HOL_OThe(X17305,hAPP(hAPP(c_COMBB(tc_fun(X17305,tc_HOL_Obool),tc_HOL_Obool,X17305),hAPP(c_fequal,X17304)),hAPP(hAPP(c_COMBC(X17305,tc_fun(X17305,tc_HOL_Obool),tc_fun(X17305,tc_HOL_Obool)),c_Set_Oinsert(X17305)),c_Orderings_Obot__class_Obot(tc_fun(X17305,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_the__elem__def]) ).

cnf(i_0_7208,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk346_2(X2,X1)),esk346_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5542]) ).

cnf(i_0_7209,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk333_2(X2,X1)),esk333_2(X2,X1))),c_Transitive__Closure_Otrancl(X1,X2)))
    | c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5501]) ).

fof(i_0_7210,plain,
    ! [X29922,X29923,X29924] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29924),tc_List_Olist(X29924))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29924),tc_List_Olist(X29924)),c_List_Olist_ONil(X29924)),X29923)),c_List_Olistrel1(X29924,X29922))),
    inference(variable_rename,[status(thm)],[i_0_5543]) ).

fof(i_0_7211,plain,
    ! [X29933,X29934,X29935] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29935),tc_List_Olist(X29935))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29935),tc_List_Olist(X29935)),c_List_Olist_ONil(X29935)),X29934)),c_List_Olex(X29935,X29933))),
    inference(variable_rename,[status(thm)],[i_0_5544]) ).

fof(i_0_7212,plain,
    ! [X21474,X21475] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21475),X21474))
        | 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),X21475)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21474)))
        | ~ c_Nat__Transfer_Onat__set(X21474)
        | ~ c_Nat__Transfer_Onat__set(X21475) )
      & ( ~ 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),X21475)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21474)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21475),X21474))
        | ~ c_Nat__Transfer_Onat__set(X21474)
        | ~ c_Nat__Transfer_Onat__set(X21475) ) ),
    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_7213,plain,
    ! [X21476,X21477] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21477),X21476))
        | 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),X21477)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21476)))
        | ~ c_Nat__Transfer_Onat__set(X21476)
        | ~ c_Nat__Transfer_Onat__set(X21477) )
      & ( ~ 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),X21477)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21476)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X21477),X21476))
        | ~ c_Nat__Transfer_Onat__set(X21476)
        | ~ c_Nat__Transfer_Onat__set(X21477) ) ),
    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_7214,plain,
    ! [X27930,X27931,X27932,X27933] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X27933,X27933,X27933),X27932),X27931) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27933,X27933),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27933,X27933,X27933),X27930),X27931) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27933,X27933),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27933,X27933,X27933),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27933,X27933),tc_HOL_Obool)),X27932),X27930)),X27931) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27933,X27933),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyL])]) ).

fof(i_0_7215,plain,
    ! [X24226] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24226) = 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),X24226),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_7216,plain,
    ! [X25204,X25205,X25206,X25207] :
      ( ~ class_Lattices_Olattice(X25207)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25207),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25207),X25206),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25207),X25205),X25204))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25207),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25207),X25206),X25205)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25207),X25206),X25204)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distrib__sup__le])]) ).

fof(i_0_7217,plain,
    ! [X22647,X22648,X22649,X22650] :
      ( ~ class_Orderings_Olinorder(X22650)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22650),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22650),X22649),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22650),X22648),X22647))),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22650),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22650),X22649),X22648)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22650),X22649),X22647)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Odistrib__sup__le])]) ).

fof(i_0_7218,plain,
    ! [X25395,X25396,X25397,X25398] :
      ( ~ class_Lattices_Osemilattice__inf(X25398)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25398),X25397))
      | ~ hBOOL(hAPP(hAPP(c_member(X25398),X25396),X25397))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25398),hAPP(hAPP(c_Finite__Set_Ofold(X25398,X25398,c_Lattices_Osemilattice__inf__class_Oinf(X25398)),X25395),X25397)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25398),X25396),X25395))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__le__inf])]) ).

fof(i_0_7219,plain,
    ! [X21714,X21715,X21716,X21717] :
      ( ~ class_Orderings_Olinorder(X21717)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21717),X21716))
      | ~ hBOOL(hAPP(hAPP(c_member(X21717),X21715),X21716))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21717),hAPP(hAPP(c_Finite__Set_Ofold(X21717,X21717,c_Orderings_Oord__class_Omin(X21717)),X21714),X21716)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21717),X21715),X21714))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__le__inf])]) ).

fof(i_0_7220,plain,
    ! [X29722,X29723,X29724,X29725,X29726] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29726,tc_HOL_Obool)),hAPP(c_List_Oset(X29726),X29725)),X29724))
      | ~ hBOOL(hAPP(hAPP(c_member(X29726),X29723),X29724))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29726,tc_HOL_Obool)),hAPP(c_List_Oset(X29726),hAPP(hAPP(c_List_Olist__update(X29726,X29725),X29722),X29723))),X29724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__subsetI])]) ).

fof(i_0_7221,plain,
    ! [X24632,X24633,X24634,X24635,X24636] :
      ( ~ class_Groups_Ocomm__monoid__add(X24636)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24635),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24634),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24636),X24633),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24635,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24634),X24632))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24636),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24636),X24633),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24635,X24634))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24636),X24633),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24634),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24634),X24632)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__ub__add__nat])]) ).

fof(i_0_7222,plain,
    ! [X32853,X32854] :
      ( ~ c_Relation_Otrans(X32854,X32853)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32854,X32854),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X32854,X32854,X32854),X32853),X32853)),X32853)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__O__subset])]) ).

fof(i_0_7223,plain,
    ! [X27224,X27225,X27226,X27227,X27228] : hAPP(hAPP(c_Product__Type_OSigma(X27228,X27227),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27228,tc_HOL_Obool)),X27226),X27225)),hAPP(c_COMBK(tc_fun(X27227,tc_HOL_Obool),X27228),X27224)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27228,X27227),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27228,X27227),X27226),hAPP(c_COMBK(tc_fun(X27227,tc_HOL_Obool),X27228),X27224))),hAPP(hAPP(c_Product__Type_OSigma(X27228,X27227),X27225),hAPP(c_COMBK(tc_fun(X27227,tc_HOL_Obool),X27228),X27224))),
    inference(variable_rename,[status(thm)],[fact_Times__Int__distrib1]) ).

fof(i_0_7224,plain,
    ! [X27198,X27199,X27200,X27201,X27202] : hAPP(hAPP(c_Product__Type_OSigma(X27202,X27201),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27202,tc_HOL_Obool)),X27200),X27199)),hAPP(c_COMBK(tc_fun(X27201,tc_HOL_Obool),X27202),X27198)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27202,X27201),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27202,X27201),X27200),hAPP(c_COMBK(tc_fun(X27201,tc_HOL_Obool),X27202),X27198))),hAPP(hAPP(c_Product__Type_OSigma(X27202,X27201),X27199),hAPP(c_COMBK(tc_fun(X27201,tc_HOL_Obool),X27202),X27198))),
    inference(variable_rename,[status(thm)],[fact_Times__Un__distrib1]) ).

fof(i_0_7225,plain,
    ! [X27141,X27142,X27143,X27144,X27145] : hAPP(hAPP(c_Product__Type_OSigma(X27145,X27144),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27145,tc_HOL_Obool)),X27143),X27142)),hAPP(c_COMBK(tc_fun(X27144,tc_HOL_Obool),X27145),X27141)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27145,X27144),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27145,X27144),X27143),hAPP(c_COMBK(tc_fun(X27144,tc_HOL_Obool),X27145),X27141))),hAPP(hAPP(c_Product__Type_OSigma(X27145,X27144),X27142),hAPP(c_COMBK(tc_fun(X27144,tc_HOL_Obool),X27145),X27141))),
    inference(variable_rename,[status(thm)],[fact_Times__Diff__distrib1]) ).

fof(i_0_7226,plain,
    ! [X18189,X18190,X18191,X18192,X18193] :
      ( ~ c_Fun_Oinj__on(X18193,X18192,X18191,X18190)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18192,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18193,X18192,X18191),X18190)),X18189))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18192),X18189))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18193),X18190)),hAPP(c_Finite__Set_Ocard(X18192),X18189))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__inj__on__le])]) ).

fof(i_0_7227,plain,
    ! [X19396,X19397,X19398,X19399] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19398),esk48_4(X19396,X19397,X19398,X19399)),X19397))
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19399,X19398,c_Groups_Otimes__class_Otimes(X19399)),X19396),c_Groups_Oone__class_Oone(X19399)),X19397) = c_Groups_Oone__class_Oone(X19399)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19398),X19397))
        | ~ class_Groups_Ocomm__monoid__mult(X19399) )
      & ( hAPP(X19396,esk48_4(X19396,X19397,X19398,X19399)) != c_Groups_Oone__class_Oone(X19399)
        | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19399,X19398,c_Groups_Otimes__class_Otimes(X19399)),X19396),c_Groups_Oone__class_Oone(X19399)),X19397) = c_Groups_Oone__class_Oone(X19399)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19398),X19397))
        | ~ class_Groups_Ocomm__monoid__mult(X19399) ) ),
    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_7228,plain,
    ! [X32222,X32223,X32224,X32225] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32224),esk464_4(X32222,X32223,X32224,X32225)),hAPP(c_List_Oset(X32224),X32223)))
        | hBOOL(hAPP(X32222,hAPP(hAPP(c_List_Onth(X32224),X32223),X32225)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32225),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32224)),X32223))) )
      & ( ~ hBOOL(hAPP(X32222,esk464_4(X32222,X32223,X32224,X32225)))
        | hBOOL(hAPP(X32222,hAPP(hAPP(c_List_Onth(X32224),X32223),X32225)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_list__ball__nth])])])]) ).

fof(i_0_7229,plain,
    ! [X29824,X29825,X29826] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29826),tc_List_Olist(X29826))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29826),tc_List_Olist(X29826)),X29825),c_List_Olist_ONil(X29826))),c_List_Olistrel(X29826,X29824)))
      | X29825 = c_List_Olist_ONil(X29826) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__Nil2])]) ).

fof(i_0_7230,plain,
    ! [X26451,X26452,X26453,X26454,X26455,X26456] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26456)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26455,X26456),X26454),hAPP(hAPP(c_COMBB(tc_fun(X26453,X26456),X26456,X26455),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26453,X26456),X26452)),X26451)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26453,X26456),X26452),hAPP(hAPP(c_COMBB(tc_fun(X26455,X26456),X26456,X26453),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26455,X26456),X26454)),hAPP(c_COMBC(X26455,X26453,X26456),X26451))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__commute])]) ).

fof(i_0_7231,plain,
    ! [X23833,X23834,X23835,X23836,X23837,X23838] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X23838)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23837,X23838),X23836),hAPP(hAPP(c_COMBB(tc_fun(X23835,X23838),X23838,X23837),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23835,X23838),X23834)),X23833)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23835,X23838),X23834),hAPP(hAPP(c_COMBB(tc_fun(X23837,X23838),X23838,X23835),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23837,X23838),X23836)),hAPP(c_COMBC(X23837,X23835,X23838),X23833))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__commute])]) ).

fof(i_0_7232,plain,
    ! [X29919,X29920,X29921] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29921),tc_List_Olist(X29921))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29921),tc_List_Olist(X29921)),X29920),c_List_Olist_ONil(X29921))),c_List_Olistrel1(X29921,X29919))),
    inference(variable_rename,[status(thm)],[i_0_5545]) ).

fof(i_0_7233,plain,
    ! [X29927,X29928,X29929] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29929),tc_List_Olist(X29929))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29929),tc_List_Olist(X29929)),X29928),c_List_Olist_ONil(X29929))),c_List_Olexord(X29929,X29927))),
    inference(variable_rename,[status(thm)],[i_0_5546]) ).

fof(i_0_7234,plain,
    ! [X29930,X29931,X29932] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29932),tc_List_Olist(X29932))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29932),tc_List_Olist(X29932)),X29931),c_List_Olist_ONil(X29932))),c_List_Olex(X29932,X29930))),
    inference(variable_rename,[status(thm)],[i_0_5547]) ).

fof(i_0_7235,plain,
    ! [X24721,X24722,X24723,X24724,X24725] :
      ( ( hAPP(c_Relation_OImage(X24725,X24725,X24723),hAPP(hAPP(c_Set_Oinsert(X24725),X24722),c_Orderings_Obot__class_Obot(tc_fun(X24725,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X24725,X24725,X24723),hAPP(hAPP(c_Set_Oinsert(X24725),X24721),c_Orderings_Obot__class_Obot(tc_fun(X24725,tc_HOL_Obool))))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24725,X24725)),hAPP(hAPP(c_Product__Type_OPair(X24725,X24725),X24722),X24721)),X24723))
        | ~ hBOOL(hAPP(hAPP(c_member(X24725),X24721),X24724))
        | ~ hBOOL(hAPP(hAPP(c_member(X24725),X24722),X24724))
        | ~ c_Equiv__Relations_Oequiv(X24725,X24724,X24723) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24725,X24725)),hAPP(hAPP(c_Product__Type_OPair(X24725,X24725),X24722),X24721)),X24723))
        | hAPP(c_Relation_OImage(X24725,X24725,X24723),hAPP(hAPP(c_Set_Oinsert(X24725),X24722),c_Orderings_Obot__class_Obot(tc_fun(X24725,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X24725,X24725,X24723),hAPP(hAPP(c_Set_Oinsert(X24725),X24721),c_Orderings_Obot__class_Obot(tc_fun(X24725,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24725),X24721),X24724))
        | ~ hBOOL(hAPP(hAPP(c_member(X24725),X24722),X24724))
        | ~ c_Equiv__Relations_Oequiv(X24725,X24724,X24723) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class__iff])])]) ).

fof(i_0_7236,plain,
    ! [X24672,X24673,X24674] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24674),esk185_3(X24672,X24673,X24674)),X24673))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24674,tc_Int_Oint),X24672),X24673) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24674,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X24674),c_Int_Onat),X24672)),X24673)) )
      & ( ~ c_Nat__Transfer_Ois__nat(hAPP(X24672,esk185_3(X24672,X24673,X24674)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24674,tc_Int_Oint),X24672),X24673) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24674,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X24674),c_Int_Onat),X24672)),X24673)) ) ),
    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_7237,plain,
    ! [X22205,X22206,X22207] :
      ( ( hBOOL(hAPP(hAPP(c_member(X22207),esk90_3(X22205,X22206,X22207)),X22206))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22207,tc_Int_Oint),X22205),X22206) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22207,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X22207),c_Int_Onat),X22205)),X22206)) )
      & ( ~ c_Nat__Transfer_Ois__nat(hAPP(X22205,esk90_3(X22205,X22206,X22207)))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22207,tc_Int_Oint),X22205),X22206) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22207,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,X22207),c_Int_Onat),X22205)),X22206)) ) ),
    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_7238,plain,
    ! [X29319,X29320,X29321,X29322] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29322),tc_List_Olist(X29322))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29322),tc_List_Olist(X29322)),X29321),X29320)),c_List_Olistrel(X29322,X29319)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29322)),X29321) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29322)),X29320) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__eq__len])]) ).

fof(i_0_7239,plain,
    ! [X29278,X29279,X29280,X29281] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29281),tc_List_Olist(X29281))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29281),tc_List_Olist(X29281)),X29280),X29279)),c_List_Olistrel1(X29281,X29278)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29281)),X29280) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29281)),X29279) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__eq__len])]) ).

fof(i_0_7240,plain,
    ! [X33010,X33011,X33012,X33013] :
      ( ~ c_Relation_Osym(X33013,X33012)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33013,X33013)),hAPP(hAPP(c_Product__Type_OPair(X33013,X33013),X33011),X33010)),X33012))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X33013,X33013)),hAPP(hAPP(c_Product__Type_OPair(X33013,X33013),X33010),X33011)),X33012)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_symD])]) ).

fof(i_0_7241,plain,
    ! [X33002,X33003,X33004,X33005,X33006,X33007] :
      ( ( ~ c_Relation_Osym(X33003,X33002)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33003,X33003)),hAPP(hAPP(c_Product__Type_OPair(X33003,X33003),X33004),X33005)),X33002))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X33003,X33003)),hAPP(hAPP(c_Product__Type_OPair(X33003,X33003),X33005),X33004)),X33002)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X33007,X33007)),hAPP(hAPP(c_Product__Type_OPair(X33007,X33007),esk513_2(X33006,X33007)),esk514_2(X33006,X33007))),X33006))
        | c_Relation_Osym(X33007,X33006) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X33007,X33007)),hAPP(hAPP(c_Product__Type_OPair(X33007,X33007),esk514_2(X33006,X33007)),esk513_2(X33006,X33007))),X33006))
        | c_Relation_Osym(X33007,X33006) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__def])])])])])]) ).

cnf(i_0_7242,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_5548]) ).

cnf(i_0_7243,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_5549]) ).

fof(i_0_7244,plain,
    ! [X17793,X17794,X17795] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X17795),esk17_3(X17793,X17794,X17795)))
        | hBOOL(hAPP(X17793,X17794))
        | ~ hBOOL(hAPP(X17793,c_Orderings_Obot__class_Obot(tc_fun(X17795,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17795),X17794)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17795),esk16_3(X17793,X17794,X17795)),esk17_3(X17793,X17794,X17795)))
        | hBOOL(hAPP(X17793,X17794))
        | ~ hBOOL(hAPP(X17793,c_Orderings_Obot__class_Obot(tc_fun(X17795,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17795),X17794)) )
      & ( hBOOL(hAPP(X17793,esk17_3(X17793,X17794,X17795)))
        | hBOOL(hAPP(X17793,X17794))
        | ~ hBOOL(hAPP(X17793,c_Orderings_Obot__class_Obot(tc_fun(X17795,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17795),X17794)) )
      & ( ~ hBOOL(hAPP(X17793,hAPP(hAPP(c_Set_Oinsert(X17795),esk16_3(X17793,X17794,X17795)),esk17_3(X17793,X17794,X17795))))
        | hBOOL(hAPP(X17793,X17794))
        | ~ hBOOL(hAPP(X17793,c_Orderings_Obot__class_Obot(tc_fun(X17795,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17795),X17794)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5550])])])]) ).

fof(i_0_7245,plain,
    ! [X31955,X31956,X31957,X31958,X31959] :
      ( ~ class_Orderings_Olinorder(X31959)
      | ~ c_List_Olinorder__class_Osorted(X31959,hAPP(c_List_Orev(X31959),hAPP(hAPP(c_List_Omap(X31958,X31959),X31957),X31956)))
      | hAPP(c_List_Ofilter(X31958,hAPP(hAPP(c_COMBB(X31959,tc_HOL_Obool,X31958),hAPP(c_Orderings_Oord__class_Oless(X31959),X31955)),X31957)),X31956) = c_List_OtakeWhile(X31958,hAPP(hAPP(c_COMBB(X31959,tc_HOL_Obool,X31958),hAPP(c_Orderings_Oord__class_Oless(X31959),X31955)),X31957),X31956) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev])]) ).

fof(i_0_7246,plain,
    ! [X27160,X27161,X27162,X27163] : hAPP(hAPP(c_Product__Type_OSigma(X27163,X27162),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27163,tc_HOL_Obool),X27161)),X27160) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X27163,tc_HOL_Obool),tc_fun(tc_prod(X27163,X27162),tc_HOL_Obool)),X27161),hAPP(hAPP(c_COMBC(tc_fun(X27163,tc_HOL_Obool),tc_fun(X27163,tc_fun(X27162,tc_HOL_Obool)),tc_fun(tc_prod(X27163,X27162),tc_HOL_Obool)),c_Product__Type_OSigma(X27163,X27162)),X27160)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Union]) ).

fof(i_0_7247,plain,
    ! [X24298,X24299,X24300,X24301] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk160_4(X24298,X24299,X24300,X24301)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24300)))
        | X24301 = X24299
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24301),X24300) != X24299
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24299),X24298))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24300)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk161_4(X24298,X24299,X24300,X24301)),X24298))
        | X24301 = X24299
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24301),X24300) != X24299
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24299),X24298))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24300)) )
      & ( X24301 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk161_4(X24298,X24299,X24300,X24301)),esk160_4(X24298,X24299,X24300,X24301))
        | X24301 = X24299
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24301),X24300) != X24299
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24299),X24298))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24300)) ) ),
    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_7248,plain,
    ! [X24292,X24293,X24294,X24295] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk158_4(X24292,X24293,X24294,X24295)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24294)))
        | X24295 = X24293
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24295),X24294) != X24293
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24293),X24292))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24294)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk159_4(X24292,X24293,X24294,X24295)),X24292))
        | X24295 = X24293
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24295),X24294) != X24293
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24293),X24292))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24294)) )
      & ( X24295 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk159_4(X24292,X24293,X24294,X24295)),esk158_4(X24292,X24293,X24294,X24295))
        | X24295 = X24293
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24295),X24294) != X24293
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X24293),X24292))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24294)) ) ),
    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_7249,plain,
    ! [X19611,X19612,X19613,X19614,X19615] : hAPP(hAPP(c_Finite__Set_Ofold(X19615,X19614,X19613),X19612),X19611) = c_HOL_OThe(X19614,c_Finite__Set_Ofold__graph(X19615,X19614,X19613,X19612,X19611)),
    inference(variable_rename,[status(thm)],[fact_fold__def]) ).

fof(i_0_7250,plain,
    ! [X22097,X22098,X22099,X22101,X22102,X22103,X22104,X22105,X22108] :
      ( ( ~ hBOOL(hAPP(X22099,esk86_3(X22097,X22098,X22099)))
        | hBOOL(hAPP(X22099,hAPP(hAPP(c_Product__Type_OPair(X22098,X22097),X22101),X22102))) )
      & ( ~ hBOOL(hAPP(X22105,hAPP(hAPP(c_Product__Type_OPair(X22104,X22103),esk87_3(X22103,X22104,X22105)),esk88_3(X22103,X22104,X22105))))
        | hBOOL(hAPP(X22105,X22108)) ) ),
    inference(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_7251,plain,
    ! [X33251,X33252,X33253,X33254,X33255] :
      ( ~ hBOOL(hAPP(X33255,hAPP(hAPP(c_Product__Type_OPair(X33254,X33253),X33252),X33251)))
      | hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X33254,X33253,tc_HOL_Obool,X33255),X33252),X33251)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_curryI])]) ).

fof(i_0_7252,plain,
    ! [X17480,X17481,X17482] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17482),X17481))
      | 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(X17482),X17480)),hAPP(c_Finite__Set_Ocard(X17482),X17481))),hAPP(c_Finite__Set_Ocard(X17482),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17482,tc_HOL_Obool)),X17480),X17481)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__card__le__card__Diff])]) ).

fof(i_0_7253,plain,
    ! [X27115,X27116,X27117,X27118] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27117,tc_HOL_Obool)),esk255_4(X27115,X27116,X27117,X27118)),X27118))
        | c_Fun_Oinj__on(X27117,X27116,X27115,c_Complete__Lattice_OInf__class_OInf(tc_fun(X27117,tc_HOL_Obool),X27118))
        | X27118 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X27117,tc_HOL_Obool),tc_HOL_Obool)) )
      & ( ~ c_Fun_Oinj__on(X27117,X27116,X27115,esk255_4(X27115,X27116,X27117,X27118))
        | c_Fun_Oinj__on(X27117,X27116,X27115,c_Complete__Lattice_OInf__class_OInf(tc_fun(X27117,tc_HOL_Obool),X27118))
        | X27118 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X27117,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_7254,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_5551]) ).

fof(i_0_7255,plain,
    ! [X32551,X32552,X32553,X32554,X32555,X32556,X32557,X32558,X32559] :
      ( ( hBOOL(hAPP(X32551,X32552))
        | ~ hBOOL(hAPP(hAPP(c_member(X32554),X32555),hAPP(c_List_Oset(X32554),c_List_Oreplicate(X32554,X32553,X32552))))
        | ~ hBOOL(hAPP(X32551,X32555)) )
      & ( X32553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X32554),X32555),hAPP(c_List_Oset(X32554),c_List_Oreplicate(X32554,X32553,X32552))))
        | ~ hBOOL(hAPP(X32551,X32555)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32559),esk480_4(X32556,X32557,X32558,X32559)),hAPP(c_List_Oset(X32559),c_List_Oreplicate(X32559,X32558,X32557))))
        | ~ hBOOL(hAPP(X32556,X32557))
        | X32558 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(X32556,esk480_4(X32556,X32557,X32558,X32559)))
        | ~ hBOOL(hAPP(X32556,X32557))
        | X32558 = 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_7256,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_7257,plain,
    ! [X22181,X22182,X22183,X22184,X22185] :
      ( ( ~ c_Nitpick_Orefl_H(X22182,X22181)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22182,X22182)),hAPP(hAPP(c_Product__Type_OPair(X22182,X22182),X22183),X22183)),X22181)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22185,X22185)),hAPP(hAPP(c_Product__Type_OPair(X22185,X22185),esk89_2(X22184,X22185)),esk89_2(X22184,X22185))),X22184))
        | c_Nitpick_Orefl_H(X22185,X22184) ) ),
    inference(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_7258,plain,
    ! [X23621,X23622,X23623,X23625] :
      ( ( hBOOL(hAPP(X23622,esk124_3(X23621,X23622,X23623)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23621))
        | ~ hBOOL(hAPP(X23622,X23625))
        | hBOOL(hAPP(X23622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23621),X23623))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23623)) )
      & ( ~ hBOOL(hAPP(X23622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk124_3(X23621,X23622,X23623)),X23623)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23621))
        | ~ hBOOL(hAPP(X23622,X23625))
        | hBOOL(hAPP(X23622,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X23625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23621),X23623))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23623)) ) ),
    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_7259,plain,
    ! [X23605,X23606,X23607,X23609] :
      ( ( hBOOL(hAPP(X23606,esk120_3(X23605,X23606,X23607)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23605))
        | ~ hBOOL(hAPP(X23606,X23609))
        | hBOOL(hAPP(X23606,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23605),X23607))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23607)) )
      & ( ~ hBOOL(hAPP(X23606,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk120_3(X23605,X23606,X23607)),X23607)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23605))
        | ~ hBOOL(hAPP(X23606,X23609))
        | hBOOL(hAPP(X23606,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23609),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X23605),X23607))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23607)) ) ),
    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_7260,plain,
    ! [X32106,X32107,X32108,X32109,X32110] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X32110,X32109)),hAPP(X32110,X32108)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X32107,X32107)),hAPP(hAPP(c_Product__Type_OPair(X32107,X32107),X32109),X32108)),c_List_Omeasures(X32107,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X32107,tc_Nat_Onat)),X32110),X32106)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_measures__less])]) ).

cnf(i_0_7261,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_7262,plain,
    ! [X19895,X19896,X19897,X19898,X19899,X19900,X19901] :
      ( ~ c_Finite__Set_Ofolding__idem(X19901,X19900,X19899,X19898)
      | hAPP(c_Fun_Ocomp(X19900,X19900,X19897,hAPP(X19899,X19896)),hAPP(c_Fun_Ocomp(X19900,X19900,X19897,hAPP(X19899,X19896)),X19895)) = hAPP(c_Fun_Ocomp(X19900,X19900,X19897,hAPP(X19899,X19896)),X19895) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__left__comp])]) ).

fof(i_0_7263,plain,
    ! [X22061,X22062,X22063,X22064,X22065,X22066,X22067] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X22067),X22066),hAPP(hAPP(X22065,X22064),X22063)))
      | hBOOL(hAPP(hAPP(c_member(X22067),X22066),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22062,X22061,tc_fun(X22067,tc_HOL_Obool)),X22065),hAPP(hAPP(c_Product__Type_OPair(X22062,X22061),X22064),X22063)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__splitI])]) ).

fof(i_0_7264,plain,
    ! [X32561,X32562,X32563,X32564,X32566,X32567,X32568,X32569,X32570] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32564),esk481_4(X32561,X32562,X32563,X32564)),hAPP(c_List_Oset(X32564),c_List_Oreplicate(X32564,X32563,X32562))))
        | hBOOL(hAPP(X32561,X32562))
        | X32563 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(X32561,esk481_4(X32561,X32562,X32563,X32564)))
        | hBOOL(hAPP(X32561,X32562))
        | X32563 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(X32566,X32567))
        | ~ hBOOL(hAPP(hAPP(c_member(X32569),X32570),hAPP(c_List_Oset(X32569),c_List_Oreplicate(X32569,X32568,X32567))))
        | hBOOL(hAPP(X32566,X32570)) )
      & ( X32568 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X32569),X32570),hAPP(c_List_Oset(X32569),c_List_Oreplicate(X32569,X32568,X32567))))
        | hBOOL(hAPP(X32566,X32570)) ) ),
    inference(distribute,[status(thm)],[inference(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_7265,plain,
    ! [X29301,X29302,X29303,X29304] : hAPP(c_Relation_OImage(tc_List_Olist(X29304),tc_List_Olist(X29304),c_List_Olistrel(X29304,X29303)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29304)),hAPP(hAPP(c_List_Olist_OCons(X29304),X29302),X29301)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29304),tc_HOL_Obool)))) = c_List_Oset__Cons(X29304,hAPP(c_Relation_OImage(X29304,X29304,X29303),hAPP(hAPP(c_Set_Oinsert(X29304),X29302),c_Orderings_Obot__class_Obot(tc_fun(X29304,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(X29304),tc_List_Olist(X29304),c_List_Olistrel(X29304,X29303)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29304)),X29301),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29304),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_listrel__Cons]) ).

fof(i_0_7266,plain,
    ! [X25347,X25348,X25349,X25350] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X25350,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25349)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X25350,tc_HOL_Obool),tc_Nat_Onat),X25348),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X25347))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X25350,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X25347,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X25349),X25347))),X25348),
    inference(variable_rename,[status(thm)],[fact_UN__le__add__shift]) ).

cnf(i_0_7267,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_7268,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_7269,plain,
    ! [X33325,X33326,X33327,X33328] :
      ( ~ c_Fun_Obij__betw(X33328,X33327,X33326,c_Orderings_Otop__class_Otop(tc_fun(X33328,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33327,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33328,X33327,X33326),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X33328,tc_HOL_Obool)),X33325)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X33327,tc_HOL_Obool)),hAPP(c_Set_Oimage(X33328,X33327,X33326),X33325)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__image__Compl__eq])]) ).

cnf(i_0_7270,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_5552]) ).

cnf(i_0_7271,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_5553]) ).

fof(i_0_7272,plain,
    ! [X30454,X30455,X30456,X30457,X30458,X30459] :
      ( X30457 != hAPP(hAPP(c_List_Olist_OCons(X30456),X30458),X30459)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X30456),tc_List_Olist(X30456))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X30456),tc_List_Olist(X30456)),X30455),hAPP(hAPP(c_List_Oappend(X30456),X30455),X30457))),c_List_Olexord(X30456,X30454))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__append__rightI])])]) ).

fof(i_0_7273,plain,
    ! [X29593,X29594,X29595,X29596,X29597,X29598,X29599] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29593)),X29595) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29593)),X29594)
        | X29595 != X29594 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X29593,X29593)),X29596),hAPP(c_List_Oset(tc_prod(X29593,X29593)),hAPP(hAPP(c_List_Ozip(X29593,X29593),X29595),X29594))))
        | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29593,X29593,tc_HOL_Obool),c_fequal),X29596))
        | X29595 != X29594 )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X29597,X29597)),esk389_3(X29597,X29598,X29599)),hAPP(c_List_Oset(tc_prod(X29597,X29597)),hAPP(hAPP(c_List_Ozip(X29597,X29597),X29599),X29598))))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29597)),X29599) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29597)),X29598)
        | X29599 = X29598 )
      & ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X29597,X29597,tc_HOL_Obool),c_fequal),esk389_3(X29597,X29598,X29599)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29597)),X29599) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29597)),X29598)
        | X29599 = X29598 ) ),
    inference(distribute,[status(thm)],[inference(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_7274,plain,
    ! [X26034,X26035,X26036] :
      ( ( 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),esk221_3(X26034,X26035,X26036)),esk222_3(X26034,X26035,X26036))))
        | hBOOL(hAPP(hAPP(X26034,X26036),X26035))
        | ~ 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),X26036),X26035))) )
      & ( esk222_3(X26034,X26035,X26036) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(X26034,esk222_3(X26034,X26035,X26036)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk221_3(X26034,X26035,X26036),esk222_3(X26034,X26035,X26036))))
        | hBOOL(hAPP(hAPP(X26034,X26036),X26035))
        | ~ 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),X26036),X26035))) )
      & ( ~ hBOOL(hAPP(hAPP(X26034,esk221_3(X26034,X26035,X26036)),esk222_3(X26034,X26035,X26036)))
        | hBOOL(hAPP(hAPP(X26034,X26036),X26035))
        | ~ 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),X26036),X26035))) ) ),
    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_7275,plain,
    ! [X18624,X18625,X18626,X18627,X18628] :
      ( ~ c_Fun_Oinj__on(X18628,X18627,X18626,X18625)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18628,tc_HOL_Obool)),X18624),X18625))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18627,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18628,X18627,X18626),X18624)),hAPP(c_Set_Oimage(X18628,X18627,X18626),X18625))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__strict__subset])]) ).

fof(i_0_7276,plain,
    ! [X25324,X25325,X25326,X25327,X25328,X25329] :
      ( ~ c_Fun_Oinj__on(X25329,X25328,X25327,X25326)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25329,tc_HOL_Obool)),X25325),X25326))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25329,tc_HOL_Obool)),X25324),X25326))
      | hAPP(c_Set_Oimage(X25329,X25328,X25327),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25329,tc_HOL_Obool)),X25325),X25324)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25328,tc_HOL_Obool)),hAPP(c_Set_Oimage(X25329,X25328,X25327),X25325)),hAPP(c_Set_Oimage(X25329,X25328,X25327),X25324)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__Int])]) ).

fof(i_0_7277,plain,
    ! [X18675,X18676,X18677,X18678,X18679,X18680] :
      ( ~ c_Fun_Oinj__on(X18680,X18679,X18678,X18677)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18680,tc_HOL_Obool)),X18676),X18677))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18680,tc_HOL_Obool)),X18675),X18677))
      | hAPP(c_Set_Oimage(X18680,X18679,X18678),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18680,tc_HOL_Obool)),X18676),X18675)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18679,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18680,X18679,X18678),X18676)),hAPP(c_Set_Oimage(X18680,X18679,X18678),X18675)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__image__set__diff])]) ).

fof(i_0_7278,plain,
    ! [X31502,X31503,X31504] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31504),X31503))
      | hAPP(c_List_Ofilter(X31504,hAPP(hAPP(c_COMBC(X31504,tc_fun(X31504,tc_HOL_Obool),tc_HOL_Obool),c_member(X31504)),hAPP(c_List_Oset(X31504),c_List_Osublist(X31504,X31503,X31502)))),X31503) = c_List_Osublist(X31504,X31503,X31502) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__in__sublist])]) ).

cnf(i_0_7279,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_5554]) ).

cnf(i_0_7280,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk339_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_5485]) ).

cnf(i_0_7281,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oconcat(X2,X1)))
    | esk446_2(X1,X2) != esk447_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),esk445_2(X1,X2)))
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_5498]) ).

fof(i_0_7282,plain,
    ! [X33126,X33127,X33128,X33129,X33130,X33131,X33132] :
      ( ( hAPP(c_Set_Oimage(X33128,X33127,X33126),c_Orderings_Otop__class_Otop(tc_fun(X33128,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33127,tc_HOL_Obool))
        | hAPP(X33126,hAPP(c_Hilbert__Choice_Oinv__into(X33128,X33127,c_Orderings_Otop__class_Otop(tc_fun(X33128,tc_HOL_Obool)),X33126),X33129)) = X33129 )
      & ( hAPP(X33130,hAPP(c_Hilbert__Choice_Oinv__into(X33132,X33131,c_Orderings_Otop__class_Otop(tc_fun(X33132,tc_HOL_Obool)),X33130),esk521_3(X33130,X33131,X33132))) != esk521_3(X33130,X33131,X33132)
        | hAPP(c_Set_Oimage(X33132,X33131,X33130),c_Orderings_Otop__class_Otop(tc_fun(X33132,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33131,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_7283,plain,
    ! [X32709,X32710,X32711,X32713,X32714,X32715,X32716,X32717] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32711),esk486_3(X32709,X32710,X32711)),hAPP(c_List_Oset(X32711),X32709)))
        | ~ c_List_Olist__ex1(X32711,X32710,X32709) )
      & ( hBOOL(hAPP(X32710,esk486_3(X32709,X32710,X32711)))
        | ~ c_List_Olist__ex1(X32711,X32710,X32709) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32711),X32713),hAPP(c_List_Oset(X32711),X32709)))
        | ~ hBOOL(hAPP(X32710,X32713))
        | X32713 = esk486_3(X32709,X32710,X32711)
        | ~ c_List_Olist__ex1(X32711,X32710,X32709) )
      & ( hBOOL(hAPP(hAPP(c_member(X32716),esk487_4(X32714,X32715,X32716,X32717)),hAPP(c_List_Oset(X32716),X32714)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32716),X32717),hAPP(c_List_Oset(X32716),X32714)))
        | ~ hBOOL(hAPP(X32715,X32717))
        | c_List_Olist__ex1(X32716,X32715,X32714) )
      & ( hBOOL(hAPP(X32715,esk487_4(X32714,X32715,X32716,X32717)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32716),X32717),hAPP(c_List_Oset(X32716),X32714)))
        | ~ hBOOL(hAPP(X32715,X32717))
        | c_List_Olist__ex1(X32716,X32715,X32714) )
      & ( esk487_4(X32714,X32715,X32716,X32717) != X32717
        | ~ hBOOL(hAPP(hAPP(c_member(X32716),X32717),hAPP(c_List_Oset(X32716),X32714)))
        | ~ hBOOL(hAPP(X32715,X32717))
        | c_List_Olist__ex1(X32716,X32715,X32714) ) ),
    inference(distribute,[status(thm)],[inference(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_7284,plain,
    ! [X32354,X32355,X32356,X32358,X32359,X32360,X32361,X32362] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32356),esk478_3(X32354,X32355,X32356)),hAPP(c_List_Oset(X32356),X32354)))
        | ~ c_List_Olist__ex1(X32356,X32355,X32354) )
      & ( hBOOL(hAPP(X32355,esk478_3(X32354,X32355,X32356)))
        | ~ c_List_Olist__ex1(X32356,X32355,X32354) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32356),X32358),hAPP(c_List_Oset(X32356),X32354)))
        | ~ hBOOL(hAPP(X32355,X32358))
        | X32358 = esk478_3(X32354,X32355,X32356)
        | ~ c_List_Olist__ex1(X32356,X32355,X32354) )
      & ( hBOOL(hAPP(hAPP(c_member(X32361),esk479_4(X32359,X32360,X32361,X32362)),hAPP(c_List_Oset(X32361),X32359)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32361),X32362),hAPP(c_List_Oset(X32361),X32359)))
        | ~ hBOOL(hAPP(X32360,X32362))
        | c_List_Olist__ex1(X32361,X32360,X32359) )
      & ( hBOOL(hAPP(X32360,esk479_4(X32359,X32360,X32361,X32362)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32361),X32362),hAPP(c_List_Oset(X32361),X32359)))
        | ~ hBOOL(hAPP(X32360,X32362))
        | c_List_Olist__ex1(X32361,X32360,X32359) )
      & ( esk479_4(X32359,X32360,X32361,X32362) != X32362
        | ~ hBOOL(hAPP(hAPP(c_member(X32361),X32362),hAPP(c_List_Oset(X32361),X32359)))
        | ~ hBOOL(hAPP(X32360,X32362))
        | c_List_Olist__ex1(X32361,X32360,X32359) ) ),
    inference(distribute,[status(thm)],[inference(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_7285,plain,
    ! [X18799,X18800,X18801] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18801),X18800))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18801,tc_HOL_Obool)),hAPP(c_Set_Oimage(X18801,X18801,X18799),X18800)),X18800))
      | ~ c_Fun_Oinj__on(X18801,X18801,X18799,X18800)
      | hAPP(c_Set_Oimage(X18801,X18801,X18799),X18800) = X18800 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_endo__inj__surj])]) ).

fof(i_0_7286,plain,
    ! [X30606,X30607,X30608,X30609,X30610] :
      ( ~ class_Orderings_Olinorder(X30610)
      | ~ hBOOL(hAPP(hAPP(c_member(X30610),hAPP(X30609,X30608)),hAPP(c_Set_Oimage(X30607,X30610,X30609),hAPP(c_List_Oset(X30607),X30606))))
      | c_List_Olinorder__class_Oinsort__insert__key(X30607,X30610,X30609,X30608,X30606) = X30606 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__key__triv])]) ).

fof(i_0_7287,plain,
    ! [X30603,X30604,X30605] :
      ( ~ class_Orderings_Olinorder(X30605)
      | hAPP(c_List_Oset(X30605),c_List_Olinorder__class_Oinsort__insert__key(X30605,X30605,c_COMBI(X30605),X30604,X30603)) = hAPP(hAPP(c_Set_Oinsert(X30605),X30604),hAPP(c_List_Oset(X30605),X30603)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort__insert])]) ).

fof(i_0_7288,plain,
    ! [X29334,X29335,X29336] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29336,X29336),tc_HOL_Obool)),X29335),X29334))
      | ~ c_Relation_Orefl__on(X29336,c_Orderings_Otop__class_Otop(tc_fun(X29336,tc_HOL_Obool)),X29334)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29336),tc_List_Olist(X29336)),tc_HOL_Obool)),c_List_Olistrel1(X29336,X29335)),c_List_Olistrel(X29336,X29334))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__subset__listrel])]) ).

cnf(i_0_7289,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_5555]) ).

cnf(i_0_7290,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_5541]) ).

fof(i_0_7291,plain,
    ! [X21725,X21726,X21727,X21728,X21729,X21730,X21731] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21730),X21726))
        | hAPP(hAPP(X21727,X21725),X21726) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X21731,X21730,X21729),X21725),X21728),X21726)
        | ~ c_Big__Operators_Ocomm__monoid__big(X21731,X21730,X21729,X21728,X21727) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X21730),X21726))
        | hAPP(hAPP(X21727,X21725),X21726) = X21728
        | ~ c_Big__Operators_Ocomm__monoid__big(X21731,X21730,X21729,X21728,X21727) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5556])])]) ).

fof(i_0_7292,plain,
    ! [X19911,X19912,X19913,X19914,X19915,X19916,X19917] :
      ( ~ c_Finite__Set_Ofolding__image(X19917,X19916,X19915,X19914,X19913)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19916),X19912))
      | hAPP(hAPP(X19913,X19911),X19912) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19917,X19916,X19915),X19911),X19914),X19912) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__image_Oeq__fold])]) ).

fof(i_0_7293,plain,
    ! [X19706,X19707,X19708,X19709,X19710,X19711] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19711,X19710,X19709)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19711),X19708))
      | ~ hBOOL(hAPP(hAPP(c_member(X19711),X19707),X19708))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19711,X19710,X19709),X19706),X19708) = hAPP(hAPP(X19709,X19707),hAPP(hAPP(c_Finite__Set_Ofold(X19711,X19710,X19709),X19706),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19711,tc_HOL_Obool)),X19708),hAPP(hAPP(c_Set_Oinsert(X19711),X19707),c_Orderings_Obot__class_Obot(tc_fun(X19711,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__rec])]) ).

fof(i_0_7294,plain,
    ! [X26813,X26814,X26815,X26816,X26817,X26818] : hAPP(c_Set_Ovimage(X26818,X26817,hAPP(c_Fun_Ocomp(X26816,X26817,X26818,X26815),X26814)),X26813) = hAPP(c_Set_Ovimage(X26818,X26816,X26814),hAPP(c_Set_Ovimage(X26816,X26817,X26815),X26813)),
    inference(variable_rename,[status(thm)],[fact_vimage__compose]) ).

fof(i_0_7295,plain,
    ! [X19562,X19563,X19564,X19565,X19566,X19567] : hAPP(c_Set_Oimage(X19567,X19566,hAPP(c_Fun_Ocomp(X19565,X19566,X19567,X19564),X19563)),X19562) = hAPP(c_Set_Oimage(X19565,X19566,X19564),hAPP(c_Set_Oimage(X19567,X19565,X19563),X19562)),
    inference(variable_rename,[status(thm)],[fact_image__compose]) ).

fof(i_0_7296,plain,
    ! [X28960,X28961,X28962,X28964,X28965,X28966,X28967] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28962,X28962)),X28961),c_Transitive__Closure_Ortrancl(X28962,X28960)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28962,X28962)),X28961),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28962,X28962),tc_HOL_Obool),esk338_3(X28960,X28961,X28962)),X28960))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28966,X28966)),X28965),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28966,X28966),tc_HOL_Obool),X28967),X28964)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28966,X28966)),X28965),c_Transitive__Closure_Ortrancl(X28966,X28964))) ) ),
    inference(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_7297,plain,
    ! [X28477,X28478,X28479,X28480,X28481,X28482,X28483] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28483,X28482,X28481,X28480),X28479),X28478),X28477) = hAPP(hAPP(X28478,hAPP(c_Product__Type_Ofst(X28482,X28481),hAPP(X28479,X28477))),hAPP(c_Product__Type_Osnd(X28482,X28481),hAPP(X28479,X28477))),
    inference(variable_rename,[status(thm)],[fact_scomp__unfold]) ).

fof(i_0_7298,plain,
    ! [X24731,X24732,X24733,X24734,X24735] :
      ( ( hAPP(c_Relation_OImage(X24735,X24735,X24733),hAPP(hAPP(c_Set_Oinsert(X24735),X24732),c_Orderings_Obot__class_Obot(tc_fun(X24735,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X24735,X24735,X24733),hAPP(hAPP(c_Set_Oinsert(X24735),X24731),c_Orderings_Obot__class_Obot(tc_fun(X24735,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24735,X24735)),hAPP(hAPP(c_Product__Type_OPair(X24735,X24735),X24732),X24731)),X24733))
        | ~ c_Equiv__Relations_Oequiv(X24735,X24734,X24733) )
      & ( hBOOL(hAPP(hAPP(c_member(X24735),X24732),X24734))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24735,X24735)),hAPP(hAPP(c_Product__Type_OPair(X24735,X24735),X24732),X24731)),X24733))
        | ~ c_Equiv__Relations_Oequiv(X24735,X24734,X24733) )
      & ( hBOOL(hAPP(hAPP(c_member(X24735),X24731),X24734))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24735,X24735)),hAPP(hAPP(c_Product__Type_OPair(X24735,X24735),X24732),X24731)),X24733))
        | ~ c_Equiv__Relations_Oequiv(X24735,X24734,X24733) )
      & ( hAPP(c_Relation_OImage(X24735,X24735,X24733),hAPP(hAPP(c_Set_Oinsert(X24735),X24732),c_Orderings_Obot__class_Obot(tc_fun(X24735,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X24735,X24735,X24733),hAPP(hAPP(c_Set_Oinsert(X24735),X24731),c_Orderings_Obot__class_Obot(tc_fun(X24735,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(X24735),X24732),X24734))
        | ~ hBOOL(hAPP(hAPP(c_member(X24735),X24731),X24734))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24735,X24735)),hAPP(hAPP(c_Product__Type_OPair(X24735,X24735),X24732),X24731)),X24733))
        | ~ c_Equiv__Relations_Oequiv(X24735,X24734,X24733) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq__iff])])]) ).

fof(i_0_7299,plain,
    ! [X18496,X18497,X18498] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18498),c_Groups_Ozero__class_Ozero(X18498)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18498),X18497),X18497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18498),X18496),X18496))))
        | X18497 != c_Groups_Ozero__class_Ozero(X18498)
        | X18496 != c_Groups_Ozero__class_Ozero(X18498)
        | ~ class_Rings_Olinordered__ring__strict(X18498) )
      & ( X18497 = c_Groups_Ozero__class_Ozero(X18498)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18498),c_Groups_Ozero__class_Ozero(X18498)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18498),X18497),X18497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18498),X18496),X18496))))
        | ~ class_Rings_Olinordered__ring__strict(X18498) )
      & ( X18496 = c_Groups_Ozero__class_Ozero(X18498)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18498),c_Groups_Ozero__class_Ozero(X18498)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18498),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18498),X18497),X18497)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18498),X18496),X18496))))
        | ~ class_Rings_Olinordered__ring__strict(X18498) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff])])]) ).

fof(i_0_7300,plain,
    ! [X29028,X29029] : c_Transitive__Closure_Ortrancl(X29029,X29028) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(X29029,X29029),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(X29029,X29029),tc_HOL_Obool),tc_fun(tc_prod(X29029,X29029),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(X29029,X29029),tc_HOL_Obool)),X29028)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__is__UN__rel__pow]) ).

fof(i_0_7301,plain,
    ! [X32164,X32165,X32166,X32167] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32167),esk454_4(X32164,X32165,X32166,X32167)),hAPP(c_List_Oset(X32167),X32166)))
        | c_List_OtakeWhile(X32167,X32165,hAPP(hAPP(c_List_Oappend(X32167),X32166),X32164)) = hAPP(hAPP(c_List_Oappend(X32167),X32166),c_List_OtakeWhile(X32167,X32165,X32164)) )
      & ( ~ hBOOL(hAPP(X32165,esk454_4(X32164,X32165,X32166,X32167)))
        | c_List_OtakeWhile(X32167,X32165,hAPP(hAPP(c_List_Oappend(X32167),X32166),X32164)) = hAPP(hAPP(c_List_Oappend(X32167),X32166),c_List_OtakeWhile(X32167,X32165,X32164)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__append2])])])]) ).

fof(i_0_7302,plain,
    ! [X19593,X19594,X19595,X19596,X19597,X19598] :
      ( ~ c_Fun_Oinj__on(X19598,X19597,hAPP(c_Fun_Ocomp(X19596,X19597,X19598,X19595),X19594),X19593)
      | c_Fun_Oinj__on(X19596,X19597,X19595,hAPP(c_Set_Oimage(X19598,X19596,X19594),X19593)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI])]) ).

fof(i_0_7303,plain,
    ! [X24511,X24512,X24513,X24515,X24516] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24513),esk181_3(X24511,X24512,X24513)),X24512))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24513,tc_Nat_Onat),X24511),X24512) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24513),X24512)) )
      & ( hAPP(X24511,esk181_3(X24511,X24512,X24513)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24513,tc_Nat_Onat),X24511),X24512) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24513),X24512)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X24513),X24515),X24512))
        | esk181_3(X24511,X24512,X24513) = X24515
        | hAPP(X24511,X24515) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24513,tc_Nat_Onat),X24511),X24512) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24513),X24512)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24513),esk182_4(X24511,X24512,X24513,X24516)),X24512))
        | ~ hBOOL(hAPP(hAPP(c_member(X24513),X24516),X24512))
        | hAPP(X24511,X24516) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24513,tc_Nat_Onat),X24511),X24512) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24513),X24512)) )
      & ( X24516 != esk182_4(X24511,X24512,X24513,X24516)
        | ~ hBOOL(hAPP(hAPP(c_member(X24513),X24516),X24512))
        | hAPP(X24511,X24516) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24513,tc_Nat_Onat),X24511),X24512) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24513),X24512)) )
      & ( hAPP(X24511,esk182_4(X24511,X24512,X24513,X24516)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X24513),X24516),X24512))
        | hAPP(X24511,X24516) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24513,tc_Nat_Onat),X24511),X24512) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24513),X24512)) ) ),
    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_7304,plain,
    ! [X31663,X31664,X31665] :
      ( ~ class_Orderings_Olinorder(X31665)
      | ~ c_List_Olinorder__class_Osorted(X31665,X31664)
      | c_List_Olinorder__class_Osorted(X31665,c_List_Olinorder__class_Oinsort__insert__key(X31665,X31665,c_COMBI(X31665),X31663,X31664)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__insert])]) ).

fof(i_0_7305,plain,
    ! [X25899,X25900,X25901,X25902,X25903] :
      ( ~ class_Rings_Olinordered__idom(X25903)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25903),hAPP(c_Groups_Oabs__class_Oabs(X25903),X25902)),X25901))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25903),hAPP(c_Groups_Oabs__class_Oabs(X25903),X25900)),X25899))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25903),hAPP(c_Groups_Oabs__class_Oabs(X25903),X25902)),hAPP(c_Groups_Oabs__class_Oabs(X25903),X25900))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25903),X25901),X25899))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__less])]) ).

fof(i_0_7306,plain,
    ! [X19842,X19843,X19844,X19845,X19846,X19847] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19847,X19846,X19845)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19847),X19844))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19847,X19846,X19845),X19843),hAPP(hAPP(c_Set_Oinsert(X19847),X19842),X19844)) = hAPP(hAPP(X19845,X19842),hAPP(hAPP(c_Finite__Set_Ofold(X19847,X19846,X19845),X19843),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X19847,tc_HOL_Obool)),X19844),hAPP(hAPP(c_Set_Oinsert(X19847),X19842),c_Orderings_Obot__class_Obot(tc_fun(X19847,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__insert__remove])]) ).

fof(i_0_7307,plain,
    ! [X31918,X31919,X31920,X31921,X31922] : c_List_OtakeWhile(X31922,X31921,hAPP(hAPP(c_List_Omap(X31920,X31922),X31919),X31918)) = hAPP(hAPP(c_List_Omap(X31920,X31922),X31919),c_List_OtakeWhile(X31920,hAPP(c_Fun_Ocomp(X31922,tc_HOL_Obool,X31920,X31921),X31919),X31918)),
    inference(variable_rename,[status(thm)],[fact_takeWhile__map]) ).

fof(i_0_7308,plain,
    ! [X19192,X19193,X19194,X19195,X19196,X19197] :
      ( ( X19197 != X19196
        | hAPP(c_Fun_Ofun__upd(X19195,X19194,X19193,X19196,X19192),X19197) = X19192 )
      & ( X19197 = X19196
        | hAPP(c_Fun_Ofun__upd(X19195,X19194,X19193,X19196,X19192),X19197) = hAPP(X19193,X19197) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__def])]) ).

fof(i_0_7309,plain,
    ! [X19170,X19171,X19172,X19173,X19174,X19175] :
      ( ( X19175 != X19174
        | hAPP(c_Fun_Ofun__upd(X19173,X19172,X19171,X19174,X19170),X19175) = X19170 )
      & ( X19175 = X19174
        | hAPP(c_Fun_Ofun__upd(X19173,X19172,X19171,X19174,X19170),X19175) = hAPP(X19171,X19175) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__apply])]) ).

fof(i_0_7310,plain,
    ! [X19157,X19158,X19159,X19160,X19161,X19162] :
      ( X19162 = X19161
      | hAPP(c_Fun_Ofun__upd(X19160,X19159,X19158,X19161,X19157),X19162) = hAPP(X19158,X19162) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__other])]) ).

fof(i_0_7311,plain,
    ! [X24524,X24525,X24526,X24528,X24529] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24526),esk183_3(X24524,X24525,X24526)),X24525))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24526,tc_Nat_Onat),X24524),X24525) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24526),X24525)) )
      & ( hAPP(X24524,esk183_3(X24524,X24525,X24526)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24526,tc_Nat_Onat),X24524),X24525) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24526),X24525)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X24526),X24528),X24525))
        | esk183_3(X24524,X24525,X24526) = X24528
        | hAPP(X24524,X24528) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24526,tc_Nat_Onat),X24524),X24525) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24526),X24525)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24526),esk184_4(X24524,X24525,X24526,X24529)),X24525))
        | ~ hBOOL(hAPP(hAPP(c_member(X24526),X24529),X24525))
        | hAPP(X24524,X24529) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24526,tc_Nat_Onat),X24524),X24525) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24526),X24525)) )
      & ( X24529 != esk184_4(X24524,X24525,X24526,X24529)
        | ~ hBOOL(hAPP(hAPP(c_member(X24526),X24529),X24525))
        | hAPP(X24524,X24529) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24526,tc_Nat_Onat),X24524),X24525) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24526),X24525)) )
      & ( hAPP(X24524,esk184_4(X24524,X24525,X24526,X24529)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X24526),X24529),X24525))
        | hAPP(X24524,X24529) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24526,tc_Nat_Onat),X24524),X24525) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24526),X24525)) ) ),
    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_7312,plain,
    ! [X28864,X28865,X28866] :
      ( ~ c_Relation_Orefl__on(X28866,X28865,X28864)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28866,X28866),tc_HOL_Obool)),X28864),hAPP(hAPP(c_Relation_Orel__comp(X28866,X28866,X28866),hAPP(c_Relation_Oconverse(X28866,X28866),X28864)),X28864))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__comp__subset])]) ).

fof(i_0_7313,plain,
    ! [X19176,X19177,X19178,X19179,X19180] : hAPP(c_Fun_Ofun__upd(X19180,X19179,X19178,X19177,X19176),X19177) = X19176,
    inference(variable_rename,[status(thm)],[fact_fun__upd__same]) ).

fof(i_0_7314,plain,
    ! [X19599,X19600,X19601,X19602,X19603,X19604] :
      ( ~ c_Fun_Oinj__on(X19604,X19603,X19602,X19601)
      | ~ c_Fun_Oinj__on(X19603,X19600,X19599,hAPP(c_Set_Oimage(X19604,X19603,X19602),X19601))
      | c_Fun_Oinj__on(X19604,X19600,hAPP(c_Fun_Ocomp(X19603,X19600,X19604,X19599),X19602),X19601) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__inj__on])]) ).

fof(i_0_7315,plain,
    ! [X31072,X31073,X31074,X31075,X31076] : c_Enum_Oproduct(X31076,X31075,hAPP(hAPP(c_List_Olist_OCons(X31076),X31074),X31073),X31072) = hAPP(hAPP(c_List_Oappend(tc_prod(X31076,X31075)),hAPP(hAPP(c_List_Omap(X31075,tc_prod(X31076,X31075)),hAPP(c_Product__Type_OPair(X31076,X31075),X31074)),X31072)),c_Enum_Oproduct(X31076,X31075,X31073,X31072)),
    inference(variable_rename,[status(thm)],[fact_product_Osimps_I2_J]) ).

cnf(i_0_7316,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_5557]) ).

cnf(i_0_7317,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_5558]) ).

fof(i_0_7318,plain,
    ! [X30528,X30529] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30529),hAPP(c_List_Oset(tc_Nat_Onat),X30528)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30529),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)),X30528))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__sum])]) ).

fof(i_0_7319,plain,
    ! [X24132,X24133,X24134,X24135,X24136,X24137] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X24137),X24136),X24135))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24137,X24134)),hAPP(hAPP(c_Product__Type_OPair(X24137,X24134),X24136),X24133)),X24132))
      | hBOOL(hAPP(hAPP(c_member(X24134),X24133),hAPP(c_Relation_OImage(X24137,X24134,X24132),X24135))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__ImageI])]) ).

fof(i_0_7320,plain,
    ! [X30845,X30846,X30847,X30848,X30849,X30850] : hAPP(hAPP(c_List_Omap(X30850,X30849),X30848),hAPP(hAPP(c_List_Omap(X30847,X30850),X30846),X30845)) = hAPP(hAPP(c_List_Omap(X30847,X30849),hAPP(c_Fun_Ocomp(X30850,X30849,X30847,X30848),X30846)),X30845),
    inference(variable_rename,[status(thm)],[fact_map__map]) ).

fof(i_0_7321,plain,
    ! [X30839,X30840,X30841,X30842,X30843,X30844] : hAPP(hAPP(c_List_Omap(X30844,X30843),X30842),hAPP(hAPP(c_List_Omap(X30841,X30844),X30840),X30839)) = hAPP(hAPP(c_List_Omap(X30841,X30843),hAPP(c_Fun_Ocomp(X30844,X30843,X30841,X30842),X30840)),X30839),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Ocompositionality]) ).

fof(i_0_7322,plain,
    ! [X29936,X29937,X29938,X29939] : hAPP(hAPP(c_List_Otake(X29939),X29938),hAPP(hAPP(c_List_Olist_OCons(X29939),X29937),X29936)) = c_Nat_Onat_Onat__case(tc_List_Olist(X29939),c_List_Olist_ONil(X29939),hAPP(hAPP(c_COMBB(tc_List_Olist(X29939),tc_List_Olist(X29939),tc_Nat_Onat),hAPP(c_List_Olist_OCons(X29939),X29937)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X29939),tc_List_Olist(X29939)),c_List_Otake(X29939)),X29936)),X29938),
    inference(variable_rename,[status(thm)],[fact_take__Cons]) ).

fof(i_0_7323,plain,
    ! [X24066,X24067,X24068,X24069,X24070] : hAPP(c_Relation_OImage(X24070,X24069,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X24070,X24069),tc_HOL_Obool)),X24068),X24067)),X24066) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24069,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24070,X24069,X24068),X24066)),hAPP(c_Relation_OImage(X24070,X24069,X24067),X24066)),
    inference(variable_rename,[status(thm)],[fact_Un__Image]) ).

fof(i_0_7324,plain,
    ! [X28583,X28584,X28585,X28586,X28587] :
      ( ( X28587 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Random_Oiterate(X28586,X28585,X28587,X28584),X28583) = hAPP(c_Product__Type_OPair(X28586,X28585),X28583) )
      & ( X28587 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_Random_Oiterate(X28586,X28585,X28587,X28584),X28583) = hAPP(hAPP(c_Product__Type_Oscomp(X28585,X28586,X28585,tc_prod(X28586,X28585)),hAPP(X28584,X28583)),c_Random_Oiterate(X28586,X28585,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28587),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X28584)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iterate_Osimps])]) ).

fof(i_0_7325,plain,
    ! [X24702,X24703,X24704,X24705,X24706] :
      ( ~ c_Equiv__Relations_Oequiv(X24706,X24705,X24704)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24706,X24706)),hAPP(hAPP(c_Product__Type_OPair(X24706,X24706),X24703),X24702)),X24704))
      | hAPP(c_Relation_OImage(X24706,X24706,X24704),hAPP(hAPP(c_Set_Oinsert(X24706),X24703),c_Orderings_Obot__class_Obot(tc_fun(X24706,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(X24706,X24706,X24704),hAPP(hAPP(c_Set_Oinsert(X24706),X24702),c_Orderings_Obot__class_Obot(tc_fun(X24706,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__eq])]) ).

fof(i_0_7326,plain,
    ! [X27256,X27257,X27258,X27259,X27260,X27261] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27261),X27259),X27257))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27261,X27260)),hAPP(hAPP(c_Product__Type_OPair(X27261,X27260),X27259),X27258)),hAPP(hAPP(c_Product__Type_OSigma(X27261,X27260),X27257),X27256))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27260),X27258),hAPP(X27256,X27259)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27261,X27260)),hAPP(hAPP(c_Product__Type_OPair(X27261,X27260),X27259),X27258)),hAPP(hAPP(c_Product__Type_OSigma(X27261,X27260),X27257),X27256))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5559])])]) ).

fof(i_0_7327,plain,
    ! [X27238,X27239,X27240,X27241,X27242,X27243] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27243),X27241),X27239))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27243,X27242)),hAPP(hAPP(c_Product__Type_OPair(X27243,X27242),X27241),X27240)),hAPP(hAPP(c_Product__Type_OSigma(X27243,X27242),X27239),X27238))) )
      & ( hBOOL(hAPP(hAPP(c_member(X27242),X27240),hAPP(X27238,X27241)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27243,X27242)),hAPP(hAPP(c_Product__Type_OPair(X27243,X27242),X27241),X27240)),hAPP(hAPP(c_Product__Type_OSigma(X27243,X27242),X27239),X27238))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27243),X27241),X27239))
        | ~ hBOOL(hAPP(hAPP(c_member(X27242),X27240),hAPP(X27238,X27241)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X27243,X27242)),hAPP(hAPP(c_Product__Type_OPair(X27243,X27242),X27241),X27240)),hAPP(hAPP(c_Product__Type_OSigma(X27243,X27242),X27239),X27238))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Sigma__iff])])]) ).

fof(i_0_7328,plain,
    ! [X27250,X27251,X27252,X27253,X27254,X27255] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27255,X27254)),hAPP(hAPP(c_Product__Type_OPair(X27255,X27254),X27253),X27252)),hAPP(hAPP(c_Product__Type_OSigma(X27255,X27254),X27251),X27250)))
      | hBOOL(hAPP(hAPP(c_member(X27254),X27252),hAPP(X27250,X27253))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD2])]) ).

fof(i_0_7329,plain,
    ! [X29314,X29315,X29316] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29316,X29316),tc_HOL_Obool)),X29315),X29314))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29316),tc_List_Olist(X29316)),tc_HOL_Obool)),c_List_Olistrel(X29316,X29315)),c_List_Olistrel(X29316,X29314))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__mono])]) ).

fof(i_0_7330,plain,
    ! [X29263,X29264,X29265] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X29265,X29265),tc_HOL_Obool)),X29264),X29263))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29265),tc_List_Olist(X29265)),tc_HOL_Obool)),c_List_Olistrel1(X29265,X29264)),c_List_Olistrel1(X29265,X29263))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel1__mono])]) ).

fof(i_0_7331,plain,
    ! [X33411,X33412,X33413] :
      ( ( c_Fun_Oinj__on(X33413,X33412,X33411,c_Orderings_Otop__class_Otop(tc_fun(X33413,tc_HOL_Obool)))
        | ~ c_Fun_Obij__betw(X33413,X33412,X33411,c_Orderings_Otop__class_Otop(tc_fun(X33413,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33412,tc_HOL_Obool))) )
      & ( hAPP(c_Set_Oimage(X33413,X33412,X33411),c_Orderings_Otop__class_Otop(tc_fun(X33413,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33412,tc_HOL_Obool))
        | ~ c_Fun_Obij__betw(X33413,X33412,X33411,c_Orderings_Otop__class_Otop(tc_fun(X33413,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33412,tc_HOL_Obool))) )
      & ( ~ c_Fun_Oinj__on(X33413,X33412,X33411,c_Orderings_Otop__class_Otop(tc_fun(X33413,tc_HOL_Obool)))
        | hAPP(c_Set_Oimage(X33413,X33412,X33411),c_Orderings_Otop__class_Otop(tc_fun(X33413,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33412,tc_HOL_Obool))
        | c_Fun_Obij__betw(X33413,X33412,X33411,c_Orderings_Otop__class_Otop(tc_fun(X33413,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33412,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__def])])]) ).

fof(i_0_7332,plain,
    ! [X33380,X33381,X33382] :
      ( ~ c_Fun_Obij__betw(X33382,X33381,X33380,c_Orderings_Otop__class_Otop(tc_fun(X33382,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33381,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X33382,X33381,X33380,c_Orderings_Otop__class_Otop(tc_fun(X33382,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__is__inj])]) ).

cnf(i_0_7333,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_5560]) ).

fof(i_0_7334,plain,
    ! [X28522,X28523,X28524,X28525,X28526,X28527,X28528] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28528,X28527,X28526,X28525),X28524),X28523),X28522) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28527,X28526,X28525),X28523),hAPP(X28524,X28522)),
    inference(variable_rename,[status(thm)],[fact_scomp__def]) ).

fof(i_0_7335,plain,
    ! [X28513,X28514,X28515,X28516,X28517,X28518,X28519] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(X28519,X28518,X28517,X28516),X28515),X28514),X28513) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X28518,X28517,X28516),X28514),hAPP(X28515,X28513)),
    inference(variable_rename,[status(thm)],[fact_scomp__apply]) ).

fof(i_0_7336,plain,
    ! [X23357,X23358,X23359,X23360] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23360,tc_HOL_Obool)),X23359),X23358))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23360,tc_HOL_Obool)),X23357),X23358))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23360,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23360,tc_HOL_Obool)),X23359),X23357)),X23358)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__least])]) ).

fof(i_0_7337,plain,
    ! [X25463,X25464,X25465,X25466,X25467] :
      ( ~ c_Finite__Set_Ofolding__one(X25467,X25466,X25465)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25467),X25464))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25467),X25463))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25467,tc_HOL_Obool)),X25464),X25463) = c_Orderings_Obot__class_Obot(tc_fun(X25467,tc_HOL_Obool))
      | hAPP(hAPP(X25466,hAPP(X25465,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25467,tc_HOL_Obool)),X25464),X25463))),hAPP(X25465,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25467,tc_HOL_Obool)),X25464),X25463))) = hAPP(hAPP(X25466,hAPP(X25465,X25464)),hAPP(X25465,X25463)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__inter])]) ).

fof(i_0_7338,plain,
    ! [X19241,X19242,X19243,X19244,X19245] :
      ( ~ c_Fun_Oinj__on(X19245,X19244,X19243,X19242)
      | ~ hBOOL(hAPP(hAPP(c_member(X19244),X19241),hAPP(c_Set_Oimage(X19245,X19244,X19243),X19242)))
      | hAPP(X19243,hAPP(c_Fun_Othe__inv__into(X19245,X19244,X19242,X19243),X19241)) = X19241 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__the__inv__into__f])]) ).

cnf(i_0_7339,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_5561]) ).

cnf(i_0_7340,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_5562]) ).

fof(i_0_7341,plain,
    ! [X27023,X27024,X27025,X27026] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X27026,tc_HOL_Obool),tc_fun(X27025,tc_HOL_Obool)),X27024),hAPP(hAPP(c_COMBC(tc_fun(X27026,tc_HOL_Obool),tc_fun(X27026,tc_fun(X27025,tc_HOL_Obool)),tc_fun(X27025,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X27026,tc_fun(X27025,tc_HOL_Obool))),X27023)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X27026,tc_fun(X27025,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27026,tc_HOL_Obool),X27024)),X27023),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I8_J]) ).

fof(i_0_7342,plain,
    ! [X26991,X26992,X26993,X26994] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X26994,tc_HOL_Obool),tc_fun(X26993,tc_HOL_Obool)),X26992),hAPP(hAPP(c_COMBC(tc_fun(X26994,tc_HOL_Obool),tc_fun(X26994,tc_fun(X26993,tc_HOL_Obool)),tc_fun(X26993,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26994,tc_fun(X26993,tc_HOL_Obool))),X26991)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26994,tc_fun(X26993,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X26994,tc_HOL_Obool),X26992)),X26991),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I8_J]) ).

fof(i_0_7343,plain,
    ! [X27019,X27020,X27021,X27022] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X27022,tc_fun(X27021,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27022,tc_HOL_Obool),X27020)),X27019) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X27022,tc_HOL_Obool),tc_fun(X27021,tc_HOL_Obool)),X27020),hAPP(hAPP(c_COMBC(tc_fun(X27022,tc_HOL_Obool),tc_fun(X27022,tc_fun(X27021,tc_HOL_Obool)),tc_fun(X27021,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X27022,tc_fun(X27021,tc_HOL_Obool))),X27019)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I8_J]) ).

fof(i_0_7344,plain,
    ! [X26995,X26996,X26997,X26998] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26998,tc_fun(X26997,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X26998,tc_HOL_Obool),X26996)),X26995) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X26998,tc_HOL_Obool),tc_fun(X26997,tc_HOL_Obool)),X26996),hAPP(hAPP(c_COMBC(tc_fun(X26998,tc_HOL_Obool),tc_fun(X26998,tc_fun(X26997,tc_HOL_Obool)),tc_fun(X26997,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26998,tc_fun(X26997,tc_HOL_Obool))),X26995)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I8_J]) ).

fof(i_0_7345,plain,
    ! [X18337,X18338,X18339,X18340,X18341,X18342,X18343,X18344,X18345,X18346] :
      ( ( ~ c_Fun_Oinj__on(X18340,X18339,X18338,X18337)
        | ~ hBOOL(hAPP(hAPP(c_member(X18340),X18341),X18337))
        | ~ hBOOL(hAPP(hAPP(c_member(X18340),X18342),X18337))
        | hAPP(X18338,X18341) != hAPP(X18338,X18342)
        | X18341 = X18342 )
      & ( hBOOL(hAPP(hAPP(c_member(X18346),esk22_4(X18343,X18344,X18345,X18346)),X18343))
        | c_Fun_Oinj__on(X18346,X18345,X18344,X18343) )
      & ( hBOOL(hAPP(hAPP(c_member(X18346),esk23_4(X18343,X18344,X18345,X18346)),X18343))
        | c_Fun_Oinj__on(X18346,X18345,X18344,X18343) )
      & ( hAPP(X18344,esk22_4(X18343,X18344,X18345,X18346)) = hAPP(X18344,esk23_4(X18343,X18344,X18345,X18346))
        | c_Fun_Oinj__on(X18346,X18345,X18344,X18343) )
      & ( esk22_4(X18343,X18344,X18345,X18346) != esk23_4(X18343,X18344,X18345,X18346)
        | c_Fun_Oinj__on(X18346,X18345,X18344,X18343) ) ),
    inference(distribute,[status(thm)],[inference(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_7346,plain,
    ! [X28640,X28641,X28642] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28642,X28642),tc_HOL_Obool)),X28641),X28640))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28642,X28642),tc_HOL_Obool)),X28640),c_Transitive__Closure_Ortrancl(X28642,X28641)))
      | c_Transitive__Closure_Ortrancl(X28642,X28640) = c_Transitive__Closure_Ortrancl(X28642,X28641) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset])]) ).

fof(i_0_7347,plain,
    ! [X24726,X24727,X24728,X24729,X24730] :
      ( hAPP(c_Relation_OImage(X24730,X24730,X24729),hAPP(hAPP(c_Set_Oinsert(X24730),X24728),c_Orderings_Obot__class_Obot(tc_fun(X24730,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(X24730,X24730,X24729),hAPP(hAPP(c_Set_Oinsert(X24730),X24727),c_Orderings_Obot__class_Obot(tc_fun(X24730,tc_HOL_Obool))))
      | ~ c_Equiv__Relations_Oequiv(X24730,X24726,X24729)
      | ~ hBOOL(hAPP(hAPP(c_member(X24730),X24727),X24726))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X24730,X24730)),hAPP(hAPP(c_Product__Type_OPair(X24730,X24730),X24728),X24727)),X24729)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__equiv__class])]) ).

fof(i_0_7348,plain,
    ! [X27244,X27245,X27246,X27247,X27248,X27249] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27249,X27248)),hAPP(hAPP(c_Product__Type_OPair(X27249,X27248),X27247),X27246)),hAPP(hAPP(c_Product__Type_OSigma(X27249,X27248),X27245),X27244)))
      | hBOOL(hAPP(hAPP(c_member(X27249),X27247),X27245)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaD1])]) ).

fof(i_0_7349,plain,
    ! [X21885,X21886,X21887,X21888,X21890] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21887),esk83_4(X21885,X21886,X21887,X21888)),X21886))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21887,X21888),X21885),X21886) != c_Groups_Ozero__class_Ozero(X21888)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21887),X21886))
        | ~ class_Rings_Ocomm__semiring__1(X21888)
        | ~ class_Rings_Ono__zero__divisors(X21888) )
      & ( hAPP(X21885,esk83_4(X21885,X21886,X21887,X21888)) = c_Groups_Ozero__class_Ozero(X21888)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21887,X21888),X21885),X21886) != c_Groups_Ozero__class_Ozero(X21888)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21887),X21886))
        | ~ class_Rings_Ocomm__semiring__1(X21888)
        | ~ class_Rings_Ono__zero__divisors(X21888) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21887),X21890),X21886))
        | hAPP(X21885,X21890) != c_Groups_Ozero__class_Ozero(X21888)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21887,X21888),X21885),X21886) = c_Groups_Ozero__class_Ozero(X21888)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21887),X21886))
        | ~ class_Rings_Ocomm__semiring__1(X21888)
        | ~ class_Rings_Ono__zero__divisors(X21888) ) ),
    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_7350,plain,
    ! [X17113,X17114,X17115,X17116] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17116),X17115))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17114),hAPP(c_Set_Oimage(X17116,X17114,X17113),X17115))),hAPP(c_Finite__Set_Ocard(X17116),X17115))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image__le])]) ).

fof(i_0_7351,plain,
    ! [X30587,X30588,X30589,X30590,X30591] :
      ( ~ class_Orderings_Olinorder(X30591)
      | hBOOL(hAPP(hAPP(c_member(X30591),hAPP(X30590,X30589)),hAPP(c_Set_Oimage(X30588,X30591,X30590),hAPP(c_List_Oset(X30588),X30587))))
      | c_List_Olinorder__class_Oinsort__insert__key(X30588,X30591,X30590,X30589,X30587) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30588,X30591,X30590),X30589),X30587) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5563])]) ).

cnf(i_0_7352,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_5564]) ).

fof(i_0_7353,plain,
    ! [X26346,X26347,X26348,X26349,X26350,X26351,X26352,X26353,X26354] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26349,tc_fun(X26348,tc_HOL_Obool)),X26347),X26346) != c_Orderings_Otop__class_Otop(tc_fun(X26348,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X26349),X26350),X26347))
        | hAPP(X26346,X26350) = c_Orderings_Otop__class_Otop(tc_fun(X26348,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26354),esk229_4(X26351,X26352,X26353,X26354)),X26352))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26354,tc_fun(X26353,tc_HOL_Obool)),X26352),X26351) = c_Orderings_Otop__class_Otop(tc_fun(X26353,tc_HOL_Obool)) )
      & ( hAPP(X26351,esk229_4(X26351,X26352,X26353,X26354)) != c_Orderings_Otop__class_Otop(tc_fun(X26353,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26354,tc_fun(X26353,tc_HOL_Obool)),X26352),X26351) = c_Orderings_Otop__class_Otop(tc_fun(X26353,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_7354,plain,
    ! [X23766,X23767,X23768,X23769,X23770,X23771,X23772,X23773,X23774] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23769,tc_fun(X23768,tc_HOL_Obool)),X23767),X23766) != c_Orderings_Obot__class_Obot(tc_fun(X23768,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X23769),X23770),X23767))
        | hAPP(X23766,X23770) = c_Orderings_Obot__class_Obot(tc_fun(X23768,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23774),esk134_4(X23771,X23772,X23773,X23774)),X23772))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23774,tc_fun(X23773,tc_HOL_Obool)),X23772),X23771) = c_Orderings_Obot__class_Obot(tc_fun(X23773,tc_HOL_Obool)) )
      & ( hAPP(X23771,esk134_4(X23771,X23772,X23773,X23774)) != c_Orderings_Obot__class_Obot(tc_fun(X23773,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23774,tc_fun(X23773,tc_HOL_Obool)),X23772),X23771) = c_Orderings_Obot__class_Obot(tc_fun(X23773,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_7355,plain,
    ! [X26356,X26357,X26358,X26359,X26360,X26361,X26362,X26363,X26364] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(X26359,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26358,tc_fun(X26359,tc_HOL_Obool)),X26357),X26356)
        | ~ hBOOL(hAPP(hAPP(c_member(X26358),X26360),X26357))
        | hAPP(X26356,X26360) = c_Orderings_Otop__class_Otop(tc_fun(X26359,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26363),esk230_4(X26361,X26362,X26363,X26364)),X26362))
        | c_Orderings_Otop__class_Otop(tc_fun(X26364,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26363,tc_fun(X26364,tc_HOL_Obool)),X26362),X26361) )
      & ( hAPP(X26361,esk230_4(X26361,X26362,X26363,X26364)) != c_Orderings_Otop__class_Otop(tc_fun(X26364,tc_HOL_Obool))
        | c_Orderings_Otop__class_Otop(tc_fun(X26364,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26363,tc_fun(X26364,tc_HOL_Obool)),X26362),X26361) ) ),
    inference(distribute,[status(thm)],[inference(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_7356,plain,
    ! [X23783,X23784,X23785,X23786,X23787,X23788,X23789,X23790,X23791] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X23786,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23785,tc_fun(X23786,tc_HOL_Obool)),X23784),X23783)
        | ~ hBOOL(hAPP(hAPP(c_member(X23785),X23787),X23784))
        | hAPP(X23783,X23787) = c_Orderings_Obot__class_Obot(tc_fun(X23786,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X23790),esk135_4(X23788,X23789,X23790,X23791)),X23789))
        | c_Orderings_Obot__class_Obot(tc_fun(X23791,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23790,tc_fun(X23791,tc_HOL_Obool)),X23789),X23788) )
      & ( hAPP(X23788,esk135_4(X23788,X23789,X23790,X23791)) != c_Orderings_Obot__class_Obot(tc_fun(X23791,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(X23791,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23790,tc_fun(X23791,tc_HOL_Obool)),X23789),X23788) ) ),
    inference(distribute,[status(thm)],[inference(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_7357,plain,
    ! [X28356,X28357,X28358,X28359] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28359),esk313_4(X28356,X28357,X28358,X28359)),X28357))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28359,tc_Nat_Onat),X28358),X28357) != hAPP(c_Nat_OSuc,X28356) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X28358,esk313_4(X28356,X28357,X28358,X28359))))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X28359,tc_Nat_Onat),X28358),X28357) != hAPP(c_Nat_OSuc,X28356) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__SucD])])])]) ).

fof(i_0_7358,plain,
    ! [X25680,X25681,X25682] :
      ( ~ class_Lattices_Olattice(X25682)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25682),X25681))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25682),X25680))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25682,tc_HOL_Obool)),X25681),X25680) = c_Orderings_Obot__class_Obot(tc_fun(X25682,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25682),c_Big__Operators_Olattice__class_OInf__fin(X25682,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25682,tc_HOL_Obool)),X25681),X25680))),c_Big__Operators_Olattice__class_OInf__fin(X25682,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25682,tc_HOL_Obool)),X25681),X25680))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25682),c_Big__Operators_Olattice__class_OInf__fin(X25682,X25681)),c_Big__Operators_Olattice__class_OInf__fin(X25682,X25680)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__inter])]) ).

fof(i_0_7359,plain,
    ! [X25510,X25511,X25512] :
      ( ~ class_Lattices_Olattice(X25512)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25512),X25511))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25512),X25510))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25512,tc_HOL_Obool)),X25511),X25510) = c_Orderings_Obot__class_Obot(tc_fun(X25512,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25512),c_Big__Operators_Olattice__class_OSup__fin(X25512,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25512,tc_HOL_Obool)),X25511),X25510))),c_Big__Operators_Olattice__class_OSup__fin(X25512,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25512,tc_HOL_Obool)),X25511),X25510))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25512),c_Big__Operators_Olattice__class_OSup__fin(X25512,X25511)),c_Big__Operators_Olattice__class_OSup__fin(X25512,X25510)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__inter])]) ).

fof(i_0_7360,plain,
    ! [X25519,X25520,X25521] :
      ( ~ class_Orderings_Olinorder(X25521)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25521),X25520))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25521),X25519))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25521,tc_HOL_Obool)),X25520),X25519) = c_Orderings_Obot__class_Obot(tc_fun(X25521,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X25521),c_Big__Operators_Olinorder__class_OMax(X25521,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25521,tc_HOL_Obool)),X25520),X25519))),c_Big__Operators_Olinorder__class_OMax(X25521,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25521,tc_HOL_Obool)),X25520),X25519))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25521),c_Big__Operators_Olinorder__class_OMax(X25521,X25520)),c_Big__Operators_Olinorder__class_OMax(X25521,X25519)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__inter])]) ).

fof(i_0_7361,plain,
    ! [X25513,X25514,X25515] :
      ( ~ class_Orderings_Olinorder(X25515)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25515),X25514))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25515),X25513))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25515,tc_HOL_Obool)),X25514),X25513) = c_Orderings_Obot__class_Obot(tc_fun(X25515,tc_HOL_Obool))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X25515),c_Big__Operators_Olinorder__class_OMin(X25515,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25515,tc_HOL_Obool)),X25514),X25513))),c_Big__Operators_Olinorder__class_OMin(X25515,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25515,tc_HOL_Obool)),X25514),X25513))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25515),c_Big__Operators_Olinorder__class_OMin(X25515,X25514)),c_Big__Operators_Olinorder__class_OMin(X25515,X25513)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__inter])]) ).

fof(i_0_7362,plain,
    ! [X32045,X32046,X32049,X32050,X32051] :
      ( ( X32045 = hAPP(hAPP(c_List_Olist_OCons(X32046),esk443_2(X32045,X32046)),esk442_2(X32045,X32046))
        | X32045 = c_List_Olist_ONil(X32046)
        | ~ c_List_Olinorder__class_Osorted(X32046,X32045)
        | ~ class_Orderings_Olinorder(X32046) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32046),X32049),hAPP(c_List_Oset(X32046),esk442_2(X32045,X32046))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32046),esk443_2(X32045,X32046)),X32049))
        | X32045 = c_List_Olist_ONil(X32046)
        | ~ c_List_Olinorder__class_Osorted(X32046,X32045)
        | ~ class_Orderings_Olinorder(X32046) )
      & ( c_List_Olinorder__class_Osorted(X32046,esk442_2(X32045,X32046))
        | X32045 = c_List_Olist_ONil(X32046)
        | ~ c_List_Olinorder__class_Osorted(X32046,X32045)
        | ~ class_Orderings_Olinorder(X32046) )
      & ( X32045 != c_List_Olist_ONil(X32046)
        | c_List_Olinorder__class_Osorted(X32046,X32045)
        | ~ class_Orderings_Olinorder(X32046) )
      & ( hBOOL(hAPP(hAPP(c_member(X32046),esk444_4(X32045,X32046,X32050,X32051)),hAPP(c_List_Oset(X32046),X32050)))
        | X32045 != hAPP(hAPP(c_List_Olist_OCons(X32046),X32051),X32050)
        | ~ c_List_Olinorder__class_Osorted(X32046,X32050)
        | c_List_Olinorder__class_Osorted(X32046,X32045)
        | ~ class_Orderings_Olinorder(X32046) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32046),X32051),esk444_4(X32045,X32046,X32050,X32051)))
        | X32045 != hAPP(hAPP(c_List_Olist_OCons(X32046),X32051),X32050)
        | ~ c_List_Olinorder__class_Osorted(X32046,X32050)
        | c_List_Olinorder__class_Osorted(X32046,X32045)
        | ~ class_Orderings_Olinorder(X32046) ) ),
    inference(distribute,[status(thm)],[inference(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_7363,plain,
    ! [X26709,X26710,X26711,X26712,X26713,X26714,X26715] :
      ( ( hAPP(X26712,X26710) != hAPP(X26712,X26709)
        | X26710 = X26709
        | ~ hBOOL(hAPP(hAPP(c_member(X26714),X26709),X26711))
        | ~ hBOOL(hAPP(hAPP(c_member(X26714),X26710),X26711))
        | ~ c_Typedef_Otype__definition(X26715,X26714,X26713,X26712,X26711) )
      & ( X26710 != X26709
        | hAPP(X26712,X26710) = hAPP(X26712,X26709)
        | ~ hBOOL(hAPP(hAPP(c_member(X26714),X26709),X26711))
        | ~ hBOOL(hAPP(hAPP(c_member(X26714),X26710),X26711))
        | ~ c_Typedef_Otype__definition(X26715,X26714,X26713,X26712,X26711) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inject])])]) ).

fof(i_0_7364,plain,
    ! [X32457,X32458] :
      ( ( ~ c_Wellfounded_Oacyclic(X32458,hAPP(c_Set_OCollect(tc_prod(X32458,X32458)),hAPP(c_Product__Type_Oprod_Oprod__case(X32458,X32458,tc_HOL_Obool),c_Predicate_Oconversep(X32458,X32458,X32457))))
        | c_Wellfounded_Oacyclic(X32458,hAPP(c_Set_OCollect(tc_prod(X32458,X32458)),hAPP(c_Product__Type_Oprod_Oprod__case(X32458,X32458,tc_HOL_Obool),X32457))) )
      & ( ~ c_Wellfounded_Oacyclic(X32458,hAPP(c_Set_OCollect(tc_prod(X32458,X32458)),hAPP(c_Product__Type_Oprod_Oprod__case(X32458,X32458,tc_HOL_Obool),X32457)))
        | c_Wellfounded_Oacyclic(X32458,hAPP(c_Set_OCollect(tc_prod(X32458,X32458)),hAPP(c_Product__Type_Oprod_Oprod__case(X32458,X32458,tc_HOL_Obool),c_Predicate_Oconversep(X32458,X32458,X32457)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclicP__converse])]) ).

cnf(i_0_7365,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_5503]) ).

fof(i_0_7366,plain,
    ! [X23559,X23560,X23561,X23562] : hAPP(c_Relation_OField(X23562),hAPP(hAPP(c_Set_Oinsert(tc_prod(X23562,X23562)),hAPP(hAPP(c_Product__Type_OPair(X23562,X23562),X23561),X23560)),X23559)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23562,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23562),X23561),hAPP(hAPP(c_Set_Oinsert(X23562),X23560),c_Orderings_Obot__class_Obot(tc_fun(X23562,tc_HOL_Obool))))),hAPP(c_Relation_OField(X23562),X23559)),
    inference(variable_rename,[status(thm)],[fact_Field__insert]) ).

fof(i_0_7367,plain,
    ! [X30464,X30465,X30466] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30466),X30465))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30466),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30465),X30464))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_start__le__sum])]) ).

cnf(i_0_7368,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_5565]) ).

fof(i_0_7369,plain,
    ! [X19413,X19414,X19415,X19416,X19417,X19418] : c_Nitpick_Opair__box_Opair__box__size(X19418,X19417,X19416,X19415,c_Nitpick_Opair__box_OPairBox(X19418,X19417,X19414,X19413)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X19416,X19414)),hAPP(X19415,X19413))),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_7370,plain,
    ! [X27109,X27110,X27111] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27111,tc_HOL_Obool)),esk253_3(X27109,X27110,X27111)),X27110))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27109),hAPP(c_Finite__Set_Ocard(tc_fun(X27111,tc_HOL_Obool)),X27110)) = hAPP(c_Finite__Set_Ocard(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X27111,tc_HOL_Obool)),esk252_3(X27109,X27110,X27111)),X27110))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27111,tc_HOL_Obool)),X27110)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27111,tc_HOL_Obool)),esk254_3(X27109,X27110,X27111)),X27110))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27109),hAPP(c_Finite__Set_Ocard(tc_fun(X27111,tc_HOL_Obool)),X27110)) = hAPP(c_Finite__Set_Ocard(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X27111,tc_HOL_Obool)),esk252_3(X27109,X27110,X27111)),X27110))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27111,tc_HOL_Obool)),X27110)) )
      & ( esk253_3(X27109,X27110,X27111) != esk254_3(X27109,X27110,X27111)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27109),hAPP(c_Finite__Set_Ocard(tc_fun(X27111,tc_HOL_Obool)),X27110)) = hAPP(c_Finite__Set_Ocard(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X27111,tc_HOL_Obool)),esk252_3(X27109,X27110,X27111)),X27110))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27111,tc_HOL_Obool)),X27110)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27111,tc_HOL_Obool)),esk253_3(X27109,X27110,X27111)),esk254_3(X27109,X27110,X27111)) != c_Orderings_Obot__class_Obot(tc_fun(X27111,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27109),hAPP(c_Finite__Set_Ocard(tc_fun(X27111,tc_HOL_Obool)),X27110)) = hAPP(c_Finite__Set_Ocard(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X27111,tc_HOL_Obool)),esk252_3(X27109,X27110,X27111)),X27110))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27111,tc_HOL_Obool)),X27110)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27111,tc_HOL_Obool)),esk253_3(X27109,X27110,X27111)),X27110))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27109),hAPP(c_Finite__Set_Ocard(tc_fun(X27111,tc_HOL_Obool)),X27110)) = hAPP(c_Finite__Set_Ocard(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110))
        | hAPP(c_Finite__Set_Ocard(X27111),esk252_3(X27109,X27110,X27111)) != X27109
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27111,tc_HOL_Obool)),X27110)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27111,tc_HOL_Obool)),esk254_3(X27109,X27110,X27111)),X27110))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27109),hAPP(c_Finite__Set_Ocard(tc_fun(X27111,tc_HOL_Obool)),X27110)) = hAPP(c_Finite__Set_Ocard(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110))
        | hAPP(c_Finite__Set_Ocard(X27111),esk252_3(X27109,X27110,X27111)) != X27109
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27111,tc_HOL_Obool)),X27110)) )
      & ( esk253_3(X27109,X27110,X27111) != esk254_3(X27109,X27110,X27111)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27109),hAPP(c_Finite__Set_Ocard(tc_fun(X27111,tc_HOL_Obool)),X27110)) = hAPP(c_Finite__Set_Ocard(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110))
        | hAPP(c_Finite__Set_Ocard(X27111),esk252_3(X27109,X27110,X27111)) != X27109
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27111,tc_HOL_Obool)),X27110)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27111,tc_HOL_Obool)),esk253_3(X27109,X27110,X27111)),esk254_3(X27109,X27110,X27111)) != c_Orderings_Obot__class_Obot(tc_fun(X27111,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27109),hAPP(c_Finite__Set_Ocard(tc_fun(X27111,tc_HOL_Obool)),X27110)) = hAPP(c_Finite__Set_Ocard(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110))
        | hAPP(c_Finite__Set_Ocard(X27111),esk252_3(X27109,X27110,X27111)) != X27109
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27111),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27111,tc_HOL_Obool),X27110)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27111,tc_HOL_Obool)),X27110)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__partition])])])]) ).

fof(i_0_7371,plain,
    ! [X33401,X33402,X33403] :
      ( ~ c_Fun_Obij__betw(X33403,X33402,X33401,c_Orderings_Otop__class_Otop(tc_fun(X33403,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33402,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33403,X33402,X33401),c_Orderings_Otop__class_Otop(tc_fun(X33403,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33402,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__is__surj])]) ).

fof(i_0_7372,plain,
    ! [X31727,X31728,X31729] :
      ( ~ class_Orderings_Olinorder(X31729)
      | c_List_Olinorder__class_Osorted(X31729,hAPP(c_List_Ofilter(X31729,hAPP(hAPP(c_COMBC(X31729,X31729,tc_HOL_Obool),c_fequal),hAPP(X31728,X31727))),X31727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__same])]) ).

fof(i_0_7373,plain,
    ! [X26179,X26180,X26181,X26182,X26183] :
      ( ~ c_Fun_Oinj__on(X26183,X26182,X26181,c_Orderings_Otop__class_Otop(tc_fun(X26183,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(X26180,X26183,X26179,c_Orderings_Otop__class_Otop(tc_fun(X26180,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X26180,X26182,hAPP(c_Fun_Ocomp(X26183,X26182,X26180,X26181),X26179),c_Orderings_Otop__class_Otop(tc_fun(X26180,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__comp])]) ).

fof(i_0_7374,plain,
    ! [X29727,X29728,X29729,X29730] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29730,tc_HOL_Obool)),hAPP(c_List_Oset(X29730),hAPP(hAPP(c_List_Olist__update(X29730,X29729),X29728),X29727))),hAPP(hAPP(c_Set_Oinsert(X29730),X29727),hAPP(c_List_Oset(X29730),X29729)))),
    inference(variable_rename,[status(thm)],[fact_set__update__subset__insert]) ).

cnf(i_0_7375,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_5566]) ).

fof(i_0_7376,plain,
    ! [X22987,X22988,X22989] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22989,tc_HOL_Obool)),X22988),hAPP(hAPP(c_Set_Oinsert(X22989),X22987),c_Orderings_Obot__class_Obot(tc_fun(X22989,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X22989,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X22989,c_Orderings_Oord__class_Omax(X22989),X22988) = X22987
        | ~ hBOOL(hAPP(hAPP(c_member(X22989),X22987),X22988))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22989),X22988))
        | ~ class_Orderings_Olinorder(X22989) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22989,tc_HOL_Obool)),X22988),hAPP(hAPP(c_Set_Oinsert(X22989),X22987),c_Orderings_Obot__class_Obot(tc_fun(X22989,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X22989,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X22989,c_Orderings_Oord__class_Omax(X22989),X22988) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22989),X22987),c_Big__Operators_Olattice_OSup__fin(X22989,c_Orderings_Oord__class_Omax(X22989),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22989,tc_HOL_Obool)),X22988),hAPP(hAPP(c_Set_Oinsert(X22989),X22987),c_Orderings_Obot__class_Obot(tc_fun(X22989,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X22989),X22987),X22988))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22989),X22988))
        | ~ class_Orderings_Olinorder(X22989) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oremove])])]) ).

fof(i_0_7377,plain,
    ! [X21747,X21748,X21749] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21749,tc_HOL_Obool)),X21748),hAPP(hAPP(c_Set_Oinsert(X21749),X21747),c_Orderings_Obot__class_Obot(tc_fun(X21749,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X21749,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X21749,c_Orderings_Oord__class_Omin(X21749),X21748) = X21747
        | ~ hBOOL(hAPP(hAPP(c_member(X21749),X21747),X21748))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21749),X21748))
        | ~ class_Orderings_Olinorder(X21749) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21749,tc_HOL_Obool)),X21748),hAPP(hAPP(c_Set_Oinsert(X21749),X21747),c_Orderings_Obot__class_Obot(tc_fun(X21749,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X21749,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X21749,c_Orderings_Oord__class_Omin(X21749),X21748) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21749),X21747),c_Big__Operators_Olattice_OInf__fin(X21749,c_Orderings_Oord__class_Omin(X21749),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21749,tc_HOL_Obool)),X21748),hAPP(hAPP(c_Set_Oinsert(X21749),X21747),c_Orderings_Obot__class_Obot(tc_fun(X21749,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X21749),X21747),X21748))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21749),X21748))
        | ~ class_Orderings_Olinorder(X21749) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oremove])])]) ).

fof(i_0_7378,plain,
    ! [X24424,X24425,X24426] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24426,tc_Nat_Onat),X24425),X24424) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24426,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X24426),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24425)),X24424)),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I1_J]) ).

fof(i_0_7379,plain,
    ! [X21852,X21853,X21854] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21854,tc_Nat_Onat),X21853),X21852) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21854,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X21854),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X21853)),X21852)),
    inference(variable_rename,[status(thm)],[fact_transfer__nat__int__sum__prod2_I2_J]) ).

fof(i_0_7380,plain,
    ! [X26884,X26885,X26886,X26887,X26888] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26888),X26887),hAPP(c_Set_Ovimage(X26888,X26886,X26885),hAPP(hAPP(c_Set_Oinsert(X26886),X26884),c_Orderings_Obot__class_Obot(tc_fun(X26886,tc_HOL_Obool))))))
        | hAPP(X26885,X26887) = X26884 )
      & ( hAPP(X26885,X26887) != X26884
        | hBOOL(hAPP(hAPP(c_member(X26888),X26887),hAPP(c_Set_Ovimage(X26888,X26886,X26885),hAPP(hAPP(c_Set_Oinsert(X26886),X26884),c_Orderings_Obot__class_Obot(tc_fun(X26886,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__singleton__eq])]) ).

cnf(i_0_7381,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_5567]) ).

fof(i_0_7382,plain,
    ! [X19568,X19569,X19570,X19571,X19572,X19573] :
      ( ~ c_Fun_Oinj__on(X19573,X19572,hAPP(c_Fun_Ocomp(X19571,X19572,X19573,X19570),X19569),X19568)
      | c_Fun_Oinj__on(X19573,X19571,X19569,X19568) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imageI2])]) ).

cnf(i_0_7383,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_5568]) ).

fof(i_0_7384,plain,
    ! [X17422,X17423,X17424,X17425] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17425,tc_HOL_Obool)),X17424),hAPP(hAPP(c_Set_Oinsert(X17425),X17423),X17422))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17425,tc_HOL_Obool)),X17424),X17422))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17425,tc_HOL_Obool)),X17424),X17422)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17425),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17425,tc_HOL_Obool)),X17424),hAPP(hAPP(c_Set_Oinsert(X17425),X17423),X17422)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff__insert])]) ).

fof(i_0_7385,plain,
    ! [X27655,X27656,X27657] : hAPP(hAPP(c_Set_Oinsert(X27657),X27656),X27655) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27657,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27657),hAPP(hAPP(c_COMBC(X27657,X27657,tc_HOL_Obool),c_fequal),X27656))),X27655),
    inference(variable_rename,[status(thm)],[fact_insert__def]) ).

cnf(i_0_7386,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_5569]) ).

cnf(i_0_7387,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_5570]) ).

cnf(i_0_7388,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_5571]) ).

cnf(i_0_7389,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_5572]) ).

cnf(i_0_7390,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_5508]) ).

cnf(i_0_7391,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_5509]) ).

cnf(i_0_7392,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_5510]) ).

cnf(i_0_7393,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_5511]) ).

fof(i_0_7394,plain,
    ! [X18612,X18613,X18614,X18615,X18616,X18617] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),X18616),X18615)),X18614) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),X18613),X18615)),X18612)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18617),X18616),X18613)),X18615)),X18614) = X18612
        | ~ class_Rings_Oring(X18617) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18617),X18616),X18613)),X18615)),X18614) != X18612
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),X18616),X18615)),X18614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18617),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18617),X18613),X18615)),X18612)
        | ~ class_Rings_Oring(X18617) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff1])])]) ).

fof(i_0_7395,plain,
    ! [X18618,X18619,X18620,X18621,X18622,X18623] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18623),X18622),X18621)),X18620) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18623),X18619),X18621)),X18618)
        | X18620 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18623),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18623),X18619),X18622)),X18621)),X18618)
        | ~ class_Rings_Oring(X18623) )
      & ( X18620 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18623),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18623),X18619),X18622)),X18621)),X18618)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18623),X18622),X18621)),X18620) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18623),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18623),X18619),X18621)),X18618)
        | ~ class_Rings_Oring(X18623) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__add__iff2])])]) ).

fof(i_0_7396,plain,
    ! [X28875,X28876,X28877,X28878,X28879,X28880] :
      ( ~ c_Relation_Osingle__valued(X28880,X28879,hAPP(c_Relation_Oconverse(X28879,X28880),X28878))
      | X28877 = c_Orderings_Obot__class_Obot(tc_fun(X28876,tc_HOL_Obool))
      | hAPP(c_Relation_OImage(X28879,X28880,X28878),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28876,tc_fun(X28879,tc_HOL_Obool)),X28877),X28875)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X28876,tc_fun(X28880,tc_HOL_Obool)),X28877),hAPP(hAPP(c_COMBB(tc_fun(X28879,tc_HOL_Obool),tc_fun(X28880,tc_HOL_Obool),X28876),c_Relation_OImage(X28879,X28880,X28878)),X28875)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__INT__eq])]) ).

fof(i_0_7397,plain,
    ! [X31421,X31422,X31423] : hAPP(c_Product__Type_Osnd(tc_List_Olist(X31423),tc_List_Olist(X31423)),c_List_Opartition(X31423,X31422,X31421)) = hAPP(c_List_Ofilter(X31423,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,X31423,c_fNot),X31422)),X31421),
    inference(variable_rename,[status(thm)],[fact_partition__filter2]) ).

cnf(i_0_7398,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5573]) ).

fof(i_0_7399,plain,
    ! [X33101,X33102,X33103,X33104,X33105] :
      ( ~ c_Fun_Oinj__on(X33105,X33104,X33103,X33102)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33105,tc_HOL_Obool)),X33101),X33102))
      | hAPP(c_Set_Oimage(X33104,X33105,c_Hilbert__Choice_Oinv__into(X33105,X33104,X33102,X33103)),hAPP(c_Set_Oimage(X33105,X33104,X33103),X33101)) = X33101 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__image__cancel])]) ).

fof(i_0_7400,plain,
    ! [X26808,X26809,X26810,X26811,X26812] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26812,tc_HOL_Obool)),X26811),X26810))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26809,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26809,X26812,X26808),X26811)),hAPP(c_Set_Ovimage(X26809,X26812,X26808),X26810))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__mono])]) ).

fof(i_0_7401,plain,
    ! [X17056,X17057,X17058,X17059,X17060] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17060,tc_HOL_Obool)),X17059),X17058))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17057,tc_HOL_Obool)),hAPP(c_Set_Oimage(X17060,X17057,X17056),X17059)),hAPP(c_Set_Oimage(X17060,X17057,X17056),X17058))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__mono])]) ).

fof(i_0_7402,plain,
    ! [X24756,X24757,X24758,X24759,X24760,X24761] :
      ( ~ c_Equiv__Relations_Oequiv(X24761,X24760,X24759)
      | ~ c_Equiv__Relations_Ocongruent(X24761,tc_fun(X24758,tc_HOL_Obool),X24759,X24757)
      | ~ hBOOL(hAPP(hAPP(c_member(X24761),X24756),X24760))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24761,tc_fun(X24758,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24761,X24761,X24759),hAPP(hAPP(c_Set_Oinsert(X24761),X24756),c_Orderings_Obot__class_Obot(tc_fun(X24761,tc_HOL_Obool))))),X24757) = hAPP(X24757,X24756) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__equiv__class])]) ).

fof(i_0_7403,plain,
    ! [X23044,X23045,X23046] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23046,tc_HOL_Obool)),X23045),hAPP(hAPP(c_Set_Oinsert(X23046),X23044),c_Orderings_Obot__class_Obot(tc_fun(X23046,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X23046,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X23046,c_Orderings_Oord__class_Omax(X23046),hAPP(hAPP(c_Set_Oinsert(X23046),X23044),X23045)) = X23044
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23046),X23045))
        | ~ class_Orderings_Olinorder(X23046) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23046,tc_HOL_Obool)),X23045),hAPP(hAPP(c_Set_Oinsert(X23046),X23044),c_Orderings_Obot__class_Obot(tc_fun(X23046,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X23046,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OSup__fin(X23046,c_Orderings_Oord__class_Omax(X23046),hAPP(hAPP(c_Set_Oinsert(X23046),X23044),X23045)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X23046),X23044),c_Big__Operators_Olattice_OSup__fin(X23046,c_Orderings_Oord__class_Omax(X23046),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23046,tc_HOL_Obool)),X23045),hAPP(hAPP(c_Set_Oinsert(X23046),X23044),c_Orderings_Obot__class_Obot(tc_fun(X23046,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23046),X23045))
        | ~ class_Orderings_Olinorder(X23046) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__remove])])]) ).

fof(i_0_7404,plain,
    ! [X21811,X21812,X21813] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21813,tc_HOL_Obool)),X21812),hAPP(hAPP(c_Set_Oinsert(X21813),X21811),c_Orderings_Obot__class_Obot(tc_fun(X21813,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X21813,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X21813,c_Orderings_Oord__class_Omin(X21813),hAPP(hAPP(c_Set_Oinsert(X21813),X21811),X21812)) = X21811
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21813),X21812))
        | ~ class_Orderings_Olinorder(X21813) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21813,tc_HOL_Obool)),X21812),hAPP(hAPP(c_Set_Oinsert(X21813),X21811),c_Orderings_Obot__class_Obot(tc_fun(X21813,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X21813,tc_HOL_Obool))
        | c_Big__Operators_Olattice_OInf__fin(X21813,c_Orderings_Oord__class_Omin(X21813),hAPP(hAPP(c_Set_Oinsert(X21813),X21811),X21812)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21813),X21811),c_Big__Operators_Olattice_OInf__fin(X21813,c_Orderings_Oord__class_Omin(X21813),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21813,tc_HOL_Obool)),X21812),hAPP(hAPP(c_Set_Oinsert(X21813),X21811),c_Orderings_Obot__class_Obot(tc_fun(X21813,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21813),X21812))
        | ~ class_Orderings_Olinorder(X21813) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__remove])])]) ).

fof(i_0_7405,plain,
    ! [X19545,X19546,X19547,X19548,X19549,X19550,X19551,X19552,X19553,X19554,X19555] :
      ( hAPP(X19555,hAPP(X19554,X19553)) != hAPP(X19552,hAPP(X19551,X19550))
      | hAPP(hAPP(c_Fun_Ocomp(X19549,X19548,X19547,X19555),X19554),X19553) = hAPP(hAPP(c_Fun_Ocomp(X19546,X19548,X19545,X19552),X19551),X19550) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__cong])]) ).

cnf(i_0_7406,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_5574]) ).

fof(i_0_7407,plain,
    ! [X33093,X33094,X33095] :
      ( ~ c_Fun_Oinj__on(X33095,X33094,X33093,c_Orderings_Otop__class_Otop(tc_fun(X33095,tc_HOL_Obool)))
      | hAPP(c_Fun_Ocomp(X33094,X33095,X33095,c_Hilbert__Choice_Oinv__into(X33095,X33094,c_Orderings_Otop__class_Otop(tc_fun(X33095,tc_HOL_Obool)),X33093)),X33093) = c_Fun_Oid(X33095) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__o__cancel])]) ).

fof(i_0_7408,plain,
    ! [X33397,X33398,X33399,X33400] :
      ( ~ c_Fun_Obij__betw(X33400,X33399,X33398,X33397,c_Orderings_Otop__class_Otop(tc_fun(X33399,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33400,X33399,X33398),c_Orderings_Otop__class_Otop(tc_fun(X33400,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33399,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__imp__surj])]) ).

fof(i_0_7409,plain,
    ! [X17445,X17446,X17447,X17448,X17449] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17449,tc_HOL_Obool)),X17446),hAPP(hAPP(c_Set_Oinsert(X17449),X17445),c_Orderings_Obot__class_Obot(tc_fun(X17449,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X17449,tc_HOL_Obool))
        | hAPP(X17447,X17446) = X17445
        | ~ hBOOL(hAPP(hAPP(c_member(X17449),X17445),X17446))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17449),X17446))
        | ~ c_Finite__Set_Ofolding__one(X17449,X17448,X17447) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17449,tc_HOL_Obool)),X17446),hAPP(hAPP(c_Set_Oinsert(X17449),X17445),c_Orderings_Obot__class_Obot(tc_fun(X17449,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X17449,tc_HOL_Obool))
        | hAPP(X17447,X17446) = hAPP(hAPP(X17448,X17445),hAPP(X17447,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17449,tc_HOL_Obool)),X17446),hAPP(hAPP(c_Set_Oinsert(X17449),X17445),c_Orderings_Obot__class_Obot(tc_fun(X17449,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X17449),X17445),X17446))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17449),X17446))
        | ~ c_Finite__Set_Ofolding__one(X17449,X17448,X17447) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oremove])])]) ).

fof(i_0_7410,plain,
    ! [X25422,X25423,X25424] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25424),X25423))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25424),X25422))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25424),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25424,tc_HOL_Obool)),X25423),X25422))),hAPP(c_Finite__Set_Ocard(X25424),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25424,tc_HOL_Obool)),X25423),X25422))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25424),X25423)),hAPP(c_Finite__Set_Ocard(X25424),X25422)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Ounion__inter])]) ).

fof(i_0_7411,plain,
    ! [X25425,X25426,X25427] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25427),X25426))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25427),X25425))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25427),X25426)),hAPP(c_Finite__Set_Ocard(X25427),X25425)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25427),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25427,tc_HOL_Obool)),X25426),X25425))),hAPP(c_Finite__Set_Ocard(X25427),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25427,tc_HOL_Obool)),X25426),X25425))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__Int])]) ).

fof(i_0_7412,plain,
    ! [X28236,X28237,X28238,X28239] :
      ( ( hBOOL(hAPP(X28239,esk296_4(X28236,X28237,X28238,X28239)))
        | c_Wellfounded_Owf(tc_prod(X28236,X28238),c_Recdef_Osame__fst(X28236,X28238,X28239,X28237)) )
      & ( ~ c_Wellfounded_Owf(X28238,hAPP(X28237,esk296_4(X28236,X28237,X28238,X28239)))
        | c_Wellfounded_Owf(tc_prod(X28236,X28238),c_Recdef_Osame__fst(X28236,X28238,X28239,X28237)) ) ),
    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_7413,plain,
    ! [X22174,X22175,X22176,X22177,X22178] :
      ( ( ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X22178,X22177,X22176),X22175),X22174))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X22178,X22177)),hAPP(hAPP(c_Product__Type_OPair(X22178,X22177),X22175),X22174)),X22176)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X22178,X22177)),hAPP(hAPP(c_Product__Type_OPair(X22178,X22177),X22175),X22174)),X22176))
        | hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(X22178,X22177,X22176),X22175),X22174)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).

fof(i_0_7414,plain,
    ! [X33392,X33393,X33394,X33395,X33396] :
      ( ( c_Fun_Oinj__on(X33396,X33395,X33394,X33393)
        | ~ c_Fun_Obij__betw(X33396,X33395,X33394,X33393,X33392) )
      & ( hAPP(c_Set_Oimage(X33396,X33395,X33394),X33393) = X33392
        | ~ c_Fun_Obij__betw(X33396,X33395,X33394,X33393,X33392) )
      & ( ~ c_Fun_Oinj__on(X33396,X33395,X33394,X33393)
        | hAPP(c_Set_Oimage(X33396,X33395,X33394),X33393) != X33392
        | c_Fun_Obij__betw(X33396,X33395,X33394,X33393,X33392) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__def])])]) ).

fof(i_0_7415,plain,
    ! [X33383,X33384,X33385,X33386,X33387] :
      ( ~ c_Fun_Obij__betw(X33387,X33386,X33385,X33384,X33383)
      | c_Fun_Oinj__on(X33387,X33386,X33385,X33384) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__imp__inj__on])]) ).

cnf(i_0_7416,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_5575]) ).

fof(i_0_7417,plain,
    ! [X28649,X28650,X28651] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28651,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28651,X28651,X28650),X28649)),X28649))
      | hAPP(c_Relation_OImage(X28651,X28651,c_Transitive__Closure_Ortrancl(X28651,X28650)),X28649) = X28649 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__closed__trancl])]) ).

cnf(i_0_7418,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_5576]) ).

fof(i_0_7419,plain,
    ! [X28727,X28728,X28729,X28730] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28730,X28730)),hAPP(hAPP(c_Product__Type_OPair(X28730,X28730),X28729),X28728)),c_Transitive__Closure_Ortrancl(X28730,X28727)))
      | ~ hBOOL(hAPP(hAPP(c_member(X28730),X28728),c_Wellfounded_Oacc(X28730,X28727)))
      | hBOOL(hAPP(hAPP(c_member(X28730),X28729),c_Wellfounded_Oacc(X28730,X28727))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards__aux])]) ).

fof(i_0_7420,plain,
    ! [X28731,X28732,X28733,X28734] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28734),X28733),c_Wellfounded_Oacc(X28734,X28732)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28734,X28734)),hAPP(hAPP(c_Product__Type_OPair(X28734,X28734),X28731),X28733)),c_Transitive__Closure_Ortrancl(X28734,X28732)))
      | hBOOL(hAPP(hAPP(c_member(X28734),X28731),c_Wellfounded_Oacc(X28734,X28732))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downwards])]) ).

fof(i_0_7421,plain,
    ! [X17527,X17528,X17529,X17530] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17530),X17529))
      | ~ hBOOL(hAPP(hAPP(c_member(X17530),X17528),X17529))
      | hBOOL(hAPP(hAPP(c_member(X17530),X17528),X17527))
      | hAPP(c_Finite__Set_Ocard(X17530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17530,tc_HOL_Obool)),X17529),hAPP(hAPP(c_Set_Oinsert(X17530),X17528),X17527))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17530),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17530,tc_HOL_Obool)),X17529),X17527))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5577])]) ).

cnf(i_0_7422,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_5578]) ).

fof(i_0_7423,plain,
    ! [X26538,X26539,X26540,X26541,X26542] :
      ( ( X26542 != c_Orderings_Obot__class_Obot(tc_fun(X26541,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26541,tc_fun(X26540,tc_HOL_Obool)),X26542),hAPP(hAPP(c_COMBB(tc_fun(X26540,tc_HOL_Obool),tc_fun(X26540,tc_HOL_Obool),X26541),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26540,tc_HOL_Obool)),X26539)),X26538)) = c_Orderings_Otop__class_Otop(tc_fun(X26540,tc_HOL_Obool)) )
      & ( X26542 = c_Orderings_Obot__class_Obot(tc_fun(X26541,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26541,tc_fun(X26540,tc_HOL_Obool)),X26542),hAPP(hAPP(c_COMBB(tc_fun(X26540,tc_HOL_Obool),tc_fun(X26540,tc_HOL_Obool),X26541),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26540,tc_HOL_Obool)),X26539)),X26538)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26540,tc_HOL_Obool)),X26539),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26541,tc_fun(X26540,tc_HOL_Obool)),X26542),X26538)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I2_J])]) ).

fof(i_0_7424,plain,
    ! [X26602,X26603,X26604,X26605,X26606] :
      ( ( X26606 != c_Orderings_Obot__class_Obot(tc_fun(X26605,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26605,tc_fun(X26604,tc_HOL_Obool)),X26606),hAPP(hAPP(c_COMBB(tc_fun(X26604,tc_HOL_Obool),tc_fun(X26604,tc_HOL_Obool),X26605),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26604,tc_HOL_Obool)),X26603)),X26602)) = c_Orderings_Otop__class_Otop(tc_fun(X26604,tc_HOL_Obool)) )
      & ( X26606 = c_Orderings_Obot__class_Obot(tc_fun(X26605,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26605,tc_fun(X26604,tc_HOL_Obool)),X26606),hAPP(hAPP(c_COMBB(tc_fun(X26604,tc_HOL_Obool),tc_fun(X26604,tc_HOL_Obool),X26605),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26604,tc_HOL_Obool)),X26603)),X26602)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26604,tc_HOL_Obool)),X26603),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26605,tc_fun(X26604,tc_HOL_Obool)),X26606),X26602)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__simps_I4_J])]) ).

fof(i_0_7425,plain,
    ! [X23912,X23913,X23914,X23915,X23916] :
      ( ( X23916 != c_Orderings_Obot__class_Obot(tc_fun(X23915,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23915,tc_fun(X23914,tc_HOL_Obool)),X23916),hAPP(hAPP(c_COMBB(tc_fun(X23914,tc_HOL_Obool),tc_fun(X23914,tc_HOL_Obool),X23915),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23914,tc_HOL_Obool)),X23913)),X23912)) = c_Orderings_Obot__class_Obot(tc_fun(X23914,tc_HOL_Obool)) )
      & ( X23916 = c_Orderings_Obot__class_Obot(tc_fun(X23915,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23915,tc_fun(X23914,tc_HOL_Obool)),X23916),hAPP(hAPP(c_COMBB(tc_fun(X23914,tc_HOL_Obool),tc_fun(X23914,tc_HOL_Obool),X23915),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23914,tc_HOL_Obool)),X23913)),X23912)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23914,tc_HOL_Obool)),X23913),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23915,tc_fun(X23914,tc_HOL_Obool)),X23916),X23912)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I3_J])]) ).

fof(i_0_7426,plain,
    ! [X26533,X26534,X26535,X26536,X26537] :
      ( ( X26537 != c_Orderings_Obot__class_Obot(tc_fun(X26536,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26535,tc_HOL_Obool)),X26534),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26536,tc_fun(X26535,tc_HOL_Obool)),X26537),X26533)) = X26534 )
      & ( X26537 = c_Orderings_Obot__class_Obot(tc_fun(X26536,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26535,tc_HOL_Obool)),X26534),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26536,tc_fun(X26535,tc_HOL_Obool)),X26537),X26533)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26536,tc_fun(X26535,tc_HOL_Obool)),X26537),hAPP(hAPP(c_COMBB(tc_fun(X26535,tc_HOL_Obool),tc_fun(X26535,tc_HOL_Obool),X26536),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26535,tc_HOL_Obool)),X26534)),X26533)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I2_J])]) ).

fof(i_0_7427,plain,
    ! [X23902,X23903,X23904,X23905,X23906] :
      ( ( X23906 != c_Orderings_Obot__class_Obot(tc_fun(X23905,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23904,tc_HOL_Obool)),X23903),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23905,tc_fun(X23904,tc_HOL_Obool)),X23906),X23902)) = X23903 )
      & ( X23906 = c_Orderings_Obot__class_Obot(tc_fun(X23905,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23904,tc_HOL_Obool)),X23903),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23905,tc_fun(X23904,tc_HOL_Obool)),X23906),X23902)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23905,tc_fun(X23904,tc_HOL_Obool)),X23906),hAPP(hAPP(c_COMBB(tc_fun(X23904,tc_HOL_Obool),tc_fun(X23904,tc_HOL_Obool),X23905),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23904,tc_HOL_Obool)),X23903)),X23902)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I3_J])]) ).

fof(i_0_7428,plain,
    ! [X26597,X26598,X26599,X26600,X26601] :
      ( ( X26601 != c_Orderings_Obot__class_Obot(tc_fun(X26600,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26599,tc_HOL_Obool)),X26598),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26600,tc_fun(X26599,tc_HOL_Obool)),X26601),X26597)) = X26598 )
      & ( X26601 = c_Orderings_Obot__class_Obot(tc_fun(X26600,tc_HOL_Obool))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26599,tc_HOL_Obool)),X26598),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26600,tc_fun(X26599,tc_HOL_Obool)),X26601),X26597)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26600,tc_fun(X26599,tc_HOL_Obool)),X26601),hAPP(hAPP(c_COMBB(tc_fun(X26599,tc_HOL_Obool),tc_fun(X26599,tc_HOL_Obool),X26600),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26599,tc_HOL_Obool)),X26598)),X26597)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__extend__simps_I4_J])]) ).

fof(i_0_7429,plain,
    ! [X17398,X17399,X17400,X17401,X17402] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17402,tc_HOL_Obool)),X17399),hAPP(hAPP(c_Set_Oinsert(X17402),X17398),c_Orderings_Obot__class_Obot(tc_fun(X17402,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X17402,tc_HOL_Obool))
        | hAPP(X17400,hAPP(hAPP(c_Set_Oinsert(X17402),X17398),X17399)) = X17398
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17402),X17399))
        | ~ c_Finite__Set_Ofolding__one(X17402,X17401,X17400) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17402,tc_HOL_Obool)),X17399),hAPP(hAPP(c_Set_Oinsert(X17402),X17398),c_Orderings_Obot__class_Obot(tc_fun(X17402,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X17402,tc_HOL_Obool))
        | hAPP(X17400,hAPP(hAPP(c_Set_Oinsert(X17402),X17398),X17399)) = hAPP(hAPP(X17401,X17398),hAPP(X17400,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17402,tc_HOL_Obool)),X17399),hAPP(hAPP(c_Set_Oinsert(X17402),X17398),c_Orderings_Obot__class_Obot(tc_fun(X17402,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17402),X17399))
        | ~ c_Finite__Set_Ofolding__one(X17402,X17401,X17400) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oinsert__remove])])]) ).

fof(i_0_7430,plain,
    ! [X25633,X25634,X25635] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25635,tc_HOL_Obool)),X25634),hAPP(hAPP(c_Set_Oinsert(X25635),X25633),c_Orderings_Obot__class_Obot(tc_fun(X25635,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25635,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X25635,X25634) = X25633
        | ~ hBOOL(hAPP(hAPP(c_member(X25635),X25633),X25634))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25635),X25634))
        | ~ class_Lattices_Olattice(X25635) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25635,tc_HOL_Obool)),X25634),hAPP(hAPP(c_Set_Oinsert(X25635),X25633),c_Orderings_Obot__class_Obot(tc_fun(X25635,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25635,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X25635,X25634) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25635),X25633),c_Big__Operators_Olattice__class_OInf__fin(X25635,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25635,tc_HOL_Obool)),X25634),hAPP(hAPP(c_Set_Oinsert(X25635),X25633),c_Orderings_Obot__class_Obot(tc_fun(X25635,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X25635),X25633),X25634))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25635),X25634))
        | ~ class_Lattices_Olattice(X25635) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oremove])])]) ).

fof(i_0_7431,plain,
    ! [X23469,X23470,X23471] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23471,tc_HOL_Obool)),X23470),hAPP(hAPP(c_Set_Oinsert(X23471),X23469),c_Orderings_Obot__class_Obot(tc_fun(X23471,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X23471,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X23471,X23470) = X23469
        | ~ hBOOL(hAPP(hAPP(c_member(X23471),X23469),X23470))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23471),X23470))
        | ~ class_Lattices_Olattice(X23471) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23471,tc_HOL_Obool)),X23470),hAPP(hAPP(c_Set_Oinsert(X23471),X23469),c_Orderings_Obot__class_Obot(tc_fun(X23471,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X23471,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X23471,X23470) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23471),X23469),c_Big__Operators_Olattice__class_OSup__fin(X23471,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23471,tc_HOL_Obool)),X23470),hAPP(hAPP(c_Set_Oinsert(X23471),X23469),c_Orderings_Obot__class_Obot(tc_fun(X23471,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X23471),X23469),X23470))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23471),X23470))
        | ~ class_Lattices_Olattice(X23471) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oremove])])]) ).

fof(i_0_7432,plain,
    ! [X22982,X22983,X22984] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22984,tc_HOL_Obool)),X22983),hAPP(hAPP(c_Set_Oinsert(X22984),X22982),c_Orderings_Obot__class_Obot(tc_fun(X22984,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X22984,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X22984,X22983) = X22982
        | ~ hBOOL(hAPP(hAPP(c_member(X22984),X22982),X22983))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22984),X22983))
        | ~ class_Orderings_Olinorder(X22984) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22984,tc_HOL_Obool)),X22983),hAPP(hAPP(c_Set_Oinsert(X22984),X22982),c_Orderings_Obot__class_Obot(tc_fun(X22984,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X22984,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X22984,X22983) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22984),X22982),c_Big__Operators_Olinorder__class_OMax(X22984,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22984,tc_HOL_Obool)),X22983),hAPP(hAPP(c_Set_Oinsert(X22984),X22982),c_Orderings_Obot__class_Obot(tc_fun(X22984,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X22984),X22982),X22983))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22984),X22983))
        | ~ class_Orderings_Olinorder(X22984) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oremove])])]) ).

fof(i_0_7433,plain,
    ! [X21744,X21745,X21746] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21746,tc_HOL_Obool)),X21745),hAPP(hAPP(c_Set_Oinsert(X21746),X21744),c_Orderings_Obot__class_Obot(tc_fun(X21746,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X21746,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X21746,X21745) = X21744
        | ~ hBOOL(hAPP(hAPP(c_member(X21746),X21744),X21745))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21746),X21745))
        | ~ class_Orderings_Olinorder(X21746) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21746,tc_HOL_Obool)),X21745),hAPP(hAPP(c_Set_Oinsert(X21746),X21744),c_Orderings_Obot__class_Obot(tc_fun(X21746,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X21746,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X21746,X21745) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21746),X21744),c_Big__Operators_Olinorder__class_OMin(X21746,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21746,tc_HOL_Obool)),X21745),hAPP(hAPP(c_Set_Oinsert(X21746),X21744),c_Orderings_Obot__class_Obot(tc_fun(X21746,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(X21746),X21744),X21745))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21746),X21745))
        | ~ class_Orderings_Olinorder(X21746) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oremove])])]) ).

fof(i_0_7434,plain,
    ! [X26729,X26730,X26731,X26732,X26733,X26734] :
      ( ~ c_Typedef_Otype__definition(X26734,X26733,X26732,X26731,X26730)
      | hBOOL(hAPP(hAPP(c_member(X26733),hAPP(X26732,X26729)),X26730)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep])]) ).

fof(i_0_7435,plain,
    ! [X26735,X26736,X26737,X26738,X26739,X26740] :
      ( ~ c_Typedef_Otype__definition(X26740,X26739,X26738,X26737,X26736)
      | ~ hBOOL(hAPP(hAPP(c_member(X26739),X26735),X26736))
      | hAPP(X26738,hAPP(X26737,X26735)) = X26735 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__inverse])]) ).

fof(i_0_7436,plain,
    ! [X31712,X31713,X31714,X31715,X31716] :
      ( ( ~ c_List_Olinorder__class_Osorted(X31716,hAPP(hAPP(c_List_Omap(X31715,X31716),X31714),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31715,X31716,X31714),X31713),X31712)))
        | c_List_Olinorder__class_Osorted(X31716,hAPP(hAPP(c_List_Omap(X31715,X31716),X31714),X31712))
        | ~ class_Orderings_Olinorder(X31716) )
      & ( ~ c_List_Olinorder__class_Osorted(X31716,hAPP(hAPP(c_List_Omap(X31715,X31716),X31714),X31712))
        | c_List_Olinorder__class_Osorted(X31716,hAPP(hAPP(c_List_Omap(X31715,X31716),X31714),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31715,X31716,X31714),X31713),X31712)))
        | ~ class_Orderings_Olinorder(X31716) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort__key])])]) ).

fof(i_0_7437,plain,
    ! [X28438,X28439,X28440] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk324_3(X28438,X28439,X28440)),X28440))
        | ~ hBOOL(hAPP(X28439,X28438))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28438),X28440))
        | hBOOL(hAPP(X28439,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X28439,esk324_3(X28438,X28439,X28440)))
        | ~ hBOOL(hAPP(X28439,X28438))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28438),X28440))
        | hBOOL(hAPP(X28439,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(X28439,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,esk324_3(X28438,X28439,X28440)),X28440)))
        | ~ hBOOL(hAPP(X28439,X28438))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X28438),X28440))
        | hBOOL(hAPP(X28439,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_7438,plain,
    ! [X33414,X33415,X33416] :
      ( ~ c_Fun_Oinj__on(X33416,X33415,X33414,c_Orderings_Otop__class_Otop(tc_fun(X33416,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33416,X33415,X33414),c_Orderings_Otop__class_Otop(tc_fun(X33416,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33415,tc_HOL_Obool))
      | c_Fun_Obij__betw(X33416,X33415,X33414,c_Orderings_Otop__class_Otop(tc_fun(X33416,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33415,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bijI])]) ).

fof(i_0_7439,plain,
    ! [X20909,X20910,X20911] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20911),X20910)),X20909) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20911),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20910),X20909))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20911),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20910,X20909))),X20909)),
    inference(variable_rename,[status(thm)],[fact_zdiv__zmult1__eq]) ).

fof(i_0_7440,plain,
    ! [X21300,X21301,X21302] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21302),X21301)),X21300) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21302),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21301),X21300))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21302),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21301,X21300))),X21300)),
    inference(variable_rename,[status(thm)],[fact_div__mult1__eq]) ).

fof(i_0_7441,plain,
    ! [X18921,X18922,X18923,X18924,X18925] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18924),X18923)),X18922) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18925),X18923)),X18921)
        | 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),X18924),X18925)),X18923)),X18922) = X18921
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18925),X18924)) )
      & ( 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),X18924),X18925)),X18923)),X18922) != X18921
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18924),X18923)),X18922) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18925),X18923)),X18921)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18925),X18924)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1])])]) ).

fof(i_0_7442,plain,
    ! [X18906,X18907,X18908,X18909,X18910] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18910),X18908)),X18907) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18909),X18908)),X18906)
        | X18907 = 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),X18909),X18910)),X18908)),X18906)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18910),X18909)) )
      & ( X18907 != 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),X18909),X18910)),X18908)),X18906)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18910),X18908)),X18907) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18909),X18908)),X18906)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18910),X18909)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2])])]) ).

fof(i_0_7443,plain,
    ! [X19378,X19379,X19380,X19381,X19382,X19383] :
      ( ~ class_Groups_Oab__semigroup__mult(X19383)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19382),X19381))
      | hBOOL(hAPP(hAPP(c_member(X19382),X19380),X19381))
      | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19383,X19382,c_Groups_Otimes__class_Otimes(X19383)),X19379),X19378),hAPP(hAPP(c_Set_Oinsert(X19382),X19380),X19381)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19383),hAPP(X19379,X19380)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19383,X19382,c_Groups_Otimes__class_Otimes(X19383)),X19379),X19378),X19381)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5579])]) ).

cnf(i_0_7444,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_5580]) ).

fof(i_0_7445,plain,
    ! [X25256,X25257,X25258,X25259] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25259,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25259,tc_HOL_Obool)),X25258),X25257)),X25256) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25259,tc_HOL_Obool)),X25258),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25259,tc_HOL_Obool)),X25257),X25256))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25259,tc_HOL_Obool)),X25256),X25258)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25259,tc_HOL_Obool)),X25256),X25258))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25259,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25259,tc_HOL_Obool)),X25258),X25257)),X25256) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25259,tc_HOL_Obool)),X25258),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25259,tc_HOL_Obool)),X25257),X25256)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__Int__assoc__eq])]) ).

fof(i_0_7446,plain,
    ! [X26419,X26420,X26421,X26422,X26423] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26423,tc_fun(X26422,tc_HOL_Obool)),X26421),hAPP(hAPP(c_COMBB(tc_fun(X26422,tc_HOL_Obool),tc_fun(X26422,tc_HOL_Obool),X26423),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26422,tc_HOL_Obool)),X26420)),X26419)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26422,tc_HOL_Obool)),X26420),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26423,tc_fun(X26422,tc_HOL_Obool)),X26421),X26419)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I7_J]) ).

fof(i_0_7447,plain,
    ! [X25168,X25169,X25170,X25171,X25172] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25172,tc_fun(X25171,tc_HOL_Obool)),X25170),hAPP(hAPP(c_COMBB(tc_fun(X25171,tc_HOL_Obool),tc_fun(X25171,tc_HOL_Obool),X25172),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25171,tc_HOL_Obool)),X25169)),X25168)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25171,tc_HOL_Obool)),X25169),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25172,tc_fun(X25171,tc_HOL_Obool)),X25170),X25168)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I5_J]) ).

fof(i_0_7448,plain,
    ! [X26568,X26569,X26570,X26571,X26572] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26572,tc_fun(X26571,tc_HOL_Obool)),X26570),hAPP(hAPP(c_COMBB(tc_fun(X26571,tc_HOL_Obool),tc_fun(X26571,tc_HOL_Obool),X26572),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26571,tc_HOL_Obool)),X26569)),X26568)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26571,tc_HOL_Obool)),X26569),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26572,tc_fun(X26571,tc_HOL_Obool)),X26570),X26568)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I7_J]) ).

fof(i_0_7449,plain,
    ! [X25183,X25184,X25185,X25186,X25187] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25187,tc_HOL_Obool)),X25186),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25185,tc_fun(X25187,tc_HOL_Obool)),X25184),X25183)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25185,tc_fun(X25187,tc_HOL_Obool)),X25184),hAPP(hAPP(c_COMBB(tc_fun(X25187,tc_HOL_Obool),tc_fun(X25187,tc_HOL_Obool),X25185),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25187,tc_HOL_Obool)),X25186)),X25183)),
    inference(variable_rename,[status(thm)],[fact_Int__UN__distrib]) ).

fof(i_0_7450,plain,
    ! [X25178,X25179,X25180,X25181,X25182] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25182,tc_HOL_Obool)),X25181),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25180,tc_fun(X25182,tc_HOL_Obool)),X25179),X25178)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X25180,tc_fun(X25182,tc_HOL_Obool)),X25179),hAPP(hAPP(c_COMBB(tc_fun(X25182,tc_HOL_Obool),tc_fun(X25182,tc_HOL_Obool),X25180),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25182,tc_HOL_Obool)),X25181)),X25178)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I5_J]) ).

fof(i_0_7451,plain,
    ! [X26434,X26435,X26436,X26437,X26438] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26438,tc_HOL_Obool)),X26437),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26436,tc_fun(X26438,tc_HOL_Obool)),X26435),X26434)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26436,tc_fun(X26438,tc_HOL_Obool)),X26435),hAPP(hAPP(c_COMBB(tc_fun(X26438,tc_HOL_Obool),tc_fun(X26438,tc_HOL_Obool),X26436),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26438,tc_HOL_Obool)),X26437)),X26434)),
    inference(variable_rename,[status(thm)],[fact_Un__INT__distrib]) ).

fof(i_0_7452,plain,
    ! [X26429,X26430,X26431,X26432,X26433] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26433,tc_HOL_Obool)),X26432),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26431,tc_fun(X26433,tc_HOL_Obool)),X26430),X26429)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26431,tc_fun(X26433,tc_HOL_Obool)),X26430),hAPP(hAPP(c_COMBB(tc_fun(X26433,tc_HOL_Obool),tc_fun(X26433,tc_HOL_Obool),X26431),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26433,tc_HOL_Obool)),X26432)),X26429)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I7_J]) ).

fof(i_0_7453,plain,
    ! [X26573,X26574,X26575,X26576,X26577] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26577,tc_HOL_Obool)),X26576),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26575,tc_fun(X26577,tc_HOL_Obool)),X26574),X26573)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26575,tc_fun(X26577,tc_HOL_Obool)),X26574),hAPP(hAPP(c_COMBB(tc_fun(X26577,tc_HOL_Obool),tc_fun(X26577,tc_HOL_Obool),X26575),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26577,tc_HOL_Obool)),X26576)),X26573)),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I7_J]) ).

fof(i_0_7454,plain,
    ! [X27934,X27935,X27936,X27937] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X27937,X27937,X27937),X27936),X27935) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27937,X27937),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27937,X27937,X27937),X27936),X27934) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27937,X27937),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(X27937,X27937,X27937),X27936),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27937,X27937),tc_HOL_Obool)),X27935),X27934)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27937,X27937),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__comp__emptyR])]) ).

cnf(i_0_7455,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_5534]) ).

cnf(i_0_7456,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_5535]) ).

fof(i_0_7457,plain,
    ! [X33356,X33357,X33358,X33359,X33360] :
      ( ( ~ c_Fun_Obij__betw(X33359,X33357,X33360,X33358,X33356)
        | hAPP(c_Finite__Set_Ocard(X33359),X33358) = hAPP(c_Finite__Set_Ocard(X33357),X33356)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33357),X33356))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33359),X33358)) )
      & ( hAPP(c_Finite__Set_Ocard(X33359),X33358) != hAPP(c_Finite__Set_Ocard(X33357),X33356)
        | c_Fun_Obij__betw(X33359,X33357,esk530_4(X33356,X33357,X33358,X33359),X33358,X33356)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33357),X33356))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33359),X33358)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_BIJ])])])])]) ).

fof(i_0_7458,plain,
    ! [X26704,X26705,X26706,X26707,X26708] :
      ( ~ c_Typedef_Otype__definition(X26708,X26707,X26706,X26705,X26704)
      | hAPP(c_Set_Oimage(X26708,X26707,X26706),c_Orderings_Otop__class_Otop(tc_fun(X26708,tc_HOL_Obool))) = X26704 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__range])]) ).

fof(i_0_7459,plain,
    ! [X24637,X24638,X24639] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X24639),hAPP(hAPP(c_Set_Oinsert(X24639),X24638),c_Orderings_Obot__class_Obot(tc_fun(X24639,tc_HOL_Obool)))),X24637) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X24639,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24639,X24639,X24637),hAPP(hAPP(c_Set_Oinsert(X24639),X24638),c_Orderings_Obot__class_Obot(tc_fun(X24639,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24639,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__quotient]) ).

fof(i_0_7460,plain,
    ! [X24792,X24793,X24794,X24795,X24796,X24797] :
      ( ~ c_Equiv__Relations_Ocongruent(X24797,X24796,X24795,X24794)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24797,X24797)),hAPP(hAPP(c_Product__Type_OPair(X24797,X24797),X24793),X24792)),X24795))
      | hAPP(X24794,X24793) = hAPP(X24794,X24792) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_congruentD])]) ).

fof(i_0_7461,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),v_G)),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_7])]) ).

fof(i_0_7462,plain,
    ! [X28637,X28638,X28639] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28639,X28639),tc_HOL_Obool)),X28638),c_Transitive__Closure_Ortrancl(X28639,X28637)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28639,X28639),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28639,X28638)),c_Transitive__Closure_Ortrancl(X28639,X28637))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__subset__rtrancl])]) ).

cnf(i_0_7463,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_5526]) ).

cnf(i_0_7464,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_5522]) ).

fof(i_0_7465,plain,
    ! [X28956,X28957,X28958,X28959] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28959,X28959)),X28958),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28959,X28959),tc_HOL_Obool),X28957),X28956)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28959,X28959)),X28958),c_Transitive__Closure_Ortrancl(X28959,X28956))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rel__pow__imp__rtrancl])]) ).

fof(i_0_7466,plain,
    ! [X26267,X26268,X26269,X26270] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26270),X26269),c_Wellfounded_Oacc(X26270,X26268)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X26270,X26270)),hAPP(hAPP(c_Product__Type_OPair(X26270,X26270),X26267),X26269)),X26268))
      | hBOOL(hAPP(hAPP(c_member(X26270),X26267),c_Wellfounded_Oacc(X26270,X26268))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__downward])]) ).

fof(i_0_7467,plain,
    ! [X32101,X32102,X32103] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X32103,X32103)),hAPP(hAPP(c_Product__Type_OPair(X32103,X32103),X32102),X32101)),c_List_Omeasures(X32103,c_List_Olist_ONil(tc_fun(X32103,tc_Nat_Onat))))),
    inference(variable_rename,[status(thm)],[i_0_5581]) ).

fof(i_0_7468,plain,
    ! [X25674,X25675,X25676] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25676,tc_HOL_Obool)),X25675),hAPP(hAPP(c_Set_Oinsert(X25676),X25674),c_Orderings_Obot__class_Obot(tc_fun(X25676,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X25676,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X25676,hAPP(hAPP(c_Set_Oinsert(X25676),X25674),X25675)) = X25674
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25676),X25675))
        | ~ class_Lattices_Olattice(X25676) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25676,tc_HOL_Obool)),X25675),hAPP(hAPP(c_Set_Oinsert(X25676),X25674),c_Orderings_Obot__class_Obot(tc_fun(X25676,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X25676,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OInf__fin(X25676,hAPP(hAPP(c_Set_Oinsert(X25676),X25674),X25675)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25676),X25674),c_Big__Operators_Olattice__class_OInf__fin(X25676,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25676,tc_HOL_Obool)),X25675),hAPP(hAPP(c_Set_Oinsert(X25676),X25674),c_Orderings_Obot__class_Obot(tc_fun(X25676,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25676),X25675))
        | ~ class_Lattices_Olattice(X25676) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__remove])])]) ).

fof(i_0_7469,plain,
    ! [X23537,X23538,X23539] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23539,tc_HOL_Obool)),X23538),hAPP(hAPP(c_Set_Oinsert(X23539),X23537),c_Orderings_Obot__class_Obot(tc_fun(X23539,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X23539,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X23539,hAPP(hAPP(c_Set_Oinsert(X23539),X23537),X23538)) = X23537
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23539),X23538))
        | ~ class_Lattices_Olattice(X23539) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23539,tc_HOL_Obool)),X23538),hAPP(hAPP(c_Set_Oinsert(X23539),X23537),c_Orderings_Obot__class_Obot(tc_fun(X23539,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X23539,tc_HOL_Obool))
        | c_Big__Operators_Olattice__class_OSup__fin(X23539,hAPP(hAPP(c_Set_Oinsert(X23539),X23537),X23538)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23539),X23537),c_Big__Operators_Olattice__class_OSup__fin(X23539,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23539,tc_HOL_Obool)),X23538),hAPP(hAPP(c_Set_Oinsert(X23539),X23537),c_Orderings_Obot__class_Obot(tc_fun(X23539,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23539),X23538))
        | ~ class_Lattices_Olattice(X23539) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__remove])])]) ).

fof(i_0_7470,plain,
    ! [X23053,X23054,X23055] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23055,tc_HOL_Obool)),X23054),hAPP(hAPP(c_Set_Oinsert(X23055),X23053),c_Orderings_Obot__class_Obot(tc_fun(X23055,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X23055,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X23055,hAPP(hAPP(c_Set_Oinsert(X23055),X23053),X23054)) = X23053
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23055),X23054))
        | ~ class_Orderings_Olinorder(X23055) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23055,tc_HOL_Obool)),X23054),hAPP(hAPP(c_Set_Oinsert(X23055),X23053),c_Orderings_Obot__class_Obot(tc_fun(X23055,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X23055,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMax(X23055,hAPP(hAPP(c_Set_Oinsert(X23055),X23053),X23054)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X23055),X23053),c_Big__Operators_Olinorder__class_OMax(X23055,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23055,tc_HOL_Obool)),X23054),hAPP(hAPP(c_Set_Oinsert(X23055),X23053),c_Orderings_Obot__class_Obot(tc_fun(X23055,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23055),X23054))
        | ~ class_Orderings_Olinorder(X23055) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oinsert__remove])])]) ).

fof(i_0_7471,plain,
    ! [X21820,X21821,X21822] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21822,tc_HOL_Obool)),X21821),hAPP(hAPP(c_Set_Oinsert(X21822),X21820),c_Orderings_Obot__class_Obot(tc_fun(X21822,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X21822,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X21822,hAPP(hAPP(c_Set_Oinsert(X21822),X21820),X21821)) = X21820
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21822),X21821))
        | ~ class_Orderings_Olinorder(X21822) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21822,tc_HOL_Obool)),X21821),hAPP(hAPP(c_Set_Oinsert(X21822),X21820),c_Orderings_Obot__class_Obot(tc_fun(X21822,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X21822,tc_HOL_Obool))
        | c_Big__Operators_Olinorder__class_OMin(X21822,hAPP(hAPP(c_Set_Oinsert(X21822),X21820),X21821)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21822),X21820),c_Big__Operators_Olinorder__class_OMin(X21822,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X21822,tc_HOL_Obool)),X21821),hAPP(hAPP(c_Set_Oinsert(X21822),X21820),c_Orderings_Obot__class_Obot(tc_fun(X21822,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21822),X21821))
        | ~ class_Orderings_Olinorder(X21822) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oinsert__remove])])]) ).

fof(i_0_7472,plain,
    ! [X26699,X26700,X26701,X26702,X26703] :
      ( ~ c_Typedef_Otype__definition(X26703,X26702,X26701,X26700,X26699)
      | hAPP(c_Set_Oimage(X26702,X26703,X26700),X26699) = c_Orderings_Otop__class_Otop(tc_fun(X26703,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_OAbs__image])]) ).

fof(i_0_7473,plain,
    ! [X30889,X30890,X30891,X30892] :
      ( ~ c_Fun_Oinj__on(X30892,X30891,X30890,c_Complete__Lattice_OSup__class_OSup(tc_fun(X30892,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(X30892),tc_fun(X30892,tc_HOL_Obool),c_List_Oset(X30892)),X30889)))
      | c_Fun_Oinj__on(tc_List_Olist(X30892),tc_List_Olist(X30891),hAPP(c_List_Omap(X30892,X30891),X30890),X30889) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__mapI])]) ).

fof(i_0_7474,plain,
    ! [X22907,X22908,X22909,X22910] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)),X22909))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22907))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22907))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)),X22909))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22907))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)),X22909))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22908))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22907))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22908),c_Groups_Ozero__class_Ozero(X22910)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)),X22909))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),c_Groups_Ozero__class_Ozero(X22910)),X22907))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)),X22909))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),X22909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22910),X22907),X22908)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22910),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22910),X22909),X22908)),X22907))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22910) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5582])])]) ).

fof(i_0_7475,plain,
    ! [X22959,X22960,X22961,X22962] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),X22961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)),X22961))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22959))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22959))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)),X22961))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22959))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)),X22961))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22960))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),X22961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),X22961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22959))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),X22961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22962),X22960),c_Groups_Ozero__class_Ozero(X22962)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)),X22961))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),X22961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),c_Groups_Ozero__class_Ozero(X22962)),X22959))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)),X22961))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),X22961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22962),X22959),X22960)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22962),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22962),X22961),X22960)),X22959))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22962) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5583])])]) ).

fof(i_0_7476,plain,
    ! [X33113,X33114,X33115,X33116] :
      ( ~ c_Fun_Oinj__on(X33116,X33115,X33114,c_Orderings_Otop__class_Otop(tc_fun(X33116,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33115,X33116,c_Hilbert__Choice_Oinv__into(X33116,X33115,c_Orderings_Otop__class_Otop(tc_fun(X33116,tc_HOL_Obool)),X33114)),hAPP(c_Set_Oimage(X33116,X33115,X33114),X33113)) = X33113 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__inv__f__f])]) ).

fof(i_0_7477,plain,
    ! [X33109,X33110,X33111,X33112] :
      ( ~ c_Fun_Oinj__on(X33112,X33111,X33110,c_Orderings_Otop__class_Otop(tc_fun(X33112,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33111,X33112,c_Hilbert__Choice_Oinv__into(X33112,X33111,c_Orderings_Otop__class_Otop(tc_fun(X33112,tc_HOL_Obool)),X33110)),hAPP(c_Set_Oimage(X33112,X33111,X33110),X33109)) = X33109 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__image__comp])]) ).

fof(i_0_7478,plain,
    ! [X29688,X29689,X29690,X29691,X29692,X29693] : hAPP(hAPP(c_List_Olist__update(tc_prod(X29693,X29692),hAPP(hAPP(c_List_Ozip(X29693,X29692),X29691),X29690)),X29689),X29688) = hAPP(hAPP(c_List_Ozip(X29693,X29692),hAPP(hAPP(c_List_Olist__update(X29693,X29691),X29689),hAPP(c_Product__Type_Ofst(X29693,X29692),X29688))),hAPP(hAPP(c_List_Olist__update(X29692,X29690),X29689),hAPP(c_Product__Type_Osnd(X29693,X29692),X29688))),
    inference(variable_rename,[status(thm)],[fact_update__zip]) ).

cnf(i_0_7479,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_5528]) ).

cnf(i_0_7480,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_5529]) ).

cnf(i_0_7481,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_5531]) ).

cnf(i_0_7482,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_5530]) ).

cnf(i_0_7483,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_5532]) ).

cnf(i_0_7484,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_5584]) ).

fof(i_0_7485,plain,
    ! [X27569] : 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)),X27569)))),
    inference(variable_rename,[status(thm)],[fact_finite__Collect__less__nat]) ).

fof(i_0_7486,plain,
    ! [X27570] : 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)),X27570)))),
    inference(variable_rename,[status(thm)],[fact_finite__Collect__le__nat]) ).

fof(i_0_7487,plain,
    ! [X27882,X27883,X27884,X27885,X27886,X27887,X27888] : hAPP(hAPP(c_Relation_Orel__comp(X27888,X27887,X27886),hAPP(hAPP(c_Relation_Orel__comp(X27888,X27885,X27887),X27884),X27883)),X27882) = hAPP(hAPP(c_Relation_Orel__comp(X27888,X27885,X27886),X27884),hAPP(hAPP(c_Relation_Orel__comp(X27885,X27887,X27886),X27883),X27882)),
    inference(variable_rename,[status(thm)],[fact_O__assoc]) ).

fof(i_0_7488,plain,
    ! [X24645,X24646,X24647,X24648,X24649] :
      ( ~ class_Groups_Ocomm__monoid__add(X24649)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24648),X24647))
      | ~ hBOOL(hAPP(hAPP(c_member(X24648),X24646),X24647))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24648,X24649),X24645),X24647) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24649),hAPP(X24645,X24646)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24648,X24649),X24645),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24648,tc_HOL_Obool)),X24647),hAPP(hAPP(c_Set_Oinsert(X24648),X24646),c_Orderings_Obot__class_Obot(tc_fun(X24648,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1_H])]) ).

fof(i_0_7489,plain,
    ! [X24640,X24641,X24642,X24643,X24644] :
      ( ~ class_Groups_Ocomm__monoid__add(X24644)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24643),X24642))
      | ~ hBOOL(hAPP(hAPP(c_member(X24643),X24641),X24642))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24643,X24644),X24640),X24642) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24644),hAPP(X24640,X24641)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24643,X24644),X24640),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24643,tc_HOL_Obool)),X24642),hAPP(hAPP(c_Set_Oinsert(X24643),X24641),c_Orderings_Obot__class_Obot(tc_fun(X24643,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oremove])]) ).

fof(i_0_7490,plain,
    ! [X22015,X22016,X22017,X22018,X22019] :
      ( ~ class_Groups_Ocomm__monoid__mult(X22019)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22018),X22017))
      | ~ hBOOL(hAPP(hAPP(c_member(X22018),X22016),X22017))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22018,X22019),X22015),X22017) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22019),hAPP(X22015,X22016)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22018,X22019),X22015),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22018,tc_HOL_Obool)),X22017),hAPP(hAPP(c_Set_Oinsert(X22018),X22016),c_Orderings_Obot__class_Obot(tc_fun(X22018,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oremove])]) ).

fof(i_0_7491,plain,
    ! [X26463,X26464,X26465,X26466] : hAPP(c_Set_OPow(X26466),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26465,tc_fun(X26466,tc_HOL_Obool)),X26464),X26463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26465,tc_fun(tc_fun(X26466,tc_HOL_Obool),tc_HOL_Obool)),X26464),hAPP(hAPP(c_COMBB(tc_fun(X26466,tc_HOL_Obool),tc_fun(tc_fun(X26466,tc_HOL_Obool),tc_HOL_Obool),X26465),c_Set_OPow(X26466)),X26463)),
    inference(variable_rename,[status(thm)],[fact_Pow__INT__eq]) ).

fof(i_0_7492,plain,
    ! [X19676,X19677,X19678] :
      ( ~ 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),X19678),X19677)),X19676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19676),X19678))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19678))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19677)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_q__pos__lemma])]) ).

fof(i_0_7493,plain,
    ! [X33351,X33352,X33353,X33354,X33355] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33355),X33352))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33354),X33351))
        | ~ c_Fun_Obij__betw(X33355,X33354,X33353,X33352,X33351) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33354),X33351))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X33355),X33352))
        | ~ c_Fun_Obij__betw(X33355,X33354,X33353,X33352,X33351) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__finite])])]) ).

fof(i_0_7494,plain,
    ! [X33362,X33363,X33364,X33365] :
      ( ~ c_Fun_Obij__betw(X33365,X33364,X33363,c_Orderings_Obot__class_Obot(tc_fun(X33365,tc_HOL_Obool)),X33362)
      | X33362 = c_Orderings_Obot__class_Obot(tc_fun(X33364,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__empty1])]) ).

fof(i_0_7495,plain,
    ! [X33366,X33367,X33368,X33369] :
      ( ~ c_Fun_Obij__betw(X33369,X33368,X33367,X33366,c_Orderings_Obot__class_Obot(tc_fun(X33368,tc_HOL_Obool)))
      | X33366 = c_Orderings_Obot__class_Obot(tc_fun(X33369,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__empty2])]) ).

fof(i_0_7496,plain,
    ! [X25547,X25548,X25549] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X25549,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25548)),X25547) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25549,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(X25549,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X25548)),X25547)),hAPP(X25547,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[fact_UN__le__eq__Un0]) ).

fof(i_0_7497,plain,
    ! [X25428,X25429,X25430] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25430),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25430,tc_HOL_Obool)),X25429),X25428)))
      | hAPP(c_Finite__Set_Ocard(X25430),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25430,tc_HOL_Obool)),X25429),X25428)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25430),X25429)),hAPP(c_Finite__Set_Ocard(X25430),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25430,tc_HOL_Obool)),X25429),X25428))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset__Int])]) ).

cnf(i_0_7498,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_7499,plain,
    ! [X26563,X26564,X26565,X26566,X26567] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26567,tc_fun(X26566,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26567,tc_HOL_Obool)),X26565),X26564)),X26563) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26566,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26567,tc_fun(X26566,tc_HOL_Obool)),X26565),X26563)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26567,tc_fun(X26566,tc_HOL_Obool)),X26564),X26563)),
    inference(variable_rename,[status(thm)],[fact_INT__Un]) ).

fof(i_0_7500,plain,
    ! [X23823,X23824,X23825,X23826,X23827] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23827,tc_fun(X23826,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23827,tc_HOL_Obool)),X23825),X23824)),X23823) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23826,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23827,tc_fun(X23826,tc_HOL_Obool)),X23825),X23823)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23827,tc_fun(X23826,tc_HOL_Obool)),X23824),X23823)),
    inference(variable_rename,[status(thm)],[fact_UN__Un]) ).

cnf(i_0_7501,plain,
    ( ~ c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Oupt(X2,X3))
    | ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5585]) ).

fof(i_0_7502,plain,
    ! [X28723,X28724,X28725,X28726] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28726,X28726)),hAPP(hAPP(c_Product__Type_OPair(X28726,X28726),X28725),X28723)),c_Transitive__Closure_Ortrancl(X28726,X28724)))
        | X28725 = X28723
        | hBOOL(hAPP(hAPP(c_member(X28726),X28725),hAPP(c_Relation_ODomain(X28726,X28726),X28724))) )
      & ( X28725 != X28723
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X28726,X28726)),hAPP(hAPP(c_Product__Type_OPair(X28726,X28726),X28725),X28723)),c_Transitive__Closure_Ortrancl(X28726,X28724)))
        | hBOOL(hAPP(hAPP(c_member(X28726),X28725),hAPP(c_Relation_ODomain(X28726,X28726),X28724))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5586])])]) ).

cnf(i_0_7503,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_5587]) ).

fof(i_0_7504,plain,
    ! [X21733,X21734,X21735,X21736,X21737,X21738,X21739] :
      ( ~ c_Big__Operators_Ocomm__monoid__big(X21739,X21738,X21737,X21736,X21735)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X21738),X21734))
      | hAPP(hAPP(X21735,X21733),X21734) = X21736 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5588])]) ).

fof(i_0_7505,plain,
    ! [X21453,X21454,X21455] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21455,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21455,tc_HOL_Obool)),X21454)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21455,tc_HOL_Obool)),X21453)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21455,tc_HOL_Obool)),X21453),X21454)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21455,tc_HOL_Obool)),X21453),X21454))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21455,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21455,tc_HOL_Obool)),X21454)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21455,tc_HOL_Obool)),X21453))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__subset__Compl__iff])]) ).

fof(i_0_7506,plain,
    ! [X26514,X26515,X26516,X26517,X26518] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26518),X26517),X26516))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26515,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26518,tc_fun(X26515,tc_HOL_Obool)),X26516),X26514)),hAPP(X26514,X26517))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__lower])]) ).

fof(i_0_7507,plain,
    ! [X28643,X28644,X28645] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28645,X28645),tc_HOL_Obool)),X28644),X28643))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28645,X28645),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28645,X28644)),c_Transitive__Closure_Ortrancl(X28645,X28643))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rtrancl__mono])]) ).

fof(i_0_7508,plain,
    ! [X26779,X26780,X26781,X26782,X26783,X26784] : hAPP(c_Set_Ovimage(X26784,X26783,X26782),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26781,tc_fun(X26783,tc_HOL_Obool)),X26780),X26779)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26781,tc_fun(X26784,tc_HOL_Obool)),X26780),hAPP(hAPP(c_COMBB(tc_fun(X26783,tc_HOL_Obool),tc_fun(X26784,tc_HOL_Obool),X26781),c_Set_Ovimage(X26784,X26783,X26782)),X26779)),
    inference(variable_rename,[status(thm)],[fact_vimage__INT]) ).

fof(i_0_7509,plain,
    ! [X26835,X26836,X26837,X26838,X26839,X26840] : hAPP(c_Set_Ovimage(X26840,X26839,X26838),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26837,tc_fun(X26839,tc_HOL_Obool)),X26836),X26835)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26837,tc_fun(X26840,tc_HOL_Obool)),X26836),hAPP(hAPP(c_COMBB(tc_fun(X26839,tc_HOL_Obool),tc_fun(X26840,tc_HOL_Obool),X26837),c_Set_Ovimage(X26840,X26839,X26838)),X26835)),
    inference(variable_rename,[status(thm)],[fact_vimage__UN]) ).

fof(i_0_7510,plain,
    ! [X24046,X24047,X24048,X24049,X24050,X24051] : hAPP(c_Relation_OImage(X24051,X24050,X24049),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24048,tc_fun(X24051,tc_HOL_Obool)),X24047),X24046)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X24048,tc_fun(X24050,tc_HOL_Obool)),X24047),hAPP(hAPP(c_COMBB(tc_fun(X24051,tc_HOL_Obool),tc_fun(X24050,tc_HOL_Obool),X24048),c_Relation_OImage(X24051,X24050,X24049)),X24046)),
    inference(variable_rename,[status(thm)],[fact_Image__UN]) ).

fof(i_0_7511,plain,
    ! [X23811,X23812,X23813,X23814,X23815,X23816] : hAPP(c_Set_Oimage(X23816,X23815,X23814),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23813,tc_fun(X23816,tc_HOL_Obool)),X23812),X23811)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23813,tc_fun(X23815,tc_HOL_Obool)),X23812),hAPP(hAPP(c_COMBB(tc_fun(X23816,tc_HOL_Obool),tc_fun(X23815,tc_HOL_Obool),X23813),c_Set_Oimage(X23816,X23815,X23814)),X23811)),
    inference(variable_rename,[status(thm)],[fact_image__UN]) ).

fof(i_0_7512,plain,
    ! [X22931,X22932,X22933,X22934,X22935] :
      ( ~ class_Fields_Ofield(X22935)
      | X22934 = c_Groups_Ozero__class_Ozero(X22935)
      | X22933 = c_Groups_Ozero__class_Ozero(X22935)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22935),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22935),X22932),X22934)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22935),X22931),X22933)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22935),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22935),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22935),X22932),X22933)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22935),X22931),X22934))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22935),X22934),X22933)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__eq])]) ).

fof(i_0_7513,plain,
    ! [X22936,X22937,X22938,X22939,X22940] :
      ( ~ class_Fields_Ofield(X22940)
      | X22939 = c_Groups_Ozero__class_Ozero(X22940)
      | X22938 = c_Groups_Ozero__class_Ozero(X22940)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22940),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22940),X22937),X22939)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22940),X22936),X22938)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22940),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22940),X22937),X22938)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22940),X22936),X22939))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22940),X22939),X22938)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__frac__eq])]) ).

fof(i_0_7514,plain,
    ! [X27658,X27659] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27659,tc_HOL_Obool)),X27658) = hAPP(c_Set_OCollect(X27659),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27659),c_fNot),hAPP(hAPP(c_COMBC(X27659,tc_fun(X27659,tc_HOL_Obool),tc_HOL_Obool),c_member(X27659)),X27658))),
    inference(variable_rename,[status(thm)],[fact_Compl__eq]) ).

cnf(i_0_7515,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_5589]) ).

fof(i_0_7516,plain,
    ! [X31139,X31140,X31141,X31142,X31143] :
      ( ~ c_List_Olist__all2(X31143,X31142,X31141,X31140,X31139)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31143)),X31140) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31142)),X31139) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__lengthD])]) ).

fof(i_0_7517,plain,
    ! [X18716,X18717,X18718] :
      ( ( ~ 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,X18718)),X18717)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18718)),X18716)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18717),X18716)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18717),X18716))
        | 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,X18718)),X18717)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18718)),X18716))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__less__cancel1])]) ).

fof(i_0_7518,plain,
    ! [X18724,X18725,X18726] :
      ( ( ~ 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,X18726)),X18725)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18726)),X18724)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18725),X18724)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18725),X18724))
        | 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,X18726)),X18725)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18726)),X18724))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1])]) ).

fof(i_0_7519,plain,
    ! [X21048,X21049,X21050,X21051,X21052] :
      ( ( ~ hBOOL(hAPP(hAPP(X21049,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21048),X21050)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21048,X21050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21052),X21050))
        | X21048 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21050),X21051)),X21052)
        | hBOOL(hAPP(hAPP(X21049,X21051),X21052))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21050)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk70_3(X21048,X21049,X21050)))
        | hBOOL(hAPP(hAPP(X21049,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21048),X21050)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21048,X21050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21050)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk70_3(X21048,X21049,X21050)),X21050))
        | hBOOL(hAPP(hAPP(X21049,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21048),X21050)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21048,X21050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21050)) )
      & ( X21048 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21050),esk69_3(X21048,X21049,X21050))),esk70_3(X21048,X21049,X21050))
        | hBOOL(hAPP(hAPP(X21049,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21048),X21050)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21048,X21050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21050)) )
      & ( ~ hBOOL(hAPP(hAPP(X21049,esk69_3(X21048,X21049,X21050)),esk70_3(X21048,X21049,X21050)))
        | hBOOL(hAPP(hAPP(X21049,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21048),X21050)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21048,X21050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21050)) ) ),
    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_7520,plain,
    ! [X30582,X30583,X30584,X30585,X30586] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30585),X30583),hAPP(c_List_Oset(X30585),X30582)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30585),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30585,X30586,X30584),X30583),X30582)))
        | ~ class_Orderings_Olinorder(X30586) )
      & ( hBOOL(hAPP(c_List_Odistinct(X30585),X30582))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30585),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30585,X30586,X30584),X30583),X30582)))
        | ~ class_Orderings_Olinorder(X30586) )
      & ( hBOOL(hAPP(hAPP(c_member(X30585),X30583),hAPP(c_List_Oset(X30585),X30582)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30585),X30582))
        | hBOOL(hAPP(c_List_Odistinct(X30585),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30585,X30586,X30584),X30583),X30582)))
        | ~ class_Orderings_Olinorder(X30586) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5590])])]) ).

fof(i_0_7521,plain,
    ! [X33096,X33097,X33098,X33099,X33100] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33100,tc_HOL_Obool)),X33099),hAPP(c_Set_Oimage(X33098,X33100,X33097),X33096)))
      | c_Fun_Oinj__on(X33100,X33098,c_Hilbert__Choice_Oinv__into(X33098,X33100,X33096,X33097),X33099) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__inv__into])]) ).

fof(i_0_7522,plain,
    ! [X23661,X23662,X23663,X23664,X23665,X23666] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23666,tc_fun(X23665,tc_HOL_Obool)),X23664),hAPP(c_Fun_Ocomp(X23663,tc_fun(X23665,tc_HOL_Obool),X23666,X23662),X23661)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23663,tc_fun(X23665,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23666,X23663,X23661),X23664)),X23662),
    inference(variable_rename,[status(thm)],[fact_UN__o]) ).

fof(i_0_7523,plain,
    ! [X24611,X24612,X24613,X24614,X24615] :
      ( ~ class_Groups_Ocomm__monoid__add(X24615)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24614),X24613))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24614,X24615),X24612),hAPP(hAPP(c_Set_Oinsert(X24614),X24611),X24613)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24615),hAPP(X24612,X24611)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24614,X24615),X24612),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24614,tc_HOL_Obool)),X24613),hAPP(hAPP(c_Set_Oinsert(X24614),X24611),c_Orderings_Obot__class_Obot(tc_fun(X24614,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oinsert__remove])]) ).

fof(i_0_7524,plain,
    ! [X22008,X22009,X22010,X22011,X22012] :
      ( ~ class_Groups_Ocomm__monoid__mult(X22012)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22011),X22010))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22011,X22012),X22009),hAPP(hAPP(c_Set_Oinsert(X22011),X22008),X22010)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22012),hAPP(X22009,X22008)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22011,X22012),X22009),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22011,tc_HOL_Obool)),X22010),hAPP(hAPP(c_Set_Oinsert(X22011),X22008),c_Orderings_Obot__class_Obot(tc_fun(X22011,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oinsert__remove])]) ).

fof(i_0_7525,plain,
    ! [X33153,X33154,X33155,X33156,X33157] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33157),X33156),hAPP(c_Set_Oimage(X33155,X33157,X33154),X33153)))
      | hAPP(X33154,hAPP(c_Hilbert__Choice_Oinv__into(X33155,X33157,X33153,X33154),X33156)) = X33156 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_f__inv__into__f])]) ).

fof(i_0_7526,plain,
    ! [X21041,X21042,X21043,X21044,X21045] :
      ( ( ~ hBOOL(hAPP(hAPP(X21042,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21041),X21043)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21041,X21043)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21043),X21045))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21045),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X21041 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21043),X21044)),X21045)
        | hBOOL(hAPP(hAPP(X21042,X21044),X21045))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21043),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21043),esk68_3(X21041,X21042,X21043)))
        | hBOOL(hAPP(hAPP(X21042,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21041),X21043)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21041,X21043)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21043),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk68_3(X21041,X21042,X21043)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(X21042,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21041),X21043)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21041,X21043)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21043),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( X21041 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21043),esk67_3(X21041,X21042,X21043))),esk68_3(X21041,X21042,X21043))
        | hBOOL(hAPP(hAPP(X21042,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21041),X21043)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21041,X21043)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21043),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(X21042,esk67_3(X21041,X21042,X21043)),esk68_3(X21041,X21042,X21043)))
        | hBOOL(hAPP(hAPP(X21042,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21041),X21043)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21041,X21043)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21043),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_7527,plain,
    ! [X30684,X30685] : hAPP(hAPP(c_List_Ozip(X30685,X30685),X30684),X30684) = hAPP(hAPP(c_List_Omap(X30685,tc_prod(X30685,X30685)),hAPP(hAPP(c_COMBS(X30685,X30685,tc_prod(X30685,X30685)),c_Product__Type_OPair(X30685,X30685)),c_COMBI(X30685))),X30684),
    inference(variable_rename,[status(thm)],[fact_zip__same__conv__map]) ).

fof(i_0_7528,plain,
    ! [X25275,X25276] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X25276),X25275) = 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)),X25276)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X25275))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J]) ).

fof(i_0_7529,plain,
    ! [X23483,X23484] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X23484),X23483) = 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)),X23484)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X23483))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J]) ).

fof(i_0_7530,plain,
    ! [X33200,X33201,X33202] :
      ( ( hAPP(c_Set_Oimage(X33202,X33201,X33200),c_Orderings_Otop__class_Otop(tc_fun(X33202,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33201,tc_HOL_Obool))
        | hAPP(c_Fun_Ocomp(X33202,X33201,X33201,X33200),c_Hilbert__Choice_Oinv__into(X33202,X33201,c_Orderings_Otop__class_Otop(tc_fun(X33202,tc_HOL_Obool)),X33200)) = c_Fun_Oid(X33201) )
      & ( hAPP(c_Fun_Ocomp(X33202,X33201,X33201,X33200),c_Hilbert__Choice_Oinv__into(X33202,X33201,c_Orderings_Otop__class_Otop(tc_fun(X33202,tc_HOL_Obool)),X33200)) != c_Fun_Oid(X33201)
        | hAPP(c_Set_Oimage(X33202,X33201,X33200),c_Orderings_Otop__class_Otop(tc_fun(X33202,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33201,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__iff])]) ).

fof(i_0_7531,plain,
    ! [X20346,X20347,X20348] :
      ( ~ class_Rings_Olinordered__semidom(X20348)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20348),c_Groups_Ozero__class_Ozero(X20348)),X20347))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20348),X20347),c_Groups_Oone__class_Oone(X20348)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20348),X20347),hAPP(hAPP(c_Power_Opower__class_Opower(X20348),X20347),X20346))),hAPP(hAPP(c_Power_Opower__class_Opower(X20348),X20347),X20346))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less])]) ).

fof(i_0_7532,plain,
    ! [X26716,X26717,X26718,X26719,X26720,X26721,X26722] :
      ( ( hAPP(X26720,X26717) != hAPP(X26720,X26716)
        | X26717 = X26716
        | ~ c_Typedef_Otype__definition(X26722,X26721,X26720,X26719,X26718) )
      & ( X26717 != X26716
        | hAPP(X26720,X26717) = hAPP(X26720,X26716)
        | ~ c_Typedef_Otype__definition(X26722,X26721,X26720,X26719,X26718) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inject])])]) ).

fof(i_0_7533,plain,
    ! [X27282,X27283,X27284,X27285] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27285,X27284)),hAPP(hAPP(c_Product__Type_OSigma(X27285,X27284),X27283),hAPP(c_COMBK(tc_fun(X27284,tc_HOL_Obool),X27285),X27282))))
      | X27283 = c_Orderings_Obot__class_Obot(tc_fun(X27285,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27284),X27282)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD2])]) ).

fof(i_0_7534,plain,
    ! [X27278,X27279,X27280,X27281] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27281,X27280)),hAPP(hAPP(c_Product__Type_OSigma(X27281,X27280),X27279),hAPP(c_COMBK(tc_fun(X27280,tc_HOL_Obool),X27281),X27278))))
      | X27278 = c_Orderings_Obot__class_Obot(tc_fun(X27280,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27281),X27279)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__productD1])]) ).

fof(i_0_7535,plain,
    ! [X26723,X26724,X26725,X26726,X26727,X26728] :
      ( ~ c_Typedef_Otype__definition(X26728,X26727,X26726,X26725,X26724)
      | hAPP(X26725,hAPP(X26726,X26723)) = X26723 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_type__definition_ORep__inverse])]) ).

fof(i_0_7536,plain,
    ! [X33370,X33371,X33372,X33373,X33374] :
      ( ~ c_Fun_Obij__betw(X33374,X33373,X33372,X33371,X33370)
      | hAPP(c_Finite__Set_Ocard(X33374),X33371) = hAPP(c_Finite__Set_Ocard(X33373),X33370) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__same__card])]) ).

cnf(i_0_7537,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_5591]) ).

fof(i_0_7538,plain,
    ! [X25907,X25908,X25909] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25909)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25909),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25909),hAPP(c_Groups_Oabs__class_Oabs(X25909),X25908)),hAPP(c_Groups_Oabs__class_Oabs(X25909),X25907))),hAPP(c_Groups_Oabs__class_Oabs(X25909),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25909),X25908),X25907)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2])]) ).

fof(i_0_7539,plain,
    ! [X25910,X25911,X25912] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25912)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25912),hAPP(c_Groups_Oabs__class_Oabs(X25912),X25911)),hAPP(c_Groups_Oabs__class_Oabs(X25912),X25910))),hAPP(c_Groups_Oabs__class_Oabs(X25912),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25912),X25910),X25911)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq2__sym])]) ).

cnf(i_0_7540,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_5592]) ).

fof(i_0_7541,plain,
    ! [X26896,X26897,X26898,X26899,X26900] : hAPP(c_Set_Ovimage(X26900,X26899,X26898),hAPP(hAPP(c_Set_Oinsert(X26899),X26897),X26896)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26900,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26900,X26899,X26898),hAPP(hAPP(c_Set_Oinsert(X26899),X26897),c_Orderings_Obot__class_Obot(tc_fun(X26899,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(X26900,X26899,X26898),X26896)),
    inference(variable_rename,[status(thm)],[fact_vimage__insert]) ).

fof(i_0_7542,plain,
    ! [X19187,X19188,X19189,X19190,X19191] :
      ( ( c_Fun_Ofun__upd(X19191,X19190,X19189,X19188,X19187) != X19189
        | hAPP(X19189,X19188) = X19187 )
      & ( hAPP(X19189,X19188) != X19187
        | c_Fun_Ofun__upd(X19191,X19190,X19189,X19188,X19187) = X19189 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem__iff])]) ).

fof(i_0_7543,plain,
    ! [X31144,X31145,X31146,X31147] :
      ( ( ~ c_List_Olist__all2(X31147,X31146,X31145,c_List_Olist_ONil(X31147),X31144)
        | X31144 = c_List_Olist_ONil(X31146) )
      & ( X31144 != c_List_Olist_ONil(X31146)
        | c_List_Olist__all2(X31147,X31146,X31145,c_List_Olist_ONil(X31147),X31144) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil])]) ).

fof(i_0_7544,plain,
    ! [X31148,X31149,X31150,X31151] :
      ( ( ~ c_List_Olist__all2(X31151,X31150,X31149,X31148,c_List_Olist_ONil(X31150))
        | X31148 = c_List_Olist_ONil(X31151) )
      & ( X31148 != c_List_Olist_ONil(X31151)
        | c_List_Olist__all2(X31151,X31150,X31149,X31148,c_List_Olist_ONil(X31150)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__Nil2])]) ).

fof(i_0_7545,plain,
    ! [X33348,X33349,X33350] :
      ( ( ~ c_Fun_Obij__betw(X33350,X33350,c_Fun_Oid(X33350),X33349,X33348)
        | X33349 = X33348 )
      & ( X33349 != X33348
        | c_Fun_Obij__betw(X33350,X33350,c_Fun_Oid(X33350),X33349,X33348) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bij__betw__id__iff])]) ).

fof(i_0_7546,plain,
    ! [X28070,X28071,X28072,X28073,X28074] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28074,X28073)),hAPP(hAPP(c_Product__Type_OPair(X28074,X28073),X28072),X28071)),X28070))
      | hBOOL(hAPP(hAPP(c_member(X28074),X28072),hAPP(c_Relation_ODomain(X28074,X28073),X28070))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainI])]) ).

fof(i_0_7547,plain,
    ! [X27875,X27876,X27877,X27878,X27879] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27879,X27878)),hAPP(hAPP(c_Product__Type_OPair(X27879,X27878),X27877),X27876)),X27875))
      | hBOOL(hAPP(hAPP(c_member(X27878),X27876),hAPP(c_Relation_ORange(X27879,X27878),X27875))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeI])]) ).

fof(i_0_7548,plain,
    ! [X30291,X30292,X30293,X30294] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30294),X30293))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30292,tc_HOL_Obool)),hAPP(c_List_Oset(X30292),hAPP(hAPP(c_List_Odrop(X30292),X30293),X30291))),hAPP(c_List_Oset(X30292),hAPP(hAPP(c_List_Odrop(X30292),X30294),X30291)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__drop__subset__set__drop])]) ).

fof(i_0_7549,plain,
    ! [X29466,X29467,X29468,X29469] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29469),X29468))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29467,tc_HOL_Obool)),hAPP(c_List_Oset(X29467),hAPP(hAPP(c_List_Otake(X29467),X29469),X29466))),hAPP(c_List_Oset(X29467),hAPP(hAPP(c_List_Otake(X29467),X29468),X29466)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__take__subset__set__take])]) ).

fof(i_0_7550,plain,
    ! [X31136,X31137,X31138] :
      ( ( X31138 != X31137
        | c_List_Olist__all2(X31136,X31136,c_fequal,X31138,X31137) )
      & ( ~ c_List_Olist__all2(X31136,X31136,c_fequal,X31138,X31137)
        | X31138 = X31137 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all2__eq])]) ).

fof(i_0_7551,plain,
    ! [X30530,X30531,X30532] :
      ( ~ class_Orderings_Olinorder(X30532)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X30532),X30531))
      | c_List_Olinorder__class_Osorted__list__of__set(X30532,hAPP(hAPP(c_Set_Oinsert(X30532),X30530),X30531)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30532,X30532,c_COMBI(X30532)),X30530),c_List_Olinorder__class_Osorted__list__of__set(X30532,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X30532,tc_HOL_Obool)),X30531),hAPP(hAPP(c_Set_Oinsert(X30532),X30530),c_Orderings_Obot__class_Obot(tc_fun(X30532,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__insert])]) ).

fof(i_0_7552,plain,
    ! [X20315,X20316,X20317,X20318] :
      ( ~ class_Rings_Olinordered__semidom(X20318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20318),hAPP(hAPP(c_Power_Opower__class_Opower(X20318),X20317),hAPP(c_Nat_OSuc,X20316))),hAPP(hAPP(c_Power_Opower__class_Opower(X20318),X20315),hAPP(c_Nat_OSuc,X20316))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20318),c_Groups_Ozero__class_Ozero(X20318)),X20315))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20318),X20317),X20315)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__base])]) ).

cnf(i_0_7553,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_5593]) ).

fof(i_0_7554,plain,
    ! [X23434,X23435,X23436,X23437] :
      ( ~ class_Lattices_Osemilattice__sup(X23437)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23437),X23436))
      | ~ hBOOL(hAPP(hAPP(c_member(X23437),X23435),X23436))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23437),X23435),X23434)),hAPP(hAPP(c_Finite__Set_Ofold(X23437,X23437,c_Lattices_Osemilattice__sup__class_Osup(X23437)),X23434),X23436))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__le__fold__sup])]) ).

fof(i_0_7555,plain,
    ! [X22725,X22726,X22727,X22728] :
      ( ~ class_Orderings_Olinorder(X22728)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22728),X22727))
      | ~ hBOOL(hAPP(hAPP(c_member(X22728),X22726),X22727))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22728),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22728),X22726),X22725)),hAPP(hAPP(c_Finite__Set_Ofold(X22728,X22728,c_Orderings_Oord__class_Omax(X22728)),X22725),X22727))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__le__fold__sup])]) ).

fof(i_0_7556,plain,
    ! [X28134,X28135,X28136,X28137] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28137,X28136),tc_HOL_Obool)),X28135),X28134))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28137,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X28137,X28136),X28135)),hAPP(c_Relation_ODomain(X28137,X28136),X28134))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__mono])]) ).

fof(i_0_7557,plain,
    ! [X33117,X33118,X33119] :
      ( ~ c_Fun_Oinj__on(X33119,X33118,X33117,c_Orderings_Otop__class_Otop(tc_fun(X33119,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X33118,X33119,c_Hilbert__Choice_Oinv__into(X33119,X33118,c_Orderings_Otop__class_Otop(tc_fun(X33119,tc_HOL_Obool)),X33117)),c_Orderings_Otop__class_Otop(tc_fun(X33118,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X33119,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__imp__surj__inv])]) ).

cnf(i_0_7558,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_5594]) ).

fof(i_0_7559,plain,
    ! [X22952,X22953,X22954] :
      ( ~ class_Fields_Olinordered__field(X22954)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22954),X22953),X22952))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22954),X22953),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22954),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22954),X22953),X22952)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22954),c_Groups_Oone__class_Oone(X22954)),c_Groups_Oone__class_Oone(X22954))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__half__sum])]) ).

fof(i_0_7560,plain,
    ! [X25305,X25306] :
      ( ~ c_Nat__Transfer_Onat__set(X25306)
      | ~ c_Nat__Transfer_Onat__set(X25305)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25306),X25305) = 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),X25306)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X25305))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J])]) ).

fof(i_0_7561,plain,
    ! [X23487,X23488] :
      ( ~ c_Nat__Transfer_Onat__set(X23488)
      | ~ c_Nat__Transfer_Onat__set(X23487)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23488),X23487) = 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),X23488)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X23487))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J])]) ).

fof(i_0_7562,plain,
    ! [X24164,X24165,X24166,X24167,X24168] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24165),X24167))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24167),X24166))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24168,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24167,X24166)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24165,X24164)))
        | ~ class_Orderings_Oorder(X24168) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24166),X24164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24167),X24166))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24168,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24167,X24166)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24165,X24164)))
        | ~ class_Orderings_Oorder(X24168) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24168),X24165),X24167))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24168),X24166),X24164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24167),X24166))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24168,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24167,X24166)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24165,X24164)))
        | ~ class_Orderings_Oorder(X24168) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24165),X24164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24168,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24167,X24166)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24165,X24164)))
        | ~ class_Orderings_Oorder(X24168) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24167),X24166))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24165),X24164))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24168,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24167,X24166)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24165,X24164)))
        | ~ class_Orderings_Oorder(X24168) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24168),X24165),X24167))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24165),X24167))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24166),X24164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24165),X24164))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24168,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24167,X24166)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24165,X24164)))
        | ~ class_Orderings_Oorder(X24168) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24168),X24166),X24164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24165),X24167))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24166),X24164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24168),X24165),X24164))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24168,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24167,X24166)),c_SetInterval_Oord__class_OatLeastAtMost(X24168,X24165,X24164)))
        | ~ class_Orderings_Oorder(X24168) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5595])])]) ).

fof(i_0_7563,plain,
    ! [X18421,X18422,X18423,X18424,X18425] :
      ( ~ class_Rings_Osemiring(X18425)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18425),X18424),X18423)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18425),X18422),X18423)),X18421)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18425),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18425),X18424),X18422)),X18423)),X18421) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_combine__common__factor])]) ).

fof(i_0_7564,plain,
    ! [X27234,X27235] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27235,X27235),tc_HOL_Obool)),c_Relation_OId__on(X27235,X27234)),hAPP(hAPP(c_Product__Type_OSigma(X27235,X27235),X27234),hAPP(c_COMBK(tc_fun(X27235,tc_HOL_Obool),X27235),X27234)))),
    inference(variable_rename,[status(thm)],[fact_Id__on__subset__Times]) ).

fof(i_0_7565,plain,
    ! [X31367,X31368] :
      ( ~ class_Orderings_Olinorder(X31368)
      | c_List_Olinorder__class_Osort__key(X31368,X31368,c_COMBI(X31368),X31367) = hAPP(c_List_Ofoldl(tc_List_Olist(X31368),X31368,hAPP(c_COMBC(X31368,tc_List_Olist(X31368),tc_List_Olist(X31368)),c_List_Olinorder__class_Oinsort__key(X31368,X31368,c_COMBI(X31368))),c_List_Olist_ONil(X31368)),X31367) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__foldl__insort])]) ).

fof(i_0_7566,plain,
    ! [X27864,X27865,X27866] : hAPP(c_Relation_ORange(X27866,X27865),hAPP(c_Set_OCollect(tc_prod(X27866,X27865)),hAPP(c_Product__Type_Oprod_Oprod__case(X27866,X27865,tc_HOL_Obool),X27864))) = hAPP(c_Set_OCollect(X27865),hAPP(hAPP(c_COMBB(tc_fun(X27866,tc_HOL_Obool),tc_HOL_Obool,X27865),c_HOL_OEx(X27866)),hAPP(c_COMBC(X27866,X27865,tc_HOL_Obool),X27864))),
    inference(variable_rename,[status(thm)],[fact_Range__Collect__split]) ).

fof(i_0_7567,plain,
    ! [X33388,X33389,X33390,X33391] :
      ( ~ c_Fun_Oinj__on(X33391,X33390,X33389,X33388)
      | c_Fun_Obij__betw(X33391,X33390,X33389,X33388,hAPP(c_Set_Oimage(X33391,X33390,X33389),X33388)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__imp__bij__betw])]) ).

fof(i_0_7568,plain,
    ! [X27216,X27217,X27218] :
      ( ~ c_Equiv__Relations_Oequiv(X27218,X27217,X27216)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X27218,X27218),tc_HOL_Obool)),X27216),hAPP(hAPP(c_Product__Type_OSigma(X27218,X27218),X27217),hAPP(c_COMBK(tc_fun(X27218,tc_HOL_Obool),X27218),X27217)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__type])]) ).

fof(i_0_7569,plain,
    ! [X30834,X30835,X30836,X30837,X30838] : hAPP(c_Fun_Ocomp(tc_List_Olist(X30838),tc_List_Olist(X30837),tc_List_Olist(X30836),hAPP(c_List_Omap(X30838,X30837),X30835)),hAPP(c_List_Omap(X30836,X30838),X30834)) = hAPP(c_List_Omap(X30836,X30837),hAPP(c_Fun_Ocomp(X30838,X30837,X30836,X30835),X30834)),
    inference(variable_rename,[status(thm)],[fact_map__comp__map]) ).

fof(i_0_7570,plain,
    ! [X30829,X30830,X30831,X30832,X30833] : hAPP(c_Fun_Ocomp(tc_List_Olist(X30833),tc_List_Olist(X30832),tc_List_Olist(X30831),hAPP(c_List_Omap(X30833,X30832),X30830)),hAPP(c_List_Omap(X30831,X30833),X30829)) = hAPP(c_List_Omap(X30831,X30832),hAPP(c_Fun_Ocomp(X30833,X30832,X30831,X30830),X30829)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Ocomp]) ).

fof(i_0_7571,plain,
    ! [X27515,X27516,X27517,X27518,X27519] :
      ( ~ c_Relation_Orefl__on(X27519,X27518,X27517)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27519,X27519)),hAPP(hAPP(c_Product__Type_OPair(X27519,X27519),X27516),X27515)),X27517))
      | hBOOL(hAPP(hAPP(c_member(X27519),X27516),X27518)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD1])]) ).

fof(i_0_7572,plain,
    ! [X27520,X27521,X27522,X27523,X27524] :
      ( ~ c_Relation_Orefl__on(X27524,X27523,X27522)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X27524,X27524)),hAPP(hAPP(c_Product__Type_OPair(X27524,X27524),X27521),X27520)),X27522))
      | hBOOL(hAPP(hAPP(c_member(X27524),X27520),X27523)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD2])]) ).

cnf(i_0_7573,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_5596]) ).

fof(i_0_7574,plain,
    ! [X29925,X29926] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29926),tc_List_Olist(X29926))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29926),tc_List_Olist(X29926)),c_List_Olist_ONil(X29926)),c_List_Olist_ONil(X29926))),c_List_Olistrel(X29926,X29925))),
    inference(variable_rename,[status(thm)],[fact_listrel_ONil]) ).

fof(i_0_7575,plain,
    ! [X27002,X27003,X27004] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27004,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27004,tc_HOL_Obool),X27003)),X27002) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X27004,tc_HOL_Obool),tc_fun(X27004,tc_HOL_Obool)),X27003),hAPP(hAPP(c_COMBC(tc_fun(X27004,tc_HOL_Obool),tc_fun(X27004,tc_HOL_Obool),tc_fun(X27004,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27004,tc_HOL_Obool))),X27002)),
    inference(variable_rename,[status(thm)],[fact_Int__Union2]) ).

fof(i_0_7576,plain,
    ! [X24379,X24380,X24381,X24382] :
      ( ( X24381 = X24380
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24382,X24382)),hAPP(hAPP(c_Product__Type_OPair(X24382,X24382),X24381),X24380)),c_Relation_OId__on(X24382,X24379))) )
      & ( hBOOL(hAPP(hAPP(c_member(X24382),X24381),X24379))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24382,X24382)),hAPP(hAPP(c_Product__Type_OPair(X24382,X24382),X24381),X24380)),c_Relation_OId__on(X24382,X24379))) )
      & ( X24381 != X24380
        | ~ hBOOL(hAPP(hAPP(c_member(X24382),X24381),X24379))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(X24382,X24382)),hAPP(hAPP(c_Product__Type_OPair(X24382,X24382),X24381),X24380)),c_Relation_OId__on(X24382,X24379))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__iff])])]) ).

fof(i_0_7577,plain,
    ! [X18659,X18660,X18661,X18662] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X18662),X18660))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X18662,X18661)),c_Sum__Type_OPlus(X18662,X18661,X18660,X18659))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X18661),X18659))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X18662,X18661)),c_Sum__Type_OPlus(X18662,X18661,X18660,X18659))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18662),X18660))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18661),X18659))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X18662,X18661)),c_Sum__Type_OPlus(X18662,X18661,X18660,X18659))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus__iff])])]) ).

fof(i_0_7578,plain,
    ! [X18667,X18668,X18669,X18670] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X18670,X18669)),c_Sum__Type_OPlus(X18670,X18669,X18668,X18667)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X18670),X18668)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I1_J])]) ).

fof(i_0_7579,plain,
    ! [X18671,X18672,X18673,X18674] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X18674,X18673)),c_Sum__Type_OPlus(X18674,X18673,X18672,X18671)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X18673),X18671)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__PlusD_I2_J])]) ).

fof(i_0_7580,plain,
    ! [X27130,X27131,X27132,X27133,X27134,X27135] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27135),X27134),X27133))
      | ~ hBOOL(hAPP(hAPP(c_member(X27132),X27131),hAPP(X27130,X27134)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27135,X27132)),hAPP(hAPP(c_Product__Type_OPair(X27135,X27132),X27134),X27131)),hAPP(hAPP(c_Product__Type_OSigma(X27135,X27132),X27133),X27130))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SigmaI])]) ).

fof(i_0_7581,plain,
    ! [X27104,X27105,X27106] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27106,tc_HOL_Obool)),esk250_3(X27104,X27105,X27106)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X27106,tc_HOL_Obool)),X27105),X27104)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27106,tc_HOL_Obool)),X27105),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27106,tc_HOL_Obool),X27104)) = c_Orderings_Obot__class_Obot(tc_fun(X27106,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X27106,tc_HOL_Obool)),X27105),X27104)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27106,tc_HOL_Obool)),esk251_3(X27104,X27105,X27106)),hAPP(hAPP(c_Set_Oinsert(tc_fun(X27106,tc_HOL_Obool)),X27105),X27104)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27106,tc_HOL_Obool)),X27105),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27106,tc_HOL_Obool),X27104)) = c_Orderings_Obot__class_Obot(tc_fun(X27106,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X27106,tc_HOL_Obool)),X27105),X27104)) )
      & ( esk250_3(X27104,X27105,X27106) != esk251_3(X27104,X27105,X27106)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27106,tc_HOL_Obool)),X27105),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27106,tc_HOL_Obool),X27104)) = c_Orderings_Obot__class_Obot(tc_fun(X27106,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X27106,tc_HOL_Obool)),X27105),X27104)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27106,tc_HOL_Obool)),esk250_3(X27104,X27105,X27106)),esk251_3(X27104,X27105,X27106)) != c_Orderings_Obot__class_Obot(tc_fun(X27106,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27106,tc_HOL_Obool)),X27105),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27106,tc_HOL_Obool),X27104)) = c_Orderings_Obot__class_Obot(tc_fun(X27106,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X27106,tc_HOL_Obool)),X27105),X27104)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5597])])])]) ).

fof(i_0_7582,plain,
    ! [X30470,X30471,X30472,X30473] :
      ( ~ class_Groups_Osemigroup__add(X30473)
      | hAPP(c_List_Ofoldl(X30473,X30473,c_Groups_Oplus__class_Oplus(X30473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30473),X30472),X30471)),X30470) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30473),X30472),hAPP(c_List_Ofoldl(X30473,X30473,c_Groups_Oplus__class_Oplus(X30473),X30471),X30470)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__assoc])]) ).

fof(i_0_7583,plain,
    ! [X28986,X28987,X28988] : hBOOL(hAPP(hAPP(c_member(tc_prod(X28988,X28988)),hAPP(hAPP(c_Product__Type_OPair(X28988,X28988),X28987),X28987)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28988,X28988),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X28986))),
    inference(variable_rename,[status(thm)],[fact_rel__pow__0__I]) ).

cnf(i_0_7584,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_5598]) ).

fof(i_0_7585,plain,
    ! [X30175,X30176,X30177,X30178,X30179] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30179),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30178)),X30177)))
        | hAPP(hAPP(c_List_Olist__update(X30178,hAPP(hAPP(c_List_Oappend(X30178),X30177),X30176)),X30179),X30175) = hAPP(hAPP(c_List_Oappend(X30178),hAPP(hAPP(c_List_Olist__update(X30178,X30177),X30179),X30175)),X30176) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30179),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30178)),X30177)))
        | hAPP(hAPP(c_List_Olist__update(X30178,hAPP(hAPP(c_List_Oappend(X30178),X30177),X30176)),X30179),X30175) = hAPP(hAPP(c_List_Oappend(X30178),X30177),hAPP(hAPP(c_List_Olist__update(X30178,X30176),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30179),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30178)),X30177))),X30175)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5599])]) ).

fof(i_0_7586,plain,
    ! [X25445,X25446,X25447,X25448,X25449] :
      ( ~ c_Equiv__Relations_Oequiv(X25449,X25448,X25447)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25449,tc_HOL_Obool)),X25446),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25449),X25448),X25447)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X25449,tc_HOL_Obool)),X25445),hAPP(hAPP(c_Equiv__Relations_Oquotient(X25449),X25448),X25447)))
      | X25446 = X25445
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25449,tc_HOL_Obool)),X25446),X25445) = c_Orderings_Obot__class_Obot(tc_fun(X25449,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__disj])]) ).

fof(i_0_7587,plain,
    ! [X30916,X30917,X30918] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30918),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30917)),X30916)))
      | hAPP(c_Random_Opick(X30917,hAPP(hAPP(c_List_Omap(X30917,tc_prod(tc_Code__Numeral_Ocode__numeral,X30917)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X30917),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X30916)),hAPP(c_Code__Numeral_Oof__nat,X30918)) = hAPP(hAPP(c_List_Onth(X30917),X30916),X30918) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pick__same])]) ).

fof(i_0_7588,plain,
    ! [X22911,X22912,X22913,X22914] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)),X22912))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),c_Groups_Ozero__class_Ozero(X22914)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),c_Groups_Ozero__class_Ozero(X22914)),X22911))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)),X22912))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)),X22912))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),c_Groups_Ozero__class_Ozero(X22914)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)),X22912))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22911),c_Groups_Ozero__class_Ozero(X22914)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)),X22912))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),c_Groups_Ozero__class_Ozero(X22914)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22914),X22913),X22911)),X22912))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22914),X22913),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22914),X22912),X22911)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22914) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5600])])]) ).

fof(i_0_7589,plain,
    ! [X22955,X22956,X22957,X22958] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)),X22956))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),c_Groups_Ozero__class_Ozero(X22958)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),c_Groups_Ozero__class_Ozero(X22958)),X22955))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)),X22956))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)),X22956))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),c_Groups_Ozero__class_Ozero(X22958)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)),X22956))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22958),X22955),c_Groups_Ozero__class_Ozero(X22958)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)),X22956))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),c_Groups_Ozero__class_Ozero(X22958)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22958),X22957),X22955)),X22956))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22958),X22957),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22958),X22956),X22955)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22958) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5601])])]) ).

fof(i_0_7590,plain,
    ! [X24176,X24177] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),X24177),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24176),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X24177)))))
      | X24177 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24176),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24176),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X24177))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__card__intvl__is__intvl])]) ).

fof(i_0_7591,plain,
    ! [X19129,X19130,X19131,X19132,X19133] :
      ( ( hBOOL(hAPP(hAPP(X19131,X19130),X19132))
        | ~ hBOOL(hAPP(hAPP(c_member(X19133),X19132),c_SetInterval_Oord_OgreaterThanLessThan(X19133,X19131,X19130,X19129))) )
      & ( hBOOL(hAPP(hAPP(X19131,X19132),X19129))
        | ~ hBOOL(hAPP(hAPP(c_member(X19133),X19132),c_SetInterval_Oord_OgreaterThanLessThan(X19133,X19131,X19130,X19129))) )
      & ( ~ hBOOL(hAPP(hAPP(X19131,X19130),X19132))
        | ~ hBOOL(hAPP(hAPP(X19131,X19132),X19129))
        | hBOOL(hAPP(hAPP(c_member(X19133),X19132),c_SetInterval_Oord_OgreaterThanLessThan(X19133,X19131,X19130,X19129))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThanLessThan__iff])])]) ).

fof(i_0_7592,plain,
    ! [X19124,X19125,X19126,X19127,X19128] :
      ( ( hBOOL(hAPP(hAPP(X19126,X19125),X19127))
        | ~ hBOOL(hAPP(hAPP(c_member(X19128),X19127),c_SetInterval_Oord_OatLeastAtMost(X19128,X19126,X19125,X19124))) )
      & ( hBOOL(hAPP(hAPP(X19126,X19127),X19124))
        | ~ hBOOL(hAPP(hAPP(c_member(X19128),X19127),c_SetInterval_Oord_OatLeastAtMost(X19128,X19126,X19125,X19124))) )
      & ( ~ hBOOL(hAPP(hAPP(X19126,X19125),X19127))
        | ~ hBOOL(hAPP(hAPP(X19126,X19127),X19124))
        | hBOOL(hAPP(hAPP(c_member(X19128),X19127),c_SetInterval_Oord_OatLeastAtMost(X19128,X19126,X19125,X19124))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeastAtMost__iff])])]) ).

cnf(i_0_7593,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_5602]) ).

cnf(i_0_7594,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(X1,X2,X3,X4,X5) = c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4),hAPP(c_Lazy__Sequence_Oyield(X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_5603]) ).

fof(i_0_7595,plain,
    ! [X29954,X29955] : c_List_Oset__Cons(X29955,X29954,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29955)),c_List_Olist_ONil(X29955)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29955),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(X29955,tc_List_Olist(X29955),hAPP(hAPP(c_COMBC(X29955,tc_List_Olist(X29955),tc_List_Olist(X29955)),c_List_Olist_OCons(X29955)),c_List_Olist_ONil(X29955))),X29954),
    inference(variable_rename,[status(thm)],[fact_set__Cons__sing__Nil]) ).

fof(i_0_7596,plain,
    ! [X26508,X26509,X26510,X26511,X26512,X26513] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26513),X26512),X26511))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26513,tc_fun(X26510,tc_HOL_Obool)),X26511),hAPP(hAPP(c_COMBB(tc_fun(X26510,tc_HOL_Obool),tc_fun(X26510,tc_HOL_Obool),X26513),hAPP(c_Set_Oinsert(X26510),X26509)),X26508)) = hAPP(hAPP(c_Set_Oinsert(X26510),X26509),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26513,tc_fun(X26510,tc_HOL_Obool)),X26511),X26508)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__insert__distrib])]) ).

fof(i_0_7597,plain,
    ! [X23855,X23856,X23857,X23858,X23859,X23860] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23860),X23859),X23858))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23860,tc_fun(X23857,tc_HOL_Obool)),X23858),hAPP(hAPP(c_COMBB(tc_fun(X23857,tc_HOL_Obool),tc_fun(X23857,tc_HOL_Obool),X23860),hAPP(c_Set_Oinsert(X23857),X23856)),X23855)) = hAPP(hAPP(c_Set_Oinsert(X23857),X23856),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23860,tc_fun(X23857,tc_HOL_Obool)),X23858),X23855)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__insert__distrib])]) ).

fof(i_0_7598,plain,
    ! [X27851,X27852,X27855,X27856,X27857,X27858] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27852),X27851))
        | X27851 = hAPP(c_Set_Oimage(tc_Nat_Onat,X27852,esk284_2(X27851,X27852)),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)),esk283_2(X27851,X27852)))) )
      & ( X27855 != hAPP(c_Set_Oimage(tc_Nat_Onat,X27856,X27858),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)),X27857)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27856),X27855)) ) ),
    inference(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_7599,plain,
    ! [X27682,X27683,X27684,X27685] :
      ( X27685 != hAPP(c_Set_Oimage(tc_Nat_Onat,X27684,X27683),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)),X27682)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27684),X27685)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__seg__image__imp__finite])]) ).

fof(i_0_7600,plain,
    ! [X30356,X30357,X30358] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30358),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30357)),X30356)))
      | hAPP(hAPP(c_List_Oappend(X30357),hAPP(hAPP(c_List_Otake(X30357),X30358),X30356)),hAPP(hAPP(c_List_Olist_OCons(X30357),hAPP(c_List_Ohd(X30357),hAPP(hAPP(c_List_Odrop(X30357),X30358),X30356))),c_List_Olist_ONil(X30357))) = hAPP(hAPP(c_List_Otake(X30357),hAPP(c_Nat_OSuc,X30358)),X30356) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__hd__drop])]) ).

fof(i_0_7601,plain,
    ! [X17414,X17415,X17416,X17417] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17417,tc_HOL_Obool)),X17416),hAPP(hAPP(c_Set_Oinsert(X17417),X17415),X17414)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17417,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17417,tc_HOL_Obool)),X17416),hAPP(hAPP(c_Set_Oinsert(X17417),X17415),c_Orderings_Obot__class_Obot(tc_fun(X17417,tc_HOL_Obool))))),X17414),
    inference(variable_rename,[status(thm)],[fact_Diff__insert2]) ).

fof(i_0_7602,plain,
    ! [X29311,X29312,X29313] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X29313),tc_List_Olist(X29313))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X29313),tc_List_Olist(X29313)),X29312),X29312)),c_List_Olistrel(X29313,c_Transitive__Closure_Ortrancl(X29313,X29311)))),
    inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__refl]) ).

cnf(i_0_7603,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_5604]) ).

fof(i_0_7604,plain,
    ! [X27120,X27121,X27122] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27122,tc_HOL_Obool)),esk256_3(X27120,X27121,X27122)),X27121))
        | X27121 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X27122,tc_HOL_Obool),tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27122,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X27122,tc_HOL_Obool),X27121)),X27120)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27122,tc_HOL_Obool)),esk256_3(X27120,X27121,X27122)),X27120))
        | X27121 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X27122,tc_HOL_Obool),tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27122,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X27122,tc_HOL_Obool),X27121)),X27120)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__subset])])])]) ).

fof(i_0_7605,plain,
    ! [X21030,X21031,X21032] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21032))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21031,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21030),X21032)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21030),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21031),X21030),X21032))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21031,X21030)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zmult2__eq])]) ).

fof(i_0_7606,plain,
    ! [X25024,X25025,X25026,X25027] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25027,tc_HOL_Obool)),X25026),X25025))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25027,tc_HOL_Obool)),X25026),X25024))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25027,tc_HOL_Obool)),X25026),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25027,tc_HOL_Obool)),X25025),X25024))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greatest])]) ).

fof(i_0_7607,plain,
    ! [X32772,X32773,X32774] :
      ( ( ~ c_List_Olist__ex(tc_Int_Oint,X32774,c_List_Oupto(X32773,X32772))
        | ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X32774),X32773,X32772) )
      & ( c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),X32774),X32773,X32772)
        | c_List_Olist__ex(tc_Int_Oint,X32774,c_List_Oupto(X32773,X32772)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5605])]) ).

fof(i_0_7608,plain,
    ! [X22691,X22692] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22692),hAPP(c_Nat_OSuc,X22691)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22691),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)),X22691)),X22692),
    inference(variable_rename,[status(thm)],[fact_max__Suc2]) ).

cnf(i_0_7609,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_5557]) ).

fof(i_0_7610,plain,
    ! [X28971,X28972,X28973,X28974] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28974,X28974),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28973),X28972)),X28971) = hAPP(hAPP(c_Relation_Orel__comp(X28974,X28974,X28974),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28974,X28974),tc_HOL_Obool),X28973),X28971)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28974,X28974),tc_HOL_Obool),X28972),X28971)),
    inference(variable_rename,[status(thm)],[fact_rel__pow__add]) ).

fof(i_0_7611,plain,
    ! [X27039,X27040,X27041] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X27041,tc_HOL_Obool),tc_HOL_Obool)),X27040),X27039))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27041,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27041,tc_HOL_Obool),X27040)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27041,tc_HOL_Obool),X27039))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__mono])]) ).

fof(i_0_7612,plain,
    ! [X26870,X26871,X26872] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X26872,tc_HOL_Obool),tc_HOL_Obool)),X26871),X26870))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26872,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26872,tc_HOL_Obool),X26870)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26872,tc_HOL_Obool),X26871))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__anti__mono])]) ).

fof(i_0_7613,plain,
    ! [X25896,X25897,X25898] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25898)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25898),hAPP(c_Groups_Oabs__class_Oabs(X25898),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25898),X25897),X25896))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25898),hAPP(c_Groups_Oabs__class_Oabs(X25898),X25897)),hAPP(c_Groups_Oabs__class_Oabs(X25898),X25896)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq])]) ).

fof(i_0_7614,plain,
    ! [X25945,X25946,X25947] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25947)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25947),hAPP(c_Groups_Oabs__class_Oabs(X25947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25947),X25946),X25945))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25947),hAPP(c_Groups_Oabs__class_Oabs(X25947),X25946)),hAPP(c_Groups_Oabs__class_Oabs(X25947),X25945)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__triangle__ineq4])]) ).

cnf(i_0_7615,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_5606]) ).

fof(i_0_7616,plain,
    ! [X24086,X24087,X24088,X24089,X24090] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24090),X24087),X24089))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24090),X24089),X24088))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24090,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24090,X24089,X24088)),c_SetInterval_Oord__class_OatLeastAtMost(X24090,X24087,X24086)))
        | ~ class_Orderings_Oorder(X24090) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24090),X24088),X24086))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24090),X24089),X24088))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24090,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24090,X24089,X24088)),c_SetInterval_Oord__class_OatLeastAtMost(X24090,X24087,X24086)))
        | ~ class_Orderings_Oorder(X24090) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24090),X24089),X24088))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24090,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24090,X24089,X24088)),c_SetInterval_Oord__class_OatLeastAtMost(X24090,X24087,X24086)))
        | ~ class_Orderings_Oorder(X24090) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24090),X24087),X24089))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24090),X24088),X24086))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24090,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24090,X24089,X24088)),c_SetInterval_Oord__class_OatLeastAtMost(X24090,X24087,X24086)))
        | ~ class_Orderings_Oorder(X24090) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5607])])]) ).

fof(i_0_7617,plain,
    ! [X21661,X21662] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X21662),hAPP(c_Nat_OSuc,X21661)) = 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)),X21661)),X21662),
    inference(variable_rename,[status(thm)],[fact_min__Suc2]) ).

fof(i_0_7618,plain,
    ! [X17773,X17774,X17775] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17775),X17774))
      | ~ hBOOL(hAPP(hAPP(c_member(X17775),X17773),X17774))
      | hAPP(c_Finite__Set_Ocard(X17775),X17774) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X17775),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17775,tc_HOL_Obool)),X17774),hAPP(hAPP(c_Set_Oinsert(X17775),X17773),c_Orderings_Obot__class_Obot(tc_fun(X17775,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oremove])]) ).

fof(i_0_7619,plain,
    ! [X29681,X29682,X29683,X29684,X29685,X29686,X29687] : hAPP(hAPP(c_List_Ozip(X29687,X29686),hAPP(hAPP(c_List_Olist__update(X29687,X29685),X29684),X29683)),hAPP(hAPP(c_List_Olist__update(X29686,X29682),X29684),X29681)) = hAPP(hAPP(c_List_Olist__update(tc_prod(X29687,X29686),hAPP(hAPP(c_List_Ozip(X29687,X29686),X29685),X29682)),X29684),hAPP(hAPP(c_Product__Type_OPair(X29687,X29686),X29683),X29681)),
    inference(variable_rename,[status(thm)],[fact_zip__update]) ).

fof(i_0_7620,plain,
    ! [X26245,X26246,X26247,X26248,X26249] :
      ( ~ c_Fun_Oinj__on(X26249,X26248,X26247,c_Orderings_Otop__class_Otop(tc_fun(X26249,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X26249,X26248,X26247),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26249,tc_HOL_Obool)),X26246),X26245)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26248,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26249,X26248,X26247),X26246)),hAPP(c_Set_Oimage(X26249,X26248,X26247),X26245)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Int])]) ).

fof(i_0_7621,plain,
    ! [X26250,X26251,X26252,X26253,X26254] :
      ( ~ c_Fun_Oinj__on(X26254,X26253,X26252,c_Orderings_Otop__class_Otop(tc_fun(X26254,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X26254,X26253,X26252),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26254,tc_HOL_Obool)),X26251),X26250)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26253,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26254,X26253,X26252),X26251)),hAPP(c_Set_Oimage(X26254,X26253,X26252),X26250)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__set__diff])]) ).

fof(i_0_7622,plain,
    ! [X19220,X19221,X19222,X19223] :
      ( ~ c_Fun_Oinj__on(X19223,X19222,X19221,X19220)
      | hAPP(c_Set_Oimage(X19222,X19223,c_Fun_Othe__inv__into(X19223,X19222,X19220,X19221)),hAPP(c_Set_Oimage(X19223,X19222,X19221),X19220)) = X19220 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__onto])]) ).

fof(i_0_7623,plain,
    ! [X19700,X19701,X19702,X19703,X19704,X19705] : c_Nitpick_Opair__box_Opair__box__case(X19705,X19704,X19703,X19702,c_Nitpick_Opair__box_OPairBox(X19705,X19704,X19701,X19700)) = hAPP(hAPP(X19702,X19701),X19700),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osimps_I2_J]) ).

fof(i_0_7624,plain,
    ! [X19694,X19695,X19696,X19697,X19698,X19699] : c_Nitpick_Opair__box_Opair__box__rec(X19699,X19698,X19697,X19696,c_Nitpick_Opair__box_OPairBox(X19699,X19698,X19695,X19694)) = hAPP(hAPP(X19696,X19695),X19694),
    inference(variable_rename,[status(thm)],[fact_pair__box_Orecs]) ).

fof(i_0_7625,plain,
    ! [X33618,X33619,X33620,X33621,X33622] :
      ( ~ class_Groups_Ocomm__monoid__mult(X33622)
      | ~ class_Rings_Odvd(X33622)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33621),X33620))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X33621,tc_HOL_Obool)),X33619),X33620))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33622),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33621,X33622),X33618),X33619)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33621,X33622),X33618),X33620))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__dvd__setprod__subset])]) ).

fof(i_0_7626,plain,
    ! [X31913,X31914,X31915,X31916,X31917] : hAPP(hAPP(c_List_Ozip(X31917,X31916),c_List_OtakeWhile(X31917,X31915,X31914)),X31913) = c_List_OtakeWhile(tc_prod(X31917,X31916),hAPP(c_Fun_Ocomp(X31917,tc_HOL_Obool,tc_prod(X31917,X31916),X31915),c_Product__Type_Ofst(X31917,X31916)),hAPP(hAPP(c_List_Ozip(X31917,X31916),X31914),X31913)),
    inference(variable_rename,[status(thm)],[fact_zip__takeWhile__fst]) ).

cnf(i_0_7627,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_5608]) ).

cnf(i_0_7628,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_5609]) ).

cnf(i_0_7629,plain,
    ( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk356_2(X2,X1)),esk356_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),c_Relation_OId(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5610]) ).

cnf(i_0_7630,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_5611]) ).

fof(i_0_7631,plain,
    ! [X20106,X20107,X20108] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20108),X20107))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20106))
      | 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),X20106)),X20108)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20106)),X20107))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2__lemma])]) ).

cnf(i_0_7632,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_5549]) ).

cnf(i_0_7633,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_5612]) ).

fof(i_0_7634,plain,
    ! [X24887,X24888,X24889,X24890] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24890,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24890,tc_HOL_Obool)),X24889),X24888)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24890,tc_HOL_Obool)),X24887),X24888)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24890,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24890,tc_HOL_Obool)),X24889),X24888)),X24887),
    inference(variable_rename,[status(thm)],[fact_Diff__Int2]) ).

fof(i_0_7635,plain,
    ! [X24933,X24934,X24935,X24936] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24936,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24936,tc_HOL_Obool)),X24935),X24934)),X24933) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24936,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24936,tc_HOL_Obool)),X24935),X24933)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24936,tc_HOL_Obool)),X24934),X24933)),
    inference(variable_rename,[status(thm)],[fact_Int__Un__distrib2]) ).

fof(i_0_7636,plain,
    ! [X24891,X24892,X24893,X24894] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24894,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24894,tc_HOL_Obool)),X24893),X24892)),X24891) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24894,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24894,tc_HOL_Obool)),X24893),X24891)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24894,tc_HOL_Obool)),X24892),X24891)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib2]) ).

fof(i_0_7637,plain,
    ! [X24929,X24930,X24931,X24932] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24932,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24932,tc_HOL_Obool)),X24931),X24930)),X24929) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24932,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24932,tc_HOL_Obool)),X24931),X24929)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24932,tc_HOL_Obool)),X24930),X24929)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__distrib2]) ).

fof(i_0_7638,plain,
    ! [X23165,X23166,X23167,X23168] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23168,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23168,tc_HOL_Obool)),X23167),X23166)),X23165) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23168,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23168,tc_HOL_Obool)),X23167),X23165)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23168,tc_HOL_Obool)),X23166),X23165)),
    inference(variable_rename,[status(thm)],[fact_Un__Diff]) ).

fof(i_0_7639,plain,
    ! [X24287,X24288,X24289] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk156_3(X24287,X24288,X24289)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24289)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24288),X24289) = X24288
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24288),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24287))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24289)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk157_3(X24287,X24288,X24289)),X24287))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24288),X24289) = X24288
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24288),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24287))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24289)) )
      & ( X24288 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk157_3(X24287,X24288,X24289)),esk156_3(X24287,X24288,X24289))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24288),X24289) = X24288
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24288),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24287))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24289)) ) ),
    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_7640,plain,
    ! [X24282,X24283,X24284] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk154_3(X24282,X24283,X24284)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X24284)))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24283),X24284) = X24283
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24283),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24282))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24284)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk155_3(X24282,X24283,X24284)),X24282))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24283),X24284) = X24283
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24283),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24282))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24284)) )
      & ( X24283 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk155_3(X24282,X24283,X24284)),esk154_3(X24282,X24283,X24284))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24283),X24284) = X24283
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24283),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24282))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24284)) ) ),
    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_7641,plain,
    ! [X30337,X30338,X30339,X30340] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30340),X30339)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30338)),X30337)))
      | hAPP(hAPP(c_List_Otake(X30338),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30340),X30339)),X30337) = hAPP(hAPP(c_List_Oappend(X30338),hAPP(hAPP(c_List_Otake(X30338),X30340),X30337)),hAPP(hAPP(c_List_Otake(X30338),X30339),hAPP(hAPP(c_List_Odrop(X30338),X30340),X30337))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__add])]) ).

fof(i_0_7642,plain,
    ! [X25563,X25564,X25565] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25565),esk202_3(X25563,X25564,X25565)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25565,tc_HOL_Obool)),X25564),X25563)))
        | hAPP(c_Finite__Set_Ocard(X25565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25565,tc_HOL_Obool)),X25564),X25563)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25565),X25564)),hAPP(c_Finite__Set_Ocard(X25565),X25563))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25565),X25563))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25565),X25564)) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Finite__Set_Ocard(X25565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25565,tc_HOL_Obool)),X25564),X25563)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25565),X25564)),hAPP(c_Finite__Set_Ocard(X25565),X25563))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25565),X25563))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25565),X25564)) ) ),
    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_7643,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_5613]) ).

cnf(i_0_7644,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_5614]) ).

fof(i_0_7645,plain,
    ! [X17301,X17302,X17303] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17303),X17302))
      | ~ hBOOL(hAPP(hAPP(c_member(X17303),X17301),X17302))
      | hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X17303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17303,tc_HOL_Obool)),X17302),hAPP(hAPP(c_Set_Oinsert(X17303),X17301),c_Orderings_Obot__class_Obot(tc_fun(X17303,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X17303),X17302) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Suc__Diff1])]) ).

fof(i_0_7646,plain,
    ! [X19781,X19782,X19783,X19784,X19785,X19786] :
      ( ~ c_Finite__Set_Ofolding(X19786,X19785,X19784,X19783)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19786),X19782))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19786),X19781))
      | hAPP(c_Fun_Ocomp(X19785,X19785,X19785,hAPP(X19783,X19781)),hAPP(X19783,X19782)) = hAPP(c_Fun_Ocomp(X19785,X19785,X19785,hAPP(X19783,X19782)),hAPP(X19783,X19781)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H_H])]) ).

fof(i_0_7647,plain,
    ! [X31953,X31954] :
      ( X31954 = c_List_Olist_ONil(X31953)
      | ~ hBOOL(hAPP(c_List_Odistinct(X31953),X31954))
      | c_List_OtakeWhile(X31953,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X31953),c_fNot),hAPP(hAPP(c_COMBC(X31953,X31953,tc_HOL_Obool),c_fequal),c_List_Olast(X31953,X31954))),X31954) = c_List_Obutlast(X31953,X31954) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last])]) ).

fof(i_0_7648,plain,
    ! [X26588,X26589,X26590,X26591] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26591,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26590,tc_fun(X26591,tc_HOL_Obool)),X26589),X26588)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26590,tc_fun(X26591,tc_HOL_Obool)),X26589),hAPP(hAPP(c_COMBB(tc_fun(X26591,tc_HOL_Obool),tc_fun(X26591,tc_HOL_Obool),X26590),c_Groups_Ouminus__class_Ouminus(tc_fun(X26591,tc_HOL_Obool))),X26588)),
    inference(variable_rename,[status(thm)],[fact_Compl__INT]) ).

fof(i_0_7649,plain,
    ! [X26584,X26585,X26586,X26587] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26587,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X26586,tc_fun(X26587,tc_HOL_Obool)),X26585),X26584)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26586,tc_fun(X26587,tc_HOL_Obool)),X26585),hAPP(hAPP(c_COMBB(tc_fun(X26587,tc_HOL_Obool),tc_fun(X26587,tc_HOL_Obool),X26586),c_Groups_Ouminus__class_Ouminus(tc_fun(X26587,tc_HOL_Obool))),X26584)),
    inference(variable_rename,[status(thm)],[fact_Compl__UN]) ).

fof(i_0_7650,plain,
    ! [X18876,X18877,X18878,X18879] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18879,X18878,hAPP(hAPP(c_Set_Oinsert(X18879),X18877),c_Orderings_Obot__class_Obot(tc_fun(X18879,tc_HOL_Obool)))),X18876))
        | X18877 = X18876 )
      & ( X18877 != X18876
        | hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18879,X18878,hAPP(hAPP(c_Set_Oinsert(X18879),X18877),c_Orderings_Obot__class_Obot(tc_fun(X18879,tc_HOL_Obool)))),X18876)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__sing])]) ).

fof(i_0_7651,plain,
    ! [X30592,X30593,X30594] :
      ( ~ class_Orderings_Olinorder(X30594)
      | hBOOL(hAPP(hAPP(c_member(X30594),X30593),hAPP(c_List_Oset(X30594),X30592)))
      | c_List_Olinorder__class_Oinsort__insert__key(X30594,X30594,c_COMBI(X30594),X30593,X30592) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30594,X30594,c_COMBI(X30594)),X30593),X30592) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5615])]) ).

fof(i_0_7652,plain,
    ! [X23553,X23554,X23555,X23556,X23557] :
      ( ( ~ c_Relation_Oirrefl(X23554,X23553)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X23554,X23554)),hAPP(hAPP(c_Product__Type_OPair(X23554,X23554),X23555),X23555)),X23553)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(X23557,X23557)),hAPP(hAPP(c_Product__Type_OPair(X23557,X23557),esk115_2(X23556,X23557)),esk115_2(X23556,X23557))),X23556))
        | c_Relation_Oirrefl(X23557,X23556) ) ),
    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_5616])])])])]) ).

fof(i_0_7653,plain,
    ! [X25541,X25542,X25543,X25544,X25545,X25546] :
      ( ~ c_Finite__Set_Ofolding(X25546,X25545,X25544,X25543)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25546),X25542))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25546),X25541))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25546,tc_HOL_Obool)),X25542),X25541) != c_Orderings_Obot__class_Obot(tc_fun(X25546,tc_HOL_Obool))
      | hAPP(X25543,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25546,tc_HOL_Obool)),X25542),X25541)) = hAPP(c_Fun_Ocomp(X25545,X25545,X25545,hAPP(X25543,X25542)),hAPP(X25543,X25541)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ounion])]) ).

fof(i_0_7654,plain,
    ! [X20985,X20986,X20987,X20989,X20990,X20991,X20992] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20985),esk66_3(X20985,X20986,X20987))),X20986))
        | X20985 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X20987,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20986),X20985))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20985),hAPP(c_Nat_OSuc,esk66_3(X20985,X20986,X20987)))))
        | X20985 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X20987,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20986),X20985))) )
      & ( hBOOL(hAPP(X20987,esk66_3(X20985,X20986,X20987)))
        | X20985 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X20987,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20986),X20985))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20985),esk66_3(X20985,X20986,X20987))),X20986))
        | hBOOL(hAPP(X20987,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X20987,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20986),X20985))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20985),hAPP(c_Nat_OSuc,esk66_3(X20985,X20986,X20987)))))
        | hBOOL(hAPP(X20987,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X20987,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20986),X20985))) )
      & ( hBOOL(hAPP(X20987,esk66_3(X20985,X20986,X20987)))
        | hBOOL(hAPP(X20987,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X20987,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20986),X20985))) )
      & ( X20989 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X20991,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20991,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20990),X20989))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20989),X20992)),X20990))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20989),hAPP(c_Nat_OSuc,X20992))))
        | ~ hBOOL(hAPP(X20991,X20992))
        | hBOOL(hAPP(X20991,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20990),X20989))) ) ),
    inference(distribute,[status(thm)],[inference(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_7655,plain,
    ! [X17778,X17779,X17780] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17780),X17779))
      | hAPP(c_Finite__Set_Ocard(X17780),hAPP(hAPP(c_Set_Oinsert(X17780),X17778),X17779)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X17780),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17780,tc_HOL_Obool)),X17779),hAPP(hAPP(c_Set_Oinsert(X17780),X17778),c_Orderings_Obot__class_Obot(tc_fun(X17780,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oinsert__remove])]) ).

fof(i_0_7656,plain,
    ! [X19517,X19518,X19519,X19520,X19521,X19522,X19523,X19524,X19525] :
      ( hAPP(c_Fun_Ocomp(X19525,X19524,X19523,X19522),X19521) != hAPP(c_Fun_Ocomp(X19520,X19524,X19523,X19519),X19518)
      | hAPP(X19522,hAPP(X19521,X19517)) = hAPP(X19519,hAPP(X19518,X19517)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest])]) ).

fof(i_0_7657,plain,
    ! [X19508,X19509,X19510,X19511,X19512,X19513,X19514,X19515,X19516] :
      ( hAPP(c_Fun_Ocomp(X19515,X19514,X19513,X19512),X19511) != hAPP(c_Fun_Ocomp(X19510,X19514,X19513,X19509),X19508)
      | hAPP(X19512,hAPP(X19511,X19516)) = hAPP(X19509,hAPP(X19508,X19516)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__elim])])]) ).

fof(i_0_7658,plain,
    ! [X30569,X30570,X30571,X30572] :
      ( ~ class_Orderings_Olinorder(X30572)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30572,X30572,c_COMBI(X30572)),X30571),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30572,X30572,c_COMBI(X30572)),X30570),X30569)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30572,X30572,c_COMBI(X30572)),X30570),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30572,X30572,c_COMBI(X30572)),X30571),X30569)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__left__comm])]) ).

fof(i_0_7659,plain,
    ! [X27813,X27814,X27815,X27816,X27817,X27818,X27819] :
      ( hAPP(c_Fun_Ocomp(X27819,X27818,X27817,X27816),X27815) != hAPP(c_Fun_Ocomp(X27818,X27818,X27817,c_Fun_Oid(X27818)),X27814)
      | hAPP(X27816,hAPP(X27815,X27813)) = hAPP(X27814,X27813) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__id__dest])]) ).

fof(i_0_7660,plain,
    ! [X31331,X31332,X31333,X31334] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X31333),c_List_Olinorder__class_Osort__key(X31333,X31334,X31332,X31331)))
        | hBOOL(hAPP(c_List_Odistinct(X31333),X31331))
        | ~ class_Orderings_Olinorder(X31334) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31333),X31331))
        | hBOOL(hAPP(c_List_Odistinct(X31333),c_List_Olinorder__class_Osort__key(X31333,X31334,X31332,X31331)))
        | ~ class_Orderings_Olinorder(X31334) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sort])])]) ).

fof(i_0_7661,plain,
    ! [X24695,X24696,X24697,X24698] :
      ( ~ c_Equiv__Relations_Oequiv(X24698,X24697,X24696)
      | ~ hBOOL(hAPP(hAPP(c_member(X24698),X24695),X24697))
      | hBOOL(hAPP(hAPP(c_member(X24698),X24695),hAPP(c_Relation_OImage(X24698,X24698,X24696),hAPP(hAPP(c_Set_Oinsert(X24698),X24695),c_Orderings_Obot__class_Obot(tc_fun(X24698,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__class__self])]) ).

fof(i_0_7662,plain,
    ! [X26231,X26232,X26233,X26234,X26235] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26234),hAPP(X26233,X26232)),hAPP(c_Set_Oimage(X26235,X26234,X26233),X26231)))
        | hBOOL(hAPP(hAPP(c_member(X26235),X26232),X26231))
        | ~ c_Fun_Oinj__on(X26235,X26234,X26233,c_Orderings_Otop__class_Otop(tc_fun(X26235,tc_HOL_Obool))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26235),X26232),X26231))
        | hBOOL(hAPP(hAPP(c_member(X26234),hAPP(X26233,X26232)),hAPP(c_Set_Oimage(X26235,X26234,X26233),X26231)))
        | ~ c_Fun_Oinj__on(X26235,X26234,X26233,c_Orderings_Otop__class_Otop(tc_fun(X26235,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_7663,plain,
    ! [X26592,X26593,X26594,X26595,X26596] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26596)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26595,tc_HOL_Obool)),X26594),X26593))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26596),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26595,X26596),X26593),X26592)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26595,X26596),X26594),X26592))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__subset])]) ).

fof(i_0_7664,plain,
    ! [X23687,X23688,X23689,X23690,X23691] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X23691)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23690,tc_HOL_Obool)),X23689),X23688))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23691),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23690,X23691),X23689),X23687)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23690,X23691),X23688),X23687))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__subset])]) ).

fof(i_0_7665,plain,
    ! [X28107,X28108,X28109] :
      ( ~ c_Wellfounded_Owf(X28109,X28108)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28109,X28109)),hAPP(hAPP(c_Product__Type_OPair(X28109,X28109),X28107),X28107)),X28108)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5617])]) ).

fof(i_0_7666,plain,
    ! [X28096,X28097,X28098] :
      ( ~ c_Wellfounded_Owf(X28098,X28097)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28098,X28098)),hAPP(hAPP(c_Product__Type_OPair(X28098,X28098),X28096),X28096)),X28097)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5618])]) ).

fof(i_0_7667,plain,
    ! [X23871,X23872,X23873,X23874,X23875] :
      ( ( X23875 != c_Orderings_Obot__class_Obot(tc_fun(X23874,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23874,tc_fun(X23873,tc_HOL_Obool)),X23875),hAPP(hAPP(c_COMBB(tc_fun(X23873,tc_HOL_Obool),tc_fun(X23873,tc_HOL_Obool),X23874),hAPP(c_Set_Oinsert(X23873),X23872)),X23871)) = c_Orderings_Obot__class_Obot(tc_fun(X23873,tc_HOL_Obool)) )
      & ( X23875 = c_Orderings_Obot__class_Obot(tc_fun(X23874,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23874,tc_fun(X23873,tc_HOL_Obool)),X23875),hAPP(hAPP(c_COMBB(tc_fun(X23873,tc_HOL_Obool),tc_fun(X23873,tc_HOL_Obool),X23874),hAPP(c_Set_Oinsert(X23873),X23872)),X23871)) = hAPP(hAPP(c_Set_Oinsert(X23873),X23872),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23874,tc_fun(X23873,tc_HOL_Obool)),X23875),X23871)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__simps_I1_J])]) ).

fof(i_0_7668,plain,
    ! [X23878,X23879,X23880,X23881,X23882] :
      ( ( X23882 != c_Orderings_Obot__class_Obot(tc_fun(X23881,tc_HOL_Obool))
        | hAPP(hAPP(c_Set_Oinsert(X23880),X23879),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23881,tc_fun(X23880,tc_HOL_Obool)),X23882),X23878)) = hAPP(hAPP(c_Set_Oinsert(X23880),X23879),c_Orderings_Obot__class_Obot(tc_fun(X23880,tc_HOL_Obool))) )
      & ( X23882 = c_Orderings_Obot__class_Obot(tc_fun(X23881,tc_HOL_Obool))
        | hAPP(hAPP(c_Set_Oinsert(X23880),X23879),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23881,tc_fun(X23880,tc_HOL_Obool)),X23882),X23878)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23881,tc_fun(X23880,tc_HOL_Obool)),X23882),hAPP(hAPP(c_COMBB(tc_fun(X23880,tc_HOL_Obool),tc_fun(X23880,tc_HOL_Obool),X23881),hAPP(c_Set_Oinsert(X23880),X23879)),X23878)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__extend__simps_I1_J])]) ).

cnf(i_0_7669,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_5619]) ).

fof(i_0_7670,plain,
    ! [X24432,X24433,X24434,X24435,X24436] :
      ( ~ class_Rings_Osemiring__0(X24436)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24436),X24435),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24434,X24436),X24433),X24432)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24434,X24436),hAPP(hAPP(c_COMBB(X24436,X24436,X24434),hAPP(c_Groups_Otimes__class_Otimes(X24436),X24435)),X24433)),X24432) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__right__distrib])]) ).

fof(i_0_7671,plain,
    ! [X22419,X22420,X22421,X22422,X22423] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(X22423,X22422)),hAPP(X22423,X22421)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X22420,X22420)),hAPP(hAPP(c_Product__Type_OPair(X22420,X22420),X22422),X22421)),c_Wellfounded_Omlex__prod(X22420,X22423,X22419))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mlex__less])]) ).

fof(i_0_7672,plain,
    ! [X26151,X26152,X26153,X26154,X26155] : hAPP(c_Set_Oimage(X26155,X26154,hAPP(hAPP(c_COMBB(X26153,X26154,X26155),X26152),X26151)),c_Orderings_Otop__class_Otop(tc_fun(X26155,tc_HOL_Obool))) = hAPP(c_Set_Oimage(X26153,X26154,X26152),hAPP(c_Set_Oimage(X26155,X26153,X26151),c_Orderings_Otop__class_Otop(tc_fun(X26155,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_range__composition]) ).

fof(i_0_7673,plain,
    ! [X32027,X32028] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk437_2(X32027,X32028)),esk438_2(X32027,X32028)))
        | c_List_Olinorder__class_Osorted(X32028,X32027)
        | ~ class_Orderings_Olinorder(X32028) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk438_2(X32027,X32028)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32028)),X32027)))
        | c_List_Olinorder__class_Osorted(X32028,X32027)
        | ~ class_Orderings_Olinorder(X32028) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32028),hAPP(hAPP(c_List_Onth(X32028),X32027),esk437_2(X32027,X32028))),hAPP(hAPP(c_List_Onth(X32028),X32027),esk438_2(X32027,X32028))))
        | c_List_Olinorder__class_Osorted(X32028,X32027)
        | ~ class_Orderings_Olinorder(X32028) ) ),
    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_7674,plain,
    ! [X31762,X31763,X31764,X31765] :
      ( ( ~ c_List_Olinorder__class_Osorted(X31763,X31762)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31764),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31763)),X31762)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31765),X31764))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31763),hAPP(hAPP(c_List_Onth(X31763),X31762),X31765)),hAPP(hAPP(c_List_Onth(X31763),X31762),X31764)))
        | ~ class_Orderings_Olinorder(X31763) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk432_2(X31762,X31763)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31763)),X31762)))
        | c_List_Olinorder__class_Osorted(X31763,X31762)
        | ~ class_Orderings_Olinorder(X31763) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk433_2(X31762,X31763)),esk432_2(X31762,X31763)))
        | c_List_Olinorder__class_Osorted(X31763,X31762)
        | ~ class_Orderings_Olinorder(X31763) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31763),hAPP(hAPP(c_List_Onth(X31763),X31762),esk433_2(X31762,X31763))),hAPP(hAPP(c_List_Onth(X31763),X31762),esk432_2(X31762,X31763))))
        | c_List_Olinorder__class_Osorted(X31763,X31762)
        | ~ class_Orderings_Olinorder(X31763) ) ),
    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_7675,plain,
    ! [X26307,X26308,X26309,X26310,X26311,X26312] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26312),X26311),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26310,tc_fun(X26312,tc_HOL_Obool)),X26309),X26308)))
      | hBOOL(hAPP(hAPP(c_member(X26312),X26311),hAPP(X26308,X26307)))
      | ~ hBOOL(hAPP(hAPP(c_member(X26310),X26307),X26309)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5620])]) ).

fof(i_0_7676,plain,
    ! [X26301,X26302,X26303,X26304,X26305,X26306] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26306),X26305),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26304,tc_fun(X26306,tc_HOL_Obool)),X26303),X26302)))
      | ~ hBOOL(hAPP(hAPP(c_member(X26304),X26301),X26303))
      | hBOOL(hAPP(hAPP(c_member(X26306),X26305),hAPP(X26302,X26301))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__D])]) ).

fof(i_0_7677,plain,
    ! [X30467,X30468,X30469] :
      ( ~ class_Groups_Omonoid__add(X30469)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30469),X30468),hAPP(c_List_Ofoldl(X30469,X30469,c_Groups_Oplus__class_Oplus(X30469),c_Groups_Ozero__class_Ozero(X30469)),X30467)) = hAPP(c_List_Ofoldl(X30469,X30469,c_Groups_Oplus__class_Oplus(X30469),X30468),X30467) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_foldl__absorb0])]) ).

fof(i_0_7678,plain,
    ! [X29699,X29700,X29701,X29702,X29703,X29704] :
      ( X29704 = X29703
      | hAPP(hAPP(c_List_Olist__update(X29702,hAPP(hAPP(c_List_Olist__update(X29702,X29701),X29704),X29700)),X29703),X29699) = hAPP(hAPP(c_List_Olist__update(X29702,hAPP(hAPP(c_List_Olist__update(X29702,X29701),X29703),X29699)),X29704),X29700) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__swap])]) ).

fof(i_0_7679,plain,
    ! [X28936,X28937,X28938] : hAPP(hAPP(c_Relation_Orel__comp(X28938,X28938,X28938),X28937),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28938,X28938),tc_HOL_Obool),X28936),X28937)) = hAPP(hAPP(c_Relation_Orel__comp(X28938,X28938,X28938),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28938,X28938),tc_HOL_Obool),X28936),X28937)),X28937),
    inference(variable_rename,[status(thm)],[fact_rel__pow__commute]) ).

fof(i_0_7680,plain,
    ! [X34056,X34057,X34058,X34059,X34060,X34061,X34062,X34063,X34064,X34065] :
      ( ( X34057 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X34058,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ epred1_3(X34058,X34057,X34056) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34057))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34060))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34060),X34057))
        | X34056 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34057),X34059)),X34060)
        | hBOOL(hAPP(X34058,X34059))
        | ~ epred1_3(X34058,X34057,X34056) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34057),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34057),X34062))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34062),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34056 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34057),X34061)),X34062)
        | hBOOL(hAPP(X34058,X34061))
        | ~ epred1_3(X34058,X34057,X34056) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),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)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),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)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),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)),esk566_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),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)),esk566_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | X34064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),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)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),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)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),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)),esk566_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),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)),esk566_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X34063,X34064,X34065)),X34064))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk565_3(X34063,X34064,X34065))),esk566_3(X34063,X34064,X34065))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34064),esk568_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X34063,X34064,X34065)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( X34063 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34064),esk567_3(X34063,X34064,X34065))),esk568_3(X34063,X34064,X34065))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) )
      & ( ~ hBOOL(hAPP(X34065,esk567_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,esk565_3(X34063,X34064,X34065)))
        | ~ hBOOL(hAPP(X34065,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | epred1_3(X34065,X34064,X34063) ) ),
    inference(distribute,[status(thm)],[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_5214])])])])])]) ).

fof(i_0_7681,plain,
    ! [X17496,X17497,X17498] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17498),X17497))
      | hAPP(c_Finite__Set_Ocard(X17498),hAPP(hAPP(c_Set_Oinsert(X17498),X17496),X17497)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X17498),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17498,tc_HOL_Obool)),X17497),hAPP(hAPP(c_Set_Oinsert(X17498),X17496),c_Orderings_Obot__class_Obot(tc_fun(X17498,tc_HOL_Obool)))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert])]) ).

cnf(i_0_7682,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_5621]) ).

cnf(i_0_7683,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_5622]) ).

cnf(i_0_7684,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_5623]) ).

cnf(i_0_7685,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_5624]) ).

fof(i_0_7686,plain,
    ! [X22879,X22880,X22881,X22882] :
      ( ~ class_Fields_Olinordered__field(X22882)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22882),X22881),X22880))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22882),c_Groups_Ozero__class_Ozero(X22882)),X22879))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22882),c_Groups_Ozero__class_Ozero(X22882)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22882),X22880),X22881)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22882),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22882),X22879),X22880)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22882),X22879),X22881))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono])]) ).

fof(i_0_7687,plain,
    ! [X22760,X22761,X22762,X22763] :
      ( ~ class_Fields_Olinordered__field(X22763)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22763),X22762),X22761))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22763),c_Groups_Ozero__class_Ozero(X22763)),X22760))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22763),c_Groups_Ozero__class_Ozero(X22763)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22763),X22761),X22762)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22763),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22763),X22760),X22761)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22763),X22760),X22762))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono])]) ).

fof(i_0_7688,plain,
    ! [X23592,X23593,X23594] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X23594,X23594),tc_HOL_Obool)),X23593),X23592))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23594,tc_HOL_Obool)),hAPP(c_Relation_OField(X23594),X23593)),hAPP(c_Relation_OField(X23594),X23592))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mono__Field])]) ).

fof(i_0_7689,plain,
    ! [X19767,X19768,X19769,X19770,X19771,X19772] :
      ( ~ c_Finite__Set_Ofolding(X19772,X19771,X19770,X19769)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19772),X19768))
      | hAPP(c_Fun_Ocomp(X19771,X19771,X19771,hAPP(X19770,X19767)),hAPP(X19769,X19768)) = hAPP(c_Fun_Ocomp(X19771,X19771,X19771,hAPP(X19769,X19768)),hAPP(X19770,X19767)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp_H])]) ).

fof(i_0_7690,plain,
    ! [X34070,X34071,X34072,X34073,X34074,X34075,X34076,X34077,X34078,X34079] :
      ( ( X34071 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(X34072,X34070))
        | ~ epred2_3(X34072,X34071,X34070) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34071))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34074))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34074),X34071))
        | X34070 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34071),X34073)),X34074)
        | hBOOL(hAPP(X34072,X34074))
        | ~ epred2_3(X34072,X34071,X34070) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34071),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34071),X34076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X34076),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34070 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34071),X34075)),X34076)
        | hBOOL(hAPP(X34072,X34076))
        | ~ epred2_3(X34072,X34071,X34070) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),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)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),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)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),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)),esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),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)),esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | X34078 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),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)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),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)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),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)),esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),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)),esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X34077,X34078,X34079)),X34078))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk569_3(X34077,X34078,X34079))),esk570_3(X34077,X34078,X34079))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X34078),esk572_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X34077,X34078,X34079)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( X34077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X34078),esk571_3(X34077,X34078,X34079))),esk572_3(X34077,X34078,X34079))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) )
      & ( ~ hBOOL(hAPP(X34079,esk572_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,esk570_3(X34077,X34078,X34079)))
        | ~ hBOOL(hAPP(X34079,X34077))
        | epred2_3(X34079,X34078,X34077) ) ),
    inference(distribute,[status(thm)],[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_5213])])])])])]) ).

fof(i_0_7691,plain,
    ! [X26479,X26480,X26481,X26482,X26483] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26483,tc_fun(X26482,tc_HOL_Obool)),X26481),hAPP(hAPP(c_COMBB(tc_fun(X26482,tc_HOL_Obool),tc_fun(X26482,tc_HOL_Obool),X26483),hAPP(c_Set_Oinsert(X26482),X26480)),X26479)) = hAPP(hAPP(c_Set_Oinsert(X26482),X26480),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26483,tc_fun(X26482,tc_HOL_Obool)),X26481),X26479)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I5_J]) ).

fof(i_0_7692,plain,
    ! [X26484,X26485,X26486,X26487,X26488] : hAPP(hAPP(c_Set_Oinsert(X26488),X26487),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26486,tc_fun(X26488,tc_HOL_Obool)),X26485),X26484)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26486,tc_fun(X26488,tc_HOL_Obool)),X26485),hAPP(hAPP(c_COMBB(tc_fun(X26488,tc_HOL_Obool),tc_fun(X26488,tc_HOL_Obool),X26486),hAPP(c_Set_Oinsert(X26488),X26487)),X26484)),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I5_J]) ).

fof(i_0_7693,plain,
    ! [X18950,X18951,X18952,X18953] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18953),X18952)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18951),X18952)),X18950)) = 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),X18953),X18951)),X18952)),X18950),
    inference(variable_rename,[status(thm)],[fact_left__add__mult__distrib]) ).

fof(i_0_7694,plain,
    ! [X31908,X31909,X31910,X31911,X31912] : hAPP(hAPP(c_List_Ozip(X31912,X31911),X31910),c_List_OtakeWhile(X31911,X31909,X31908)) = c_List_OtakeWhile(tc_prod(X31912,X31911),hAPP(c_Fun_Ocomp(X31911,tc_HOL_Obool,tc_prod(X31912,X31911),X31909),c_Product__Type_Osnd(X31912,X31911)),hAPP(hAPP(c_List_Ozip(X31912,X31911),X31910),X31908)),
    inference(variable_rename,[status(thm)],[fact_zip__takeWhile__snd]) ).

cnf(i_0_7695,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_5625]) ).

fof(i_0_7696,plain,
    ! [X32364,X32365,X32366,X32367,X32368] :
      ( ( X32368 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Oneg__decr__bind(X32367,X32366,X32365,X32364),X32368) = c_Lazy__Sequence_Ohit__bound(X32366) )
      & ( X32368 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Oneg__decr__bind(X32367,X32366,X32365,X32364),X32368) = c_Lazy__Sequence_Ohb__bind(X32367,X32366,hAPP(X32365,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32368),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X32367,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32366))),X32364),X32368)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Oneg__decr__bind__def])]) ).

fof(i_0_7697,plain,
    ! [X26213,X26214,X26215,X26216] :
      ( ~ c_Fun_Oinj__on(X26216,X26215,X26214,c_Orderings_Otop__class_Otop(tc_fun(X26216,tc_HOL_Obool)))
      | c_Fun_Oinj__on(X26216,tc_fun(X26213,X26215),hAPP(hAPP(c_COMBB(X26215,tc_fun(X26213,X26215),X26216),c_COMBK(X26215,X26213)),X26214),c_Orderings_Otop__class_Otop(tc_fun(X26216,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__fun])]) ).

fof(i_0_7698,plain,
    ! [X26938,X26939,X26940] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26940,tc_HOL_Obool)),X26939),X26938) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X26940,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X26940,tc_HOL_Obool)),X26939),hAPP(hAPP(c_Set_Oinsert(tc_fun(X26940,tc_HOL_Obool)),X26938),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26940,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Int__eq__Inter]) ).

fof(i_0_7699,plain,
    ! [X27074,X27075,X27076] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27076,tc_HOL_Obool)),X27075),X27074) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X27076,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X27076,tc_HOL_Obool)),X27075),hAPP(hAPP(c_Set_Oinsert(tc_fun(X27076,tc_HOL_Obool)),X27074),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X27076,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_Un__eq__Union]) ).

fof(i_0_7700,plain,
    ! [X22875,X22876,X22877,X22878] :
      ( ~ class_Fields_Olinordered__field(X22878)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22878),X22877),X22876))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22878),X22875),c_Groups_Ozero__class_Ozero(X22878)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22878),c_Groups_Ozero__class_Ozero(X22878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22878),X22877),X22876)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22878),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22878),X22875),X22877)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22878),X22875),X22876))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg])]) ).

fof(i_0_7701,plain,
    ! [X22756,X22757,X22758,X22759] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X22759)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22759),X22758),X22757))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22759),X22756),c_Groups_Ozero__class_Ozero(X22759)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22759),c_Groups_Ozero__class_Ozero(X22759)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22759),X22758),X22757)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22759),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22759),X22756),X22758)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22759),X22756),X22757))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg])]) ).

fof(i_0_7702,plain,
    ! [X32369,X32370,X32371,X32372,X32373] :
      ( ( X32373 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Opos__decr__bind(X32372,X32371,X32370,X32369),X32373) = c_Lazy__Sequence_Oempty(X32371) )
      & ( X32373 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hAPP(c_New__DSequence_Opos__decr__bind(X32372,X32371,X32370,X32369),X32373) = hAPP(c_Lazy__Sequence_Obind(X32372,X32371,hAPP(X32370,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X32373),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X32372,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32371)),X32369),X32373)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_New__DSequence_Opos__decr__bind__def])]) ).

fof(i_0_7703,plain,
    ! [X29623,X29624,X29625,X29626,X29627] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29627),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29626)),X29625)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29627),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29624)),X29623)))
      | hAPP(hAPP(c_List_Onth(tc_prod(X29626,X29624)),hAPP(hAPP(c_List_Ozip(X29626,X29624),X29625),X29623)),X29627) = hAPP(hAPP(c_Product__Type_OPair(X29626,X29624),hAPP(hAPP(c_List_Onth(X29626),X29625),X29627)),hAPP(hAPP(c_List_Onth(X29624),X29623),X29627)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__zip])]) ).

fof(i_0_7704,plain,
    ! [X21303,X21304,X21305] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21305,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21304),X21303)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21304),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21305),X21304),X21303))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21305,X21304)),
    inference(variable_rename,[status(thm)],[fact_mod__mult2__eq]) ).

cnf(i_0_7705,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_5574]) ).

fof(i_0_7706,plain,
    ! [X24206,X24207,X24208] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24208),X24207))
        | 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)),X24208)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24206),X24207)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24206),X24208)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24207),X24208)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24206),X24207))
        | 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)),X24208)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24206),X24207)) = 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),X24208),X24207)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24206),X24207))
        | 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)),X24208)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24206),X24207)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24208),X24207)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5626])])]) ).

cnf(i_0_7707,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_5627]) ).

fof(i_0_7708,plain,
    ! [X30141,X30142,X30143,X30144,X30145] : hAPP(hAPP(c_List_Olist__update(X30145,hAPP(hAPP(c_List_Oappend(X30145),X30144),hAPP(hAPP(c_List_Olist_OCons(X30145),X30143),X30142))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30145)),X30144)),X30141) = hAPP(hAPP(c_List_Oappend(X30145),X30144),hAPP(hAPP(c_List_Olist_OCons(X30145),X30141),X30142)),
    inference(variable_rename,[status(thm)],[fact_list__update__length]) ).

cnf(i_0_7709,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_5628]) ).

fof(i_0_7710,plain,
    ! [X29261,X29262] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29262),tc_List_Olist(X29262)),tc_HOL_Obool)),c_List_Olistrel1(X29262,c_Transitive__Closure_Ortrancl(X29262,X29261))),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29262),c_List_Olistrel1(X29262,X29261)))),
    inference(variable_rename,[status(thm)],[fact_listrel1__rtrancl__subset__rtrancl__listrel1]) ).

fof(i_0_7711,plain,
    ! [X28632,X28633,X28634] : c_Transitive__Closure_Ortrancl(X28634,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28634,X28634),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28634,X28633)),c_Transitive__Closure_Ortrancl(X28634,X28632))) = c_Transitive__Closure_Ortrancl(X28634,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28634,X28634),tc_HOL_Obool)),X28633),X28632)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__Un__rtrancl]) ).

fof(i_0_7712,plain,
    ! [X33752,X33753,X33754,X33755] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33755),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33755),X33753),X33754)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33755),X33752),X33754)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33755),X33753),X33752))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33755),X33754),X33752))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33755),X33754),X33753))
        | ~ class_Divides_Osemiring__div(X33755) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33755),X33753),X33752))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33755),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33755),X33753),X33754)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33755),X33752),X33754)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33755),X33754),X33752))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33755),X33754),X33753))
        | ~ class_Divides_Osemiring__div(X33755) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__dvd__div])])]) ).

cnf(i_0_7713,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_5629]) ).

cnf(i_0_7714,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_5630]) ).

fof(i_0_7715,plain,
    ! [X33916,X33917,X33918,X33919,X33921] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33918),X33916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33918),esk562_3(X33916,X33917,X33918)),c_Groups_Ozero__class_Ozero(X33918))))
        | ~ hBOOL(hAPP(X33917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33918),X33916),X33919)))
        | ~ class_Rings_Odvd(X33918)
        | ~ class_Rings_Osemiring__0(X33918) )
      & ( hBOOL(hAPP(X33917,esk562_3(X33916,X33917,X33918)))
        | ~ hBOOL(hAPP(X33917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33918),X33916),X33919)))
        | ~ class_Rings_Odvd(X33918)
        | ~ class_Rings_Osemiring__0(X33918) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33918),X33916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33918),X33921),c_Groups_Ozero__class_Ozero(X33918))))
        | ~ hBOOL(hAPP(X33917,X33921))
        | hBOOL(hAPP(X33917,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33918),X33916),esk563_3(X33916,X33917,X33918))))
        | ~ class_Rings_Odvd(X33918)
        | ~ class_Rings_Osemiring__0(X33918) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex])])])])]) ).

fof(i_0_7716,plain,
    ! [X30935,X30936,X30937] : hAPP(hAPP(c_List_Ozip(X30937,X30936),hAPP(hAPP(c_List_Omap(tc_prod(X30937,X30936),X30937),c_Product__Type_Ofst(X30937,X30936)),X30935)),hAPP(hAPP(c_List_Omap(tc_prod(X30937,X30936),X30936),c_Product__Type_Osnd(X30937,X30936)),X30935)) = X30935,
    inference(variable_rename,[status(thm)],[fact_zip__map__fst__snd]) ).

fof(i_0_7717,plain,
    ! [X21944,X21945,X21946,X21947,X21948,X21949,X21950,X21951] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21951)
      | ~ c_Fun_Oinj__on(X21950,X21949,X21948,X21947)
      | X21946 != hAPP(c_Set_Oimage(X21950,X21949,X21948),X21947)
      | X21945 != hAPP(c_Fun_Ocomp(X21949,X21951,X21950,X21944),X21948)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21949,X21951),X21944),X21946) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21950,X21951),X21945),X21947) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__cong])]) ).

fof(i_0_7718,plain,
    ! [X18490,X18491,X18492] :
      ( ~ class_Rings_Olinordered__ring(X18492)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18492),c_Groups_Ozero__class_Ozero(X18492)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18492),X18491),X18491)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18492),X18490),X18490)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero])]) ).

fof(i_0_7719,plain,
    ! [X28748,X28749] :
      ( ( ~ 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),X28749),X28748)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28749),X28748)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28749),X28748))
        | 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),X28749),X28748)),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_7720,plain,
    ! [X19738,X19739,X19740,X19741,X19742,X19743] :
      ( ~ c_Finite__Set_Ofolding(X19743,X19742,X19741,X19740)
      | hAPP(c_Fun_Ocomp(X19742,X19742,X19742,hAPP(X19741,X19739)),hAPP(X19741,X19738)) = hAPP(c_Fun_Ocomp(X19742,X19742,X19742,hAPP(X19741,X19738)),hAPP(X19741,X19739)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Ocommute__comp])]) ).

fof(i_0_7721,plain,
    ! [X27229,X27230,X27231,X27232,X27233] : hAPP(hAPP(c_Product__Type_OSigma(X27233,X27232),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27233,tc_HOL_Obool)),X27231),X27230)),X27229) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27233,X27232),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27233,X27232),X27231),X27229)),hAPP(hAPP(c_Product__Type_OSigma(X27233,X27232),X27230),X27229)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Int__distrib1]) ).

fof(i_0_7722,plain,
    ! [X27203,X27204,X27205,X27206,X27207] : hAPP(hAPP(c_Product__Type_OSigma(X27207,X27206),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27207,tc_HOL_Obool)),X27205),X27204)),X27203) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27207,X27206),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27207,X27206),X27205),X27203)),hAPP(hAPP(c_Product__Type_OSigma(X27207,X27206),X27204),X27203)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Un__distrib1]) ).

fof(i_0_7723,plain,
    ! [X27146,X27147,X27148,X27149,X27150] : hAPP(hAPP(c_Product__Type_OSigma(X27150,X27149),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X27150,tc_HOL_Obool)),X27148),X27147)),X27146) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X27150,X27149),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27150,X27149),X27148),X27146)),hAPP(hAPP(c_Product__Type_OSigma(X27150,X27149),X27147),X27146)),
    inference(variable_rename,[status(thm)],[fact_Sigma__Diff__distrib1]) ).

cnf(i_0_7724,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_5631]) ).

fof(i_0_7725,plain,
    ! [X30150,X30151,X30152,X30153] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30153),X30152),hAPP(c_List_Oset(X30153),c_List_Obutlast(X30153,X30151))))
        | hBOOL(hAPP(hAPP(c_member(X30153),X30152),hAPP(c_List_Oset(X30153),c_List_Obutlast(X30153,hAPP(hAPP(c_List_Oappend(X30153),X30151),X30150))))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X30153),X30152),hAPP(c_List_Oset(X30153),c_List_Obutlast(X30153,X30150))))
        | hBOOL(hAPP(hAPP(c_member(X30153),X30152),hAPP(c_List_Oset(X30153),c_List_Obutlast(X30153,hAPP(hAPP(c_List_Oappend(X30153),X30151),X30150))))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlast__appendI])])]) ).

fof(i_0_7726,plain,
    ! [X26210,X26211,X26212] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X26212,X26212),tc_HOL_Obool)),X26211),X26210))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26212,tc_HOL_Obool)),c_Wellfounded_Oacc(X26212,X26210)),c_Wellfounded_Oacc(X26212,X26211))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__subset])]) ).

fof(i_0_7727,plain,
    ! [X30563,X30564,X30565,X30566,X30567,X30568] :
      ( ~ class_Orderings_Olinorder(X30568)
      | hAPP(X30567,X30566) = hAPP(X30567,X30565)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30564,X30568,X30567),X30565),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30564,X30568,X30567),X30566),X30563)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30564,X30568,X30567),X30566),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30564,X30568,X30567),X30565),X30563)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key__left__comm])]) ).

fof(i_0_7728,plain,
    ! [X33134,X33135,X33136,X33137] :
      ( hAPP(c_Set_Oimage(X33137,X33136,X33135),c_Orderings_Otop__class_Otop(tc_fun(X33137,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33136,tc_HOL_Obool))
      | hAPP(X33135,hAPP(c_Hilbert__Choice_Oinv__into(X33137,X33136,c_Orderings_Otop__class_Otop(tc_fun(X33137,tc_HOL_Obool)),X33135),X33134)) = X33134 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__f__inv__f])]) ).

fof(i_0_7729,plain,
    ! [X22013,X22014] :
      ( X22014 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22013,X22014),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22013),X22014)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22013,X22014)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div__mod])]) ).

fof(i_0_7730,plain,
    ! [X26467,X26468,X26469,X26470,X26471,X26472] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26472,tc_fun(X26471,tc_HOL_Obool)),X26470),hAPP(hAPP(c_COMBB(X26469,tc_fun(X26471,tc_HOL_Obool),X26472),X26468),X26467)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26469,tc_fun(X26471,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26472,X26469,X26467),X26470)),X26468),
    inference(variable_rename,[status(thm)],[fact_INT__extend__simps_I10_J]) ).

fof(i_0_7731,plain,
    ! [X23805,X23806,X23807,X23808,X23809,X23810] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23810,tc_fun(X23809,tc_HOL_Obool)),X23808),hAPP(hAPP(c_COMBB(X23807,tc_fun(X23809,tc_HOL_Obool),X23810),X23806),X23805)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23807,tc_fun(X23809,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23810,X23807,X23805),X23808)),X23806),
    inference(variable_rename,[status(thm)],[fact_UN__extend__simps_I10_J]) ).

fof(i_0_7732,plain,
    ! [X26473,X26474,X26475,X26476,X26477,X26478] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26478,tc_fun(X26477,tc_HOL_Obool)),hAPP(c_Set_Oimage(X26476,X26478,X26475),X26474)),X26473) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26476,tc_fun(X26477,tc_HOL_Obool)),X26474),hAPP(hAPP(c_COMBB(X26478,tc_fun(X26477,tc_HOL_Obool),X26476),X26473),X26475)),
    inference(variable_rename,[status(thm)],[fact_INT__simps_I10_J]) ).

fof(i_0_7733,plain,
    ! [X23817,X23818,X23819,X23820,X23821,X23822] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23822,tc_fun(X23821,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23820,X23822,X23819),X23818)),X23817) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23820,tc_fun(X23821,tc_HOL_Obool)),X23818),hAPP(hAPP(c_COMBB(X23822,tc_fun(X23821,tc_HOL_Obool),X23820),X23817),X23819)),
    inference(variable_rename,[status(thm)],[fact_UN__simps_I10_J]) ).

fof(i_0_7734,plain,
    ! [X22287,X22288] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22288,X22287),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22288),X22287)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22288,X22287)))),
    inference(variable_rename,[status(thm)],[fact_divmod__nat__rel]) ).

cnf(i_0_7735,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_5632]) ).

fof(i_0_7736,plain,
    ! [X21450,X21451,X21452] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21452,tc_HOL_Obool)),X21451),X21450))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21452,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21452,tc_HOL_Obool)),X21450)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21452,tc_HOL_Obool)),X21451))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__anti__mono])]) ).

fof(i_0_7737,plain,
    ! [X18796,X18797,X18798] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18798),X18797))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18798,tc_HOL_Obool)),X18797),hAPP(c_Set_Oimage(X18798,X18798,X18796),X18797)))
      | c_Fun_Oinj__on(X18798,X18798,X18796,X18797) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj__inj])]) ).

fof(i_0_7738,plain,
    ! [X27181,X27182,X27183] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X27183,X27182),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27183,X27182),c_Orderings_Otop__class_Otop(tc_fun(X27183,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27182,tc_HOL_Obool),X27183),X27181))) = hAPP(hAPP(c_Product__Type_OSigma(X27183,X27182),c_Orderings_Otop__class_Otop(tc_fun(X27183,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27182,tc_HOL_Obool),X27183),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27182,tc_HOL_Obool)),X27181))),
    inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV1]) ).

fof(i_0_7739,plain,
    ! [X27184,X27185,X27186] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(X27186,X27185),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(X27186,X27185),X27184),hAPP(c_COMBK(tc_fun(X27185,tc_HOL_Obool),X27186),c_Orderings_Otop__class_Otop(tc_fun(X27185,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(X27186,X27185),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27186,tc_HOL_Obool)),X27184)),hAPP(c_COMBK(tc_fun(X27185,tc_HOL_Obool),X27186),c_Orderings_Otop__class_Otop(tc_fun(X27185,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Compl__Times__UNIV2]) ).

fof(i_0_7740,plain,
    ! [X29257,X29258,X29259,X29260] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29260),X29259),c_Wellfounded_Oacc(X29260,X29258)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29260)),X29257),c_Wellfounded_Oacc(tc_List_Olist(X29260),c_List_Olistrel1(X29260,X29258))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29260)),hAPP(hAPP(c_List_Olist_OCons(X29260),X29259),X29257)),c_Wellfounded_Oacc(tc_List_Olist(X29260),c_List_Olistrel1(X29260,X29258)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__acc__listrel1I])]) ).

fof(i_0_7741,plain,
    ! [X22883,X22884,X22885,X22886] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22886),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22886),X22884),X22885)),X22883))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22886),X22883),X22885)),X22884))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22886),X22885),c_Groups_Ozero__class_Ozero(X22886)))
        | ~ class_Fields_Olinordered__field(X22886) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22886),X22883),X22885)),X22884))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22886),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22886),X22884),X22885)),X22883))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22886),X22885),c_Groups_Ozero__class_Ozero(X22886)))
        | ~ class_Fields_Olinordered__field(X22886) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq])])]) ).

fof(i_0_7742,plain,
    ! [X22764,X22765,X22766,X22767] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22767),X22765),X22766)),X22764))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22767),X22764),X22766)),X22765))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22767),X22766),c_Groups_Ozero__class_Ozero(X22767)))
        | ~ class_Fields_Olinordered__field(X22767) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22767),X22764),X22766)),X22765))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22767),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22767),X22765),X22766)),X22764))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22767),X22766),c_Groups_Ozero__class_Ozero(X22767)))
        | ~ class_Fields_Olinordered__field(X22767) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq])])]) ).

cnf(i_0_7743,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_5564]) ).

fof(i_0_7744,plain,
    ! [X22232,X22233,X22234] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22234,tc_fun(X22234,tc_HOL_Obool))),X22233),X22232))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22234,tc_HOL_Obool)),c_Wellfounded_Oaccp(X22234,X22232)),c_Wellfounded_Oaccp(X22234,X22233))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__subset])]) ).

fof(i_0_7745,plain,
    ! [X19869,X19870,X19871,X19872,X19873,X19874] :
      ( ~ c_Finite__Set_Ofolding__idem(X19874,X19873,X19872,X19871)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19874),X19870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X19874,tc_HOL_Obool)),X19869),X19870))
      | hAPP(c_Fun_Ocomp(X19873,X19873,X19873,hAPP(X19871,X19870)),hAPP(X19871,X19869)) = hAPP(X19871,X19870) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Osubset__comp__idem])]) ).

fof(i_0_7746,plain,
    ! [X30600,X30601,X30602] :
      ( ~ class_Orderings_Olinorder(X30602)
      | ~ hBOOL(hAPP(hAPP(c_member(X30602),X30601),hAPP(c_List_Oset(X30602),X30600)))
      | c_List_Olinorder__class_Oinsort__insert__key(X30602,X30602,c_COMBI(X30602),X30601,X30600) = X30600 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__insert__triv])]) ).

fof(i_0_7747,plain,
    ! [X20982,X20983,X20984] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20984),X20983)),X20982))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20984),hAPP(c_Nat_OSuc,X20983))))
        | X20983 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20982),X20984)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20984)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20984),X20983)),X20982))
        | X20983 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20982),X20984)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20984)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20984),hAPP(c_Nat_OSuc,X20983))))
        | X20983 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20982),X20984)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20984)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__div__lemma])])]) ).

fof(i_0_7748,plain,
    ! [X24570,X24571,X24572,X24573,X24574] :
      ( ~ class_Groups_Oab__group__add(X24574)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24573),X24572))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24573,tc_HOL_Obool)),X24571),X24572))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24573,X24574),X24570),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24573,tc_HOL_Obool)),X24572),X24571)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24574),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24573,X24574),X24570),X24572)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24573,X24574),X24570),X24571)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff])]) ).

cnf(i_0_7749,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_5633]) ).

fof(i_0_7750,plain,
    ! [X30353,X30354,X30355] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30355),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30354)),X30353)))
      | X30353 = hAPP(hAPP(c_List_Oappend(X30354),hAPP(hAPP(c_List_Otake(X30354),X30355),X30353)),hAPP(hAPP(c_List_Olist_OCons(X30354),hAPP(hAPP(c_List_Onth(X30354),X30353),X30355)),hAPP(hAPP(c_List_Odrop(X30354),hAPP(c_Nat_OSuc,X30355)),X30353))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_id__take__nth__drop])]) ).

cnf(i_0_7751,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_5569]) ).

cnf(i_0_7752,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_5570]) ).

cnf(i_0_7753,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_5571]) ).

cnf(i_0_7754,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_5572]) ).

fof(i_0_7755,plain,
    ! [X23099,X23100] :
      ( ( ~ 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),X23100),X23099)),c_Wellfounded_Oless__than))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23100),X23099)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X23100),X23099))
        | 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),X23100),X23099)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__than__iff])]) ).

cnf(i_0_7756,plain,
    c_Int_Opred(c_Int_OBit0(X1)) = c_Int_OBit1(c_Int_Opred(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5634]) ).

fof(i_0_7757,plain,
    ! [X16927,X16928,X16929,X16930,X16931,X16932] : hAPP(c_Set_Oimage(X16932,X16931,X16930),hAPP(c_Set_Oimage(X16929,X16932,X16928),X16927)) = hAPP(c_Set_Oimage(X16929,X16931,hAPP(hAPP(c_COMBB(X16932,X16931,X16929),X16930),X16928)),X16927),
    inference(variable_rename,[status(thm)],[fact_image__image]) ).

fof(i_0_7758,plain,
    ! [X22448,X22449,X22450,X22451,X22452] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X22451),X22448),X22450))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22451,X22452),X22449),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22451,tc_HOL_Obool)),X22450),hAPP(hAPP(c_Set_Oinsert(X22451),X22448),c_Orderings_Obot__class_Obot(tc_fun(X22451,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22452),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22451,X22452),X22449),X22450)),hAPP(X22449,X22448))
        | hAPP(X22449,X22448) = c_Groups_Ozero__class_Ozero(X22452)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22451),X22450))
        | ~ class_Fields_Ofield(X22452) )
      & ( hBOOL(hAPP(hAPP(c_member(X22451),X22448),X22450))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22451,X22452),X22449),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X22451,tc_HOL_Obool)),X22450),hAPP(hAPP(c_Set_Oinsert(X22451),X22448),c_Orderings_Obot__class_Obot(tc_fun(X22451,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22451,X22452),X22449),X22450)
        | hAPP(X22449,X22448) = c_Groups_Ozero__class_Ozero(X22452)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22451),X22450))
        | ~ class_Fields_Ofield(X22452) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5635])])]) ).

cnf(i_0_7759,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_5576]) ).

fof(i_0_7760,plain,
    ! [X30863,X30864,X30865,X30866,X30867] :
      ( hAPP(hAPP(c_List_Omap(X30867,X30866),X30865),X30864) != hAPP(hAPP(c_List_Omap(X30867,X30866),X30865),X30863)
      | ~ c_Fun_Oinj__on(X30867,X30866,X30865,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30867,tc_HOL_Obool)),hAPP(c_List_Oset(X30867),X30864)),hAPP(c_List_Oset(X30867),X30863)))
      | X30864 = X30863 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__inj__on])]) ).

fof(i_0_7761,plain,
    ! [X30858,X30859,X30860,X30861,X30862] :
      ( ( hAPP(hAPP(c_List_Omap(X30862,X30861),X30860),X30859) != hAPP(hAPP(c_List_Omap(X30862,X30861),X30860),X30858)
        | X30859 = X30858
        | ~ c_Fun_Oinj__on(X30862,X30861,X30860,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30862,tc_HOL_Obool)),hAPP(c_List_Oset(X30862),X30859)),hAPP(c_List_Oset(X30862),X30858))) )
      & ( X30859 != X30858
        | hAPP(hAPP(c_List_Omap(X30862,X30861),X30860),X30859) = hAPP(hAPP(c_List_Omap(X30862,X30861),X30860),X30858)
        | ~ c_Fun_Oinj__on(X30862,X30861,X30860,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30862,tc_HOL_Obool)),hAPP(c_List_Oset(X30862),X30859)),hAPP(c_List_Oset(X30862),X30858))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__map__eq__map])])]) ).

fof(i_0_7762,plain,
    ! [X20125,X20126,X20127] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20125),X20126))
        | hBOOL(hAPP(X20127,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20126)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20125))))
        | ~ hBOOL(hAPP(X20127,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20126),X20125)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20126),X20125))
        | hBOOL(hAPP(X20127,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X20127,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20126),X20125)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20126),X20125))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20125),X20126))
        | hBOOL(hAPP(X20127,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20126),X20125)))) )
      & ( ~ hBOOL(hAPP(X20127,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20125),X20126))
        | hBOOL(hAPP(X20127,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20126),X20125)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20126),X20125))
        | ~ hBOOL(hAPP(X20127,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20126)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20125))))
        | hBOOL(hAPP(X20127,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20126),X20125)))) )
      & ( ~ hBOOL(hAPP(X20127,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X20127,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20126)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20125))))
        | hBOOL(hAPP(X20127,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20126),X20125)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int__split])])]) ).

fof(i_0_7763,plain,
    ! [X31034,X31035,X31036,X31037] :
      ( ~ hBOOL(hAPP(c_List_Olistsp(X31037,X31036),X31035))
      | ~ hBOOL(hAPP(c_List_Olistsp(X31037,X31034),X31035))
      | hBOOL(hAPP(c_List_Olistsp(X31037,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31037,tc_HOL_Obool)),X31036),X31034)),X31035)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__infI])]) ).

fof(i_0_7764,plain,
    ! [X33644,X33645,X33646,X33647,X33648] :
      ( ~ class_Rings_Ocomm__semiring__1(X33648)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33648),hAPP(hAPP(c_Power_Opower__class_Opower(X33648),X33647),X33646)),X33645))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33644),X33646))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33648),hAPP(hAPP(c_Power_Opower__class_Opower(X33648),X33647),X33644)),X33645)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__dvd])]) ).

fof(i_0_7765,plain,
    ! [X33440,X33441] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33441),X33440))
      | c_Fun_Obij__betw(tc_Nat_Onat,X33441,esk531_2(X33440,X33441),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X33441),X33440)),X33440) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__nat__finite__1])])]) ).

cnf(i_0_7766,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_5636]) ).

fof(i_0_7767,plain,
    ! [X28922,X28923,X28924,X28925,X28926] :
      ( ~ c_Relation_Osingle__valued(X28926,X28925,hAPP(c_Relation_Oconverse(X28925,X28926),X28924))
      | hAPP(c_Relation_OImage(X28925,X28926,X28924),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28925,tc_HOL_Obool)),X28923),X28922)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28926,tc_HOL_Obool)),hAPP(c_Relation_OImage(X28925,X28926,X28924),X28923)),hAPP(c_Relation_OImage(X28925,X28926,X28924),X28922)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Image__Int__eq])]) ).

fof(i_0_7768,plain,
    ! [X22854,X22855,X22856,X22857,X22858] :
      ( ~ class_Fields_Olinordered__field(X22858)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22858),c_Groups_Ozero__class_Ozero(X22858)),X22857))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22858),X22857),X22856))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22858),c_Groups_Ozero__class_Ozero(X22858)),X22855))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22858),X22855),X22854))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22858),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22858),X22857),X22854)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22858),X22856),X22855))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less2])]) ).

fof(i_0_7769,plain,
    ! [X22859,X22860,X22861,X22862,X22863] :
      ( ~ class_Fields_Olinordered__field(X22863)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22863),c_Groups_Ozero__class_Ozero(X22863)),X22862))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22863),X22862),X22861))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22863),c_Groups_Ozero__class_Ozero(X22863)),X22860))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22863),X22860),X22859))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22863),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22863),X22862),X22859)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22863),X22861),X22860))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__less])]) ).

fof(i_0_7770,plain,
    ! [X18440,X18441,X18442,X18443,X18444] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18444)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18444),X18443),X18442))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18444),X18441),X18440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18444),c_Groups_Ozero__class_Ozero(X18444)),X18442))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18444),c_Groups_Ozero__class_Ozero(X18444)),X18441))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18444),X18443),X18441)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18444),X18442),X18440))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono])]) ).

fof(i_0_7771,plain,
    ! [X18445,X18446,X18447,X18448,X18449] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18449)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18449),X18448),X18447))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18449),X18446),X18445))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18449),c_Groups_Ozero__class_Ozero(X18449)),X18448))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18449),c_Groups_Ozero__class_Ozero(X18449)),X18446))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18449),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18449),X18448),X18446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18449),X18447),X18445))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__mono_H])]) ).

fof(i_0_7772,plain,
    ! [X18455,X18456,X18457,X18458,X18459] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18459)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18459),X18458),X18457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18459),X18456),X18455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18459),c_Groups_Ozero__class_Ozero(X18459)),X18458))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18459),c_Groups_Ozero__class_Ozero(X18459)),X18456))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18459),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18459),X18458),X18456)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18459),X18457),X18455))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less])]) ).

fof(i_0_7773,plain,
    ! [X18450,X18451,X18452,X18453,X18454] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18454)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18454),X18453),X18452))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18454),X18451),X18450))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18454),c_Groups_Ozero__class_Ozero(X18454)),X18453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18454),c_Groups_Ozero__class_Ozero(X18454)),X18451))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18454),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18454),X18453),X18451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18454),X18452),X18450))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less])]) ).

fof(i_0_7774,plain,
    ! [X22864,X22865,X22866,X22867,X22868] :
      ( ~ class_Fields_Olinordered__field(X22868)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22868),c_Groups_Ozero__class_Ozero(X22868)),X22867))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22868),X22867),X22866))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22868),c_Groups_Ozero__class_Ozero(X22868)),X22865))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22868),X22865),X22864))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22868),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22868),X22867),X22864)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22868),X22866),X22865))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__le])]) ).

fof(i_0_7775,plain,
    ! [X18306,X18307,X18308,X18309,X18310] :
      ( ~ class_Rings_Oordered__semiring(X18310)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18310),X18309),X18308))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18310),X18307),X18306))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18310),c_Groups_Ozero__class_Ozero(X18310)),X18309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18310),c_Groups_Ozero__class_Ozero(X18310)),X18307))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18310),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18310),X18309),X18307)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18310),X18308),X18306))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono_H])]) ).

fof(i_0_7776,plain,
    ! [X18311,X18312,X18313,X18314,X18315] :
      ( ~ class_Rings_Oordered__semiring(X18315)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18315),X18314),X18313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18315),X18312),X18311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18315),c_Groups_Ozero__class_Ozero(X18315)),X18313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18315),c_Groups_Ozero__class_Ozero(X18315)),X18312))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18315),X18314),X18312)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18315),X18313),X18311))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__mono])]) ).

cnf(i_0_7777,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_5637]) ).

fof(i_0_7778,plain,
    ! [X24655,X24656,X24657,X24658,X24659] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24658),X24656),X24657))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24658,X24659),X24655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24658,tc_HOL_Obool)),X24657),hAPP(hAPP(c_Set_Oinsert(X24658),X24656),c_Orderings_Obot__class_Obot(tc_fun(X24658,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24659),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24658,X24659),X24655),X24657)),hAPP(X24655,X24656))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24658),X24657))
        | ~ class_Groups_Oab__group__add(X24659) )
      & ( hBOOL(hAPP(hAPP(c_member(X24658),X24656),X24657))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24658,X24659),X24655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24658,tc_HOL_Obool)),X24657),hAPP(hAPP(c_Set_Oinsert(X24658),X24656),c_Orderings_Obot__class_Obot(tc_fun(X24658,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24658,X24659),X24655),X24657)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24658),X24657))
        | ~ class_Groups_Oab__group__add(X24659) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5638])])]) ).

fof(i_0_7779,plain,
    ! [X24650,X24651,X24652,X24653,X24654] :
      ( ~ class_Rings_Oring(X24654)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24653),X24652))
      | ~ hBOOL(hAPP(hAPP(c_member(X24653),X24651),X24652))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24653,X24654),X24650),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24653,tc_HOL_Obool)),X24652),hAPP(hAPP(c_Set_Oinsert(X24653),X24651),c_Orderings_Obot__class_Obot(tc_fun(X24653,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24654),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24653,X24654),X24650),X24652)),hAPP(X24650,X24651)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff1__ring])]) ).

fof(i_0_7780,plain,
    ! [X24663,X24664,X24665] :
      ( ~ class_Fields_Ofield(X24665)
      | X24664 = c_Groups_Oone__class_Oone(X24665)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24665),hAPP(c_Power_Opower__class_Opower(X24665),X24664)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24663)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X24665),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24665),hAPP(hAPP(c_Power_Opower__class_Opower(X24665),X24664),X24663)),c_Groups_Oone__class_Oone(X24665))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24665),X24664),c_Groups_Oone__class_Oone(X24665))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_geometric__sum])]) ).

fof(i_0_7781,plain,
    ! [X30883,X30884] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X30884)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30884),hAPP(c_Groups_Oabs__class_Oabs(X30884),hAPP(c_List_Omonoid__add__class_Olistsum(X30884),X30883))),hAPP(c_List_Omonoid__add__class_Olistsum(X30884),hAPP(hAPP(c_List_Omap(X30884,X30884),c_Groups_Oabs__class_Oabs(X30884)),X30883)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__abs])]) ).

cnf(i_0_7782,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_5639]) ).

fof(i_0_7783,plain,
    ! [X33450,X33451] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33451),X33450))
      | c_Fun_Obij__betw(tc_Nat_Onat,X33451,esk533_2(X33450,X33451),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X33451),X33450)),X33450) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__nat__finite])])]) ).

fof(i_0_7784,plain,
    ! [X33453,X33454] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33454),X33453))
      | c_Fun_Obij__betw(X33454,tc_Nat_Onat,esk534_2(X33453,X33454),X33453,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X33454),X33453))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ex__bij__betw__finite__nat])])]) ).

fof(i_0_7785,plain,
    ! [X24038,X24039,X24040] : 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)),X24040)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24039),X24038)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24039),X24040)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24038),X24040)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastLessThan]) ).

fof(i_0_7786,plain,
    ! [X24531,X24532,X24533,X24534,X24535] :
      ( ~ class_Groups_Ocomm__monoid__add(X24535)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24534),X24533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24533),X24532))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24535),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24535),X24531),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24534),X24533))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24535),X24531),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24533),X24532))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24535),X24531),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24534),X24532)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__add__nat__ivl])]) ).

fof(i_0_7787,plain,
    ! [X24536,X24537,X24538,X24539,X24540] :
      ( ~ class_Groups_Oab__group__add(X24540)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24539),X24538))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24538),X24537))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X24540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24540),X24536),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24539),X24537))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24540),X24536),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24539),X24538))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24540),X24536),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24538),X24537)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat__ivl])]) ).

fof(i_0_7788,plain,
    ! [X18460,X18461,X18462,X18463] :
      ( ~ class_Rings_Olinordered__semiring(X18463)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18463),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18463),X18462),X18461)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18463),X18460),X18461)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18463),c_Groups_Ozero__class_Ozero(X18463)),X18461))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18463),X18462),X18460)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less])]) ).

fof(i_0_7789,plain,
    ! [X18464,X18465,X18466,X18467] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18467)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18467),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18467),X18466),X18465)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18467),X18464),X18465)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18467),c_Groups_Ozero__class_Ozero(X18467)),X18465))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18467),X18466),X18464)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right])]) ).

fof(i_0_7790,plain,
    ! [X20307,X20308,X20309,X20310] :
      ( ~ class_Rings_Olinordered__semidom(X20310)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20310),hAPP(hAPP(c_Power_Opower__class_Opower(X20310),X20309),X20308)),hAPP(hAPP(c_Power_Opower__class_Opower(X20310),X20307),X20308)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20310),c_Groups_Ozero__class_Ozero(X20310)),X20307))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20310),X20309),X20307)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__base])]) ).

fof(i_0_7791,plain,
    ! [X18468,X18469,X18470,X18471] :
      ( ~ class_Rings_Olinordered__semiring(X18471)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18471),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18471),X18470),X18469)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18471),X18470),X18468)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18471),c_Groups_Ozero__class_Ozero(X18471)),X18470))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18471),X18469),X18468)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less])]) ).

fof(i_0_7792,plain,
    ! [X18472,X18473,X18474,X18475] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18475)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18475),X18474),X18473)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18475),X18474),X18472)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18475),c_Groups_Ozero__class_Ozero(X18475)),X18474))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18475),X18473),X18472)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left])]) ).

fof(i_0_7793,plain,
    ! [X18249,X18250,X18251,X18252] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18252),X18251),X18250)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18252),X18251),X18249)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18252),X18250),X18249))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18252),c_Groups_Ozero__class_Ozero(X18252)),X18251))
        | ~ class_Rings_Olinordered__ring__strict(X18252) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18252),X18250),X18249))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18252),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18252),X18251),X18250)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18252),X18251),X18249)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18252),c_Groups_Ozero__class_Ozero(X18252)),X18251))
        | ~ class_Rings_Olinordered__ring__strict(X18252) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos])])]) ).

fof(i_0_7794,plain,
    ! [X18476,X18477,X18478,X18479] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18479)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18479),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18479),X18478),X18477)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18479),X18476),X18477)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18479),c_Groups_Ozero__class_Ozero(X18479)),X18477))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18479),X18478),X18476)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le])]) ).

fof(i_0_7795,plain,
    ! [X18480,X18481,X18482,X18483] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18483)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18483),X18482),X18481)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18483),X18482),X18480)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18483),c_Groups_Ozero__class_Ozero(X18483)),X18482))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18483),X18481),X18480)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le])]) ).

fof(i_0_7796,plain,
    ! [X18432,X18433,X18434,X18435] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18435),X18434),X18433)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18435),X18434),X18432)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18435),X18433),X18432))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18435),c_Groups_Ozero__class_Ozero(X18435)),X18434))
        | ~ class_Rings_Olinordered__ring__strict(X18435) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18435),X18433),X18432))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18435),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18435),X18434),X18433)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18435),X18434),X18432)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18435),c_Groups_Ozero__class_Ozero(X18435)),X18434))
        | ~ class_Rings_Olinordered__ring__strict(X18435) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos])])]) ).

cnf(i_0_7797,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_5640]) ).

fof(i_0_7798,plain,
    ! [X24592,X24593,X24594,X24595] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24595),X24594))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24595,tc_HOL_Obool)),X24594),X24593))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24595,tc_Nat_Onat),X24592),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24595,tc_HOL_Obool)),X24593),X24594)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24595,tc_Nat_Onat),X24592),X24593)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24595,tc_Nat_Onat),X24592),X24594)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__diff__nat])]) ).

fof(i_0_7799,plain,
    ! [X21681,X21682,X21683,X21685] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21683),esk75_3(X21681,X21682,X21683)),X21682))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21683),hAPP(c_Finite__Set_Ofold1(X21683,c_Orderings_Oord__class_Omin(X21683)),X21682)),X21681))
        | X21682 = c_Orderings_Obot__class_Obot(tc_fun(X21683,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21683),X21682))
        | ~ class_Orderings_Olinorder(X21683) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21683),esk75_3(X21681,X21682,X21683)),X21681))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21683),hAPP(c_Finite__Set_Ofold1(X21683,c_Orderings_Oord__class_Omin(X21683)),X21682)),X21681))
        | X21682 = c_Orderings_Obot__class_Obot(tc_fun(X21683,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21683),X21682))
        | ~ class_Orderings_Olinorder(X21683) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21683),X21685),X21682))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21683),X21685),X21681))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21683),hAPP(c_Finite__Set_Ofold1(X21683,c_Orderings_Oord__class_Omin(X21683)),X21682)),X21681))
        | X21682 = c_Orderings_Obot__class_Obot(tc_fun(X21683,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21683),X21682))
        | ~ class_Orderings_Olinorder(X21683) ) ),
    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_7800,plain,
    ! [X21696,X21697,X21698,X21700] :
      ( ( hBOOL(hAPP(hAPP(c_member(X21698),esk78_3(X21696,X21697,X21698)),X21697))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21698),hAPP(c_Finite__Set_Ofold1(X21698,c_Orderings_Oord__class_Omin(X21698)),X21697)),X21696))
        | X21697 = c_Orderings_Obot__class_Obot(tc_fun(X21698,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21698),X21697))
        | ~ class_Orderings_Olinorder(X21698) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21698),esk78_3(X21696,X21697,X21698)),X21696))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21698),hAPP(c_Finite__Set_Ofold1(X21698,c_Orderings_Oord__class_Omin(X21698)),X21697)),X21696))
        | X21697 = c_Orderings_Obot__class_Obot(tc_fun(X21698,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21698),X21697))
        | ~ class_Orderings_Olinorder(X21698) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X21698),X21700),X21697))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21698),X21700),X21696))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21698),hAPP(c_Finite__Set_Ofold1(X21698,c_Orderings_Oord__class_Omin(X21698)),X21697)),X21696))
        | X21697 = c_Orderings_Obot__class_Obot(tc_fun(X21698,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21698),X21697))
        | ~ class_Orderings_Olinorder(X21698) ) ),
    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_7801,plain,
    ! [X26319,X26320,X26321,X26322,X26323,X26324] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26324,tc_fun(X26323,tc_HOL_Obool)),X26322),X26321),X26320))
      | hBOOL(hAPP(hAPP(X26321,X26319),X26320))
      | ~ hBOOL(hAPP(hAPP(c_member(X26324),X26319),X26322)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5641])]) ).

fof(i_0_7802,plain,
    ! [X26313,X26314,X26315,X26316,X26317,X26318] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26318,tc_fun(X26317,tc_HOL_Obool)),X26316),X26315),X26314))
      | ~ hBOOL(hAPP(hAPP(c_member(X26318),X26313),X26316))
      | hBOOL(hAPP(hAPP(X26315,X26313),X26314)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF1__D])]) ).

fof(i_0_7803,plain,
    ! [X20334,X20335,X20336,X20337] :
      ( ~ class_Rings_Olinordered__semidom(X20337)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20337),c_Groups_Oone__class_Oone(X20337)),X20336))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20337),hAPP(hAPP(c_Power_Opower__class_Opower(X20337),X20336),X20335)),hAPP(hAPP(c_Power_Opower__class_Opower(X20337),X20336),X20334)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20335),X20334)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__imp__less__exp])]) ).

fof(i_0_7804,plain,
    ! [X20330,X20331,X20332,X20333] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20333),hAPP(hAPP(c_Power_Opower__class_Opower(X20333),X20332),X20331)),hAPP(hAPP(c_Power_Opower__class_Opower(X20333),X20332),X20330)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20331),X20330))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20333),c_Groups_Oone__class_Oone(X20333)),X20332))
        | ~ class_Rings_Olinordered__semidom(X20333) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20331),X20330))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20333),hAPP(hAPP(c_Power_Opower__class_Opower(X20333),X20332),X20331)),hAPP(hAPP(c_Power_Opower__class_Opower(X20333),X20332),X20330)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20333),c_Groups_Oone__class_Oone(X20333)),X20332))
        | ~ class_Rings_Olinordered__semidom(X20333) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff])])]) ).

fof(i_0_7805,plain,
    ! [X20227,X20228,X20229,X20230] :
      ( ~ class_Rings_Olinordered__semidom(X20230)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20230),c_Groups_Oone__class_Oone(X20230)),X20229))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20230),hAPP(hAPP(c_Power_Opower__class_Opower(X20230),X20229),X20228)),hAPP(hAPP(c_Power_Opower__class_Opower(X20230),X20229),X20227)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20228),X20227)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__le__imp__le__exp])]) ).

fof(i_0_7806,plain,
    ! [X20223,X20224,X20225,X20226] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20226),hAPP(hAPP(c_Power_Opower__class_Opower(X20226),X20225),X20224)),hAPP(hAPP(c_Power_Opower__class_Opower(X20226),X20225),X20223)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20224),X20223))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20226),c_Groups_Oone__class_Oone(X20226)),X20225))
        | ~ class_Rings_Olinordered__semidom(X20226) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20224),X20223))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20226),hAPP(hAPP(c_Power_Opower__class_Opower(X20226),X20225),X20224)),hAPP(hAPP(c_Power_Opower__class_Opower(X20226),X20225),X20223)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20226),c_Groups_Oone__class_Oone(X20226)),X20225))
        | ~ class_Rings_Olinordered__semidom(X20226) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing__iff])])]) ).

fof(i_0_7807,plain,
    ! [X29961,X29962,X29963] :
      ( X29963 = c_List_Olist_ONil(X29962)
      | hBOOL(hAPP(hAPP(c_member(X29962),hAPP(c_Product__Type_Ofst(X29962,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(X29962,X29963),X29961))),hAPP(c_List_Oset(X29962),X29963))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select])]) ).

fof(i_0_7808,plain,
    ! [X27262,X27263,X27264,X27265] : hAPP(c_Finite__Set_Ocard(tc_prod(X27265,X27264)),hAPP(hAPP(c_Product__Type_OSigma(X27265,X27264),hAPP(hAPP(c_Set_Oinsert(X27265),X27263),c_Orderings_Obot__class_Obot(tc_fun(X27265,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(X27264,tc_HOL_Obool),X27265),X27262))) = hAPP(c_Finite__Set_Ocard(X27264),X27262),
    inference(variable_rename,[status(thm)],[fact_card__cartesian__product__singleton]) ).

cnf(i_0_7809,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5642]) ).

fof(i_0_7810,plain,
    ! [X22149,X22150,X22151,X22152,X22153] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22153,X22152,tc_HOL_Obool),X22151),hAPP(hAPP(c_Product__Type_OPair(X22153,X22152),X22150),X22149)))
      | hBOOL(hAPP(hAPP(X22151,X22150),X22149)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitD])]) ).

fof(i_0_7811,plain,
    ! [X22072,X22073,X22074] : c_Fun_Oinj__on(tc_prod(X22074,X22073),tc_prod(X22073,X22074),hAPP(c_Product__Type_Oprod_Oprod__case(X22074,X22073,tc_prod(X22073,X22074)),hAPP(c_COMBC(X22073,X22074,tc_prod(X22073,X22074)),c_Product__Type_OPair(X22073,X22074))),X22072),
    inference(variable_rename,[status(thm)],[fact_swap__inj__on]) ).

fof(i_0_7812,plain,
    ! [X27534,X27535,X27536] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27536),esk273_3(X27534,X27535,X27536)),X27535))
        | 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(X27536,tc_Nat_Onat),X27534),X27535)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27536),X27535)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X27534,esk273_3(X27534,X27535,X27536))))
        | 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(X27536,tc_Nat_Onat),X27534),X27535)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27536),X27535)) ) ),
    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_7813,plain,
    ! [X21939,X21940,X21941,X21942] :
      ( ( ~ 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(X21941,tc_Nat_Onat),X21939),X21940)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21941),X21942),X21940))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X21939,X21942)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21941),X21940)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21941),esk85_3(X21939,X21940,X21941)),X21940))
        | 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(X21941,tc_Nat_Onat),X21939),X21940)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21941),X21940)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X21939,esk85_3(X21939,X21940,X21941))))
        | 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(X21941,tc_Nat_Onat),X21939),X21940)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21941),X21940)) ) ),
    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_7814,plain,
    ! [X24502,X24503,X24504,X24505] :
      ( ~ class_Groups_Ocomm__monoid__add(X24505)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24505),X24504),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24503),hAPP(c_Nat_OSuc,X24502))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24505),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24505,tc_Nat_Onat),X24504),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24503,X24502)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__cl__Suc__ivl])]) ).

fof(i_0_7815,plain,
    ! [X18230,X18231,X18232,X18233] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18233),X18232),X18231)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18233),X18232),X18230)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18233),X18230),X18231))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18233),X18232),c_Groups_Ozero__class_Ozero(X18233)))
        | ~ class_Rings_Olinordered__ring__strict(X18233) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18233),X18230),X18231))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18233),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18233),X18232),X18231)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18233),X18232),X18230)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18233),X18232),c_Groups_Ozero__class_Ozero(X18233)))
        | ~ class_Rings_Olinordered__ring__strict(X18233) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__neg])])]) ).

fof(i_0_7816,plain,
    ! [X18436,X18437,X18438,X18439] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18439),X18438),X18437)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18439),X18438),X18436)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18439),X18436),X18437))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18439),X18438),c_Groups_Ozero__class_Ozero(X18439)))
        | ~ class_Rings_Olinordered__ring__strict(X18439) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18439),X18436),X18437))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18439),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18439),X18438),X18437)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18439),X18438),X18436)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18439),X18438),c_Groups_Ozero__class_Ozero(X18439)))
        | ~ class_Rings_Olinordered__ring__strict(X18439) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__neg])])]) ).

fof(i_0_7817,plain,
    ! [X25037,X25038,X25039] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25039,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25039,tc_HOL_Obool)),X25038),X25037)),X25038)),
    inference(variable_rename,[status(thm)],[fact_Int__lower1]) ).

fof(i_0_7818,plain,
    ! [X25034,X25035,X25036] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25036,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25036,tc_HOL_Obool)),X25035),X25034)),X25034)),
    inference(variable_rename,[status(thm)],[fact_Int__lower2]) ).

fof(i_0_7819,plain,
    ! [X17387,X17388,X17389] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17389,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17389,tc_HOL_Obool)),X17388),X17387)),X17388)),
    inference(variable_rename,[status(thm)],[fact_Diff__subset]) ).

fof(i_0_7820,plain,
    ! [X30907,X30908,X30909,X30910,X30911] :
      ( ~ class_Groups_Ocomm__monoid__add(X30911)
      | ~ hBOOL(hAPP(hAPP(c_member(X30910),X30909),hAPP(c_List_Oset(X30910),X30908)))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30911),hAPP(hAPP(c_List_Omap(X30910,X30911),X30907),X30908)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30911),hAPP(X30907,X30909)),hAPP(c_List_Omonoid__add__class_Olistsum(X30911),hAPP(hAPP(c_List_Omap(X30910,X30911),X30907),c_List_Oremove1(X30910,X30909,X30908)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__map__remove1])]) ).

fof(i_0_7821,plain,
    ! [X24941,X24942,X24943,X24944] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24944,tc_HOL_Obool)),X24943),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24944,tc_HOL_Obool)),X24942),X24941)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24944,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24944,tc_HOL_Obool)),X24943),X24942)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24944,tc_HOL_Obool)),X24943),X24941)),
    inference(variable_rename,[status(thm)],[fact_Int__Un__distrib]) ).

fof(i_0_7822,plain,
    ! [X24899,X24900,X24901,X24902] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24902,tc_HOL_Obool)),X24901),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24902,tc_HOL_Obool)),X24900),X24899)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24902,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24902,tc_HOL_Obool)),X24901),X24900)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24902,tc_HOL_Obool)),X24901),X24899)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int__distrib]) ).

fof(i_0_7823,plain,
    ! [X24937,X24938,X24939,X24940] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24940,tc_HOL_Obool)),X24939),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24940,tc_HOL_Obool)),X24938),X24937)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24940,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24940,tc_HOL_Obool)),X24939),X24938)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24940,tc_HOL_Obool)),X24939),X24937)),
    inference(variable_rename,[status(thm)],[fact_Un__Int__distrib]) ).

fof(i_0_7824,plain,
    ! [X25260,X25261,X25262,X25263] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25263,tc_HOL_Obool)),X25262),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25263,tc_HOL_Obool)),X25261),X25260)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25263,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25263,tc_HOL_Obool)),X25262),X25261)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25263,tc_HOL_Obool)),X25262),X25260)),
    inference(variable_rename,[status(thm)],[fact_Diff__Int]) ).

fof(i_0_7825,plain,
    ! [X25264,X25265,X25266,X25267] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25267,tc_HOL_Obool)),X25266),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25267,tc_HOL_Obool)),X25265),X25264)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25267,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25267,tc_HOL_Obool)),X25266),X25265)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25267,tc_HOL_Obool)),X25266),X25264)),
    inference(variable_rename,[status(thm)],[fact_Diff__Un]) ).

fof(i_0_7826,plain,
    ! [X22431,X22432,X22433,X22434,X22435,X22436] : c_Product__Type_Oprod_Oprod__rec(X22436,X22435,X22434,X22433,hAPP(hAPP(c_Product__Type_OPair(X22436,X22435),X22432),X22431)) = hAPP(hAPP(X22433,X22432),X22431),
    inference(variable_rename,[status(thm)],[fact_prod_Orecs]) ).

fof(i_0_7827,plain,
    ! [X32388,X32389,X32390,X32391,X32392] : hAPP(c_New__DSequence_Oneg__bind(X32392,X32391,X32390,X32389),X32388) = c_Lazy__Sequence_Ohb__bind(X32392,X32391,hAPP(X32390,X32388),hAPP(hAPP(c_COMBC(X32392,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X32391))),X32389),X32388)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__bind__def]) ).

fof(i_0_7828,plain,
    ! [X24493,X24494,X24495,X24496] :
      ( ~ class_Groups_Ocomm__monoid__add(X24496)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24496),X24495),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24494)),hAPP(c_Nat_OSuc,X24493))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24496),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24496,tc_Nat_Onat),X24495),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24494),X24493)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__bounds__Suc__ivl])]) ).

fof(i_0_7829,plain,
    ! [X24041,X24042,X24043] : 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)),X24043)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24042,X24041)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24042),X24043),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24041),X24043)),
    inference(variable_rename,[status(thm)],[fact_image__add__atLeastAtMost]) ).

cnf(i_0_7830,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_5643]) ).

cnf(i_0_7831,plain,
    ( c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5573]) ).

cnf(i_0_7832,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Relation_OId(X1)))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5644]) ).

fof(i_0_7833,plain,
    ! [X27633,X27634,X27635,X27636] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27636),X27635),X27634))
        | ~ hBOOL(hAPP(hAPP(c_member(X27636),X27635),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27636,tc_HOL_Obool)),X27634),hAPP(c_Set_OCollect(X27636),X27633)))) )
      & ( hBOOL(hAPP(X27633,X27635))
        | ~ hBOOL(hAPP(hAPP(c_member(X27636),X27635),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27636,tc_HOL_Obool)),X27634),hAPP(c_Set_OCollect(X27636),X27633)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27636),X27635),X27634))
        | ~ hBOOL(hAPP(X27633,X27635))
        | hBOOL(hAPP(hAPP(c_member(X27636),X27635),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27636,tc_HOL_Obool)),X27634),hAPP(c_Set_OCollect(X27636),X27633)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__Collect])])]) ).

fof(i_0_7834,plain,
    ! [X31495,X31496,X31497,X31498] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31498),X31497),hAPP(c_List_Oset(X31498),X31496)))
      | hBOOL(hAPP(X31495,X31497))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31498)),hAPP(c_List_Ofilter(X31498,X31495),X31496))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31498)),X31496))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5645])]) ).

fof(i_0_7835,plain,
    ! [X24109,X24110,X24111,X24112,X24113] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24113),X24110),X24112))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24113),X24111),X24112))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24113,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24113,X24112),X24111)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24113,X24110),X24109)))
        | ~ class_Orderings_Olinorder(X24113) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24113),X24111),X24109))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24113),X24111),X24112))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24113,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24113,X24112),X24111)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24113,X24110),X24109)))
        | ~ class_Orderings_Olinorder(X24113) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__subset__iff])])]) ).

fof(i_0_7836,plain,
    ! [X23428,X23429,X23430,X23431,X23432,X23433] :
      ( ~ c_Finite__Set_Ofolding__idem(X23433,X23432,X23431,X23430)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23433),X23429))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23433),X23428))
      | hAPP(X23430,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23433,tc_HOL_Obool)),X23429),X23428)) = hAPP(c_Fun_Ocomp(X23432,X23432,X23432,hAPP(X23430,X23429)),hAPP(X23430,X23428)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Ounion__idem])]) ).

cnf(i_0_7837,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_5646]) ).

cnf(i_0_7838,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_5647]) ).

cnf(i_0_7839,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_5648]) ).

fof(i_0_7840,plain,
    ! [X28112,X28113,X28114] :
      ( ~ c_Wellfounded_Owf(X28114,X28113)
      | ~ c_Wellfounded_Owf(X28114,X28112)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X28114,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X28114,X28114),X28113)),hAPP(c_Relation_ORange(X28114,X28114),X28112)) != c_Orderings_Obot__class_Obot(tc_fun(X28114,tc_HOL_Obool))
      | c_Wellfounded_Owf(X28114,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28114,X28114),tc_HOL_Obool)),X28113),X28112)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Un])]) ).

fof(i_0_7841,plain,
    ! [X31243,X31244,X31245,X31246,X31247] :
      ( ~ c_Finite__Set_Ofun__left__comm(X31247,X31246,X31245)
      | hAPP(hAPP(c_Finite__Set_Ofold(X31247,X31246,X31245),X31244),hAPP(c_List_Oset(X31247),X31243)) = hAPP(c_List_Ofoldl(X31246,X31247,hAPP(c_COMBC(X31247,X31246,X31246),X31245),X31244),c_List_Oremdups(X31247,X31243)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups])]) ).

fof(i_0_7842,plain,
    ! [X32459,X32460,X32461,X32462] : c_Predicate_Oconversep(X32462,X32461,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32462,tc_fun(X32461,tc_HOL_Obool))),X32460),X32459)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X32461,tc_fun(X32462,tc_HOL_Obool))),c_Predicate_Oconversep(X32462,X32461,X32460)),c_Predicate_Oconversep(X32462,X32461,X32459)),
    inference(variable_rename,[status(thm)],[fact_converse__meet]) ).

fof(i_0_7843,plain,
    ! [X32463,X32464,X32465,X32466] : c_Predicate_Oconversep(X32466,X32465,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32466,tc_fun(X32465,tc_HOL_Obool))),X32464),X32463)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X32465,tc_fun(X32466,tc_HOL_Obool))),c_Predicate_Oconversep(X32466,X32465,X32464)),c_Predicate_Oconversep(X32466,X32465,X32463)),
    inference(variable_rename,[status(thm)],[fact_converse__join]) ).

fof(i_0_7844,plain,
    ! [X17769,X17770,X17771] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17770),X17771)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17769),X17771)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17770),X17769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17771),X17769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17771),X17770)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17770),X17769))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17770),X17771)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17769),X17771)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17771),X17769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17771),X17770)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__iff])])]) ).

fof(i_0_7845,plain,
    ! [X17139,X17140,X17141] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17140),X17141)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17139),X17141)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17140),X17139))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17141),X17139))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17141),X17140)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17140),X17139))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17140),X17141)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17139),X17141)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17141),X17139))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17141),X17140)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__iff])])]) ).

cnf(i_0_7846,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_5649]) ).

fof(i_0_7847,plain,
    ! [X18253,X18254,X18255,X18256] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18255),c_Groups_Ozero__class_Ozero(X18256)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),c_Groups_Ozero__class_Ozero(X18256)),X18255))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18254)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18253)))
        | ~ class_Rings_Olinordered__ring__strict(X18256) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18253),X18254))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),c_Groups_Ozero__class_Ozero(X18256)),X18255))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18254)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18253)))
        | ~ class_Rings_Olinordered__ring__strict(X18256) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18255),c_Groups_Ozero__class_Ozero(X18256)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18254),X18253))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18254)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18253)))
        | ~ class_Rings_Olinordered__ring__strict(X18256) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18253),X18254))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18254),X18253))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18254)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18253)))
        | ~ class_Rings_Olinordered__ring__strict(X18256) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),c_Groups_Ozero__class_Ozero(X18256)),X18255))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18254),X18253))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18254)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18253)))
        | ~ class_Rings_Olinordered__ring__strict(X18256) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18255),c_Groups_Ozero__class_Ozero(X18256)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),X18253),X18254))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18256),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18254)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18256),X18255),X18253)))
        | ~ class_Rings_Olinordered__ring__strict(X18256) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj])])]) ).

fof(i_0_7848,plain,
    ! [X18257,X18258,X18259,X18260] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18258),c_Groups_Ozero__class_Ozero(X18260)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),c_Groups_Ozero__class_Ozero(X18260)),X18258))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18257),X18258)))
        | ~ class_Rings_Olinordered__ring__strict(X18260) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18257),X18259))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),c_Groups_Ozero__class_Ozero(X18260)),X18258))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18257),X18258)))
        | ~ class_Rings_Olinordered__ring__strict(X18260) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18258),c_Groups_Ozero__class_Ozero(X18260)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18259),X18257))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18257),X18258)))
        | ~ class_Rings_Olinordered__ring__strict(X18260) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18257),X18259))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18259),X18257))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18257),X18258)))
        | ~ class_Rings_Olinordered__ring__strict(X18260) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),c_Groups_Ozero__class_Ozero(X18260)),X18258))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18259),X18257))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18257),X18258)))
        | ~ class_Rings_Olinordered__ring__strict(X18260) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18258),c_Groups_Ozero__class_Ozero(X18260)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),X18257),X18259))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18260),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18259),X18258)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18260),X18257),X18258)))
        | ~ class_Rings_Olinordered__ring__strict(X18260) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj])])]) ).

fof(i_0_7849,plain,
    ! [X17083,X17084,X17085,X17086] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17086),X17085),X17083))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17086,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17086),X17085),X17084)),X17083)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17086,tc_HOL_Obool)),X17084),X17083))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17086,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17086),X17085),X17084)),X17083)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17086),X17085),X17083))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17086,tc_HOL_Obool)),X17084),X17083))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17086,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17086),X17085),X17084)),X17083)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__subset])])]) ).

fof(i_0_7850,plain,
    ! [X24699,X24700,X24701] :
      ( ~ class_Groups_Ocomm__monoid__add(X24701)
      | ~ class_Groups_Ocomm__monoid__mult(X24701)
      | ~ c_Nat__Transfer_Onat__set(X24700)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X24701),X24699),X24700) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24701),hAPP(hAPP(c_COMBB(tc_Int_Oint,X24701,tc_Nat_Onat),X24699),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X24700)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I1_J])]) ).

fof(i_0_7851,plain,
    ! [X21915,X21916,X21917] :
      ( ~ class_Groups_Ocomm__monoid__add(X21917)
      | ~ class_Groups_Ocomm__monoid__mult(X21917)
      | ~ c_Nat__Transfer_Onat__set(X21916)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X21917),X21915),X21916) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X21917),hAPP(hAPP(c_COMBB(tc_Int_Oint,X21917,tc_Nat_Onat),X21915),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21916)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__sum__prod_I2_J])]) ).

fof(i_0_7852,plain,
    ! [X25471,X25472,X25473,X25474,X25475] :
      ( ~ class_Groups_Ocomm__monoid__add(X25475)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25474),X25473))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25474),X25472))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25474,tc_HOL_Obool)),X25473),X25472) != c_Orderings_Obot__class_Obot(tc_fun(X25474,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25474,X25475),X25471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25474,tc_HOL_Obool)),X25473),X25472)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25475),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25474,X25475),X25471),X25473)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X25474,X25475),X25471),X25472)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__Un__disjoint])]) ).

fof(i_0_7853,plain,
    ! [X25486,X25487,X25488,X25489,X25490] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25490)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25489),X25488))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25489),X25487))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25489,tc_HOL_Obool)),X25488),X25487) != c_Orderings_Obot__class_Obot(tc_fun(X25489,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25489,X25490),X25486),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25489,tc_HOL_Obool)),X25488),X25487)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25490),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25489,X25490),X25486),X25488)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25489,X25490),X25486),X25487)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Ounion__disjoint])]) ).

fof(i_0_7854,plain,
    ! [X25481,X25482,X25483,X25484,X25485] :
      ( ~ class_Groups_Ocomm__monoid__mult(X25485)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25484),X25483))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25484),X25482))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25484,tc_HOL_Obool)),X25483),X25482) != c_Orderings_Obot__class_Obot(tc_fun(X25484,tc_HOL_Obool))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25484,X25485),X25481),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25484,tc_HOL_Obool)),X25483),X25482)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25485),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25484,X25485),X25481),X25483)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25484,X25485),X25481),X25482)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__Un__disjoint])]) ).

fof(i_0_7855,plain,
    ! [X24692,X24693,X24694] :
      ( ~ class_Groups_Ocomm__monoid__add(X24694)
      | ~ class_Groups_Ocomm__monoid__mult(X24694)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24694),X24693),X24692) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X24694),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24694,tc_Int_Oint),X24693),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24692)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I1_J])]) ).

fof(i_0_7856,plain,
    ! [X21882,X21883,X21884] :
      ( ~ class_Groups_Ocomm__monoid__add(X21884)
      | ~ class_Groups_Ocomm__monoid__mult(X21884)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,X21884),X21883),X21882) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,X21884),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21884,tc_Int_Oint),X21883),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X21882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__sum__prod_I2_J])]) ).

cnf(i_0_7857,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_5650]) ).

fof(i_0_7858,plain,
    ! [X29317,X29318] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(X29318),tc_List_Olist(X29318)),tc_HOL_Obool)),c_List_Olistrel(X29318,X29317)),c_Transitive__Closure_Ortrancl(tc_List_Olist(X29318),c_List_Olistrel1(X29318,X29317)))),
    inference(variable_rename,[status(thm)],[fact_listrel__subset__rtrancl__listrel1]) ).

fof(i_0_7859,plain,
    ! [X22031,X22032,X22033,X22034] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22033))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22033))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22034,X22033),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22032),X22031)))
        | X22034 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22033),X22032)),X22031) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22033),X22031))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22031),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)),X22033))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22034,X22033),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22032),X22031)))
        | X22034 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22033),X22032)),X22031) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22033))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22031))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22031),X22033))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22034,X22033),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22032),X22031)))
        | X22034 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22033),X22032)),X22031) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22033),X22031))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22031),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)),X22031))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22031),X22033))
        | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22034,X22033),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22032),X22031)))
        | X22034 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X22033),X22032)),X22031) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5651])])]) ).

fof(i_0_7860,plain,
    ! [X24184,X24185] : 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)),X24185)),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),X24184),X24185))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X24185),X24184),
    inference(variable_rename,[status(thm)],[fact_image__add__int__atLeastLessThan]) ).

fof(i_0_7861,plain,
    ! [X30301,X30302,X30303,X30304] : hAPP(hAPP(c_List_Odrop(X30304),X30303),hAPP(hAPP(c_List_Oappend(X30304),X30302),X30301)) = hAPP(hAPP(c_List_Oappend(X30304),hAPP(hAPP(c_List_Odrop(X30304),X30303),X30302)),hAPP(hAPP(c_List_Odrop(X30304),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30303),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30304)),X30302))),X30301)),
    inference(variable_rename,[status(thm)],[fact_drop__append]) ).

fof(i_0_7862,plain,
    ! [X30132,X30133,X30134,X30135] : hAPP(hAPP(c_List_Otake(X30135),X30134),hAPP(hAPP(c_List_Oappend(X30135),X30133),X30132)) = hAPP(hAPP(c_List_Oappend(X30135),hAPP(hAPP(c_List_Otake(X30135),X30134),X30133)),hAPP(hAPP(c_List_Otake(X30135),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30134),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30135)),X30133))),X30132)),
    inference(variable_rename,[status(thm)],[fact_take__append]) ).

fof(i_0_7863,plain,
    ! [X29911,X29912,X29913] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29913,tc_HOL_Obool)),hAPP(c_List_Oset(X29913),c_List_Oremove1(X29913,X29912,X29911))),hAPP(c_List_Oset(X29913),X29911))),
    inference(variable_rename,[status(thm)],[fact_set__remove1__subset]) ).

fof(i_0_7864,plain,
    ! [X29470,X29471,X29472] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29472,tc_HOL_Obool)),hAPP(c_List_Oset(X29472),c_List_Osublist(X29472,X29471,X29470))),hAPP(c_List_Oset(X29472),X29471))),
    inference(variable_rename,[status(thm)],[fact_set__sublist__subset]) ).

fof(i_0_7865,plain,
    ! [X19224,X19225,X19226,X19227] :
      ( ~ c_Fun_Oinj__on(X19227,X19226,X19225,X19224)
      | c_Fun_Oinj__on(X19226,X19227,c_Fun_Othe__inv__into(X19227,X19226,X19224,X19225),hAPP(c_Set_Oimage(X19227,X19226,X19225),X19224)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__the__inv__into])]) ).

fof(i_0_7866,plain,
    ! [X28051,X28052,X28053] : hAPP(c_Relation_ODomain(X28053,X28052),hAPP(c_Set_OCollect(tc_prod(X28053,X28052)),hAPP(c_Product__Type_Oprod_Oprod__case(X28053,X28052,tc_HOL_Obool),X28051))) = hAPP(c_Set_OCollect(X28053),hAPP(hAPP(c_COMBB(tc_fun(X28052,tc_HOL_Obool),tc_HOL_Obool,X28053),c_HOL_OEx(X28052)),X28051)),
    inference(variable_rename,[status(thm)],[fact_Domain__Collect__split]) ).

cnf(i_0_7867,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_5652]) ).

fof(i_0_7868,plain,
    ! [X30493,X30494,X30495,X30496,X30497] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X30497,X30496,X30495)
      | hAPP(hAPP(c_Finite__Set_Ofold(X30497,X30496,X30495),X30494),hAPP(c_List_Oset(X30497),X30493)) = hAPP(c_List_Ofoldl(X30496,X30497,hAPP(c_COMBC(X30497,X30496,X30496),X30495),X30494),X30493) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__set])]) ).

fof(i_0_7869,plain,
    ! [X24616,X24617,X24618,X24619] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24619),X24618),X24617))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24619,tc_Nat_Onat),X24616),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24619,tc_HOL_Obool)),X24617),hAPP(hAPP(c_Set_Oinsert(X24619),X24618),c_Orderings_Obot__class_Obot(tc_fun(X24619,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24619,tc_Nat_Onat),X24616),X24617)),hAPP(X24616,X24618)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24619),X24618),X24617))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24619,tc_Nat_Onat),X24616),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24619,tc_HOL_Obool)),X24617),hAPP(hAPP(c_Set_Oinsert(X24619),X24618),c_Orderings_Obot__class_Obot(tc_fun(X24619,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24619,tc_Nat_Onat),X24616),X24617) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5653])]) ).

fof(i_0_7870,plain,
    ! [X17122,X17123] :
      ( ~ v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X17123)),X17122),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X17123)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
      | v_P(X17122,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X17123)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_assms_I2_J])]) ).

fof(i_0_7871,plain,
    ! [X24400,X24401,X24402,X24403] :
      ( ~ class_Groups_Oab__group__add(X24403)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24402,X24403),hAPP(hAPP(c_COMBB(X24403,X24403,X24402),c_Groups_Ouminus__class_Ouminus(X24403)),X24401)),X24400) = hAPP(c_Groups_Ouminus__class_Ouminus(X24403),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24402,X24403),X24401),X24400)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__negf])]) ).

fof(i_0_7872,plain,
    ! [X25877,X25878,X25879,X25880] :
      ( ~ class_Fields_Olinordered__field(X25880)
      | hAPP(c_Groups_Oabs__class_Oabs(X25880),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25879,X25880),X25878),X25877)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X25879,X25880),hAPP(hAPP(c_COMBB(X25880,X25880,X25879),c_Groups_Oabs__class_Oabs(X25880)),X25878)),X25877) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__setprod])]) ).

fof(i_0_7873,plain,
    ! [X29512,X29513,X29514,X29516,X29517,X29518,X29519,X29521] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29514),esk384_3(X29512,X29513,X29514)),hAPP(c_List_Oset(X29514),X29513)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29516),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29514)),X29513)))
        | hBOOL(hAPP(X29512,hAPP(hAPP(c_List_Onth(X29514),X29513),X29516))) )
      & ( ~ hBOOL(hAPP(X29512,esk384_3(X29512,X29513,X29514)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29516),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29514)),X29513)))
        | hBOOL(hAPP(X29512,hAPP(hAPP(c_List_Onth(X29514),X29513),X29516))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk385_3(X29517,X29518,X29519)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29519)),X29518)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29519),X29521),hAPP(c_List_Oset(X29519),X29518)))
        | hBOOL(hAPP(X29517,X29521)) )
      & ( ~ hBOOL(hAPP(X29517,hAPP(hAPP(c_List_Onth(X29519),X29518),esk385_3(X29517,X29518,X29519))))
        | ~ hBOOL(hAPP(hAPP(c_member(X29519),X29521),hAPP(c_List_Oset(X29519),X29518)))
        | hBOOL(hAPP(X29517,X29521)) ) ),
    inference(distribute,[status(thm)],[inference(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_7874,plain,
    ! [X17040,X17041,X17042,X17043] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17043,tc_HOL_Obool)),X17042),X17041))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17043,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17043),X17040),X17042)),hAPP(hAPP(c_Set_Oinsert(X17043),X17040),X17041))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__mono])]) ).

cnf(i_0_7875,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_5608]) ).

cnf(i_0_7876,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_5609]) ).

cnf(i_0_7877,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_5654]) ).

fof(i_0_7878,plain,
    ! [X31735,X31736,X31737,X31738,X31739] :
      ( ( c_List_Olinorder__class_Osorted(X31737,X31736)
        | ~ c_List_Olinorder__class_Osorted(X31737,hAPP(hAPP(c_List_Oappend(X31737),X31736),X31735))
        | ~ class_Orderings_Olinorder(X31737) )
      & ( c_List_Olinorder__class_Osorted(X31737,X31735)
        | ~ c_List_Olinorder__class_Osorted(X31737,hAPP(hAPP(c_List_Oappend(X31737),X31736),X31735))
        | ~ class_Orderings_Olinorder(X31737) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31737),X31738),hAPP(c_List_Oset(X31737),X31736)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31737),X31739),hAPP(c_List_Oset(X31737),X31735)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31737),X31738),X31739))
        | ~ c_List_Olinorder__class_Osorted(X31737,hAPP(hAPP(c_List_Oappend(X31737),X31736),X31735))
        | ~ class_Orderings_Olinorder(X31737) )
      & ( hBOOL(hAPP(hAPP(c_member(X31737),esk429_3(X31735,X31736,X31737)),hAPP(c_List_Oset(X31737),X31736)))
        | ~ c_List_Olinorder__class_Osorted(X31737,X31736)
        | ~ c_List_Olinorder__class_Osorted(X31737,X31735)
        | c_List_Olinorder__class_Osorted(X31737,hAPP(hAPP(c_List_Oappend(X31737),X31736),X31735))
        | ~ class_Orderings_Olinorder(X31737) )
      & ( hBOOL(hAPP(hAPP(c_member(X31737),esk430_3(X31735,X31736,X31737)),hAPP(c_List_Oset(X31737),X31735)))
        | ~ c_List_Olinorder__class_Osorted(X31737,X31736)
        | ~ c_List_Olinorder__class_Osorted(X31737,X31735)
        | c_List_Olinorder__class_Osorted(X31737,hAPP(hAPP(c_List_Oappend(X31737),X31736),X31735))
        | ~ class_Orderings_Olinorder(X31737) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31737),esk429_3(X31735,X31736,X31737)),esk430_3(X31735,X31736,X31737)))
        | ~ c_List_Olinorder__class_Osorted(X31737,X31736)
        | ~ c_List_Olinorder__class_Osorted(X31737,X31735)
        | c_List_Olinorder__class_Osorted(X31737,hAPP(hAPP(c_List_Oappend(X31737),X31736),X31735))
        | ~ class_Orderings_Olinorder(X31737) ) ),
    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_7879,plain,
    ! [X20322,X20323,X20324] :
      ( ~ class_Rings_Olinordered__semidom(X20324)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),c_Groups_Oone__class_Oone(X20324)),X20323))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20324),hAPP(hAPP(c_Power_Opower__class_Opower(X20324),X20323),X20322)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20324),X20323),hAPP(hAPP(c_Power_Opower__class_Opower(X20324),X20323),X20322)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__less__power__Suc])]) ).

fof(i_0_7880,plain,
    ! [X17378,X17379,X17380,X17381] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17381,tc_HOL_Obool)),X17380),X17379))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17381,tc_HOL_Obool)),X17379),X17378))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17381,tc_HOL_Obool)),X17379),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17381,tc_HOL_Obool)),X17378),X17380)) = X17380 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__diff])]) ).

fof(i_0_7881,plain,
    ! [X23963,X23964,X23965] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23965,tc_HOL_Obool)),X23964),X23963))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X23965,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X23965),X23964)),hAPP(c_Set_OPow(X23965),X23963))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__mono])]) ).

fof(i_0_7882,plain,
    ! [X26659,X26660,X26661,X26662,X26663,X26664] : hAPP(hAPP(c_Fun_Ocomp(X26664,X26663,X26662,hAPP(c_COMBK(X26663,X26664),X26661)),X26660),X26659) = X26661,
    inference(variable_rename,[status(thm)],[fact_K__record__comp]) ).

fof(i_0_7883,plain,
    ! [X30284,X30285,X30286] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X30286,tc_HOL_Obool)),hAPP(c_List_Oset(X30286),hAPP(hAPP(c_List_Odrop(X30286),X30285),X30284))),hAPP(c_List_Oset(X30286),X30284))),
    inference(variable_rename,[status(thm)],[fact_set__drop__subset]) ).

fof(i_0_7884,plain,
    ! [X29463,X29464,X29465] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29465,tc_HOL_Obool)),hAPP(c_List_Oset(X29465),hAPP(hAPP(c_List_Otake(X29465),X29464),X29463))),hAPP(c_List_Oset(X29465),X29463))),
    inference(variable_rename,[status(thm)],[fact_set__take__subset]) ).

fof(i_0_7885,plain,
    ! [X22903,X22904,X22905,X22906] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22906),X22904),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22906),X22903),X22905)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22906),X22904),X22905)),X22903))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22906),c_Groups_Ozero__class_Ozero(X22906)),X22905))
        | ~ class_Fields_Olinordered__field(X22906) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22906),X22904),X22905)),X22903))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22906),X22904),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22906),X22903),X22905)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22906),c_Groups_Ozero__class_Ozero(X22906)),X22905))
        | ~ class_Fields_Olinordered__field(X22906) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq])])]) ).

fof(i_0_7886,plain,
    ! [X22899,X22900,X22901,X22902] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22902),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22902),X22900),X22901)),X22899))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22902),X22900),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22902),X22899),X22901)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22902),c_Groups_Ozero__class_Ozero(X22902)),X22901))
        | ~ class_Fields_Olinordered__field(X22902) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22902),X22900),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22902),X22899),X22901)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22902),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22902),X22900),X22901)),X22899))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22902),c_Groups_Ozero__class_Ozero(X22902)),X22901))
        | ~ class_Fields_Olinordered__field(X22902) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq])])]) ).

fof(i_0_7887,plain,
    ! [X22891,X22892,X22893,X22894] :
      ( ~ class_Fields_Olinordered__field(X22894)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22894),c_Groups_Ozero__class_Ozero(X22894)),X22893))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22894),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22894),X22892),X22893)),X22891))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22894),X22892),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22894),X22891),X22893))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos])]) ).

fof(i_0_7888,plain,
    ! [X22963,X22964,X22965,X22966] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22966),X22964),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22966),X22963),X22965)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22966),X22964),X22965)),X22963))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22966),c_Groups_Ozero__class_Ozero(X22966)),X22965))
        | ~ class_Fields_Olinordered__field(X22966) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22966),X22964),X22965)),X22963))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22966),X22964),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22966),X22963),X22965)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22966),c_Groups_Ozero__class_Ozero(X22966)),X22965))
        | ~ class_Fields_Olinordered__field(X22966) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq])])]) ).

fof(i_0_7889,plain,
    ! [X22967,X22968,X22969,X22970] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22970),X22968),X22969)),X22967))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22970),X22968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22970),X22967),X22969)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22970),c_Groups_Ozero__class_Ozero(X22970)),X22969))
        | ~ class_Fields_Olinordered__field(X22970) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22970),X22968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22970),X22967),X22969)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22970),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22970),X22968),X22969)),X22967))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22970),c_Groups_Ozero__class_Ozero(X22970)),X22969))
        | ~ class_Fields_Olinordered__field(X22970) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq])])]) ).

fof(i_0_7890,plain,
    ! [X22772,X22773,X22774,X22775] :
      ( ~ class_Fields_Olinordered__field(X22775)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22775),c_Groups_Ozero__class_Ozero(X22775)),X22774))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22775),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22775),X22773),X22774)),X22772))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22775),X22773),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22775),X22772),X22774))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos])]) ).

fof(i_0_7891,plain,
    ! [X31949,X31950,X31951,X31952] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31952),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31951)),c_List_OtakeWhile(X31951,X31950,X31949))))
      | hAPP(hAPP(c_List_Onth(X31951),c_List_OtakeWhile(X31951,X31950,X31949)),X31952) = hAPP(hAPP(c_List_Onth(X31951),X31949),X31952) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_takeWhile__nth])]) ).

fof(i_0_7892,plain,
    ! [X21848,X21849,X21850,X21851] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21851)
      | ~ class_Rings_Oring__1(X21851)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21851),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21850,tc_Int_Oint),X21849),X21848)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21850,X21851),hAPP(hAPP(c_COMBB(tc_Int_Oint,X21851,X21850),c_Int_Oring__1__class_Oof__int(X21851)),X21849)),X21848) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setprod])]) ).

fof(i_0_7893,plain,
    ! [X21867,X21868,X21869,X21870] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21870)
      | ~ class_Rings_Osemiring__1(X21870)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21870),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21869,tc_Nat_Onat),X21868),X21867)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21869,X21870),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X21870,X21869),c_Nat_Osemiring__1__class_Oof__nat(X21870)),X21868)),X21867) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setprod])]) ).

cnf(i_0_7894,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_5584]) ).

cnf(i_0_7895,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_5655]) ).

cnf(i_0_7896,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_5656]) ).

fof(i_0_7897,plain,
    ! [X28789,X28790,X28791,X28792] : hAPP(c_Relation_Oconverse(X28792,X28791),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28792,X28791),tc_HOL_Obool)),X28790),X28789)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28791,X28792),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X28792,X28791),X28790)),hAPP(c_Relation_Oconverse(X28792,X28791),X28789)),
    inference(variable_rename,[status(thm)],[fact_converse__Int]) ).

fof(i_0_7898,plain,
    ! [X28770,X28771,X28772,X28773] : hAPP(c_Relation_Oconverse(X28773,X28772),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28773,X28772),tc_HOL_Obool)),X28771),X28770)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28772,X28773),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(X28773,X28772),X28771)),hAPP(c_Relation_Oconverse(X28773,X28772),X28770)),
    inference(variable_rename,[status(thm)],[fact_converse__Un]) ).

fof(i_0_7899,plain,
    ! [X31893,X31894,X31895] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31895)),c_List_OtakeWhile(X31895,X31894,X31893))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31895)),X31893))),
    inference(variable_rename,[status(thm)],[fact_length__takeWhile__le]) ).

fof(i_0_7900,plain,
    ! [X29004,X29005,X29006,X29007] : hAPP(hAPP(c_Nat_Ocompow(X29007,X29007),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X29006),X29005)),X29004) = hAPP(c_Fun_Ocomp(X29007,X29007,X29007,hAPP(hAPP(c_Nat_Ocompow(X29007,X29007),X29006),X29004)),hAPP(hAPP(c_Nat_Ocompow(X29007,X29007),X29005),X29004)),
    inference(variable_rename,[status(thm)],[fact_funpow__add]) ).

fof(i_0_7901,plain,
    ! [X24407,X24408,X24409,X24410] :
      ( ~ class_Rings_Oring__1(X24410)
      | hAPP(c_Int_Oring__1__class_Oof__int(X24410),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24409,tc_Int_Oint),X24408),X24407)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24409,X24410),hAPP(hAPP(c_COMBB(tc_Int_Oint,X24410,X24409),c_Int_Oring__1__class_Oof__int(X24410)),X24408)),X24407) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__setsum])]) ).

fof(i_0_7902,plain,
    ! [X24417,X24418,X24419,X24420] :
      ( ~ class_Rings_Osemiring__1(X24420)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24420),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24419,tc_Nat_Onat),X24418),X24417)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24419,X24420),hAPP(hAPP(c_COMBB(tc_Nat_Onat,X24420,X24419),c_Nat_Osemiring__1__class_Oof__nat(X24420)),X24418)),X24417) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__setsum])]) ).

fof(i_0_7903,plain,
    ! [X26273] : c_Fun_Oinj__on(X26273,tc_fun(X26273,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X26273,tc_fun(X26273,tc_HOL_Obool),tc_fun(X26273,tc_HOL_Obool)),c_Set_Oinsert(X26273)),c_Orderings_Obot__class_Obot(tc_fun(X26273,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(X26273,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__singleton]) ).

fof(i_0_7904,plain,
    ! [X27212,X27213,X27214,X27215] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27215),X27214))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27213),X27212))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27215,X27213)),hAPP(hAPP(c_Product__Type_OSigma(X27215,X27213),X27214),hAPP(c_COMBK(tc_fun(X27213,tc_HOL_Obool),X27215),X27212)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__cartesian__product])]) ).

fof(i_0_7905,plain,
    ! [X18150,X18151,X18152] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18152),X18151))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18152,tc_HOL_Obool)),X18150),X18151))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18152),X18150)),hAPP(c_Finite__Set_Ocard(X18152),X18151)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18152,tc_HOL_Obool)),X18150),X18151)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__psubset])]) ).

fof(i_0_7906,plain,
    ! [X17095,X17096,X17097,X17098,X17099] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17099),X17098))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17097,tc_HOL_Obool)),X17096),hAPP(c_Set_Oimage(X17099,X17097,X17095),X17098)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17097),X17096)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__surj])]) ).

cnf(i_0_7907,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_5657]) ).

fof(i_0_7908,plain,
    ! [X33347] : c_Fun_Obij__betw(X33347,X33347,c_Fun_Oid(X33347),c_Orderings_Otop__class_Otop(tc_fun(X33347,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X33347,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_bij__id]) ).

fof(i_0_7909,plain,
    ! [X24882,X24883,X24884,X24885,X24886] :
      ( ~ c_Fun_Oinj__on(X24886,X24885,X24884,X24883)
      | ~ c_Fun_Oinj__on(X24886,X24885,X24884,X24882)
      | c_Fun_Oinj__on(X24886,X24885,X24884,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24886,tc_HOL_Obool)),X24883),X24882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Int])]) ).

fof(i_0_7910,plain,
    ! [X30317,X30318,X30319,X30320] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30320),X30319)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30318)),X30317)))
      | hAPP(hAPP(c_List_Onth(X30318),hAPP(hAPP(c_List_Odrop(X30318),X30320),X30317)),X30319) = hAPP(hAPP(c_List_Onth(X30318),X30317),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30320),X30319)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop])]) ).

fof(i_0_7911,plain,
    ! [X24624,X24625,X24626,X24627] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24626)),X24625))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24627),X24624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24625,hAPP(c_Nat_OSuc,X24626))) = c_Groups_Ozero__class_Ozero(X24627)
        | ~ class_Groups_Ocomm__monoid__add(X24627) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24626)),X24625))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24627),X24624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24625,hAPP(c_Nat_OSuc,X24626))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24627),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24627),X24624),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24625,X24626))),hAPP(X24624,hAPP(c_Nat_OSuc,X24626)))
        | ~ class_Groups_Ocomm__monoid__add(X24627) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5658])])]) ).

fof(i_0_7912,plain,
    ! [X31876,X31877,X31878,X31879] :
      ( ~ class_Orderings_Olinorder(X31879)
      | ~ c_List_Olinorder__class_Osorted(X31879,hAPP(c_List_Orev(X31879),X31878))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31877),X31876))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31876),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31879)),X31878)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31879),hAPP(hAPP(c_List_Onth(X31879),X31878),X31876)),hAPP(hAPP(c_List_Onth(X31879),X31878),X31877))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__rev__nth__mono])]) ).

fof(i_0_7913,plain,
    ! [X30087,X30088,X30089,X30090,X30091,X30092] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30092)),X30091) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30090)),X30089)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30092)),X30088) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30090)),X30087)
      | hAPP(hAPP(c_List_Ozip(X30092,X30090),hAPP(hAPP(c_List_Oappend(X30092),X30091),X30088)),hAPP(hAPP(c_List_Oappend(X30090),X30089),X30087)) = hAPP(hAPP(c_List_Oappend(tc_prod(X30092,X30090)),hAPP(hAPP(c_List_Ozip(X30092,X30090),X30091),X30089)),hAPP(hAPP(c_List_Ozip(X30092,X30090),X30088),X30087)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__append])]) ).

fof(i_0_7914,plain,
    ! [X30852,X30853,X30854,X30855,X30856] : c_List_Olist_Olist__size(X30856,X30855,hAPP(hAPP(c_List_Omap(X30854,X30856),X30853),X30852)) = c_List_Olist_Olist__size(X30854,hAPP(c_Fun_Ocomp(X30856,tc_Nat_Onat,X30854,X30855),X30853),X30852),
    inference(variable_rename,[status(thm)],[fact_list__size__map]) ).

fof(i_0_7915,plain,
    ! [X27511,X27512,X27513,X27514] :
      ( ~ c_Relation_Orefl__on(X27514,X27513,X27512)
      | ~ hBOOL(hAPP(hAPP(c_member(X27514),X27511),X27513))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X27514,X27514)),hAPP(hAPP(c_Product__Type_OPair(X27514,X27514),X27511),X27511)),X27512)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__onD])]) ).

fof(i_0_7916,plain,
    ! [X23861,X23862,X23863,X23864,X23865] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23865),X23864),X23863))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23862,tc_HOL_Obool)),hAPP(X23861,X23864)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23865,tc_fun(X23862,tc_HOL_Obool)),X23863),X23861))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__upper])]) ).

fof(i_0_7917,plain,
    ! [X29818,X29819,X29820,X29821] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29821) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X29820),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29821)),hAPP(hAPP(c_List_Olist_OCons(X29820),X29819),X29818)) = c_List_Olist_ONil(X29820) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29821) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X29820),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29821)),hAPP(hAPP(c_List_Olist_OCons(X29820),X29819),X29818)) = hAPP(hAPP(c_List_Olist_OCons(X29820),X29819),hAPP(hAPP(c_List_Otake(X29820),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29821)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29818)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons__number__of])]) ).

fof(i_0_7918,plain,
    ! [X22091,X22092,X22093,X22094,X22095,X22096] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22096,tc_fun(X22095,tc_HOL_Obool))),X22094),X22093))
      | ~ hBOOL(hAPP(hAPP(X22094,X22092),X22091))
      | hBOOL(hAPP(hAPP(X22093,X22092),X22091)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate2D])]) ).

fof(i_0_7919,plain,
    ! [X22085,X22086,X22087,X22088,X22089,X22090] :
      ( ~ hBOOL(hAPP(hAPP(X22090,X22089),X22088))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X22087,tc_fun(X22086,tc_HOL_Obool))),X22090),X22085))
      | hBOOL(hAPP(hAPP(X22085,X22089),X22088)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate2D])]) ).

fof(i_0_7920,plain,
    ! [X21678,X21679,X21680] :
      ( ~ class_Orderings_Olinorder(X21680)
      | X21679 = c_Orderings_Obot__class_Obot(tc_fun(X21680,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21680,tc_HOL_Obool)),X21679),X21678))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21680),X21678))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21680),hAPP(c_Finite__Set_Ofold1(X21680,c_Orderings_Oord__class_Omin(X21680)),X21678)),hAPP(c_Finite__Set_Ofold1(X21680,c_Orderings_Oord__class_Omin(X21680)),X21679))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__antimono])]) ).

fof(i_0_7921,plain,
    ! [X23146,X23147,X23148,X23149] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23149),X23148),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23149,tc_HOL_Obool)),X23147),X23146)))
        | hBOOL(hAPP(hAPP(c_member(X23149),X23148),X23147))
        | hBOOL(hAPP(hAPP(c_member(X23149),X23148),X23146)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23149),X23148),X23147))
        | hBOOL(hAPP(hAPP(c_member(X23149),X23148),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23149,tc_HOL_Obool)),X23147),X23146))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23149),X23148),X23146))
        | hBOOL(hAPP(hAPP(c_member(X23149),X23148),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23149,tc_HOL_Obool)),X23147),X23146))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__iff])])]) ).

fof(i_0_7922,plain,
    ! [X23134,X23135,X23136,X23137] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23137),X23136),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23137,tc_HOL_Obool)),X23135),X23134)))
      | hBOOL(hAPP(hAPP(c_member(X23137),X23136),X23135))
      | hBOOL(hAPP(hAPP(c_member(X23137),X23136),X23134)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5659])]) ).

cnf(i_0_7923,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_5660]) ).

fof(i_0_7924,plain,
    ! [X32637,X32638,X32639] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X32639),c_Groups_Ozero__class_Ozero(X32639)),esk482_3(X32637,X32638,X32639)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32639),X32638),X32637))
        | ~ class_Fields_Olinordered__field(X32639) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32639),X32638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X32639),X32637),esk482_3(X32637,X32638,X32639))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32639),X32638),X32637))
        | ~ class_Fields_Olinordered__field(X32639) ) ),
    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_7925,plain,
    ! [X30474,X30475,X30476,X30477,X30478,X30479] : hAPP(c_List_Ofoldl(X30479,X30478,X30477,X30476),hAPP(hAPP(c_List_Olist_OCons(X30478),X30475),X30474)) = hAPP(c_List_Ofoldl(X30479,X30478,X30477,hAPP(hAPP(X30477,X30476),X30475)),X30474),
    inference(variable_rename,[status(thm)],[fact_foldl__Cons]) ).

fof(i_0_7926,plain,
    ! [X31883,X31884] :
      ( ( X31883 != c_List_Olist_ONil(tc_List_Olist(X31884))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31884))),c_List_Otranspose(X31884,X31883)) = 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(X31884),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31884))),X31883))) )
      & ( X31883 = c_List_Olist_ONil(tc_List_Olist(X31884))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31884))),c_List_Otranspose(X31884,X31883)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31884)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X31884)),X31883),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(X31884),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31884))),X31883))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__transpose__sorted])])]) ).

fof(i_0_7927,plain,
    ! [X20216,X20217,X20218,X20219] :
      ( ~ class_Rings_Olinordered__semidom(X20219)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20219),X20218),X20217))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20219),c_Groups_Ozero__class_Ozero(X20219)),X20218))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20216))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20219),hAPP(hAPP(c_Power_Opower__class_Opower(X20219),X20218),X20216)),hAPP(hAPP(c_Power_Opower__class_Opower(X20219),X20217),X20216))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__mono])]) ).

fof(i_0_7928,plain,
    ! [X20235,X20236,X20237,X20238] :
      ( ~ class_Rings_Olinordered__semidom(X20238)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20237),X20236))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20238),c_Groups_Ozero__class_Ozero(X20238)),X20235))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20238),X20235),c_Groups_Oone__class_Oone(X20238)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20238),hAPP(hAPP(c_Power_Opower__class_Opower(X20238),X20235),X20236)),hAPP(hAPP(c_Power_Opower__class_Opower(X20238),X20235),X20237))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__decreasing])]) ).

fof(i_0_7929,plain,
    ! [X20231,X20232,X20233,X20234] :
      ( ~ class_Rings_Olinordered__semidom(X20234)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20233),X20232))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20234),c_Groups_Ozero__class_Ozero(X20234)),X20231))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20234),X20231),c_Groups_Oone__class_Oone(X20234)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20234),hAPP(hAPP(c_Power_Opower__class_Opower(X20234),X20231),X20232)),hAPP(hAPP(c_Power_Opower__class_Opower(X20234),X20231),X20233))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__decreasing])]) ).

fof(i_0_7930,plain,
    ! [X26830,X26831,X26832,X26833,X26834] : hAPP(c_Set_Ovimage(X26834,X26833,X26832),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26833,tc_HOL_Obool)),X26831),X26830)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26834,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26834,X26833,X26832),X26831)),hAPP(c_Set_Ovimage(X26834,X26833,X26832),X26830)),
    inference(variable_rename,[status(thm)],[fact_vimage__Int]) ).

fof(i_0_7931,plain,
    ! [X26800,X26801,X26802,X26803,X26804] : hAPP(c_Set_Ovimage(X26804,X26803,X26802),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26803,tc_HOL_Obool)),X26801),X26800)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26804,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26804,X26803,X26802),X26801)),hAPP(c_Set_Ovimage(X26804,X26803,X26802),X26800)),
    inference(variable_rename,[status(thm)],[fact_vimage__Un]) ).

fof(i_0_7932,plain,
    ! [X26785,X26786,X26787,X26788,X26789] : hAPP(c_Set_Ovimage(X26789,X26788,X26787),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26788,tc_HOL_Obool)),X26786),X26785)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26789,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26789,X26788,X26787),X26786)),hAPP(c_Set_Ovimage(X26789,X26788,X26787),X26785)),
    inference(variable_rename,[status(thm)],[fact_vimage__Diff]) ).

fof(i_0_7933,plain,
    ! [X24003,X24004,X24005,X24006,X24007] : hAPP(c_Relation_OImage(X24007,X24006,X24005),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24007,tc_HOL_Obool)),X24004),X24003)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24006,tc_HOL_Obool)),hAPP(c_Relation_OImage(X24007,X24006,X24005),X24004)),hAPP(c_Relation_OImage(X24007,X24006,X24005),X24003)),
    inference(variable_rename,[status(thm)],[fact_Image__Un]) ).

fof(i_0_7934,plain,
    ! [X23174,X23175,X23176,X23177,X23178] : hAPP(c_Set_Oimage(X23178,X23177,X23176),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23178,tc_HOL_Obool)),X23175),X23174)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23177,tc_HOL_Obool)),hAPP(c_Set_Oimage(X23178,X23177,X23176),X23175)),hAPP(c_Set_Oimage(X23178,X23177,X23176),X23174)),
    inference(variable_rename,[status(thm)],[fact_image__Un]) ).

fof(i_0_7935,plain,
    ! [X30045,X30046,X30047,X30048] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30048)),X30047),c_List_Olists(X30048,X30045)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30048)),hAPP(hAPP(c_List_Oappend(X30048),X30047),X30046)),c_List_Olists(X30048,X30045))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30048)),X30046),c_List_Olists(X30048,X30045)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30048)),hAPP(hAPP(c_List_Oappend(X30048),X30047),X30046)),c_List_Olists(X30048,X30045))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30048)),X30047),c_List_Olists(X30048,X30045)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30048)),X30046),c_List_Olists(X30048,X30045)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30048)),hAPP(hAPP(c_List_Oappend(X30048),X30047),X30046)),c_List_Olists(X30048,X30045))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__lists__conv])])]) ).

cnf(i_0_7936,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_5648]) ).

fof(i_0_7937,plain,
    ! [X24154,X24155,X24156] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24156,tc_HOL_Obool)),X24155),X24154))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X24156,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(X24156,X24155)),c_Predicate_OPowp(X24156,X24154))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__mono])]) ).

fof(i_0_7938,plain,
    ! [X31195,X31196,X31197,X31198] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31198),X31197))
      | ~ hBOOL(hAPP(c_List_Odistinct(X31196),X31195))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X31198,X31196)),c_Enum_Oproduct(X31198,X31196,X31197,X31195))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__product])]) ).

fof(i_0_7939,plain,
    ! [X18663,X18664,X18665,X18666] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18666),X18665))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18664),X18663))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X18666,X18664)),c_Sum__Type_OPlus(X18666,X18664,X18665,X18663))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Plus])]) ).

cnf(i_0_7940,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_5661]) ).

fof(i_0_7941,plain,
    ! [X19818,X19819,X19820,X19821,X19822,X19823] :
      ( ~ c_Finite__Set_Ofolding(X19823,X19822,X19821,X19820)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19823),X19819))
      | hBOOL(hAPP(hAPP(c_member(X19823),X19818),X19819))
      | hAPP(X19820,hAPP(hAPP(c_Set_Oinsert(X19823),X19818),X19819)) = hAPP(c_Fun_Ocomp(X19822,X19822,X19822,hAPP(X19820,X19819)),hAPP(X19821,X19818)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5662])]) ).

fof(i_0_7942,plain,
    ! [X24375,X24376,X24377,X24378] :
      ( X24378 != X24377
      | ~ hBOOL(hAPP(hAPP(c_member(X24376),X24378),X24375))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X24376,X24376)),hAPP(hAPP(c_Product__Type_OPair(X24376,X24376),X24378),X24377)),c_Relation_OId__on(X24376,X24375))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__on__eqI])]) ).

fof(i_0_7943,plain,
    ! [X27538,X27539] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27539),c_Int_OInteg))
      | ~ hBOOL(hAPP(X27538,hAPP(c_Int_ORep__Integ,esk274_2(X27538,X27539))))
      | hBOOL(hAPP(X27538,X27539)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__induct])])]) ).

cnf(i_0_7944,plain,
    ( c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3)
    | c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Oupt(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5585]) ).

fof(i_0_7945,plain,
    ! [X30136,X30137,X30138,X30139,X30140] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30140),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30139)),X30138)))
      | hAPP(hAPP(c_List_Olist__update(X30139,hAPP(hAPP(c_List_Oappend(X30139),X30138),X30137)),X30140),X30136) = hAPP(hAPP(c_List_Oappend(X30139),hAPP(hAPP(c_List_Olist__update(X30139,X30138),X30140),X30136)),X30137) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__append1])]) ).

fof(i_0_7946,plain,
    ! [X33615,X33616,X33617] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33617),X33616)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33617),X33615)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33617))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33616),X33615)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel])]) ).

fof(i_0_7947,plain,
    ! [X33612,X33613,X33614] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33614),X33613)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33614),X33612)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33613),X33612))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33614)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33613),X33612))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33614),X33613)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33614),X33612)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33614)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1])])]) ).

fof(i_0_7948,plain,
    ! [X20250,X20251,X20252] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20252))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20252),X20251)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20252),X20250)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20251),X20250)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less])]) ).

fof(i_0_7949,plain,
    ! [X18963,X18964,X18965] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18965),X18964)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18965),X18963)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18964),X18963))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18965)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18964),X18963))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18965),X18964)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18965),X18963)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18965)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1])])]) ).

fof(i_0_7950,plain,
    ! [X18514,X18515,X18516] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18516),X18515)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18514),X18515)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18515))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18516),X18514)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18515))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18516),X18515)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18514),X18515))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18516),X18514))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18516),X18515)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18514),X18515))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel2])])]) ).

fof(i_0_7951,plain,
    ! [X18966,X18967,X18968] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18968),X18967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18968),X18966)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18967),X18966))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18968)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18967),X18966))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18968),X18967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18968),X18966)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18968)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1])])]) ).

fof(i_0_7952,plain,
    ! [X18511,X18512,X18513] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18513),X18512)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18513),X18511)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18513))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18512),X18511)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18513))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18513),X18512)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18513),X18511))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18512),X18511))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18513),X18512)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18513),X18511))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1])])]) ).

fof(i_0_7953,plain,
    ! [X33603,X33604,X33605] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33605),X33604)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X33605),X33603)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X33605))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33604),X33603)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le])]) ).

fof(i_0_7954,plain,
    ! [X28156,X28157,X28158] :
      ( ~ c_Wellfounded_Owf(X28158,X28157)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28158,tc_HOL_Obool)),X28156),hAPP(c_Relation_OImage(X28158,X28158,X28157),X28156)))
      | X28156 = c_Orderings_Obot__class_Obot(tc_fun(X28158,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfE__pf])]) ).

fof(i_0_7955,plain,
    ! [X24421,X24422,X24423] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24423,tc_Nat_Onat),X24422),X24421)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24423,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X24423),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X24422)),X24421),
    inference(variable_rename,[status(thm)],[fact_int__setsum]) ).

fof(i_0_7956,plain,
    ! [X21871,X21872,X21873] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21873,tc_Nat_Onat),X21872),X21871)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21873,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,X21873),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X21872)),X21871),
    inference(variable_rename,[status(thm)],[fact_int__setprod]) ).

fof(i_0_7957,plain,
    ! [X19755,X19756,X19757,X19758,X19759] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19759,X19758,X19757)
      | hAPP(c_Fun_Ocomp(X19758,X19758,X19758,hAPP(X19757,X19756)),hAPP(X19757,X19755)) = hAPP(c_Fun_Ocomp(X19758,X19758,X19758,hAPP(X19757,X19755)),hAPP(X19757,X19756)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__comp__comm])]) ).

fof(i_0_7958,plain,
    ! [X29749,X29750,X29751,X29752] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29752),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29751)),X29750)))
      | hBOOL(hAPP(hAPP(c_member(X29751),X29749),hAPP(c_List_Oset(X29751),hAPP(hAPP(c_List_Olist__update(X29751,X29750),X29752),X29749)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__update__memI])]) ).

fof(i_0_7959,plain,
    ! [X23676,X23677,X23678,X23679,X23680,X23681] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23681),X23680),X23679))
      | ~ hBOOL(hAPP(hAPP(c_member(X23678),X23677),hAPP(X23676,X23680)))
      | hBOOL(hAPP(hAPP(c_member(X23678),X23677),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23681,tc_fun(X23678,tc_HOL_Obool)),X23679),X23676))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__I])]) ).

fof(i_0_7960,plain,
    ! [X21929,X21930,X21931,X21932,X21933,X21934] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21934,X21933),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21932),X21931)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21934,X21933),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21930),X21929)))
      | X21933 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X21932 = X21930 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__quotient])]) ).

fof(i_0_7961,plain,
    ! [X21923,X21924,X21925,X21926,X21927,X21928] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21928,X21927),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21926),X21925)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21928,X21927),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21924),X21923)))
      | X21927 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X21925 = X21923 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_unique__remainder])]) ).

fof(i_0_7962,plain,
    ! [X18651,X18652,X18653,X18654] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18654),hAPP(c_Set_Oimage(X18653,X18654,X18652),X18651)))
      | ~ c_Fun_Oinj__on(X18653,X18654,X18652,X18651)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X18653),X18651)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageD])]) ).

cnf(i_0_7963,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_5663]) ).

fof(i_0_7964,plain,
    ! [X33877,X33878,X33879,X33880] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33880),X33879),X33878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33880),X33879),X33877)))
        | X33879 = c_Groups_Ozero__class_Ozero(X33880)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33880),X33878),X33877))
        | ~ class_Rings_Oidom(X33880) )
      & ( X33879 != c_Groups_Ozero__class_Ozero(X33880)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33880),X33879),X33878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33880),X33879),X33877)))
        | ~ class_Rings_Oidom(X33880) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33880),X33878),X33877))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33880),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33880),X33879),X33878)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33880),X33879),X33877)))
        | ~ class_Rings_Oidom(X33880) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left])])]) ).

fof(i_0_7965,plain,
    ! [X33881,X33882,X33883,X33884] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33884),X33883),X33882)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33884),X33881),X33882)))
        | X33882 = c_Groups_Ozero__class_Ozero(X33884)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33884),X33883),X33881))
        | ~ class_Rings_Oidom(X33884) )
      & ( X33882 != c_Groups_Ozero__class_Ozero(X33884)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33884),X33883),X33882)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33884),X33881),X33882)))
        | ~ class_Rings_Oidom(X33884) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33884),X33883),X33881))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33884),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33884),X33883),X33882)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33884),X33881),X33882)))
        | ~ class_Rings_Oidom(X33884) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right])])]) ).

fof(i_0_7966,plain,
    ! [X28893,X28894,X28895,X28896] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28896,X28895),tc_HOL_Obool)),X28894),X28893))
      | ~ c_Relation_Osingle__valued(X28896,X28895,X28893)
      | c_Relation_Osingle__valued(X28896,X28895,X28894) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__subset])]) ).

fof(i_0_7967,plain,
    ! [X32280,X32281,X32282,X32285,X32286,X32287,X32288,X32289] :
      ( ( X32280 = hAPP(hAPP(c_List_Oappend(X32282),esk472_3(X32280,X32281,X32282)),hAPP(hAPP(c_List_Olist_OCons(X32282),X32281),esk473_3(X32280,X32281,X32282)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32282),X32281),hAPP(c_List_Oset(X32282),X32280))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32282),X32281),hAPP(c_List_Oset(X32282),esk473_3(X32280,X32281,X32282))))
        | ~ hBOOL(hAPP(hAPP(c_member(X32282),X32281),hAPP(c_List_Oset(X32282),X32280))) )
      & ( X32285 != hAPP(hAPP(c_List_Oappend(X32287),X32288),hAPP(hAPP(c_List_Olist_OCons(X32287),X32286),X32289))
        | hBOOL(hAPP(hAPP(c_member(X32287),X32286),hAPP(c_List_Oset(X32287),X32289)))
        | hBOOL(hAPP(hAPP(c_member(X32287),X32286),hAPP(c_List_Oset(X32287),X32285))) ) ),
    inference(distribute,[status(thm)],[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_5664])])])])])]) ).

fof(i_0_7968,plain,
    ! [X32270,X32271,X32272,X32275,X32276,X32277,X32278,X32279] :
      ( ( X32270 = hAPP(hAPP(c_List_Oappend(X32272),esk470_3(X32270,X32271,X32272)),hAPP(hAPP(c_List_Olist_OCons(X32272),X32271),esk471_3(X32270,X32271,X32272)))
        | ~ hBOOL(hAPP(hAPP(c_member(X32272),X32271),hAPP(c_List_Oset(X32272),X32270))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32272),X32271),hAPP(c_List_Oset(X32272),esk470_3(X32270,X32271,X32272))))
        | ~ hBOOL(hAPP(hAPP(c_member(X32272),X32271),hAPP(c_List_Oset(X32272),X32270))) )
      & ( X32275 != hAPP(hAPP(c_List_Oappend(X32277),X32278),hAPP(hAPP(c_List_Olist_OCons(X32277),X32276),X32279))
        | hBOOL(hAPP(hAPP(c_member(X32277),X32276),hAPP(c_List_Oset(X32277),X32278)))
        | hBOOL(hAPP(hAPP(c_member(X32277),X32276),hAPP(c_List_Oset(X32277),X32275))) ) ),
    inference(distribute,[status(thm)],[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_5665])])])])])]) ).

cnf(i_0_7969,plain,
    c_Int_Osucc(c_Int_OBit1(X1)) = c_Int_OBit0(c_Int_Osucc(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5666]) ).

fof(i_0_7970,plain,
    ! [X17938,X17939,X17940,X17941] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17941),X17940),X17939)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17941),X17938),X17939)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17941),X17940),X17938))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17941) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17941),X17940),X17938))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17941),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17941),X17940),X17939)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17941),X17938),X17939)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17941) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right])])]) ).

fof(i_0_7971,plain,
    ! [X17917,X17918,X17919,X17920] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17920)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17920),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17920),X17919),X17918)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17920),X17917),X17918)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17920),X17919),X17917)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__right])]) ).

fof(i_0_7972,plain,
    ! [X17934,X17935,X17936,X17937] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17937),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17937),X17936),X17935)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17937),X17936),X17934)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17937),X17935),X17934))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17937) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17937),X17935),X17934))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17937),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17937),X17936),X17935)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17937),X17936),X17934)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17937) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__cancel__left])])]) ).

fof(i_0_7973,plain,
    ! [X17913,X17914,X17915,X17916] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17916)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17916),X17915),X17914)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17916),X17915),X17913)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17916),X17914),X17913)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__imp__less__left])]) ).

fof(i_0_7974,plain,
    ! [X17909,X17910,X17911,X17912] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17912),X17911),X17910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17912),X17909),X17910)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17912),X17911),X17909))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17912) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17912),X17911),X17909))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17912),X17911),X17910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17912),X17909),X17910)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17912) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right])])]) ).

fof(i_0_7975,plain,
    ! [X17888,X17889,X17890,X17891] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17891)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17891),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17891),X17890),X17889)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17891),X17888),X17889)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17891),X17890),X17888)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__right])]) ).

fof(i_0_7976,plain,
    ! [X17905,X17906,X17907,X17908] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17908),X17907),X17906)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17908),X17907),X17905)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17908),X17906),X17905))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17908) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17908),X17906),X17905))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17908),X17907),X17906)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17908),X17907),X17905)))
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17908) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__cancel__left])])]) ).

fof(i_0_7977,plain,
    ! [X17884,X17885,X17886,X17887] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X17887)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17887),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17887),X17886),X17885)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17887),X17886),X17884)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17887),X17885),X17884)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__imp__le__left])]) ).

fof(i_0_7978,plain,
    ! [X31758,X31759,X31760,X31761] :
      ( ~ class_Orderings_Olinorder(X31761)
      | ~ c_List_Olinorder__class_Osorted(X31761,X31760)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X31759),X31758))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31758),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31761)),X31760)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31761),hAPP(hAPP(c_List_Onth(X31761),X31760),X31759)),hAPP(hAPP(c_List_Onth(X31761),X31760),X31758))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__nth__mono])]) ).

fof(i_0_7979,plain,
    ! [X28968,X28969,X28970] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28970,X28970),tc_HOL_Obool),hAPP(c_Nat_OSuc,X28969)),X28968) = hAPP(hAPP(c_Relation_Orel__comp(X28970,X28970,X28970),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28970,X28970),tc_HOL_Obool),X28969),X28968)),X28968),
    inference(variable_rename,[status(thm)],[fact_relpow_Osimps_I2_J]) ).

fof(i_0_7980,plain,
    ! [X22919,X22920,X22921,X22922] :
      ( ~ class_Fields_Ofield(X22922)
      | X22921 = c_Groups_Ozero__class_Ozero(X22922)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22922),X22920),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22922),X22919),X22921)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22922),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22922),X22921),X22920)),X22919)),X22921) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff])]) ).

fof(i_0_7981,plain,
    ! [X22945,X22946,X22947,X22948] :
      ( ~ class_Fields_Ofield(X22948)
      | X22947 = c_Groups_Ozero__class_Ozero(X22948)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22948),X22946),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22948),X22945),X22947)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22948),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22948),X22947),X22946)),X22945)),X22947) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff])]) ).

fof(i_0_7982,plain,
    ! [X31742,X31743,X31744,X31745,X31746,X31747] :
      ( ~ class_Orderings_Olinorder(X31747)
      | ~ c_List_Olinorder__class_Osorted(X31747,hAPP(hAPP(c_List_Omap(X31746,X31747),X31745),X31744))
      | ~ hBOOL(hAPP(X31743,X31742))
      | hAPP(c_List_Ofilter(X31746,X31743),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31746,X31747,X31745),X31742),X31744)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31746,X31747,X31745),X31742),hAPP(c_List_Ofilter(X31746,X31743),X31744)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__insort])]) ).

cnf(i_0_7983,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_5667]) ).

cnf(i_0_7984,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_5433]) ).

fof(i_0_7985,plain,
    ! [X17092,X17093,X17094] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17094,tc_HOL_Obool)),X17093),hAPP(hAPP(c_Set_Oinsert(X17094),X17092),c_Orderings_Obot__class_Obot(tc_fun(X17094,tc_HOL_Obool)))))
      | X17093 = c_Orderings_Obot__class_Obot(tc_fun(X17094,tc_HOL_Obool))
      | X17093 = hAPP(hAPP(c_Set_Oinsert(X17094),X17092),c_Orderings_Obot__class_Obot(tc_fun(X17094,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__singletonD])]) ).

fof(i_0_7986,plain,
    ! [X17365,X17366,X17367,X17368] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17368),X17367),X17366))
        | ~ hBOOL(hAPP(hAPP(c_member(X17368),X17367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17368,tc_HOL_Obool)),X17366),X17365))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17368),X17367),X17365))
        | ~ hBOOL(hAPP(hAPP(c_member(X17368),X17367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17368,tc_HOL_Obool)),X17366),X17365))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17368),X17367),X17366))
        | hBOOL(hAPP(hAPP(c_member(X17368),X17367),X17365))
        | hBOOL(hAPP(hAPP(c_member(X17368),X17367),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17368,tc_HOL_Obool)),X17366),X17365))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5668])])]) ).

fof(i_0_7987,plain,
    ! [X17332,X17333,X17334,X17335] :
      ( ( hBOOL(hAPP(hAPP(c_member(X17335),X17334),X17333))
        | ~ hBOOL(hAPP(hAPP(c_member(X17335),X17334),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17335,tc_HOL_Obool)),X17333),X17332))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17335),X17334),X17332))
        | ~ hBOOL(hAPP(hAPP(c_member(X17335),X17334),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17335,tc_HOL_Obool)),X17333),X17332))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffE])])]) ).

fof(i_0_7988,plain,
    ! [X17357,X17358,X17359,X17360] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17360),X17359),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17360,tc_HOL_Obool)),X17358),X17357)))
      | ~ hBOOL(hAPP(hAPP(c_member(X17360),X17359),X17357)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5669])]) ).

fof(i_0_7989,plain,
    ! [X19148,X19149,X19150,X19151] : c_Fun_Ofun__upd(X19151,X19150,X19149,X19148,hAPP(X19149,X19148)) = X19149,
    inference(variable_rename,[status(thm)],[fact_fun__upd__triv]) ).

cnf(i_0_7990,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_5670]) ).

cnf(i_0_7991,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_5671]) ).

cnf(i_0_7992,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_5672]) ).

cnf(i_0_7993,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_5673]) ).

fof(i_0_7994,plain,
    ! [X19152,X19153,X19154,X19155,X19156] :
      ( hAPP(X19156,X19155) != X19154
      | c_Fun_Ofun__upd(X19153,X19152,X19156,X19155,X19154) = X19156 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__upd__idem])]) ).

fof(i_0_7995,plain,
    ! [X18989,X18990,X18991,X18994,X18995,X18996,X18997,X18998] :
      ( ( X18990 = hAPP(hAPP(c_Set_Oinsert(X18991),esk35_3(X18989,X18990,X18991)),esk36_3(X18989,X18990,X18991))
        | hAPP(c_Finite__Set_Ocard(X18991),X18990) != hAPP(c_Nat_OSuc,X18989) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X18991),esk35_3(X18989,X18990,X18991)),esk36_3(X18989,X18990,X18991)))
        | hAPP(c_Finite__Set_Ocard(X18991),X18990) != hAPP(c_Nat_OSuc,X18989) )
      & ( hAPP(c_Finite__Set_Ocard(X18991),esk36_3(X18989,X18990,X18991)) = X18989
        | hAPP(c_Finite__Set_Ocard(X18991),X18990) != hAPP(c_Nat_OSuc,X18989) )
      & ( X18989 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | esk36_3(X18989,X18990,X18991) = c_Orderings_Obot__class_Obot(tc_fun(X18991,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(X18991),X18990) != hAPP(c_Nat_OSuc,X18989) )
      & ( X18994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18995 != hAPP(hAPP(c_Set_Oinsert(X18996),X18997),X18998)
        | hBOOL(hAPP(hAPP(c_member(X18996),X18997),X18998))
        | hAPP(c_Finite__Set_Ocard(X18996),X18998) != X18994
        | hAPP(c_Finite__Set_Ocard(X18996),X18995) = hAPP(c_Nat_OSuc,X18994) )
      & ( X18998 != c_Orderings_Obot__class_Obot(tc_fun(X18996,tc_HOL_Obool))
        | X18995 != hAPP(hAPP(c_Set_Oinsert(X18996),X18997),X18998)
        | hBOOL(hAPP(hAPP(c_member(X18996),X18997),X18998))
        | hAPP(c_Finite__Set_Ocard(X18996),X18998) != X18994
        | hAPP(c_Finite__Set_Ocard(X18996),X18995) = hAPP(c_Nat_OSuc,X18994) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5674])])])])])]) ).

fof(i_0_7996,plain,
    ! [X19881,X19882,X19883,X19884,X19885,X19886] :
      ( ~ c_Finite__Set_Ofolding__idem(X19886,X19885,X19884,X19883)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19886),X19882))
      | ~ hBOOL(hAPP(hAPP(c_member(X19886),X19881),X19882))
      | hAPP(c_Fun_Ocomp(X19885,X19885,X19885,hAPP(X19883,X19882)),hAPP(X19884,X19881)) = hAPP(X19883,X19882) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oin__comp__idem])]) ).

fof(i_0_7997,plain,
    ! [X30199,X30200,X30201] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30201),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30200)),X30199)))
      | hAPP(hAPP(c_List_Otake(X30200),hAPP(c_Nat_OSuc,X30201)),X30199) = hAPP(hAPP(c_List_Oappend(X30200),hAPP(hAPP(c_List_Otake(X30200),X30201),X30199)),hAPP(hAPP(c_List_Olist_OCons(X30200),hAPP(hAPP(c_List_Onth(X30200),X30199),X30201)),c_List_Olist_ONil(X30200))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc__conv__app__nth])]) ).

fof(i_0_7998,plain,
    ! [X25534,X25535,X25536] :
      ( ~ class_Orderings_Olinorder(X25536)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25536),X25535))
      | X25535 = c_Orderings_Obot__class_Obot(tc_fun(X25536,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25536),X25534))
      | X25534 = c_Orderings_Obot__class_Obot(tc_fun(X25536,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25536,tc_HOL_Obool)),X25535),X25534) != c_Orderings_Obot__class_Obot(tc_fun(X25536,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X25536,c_Orderings_Oord__class_Omax(X25536),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25536,tc_HOL_Obool)),X25535),X25534)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25536),c_Big__Operators_Olattice_OSup__fin(X25536,c_Orderings_Oord__class_Omax(X25536),X25535)),c_Big__Operators_Olattice_OSup__fin(X25536,c_Orderings_Oord__class_Omax(X25536),X25534)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__disjoint])]) ).

fof(i_0_7999,plain,
    ! [X25528,X25529,X25530] :
      ( ~ class_Orderings_Olinorder(X25530)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25530),X25529))
      | X25529 = c_Orderings_Obot__class_Obot(tc_fun(X25530,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25530),X25528))
      | X25528 = c_Orderings_Obot__class_Obot(tc_fun(X25530,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25530,tc_HOL_Obool)),X25529),X25528) != c_Orderings_Obot__class_Obot(tc_fun(X25530,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X25530,c_Orderings_Oord__class_Omin(X25530),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25530,tc_HOL_Obool)),X25529),X25528)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25530),c_Big__Operators_Olattice_OInf__fin(X25530,c_Orderings_Oord__class_Omin(X25530),X25529)),c_Big__Operators_Olattice_OInf__fin(X25530,c_Orderings_Oord__class_Omin(X25530),X25528)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__disjoint])]) ).

fof(i_0_8000,plain,
    ! [X28949,X28950,X28951,X28952] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(X28952,X28951),tc_fun(X28952,X28951)),X28950),c_Fun_Ocomp(X28951,X28951,X28952,X28949)) = c_Fun_Ocomp(X28951,X28951,X28952,hAPP(hAPP(c_Nat_Ocompow(X28951,X28951),X28950),X28949)),
    inference(variable_rename,[status(thm)],[fact_comp__funpow]) ).

fof(i_0_8001,plain,
    ! [X32406,X32407,X32408,X32409,X32410] : hAPP(c_New__DSequence_Opos__bind(X32410,X32409,X32408,X32407),X32406) = hAPP(c_Lazy__Sequence_Obind(X32410,X32409,hAPP(X32408,X32406)),hAPP(hAPP(c_COMBC(X32410,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X32409)),X32407),X32406)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__bind__def]) ).

fof(i_0_8002,plain,
    ! [X33319,X33320,X33321,X33322,X33323,X33324] : hAPP(hAPP(c_Product__Type_Ocurry(X33324,X33323,X33322,X33321),X33320),X33319) = hAPP(X33321,hAPP(hAPP(c_Product__Type_OPair(X33324,X33323),X33320),X33319)),
    inference(variable_rename,[status(thm)],[fact_curry__conv]) ).

fof(i_0_8003,plain,
    ! [X33245,X33246,X33247,X33248,X33249,X33250] : hAPP(hAPP(c_Product__Type_Ocurry(X33250,X33249,X33248,X33247),X33246),X33245) = hAPP(X33247,hAPP(hAPP(c_Product__Type_OPair(X33250,X33249),X33246),X33245)),
    inference(variable_rename,[status(thm)],[fact_curry__def]) ).

fof(i_0_8004,plain,
    ! [X23401,X23402,X23403,X23404,X23405] :
      ( ( hAPP(c_Set_Oimage(X23405,X23404,X23403),X23402) != hAPP(c_Set_Oimage(X23405,X23404,X23403),X23401)
        | X23402 = X23401
        | ~ c_Fun_Oinj__on(X23405,X23404,X23403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23405,tc_HOL_Obool)),X23402),X23401)) )
      & ( X23402 != X23401
        | hAPP(c_Set_Oimage(X23405,X23404,X23403),X23402) = hAPP(c_Set_Oimage(X23405,X23404,X23403),X23401)
        | ~ c_Fun_Oinj__on(X23405,X23404,X23403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23405,tc_HOL_Obool)),X23402),X23401)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__Un__image__eq__iff])])]) ).

cnf(i_0_8005,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk435_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_5660]) ).

fof(i_0_8006,plain,
    ! [X22895,X22896,X22897,X22898] :
      ( ~ class_Fields_Olinordered__field(X22898)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22898),c_Groups_Ozero__class_Ozero(X22898)),X22897))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22898),X22896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22898),X22895),X22897)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22898),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22898),X22896),X22897)),X22895)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less])]) ).

fof(i_0_8007,plain,
    ! [X22971,X22972,X22973,X22974] :
      ( ~ class_Fields_Olinordered__field(X22974)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22974),c_Groups_Ozero__class_Ozero(X22974)),X22973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22974),X22972),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22974),X22971),X22973)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22974),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22974),X22972),X22973)),X22971)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le])]) ).

fof(i_0_8008,plain,
    ! [X27506,X27507,X27508,X27509,X27510] :
      ( ~ c_Relation_Orefl__on(X27510,X27509,X27508)
      | ~ c_Relation_Orefl__on(X27510,X27507,X27506)
      | c_Relation_Orefl__on(X27510,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27510,tc_HOL_Obool)),X27509),X27507),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X27510,X27510),tc_HOL_Obool)),X27508),X27506)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Int])]) ).

fof(i_0_8009,plain,
    ! [X27501,X27502,X27503,X27504,X27505] :
      ( ~ c_Relation_Orefl__on(X27505,X27504,X27503)
      | ~ c_Relation_Orefl__on(X27505,X27502,X27501)
      | c_Relation_Orefl__on(X27505,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27505,tc_HOL_Obool)),X27504),X27502),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27505,X27505),tc_HOL_Obool)),X27503),X27501)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__Un])]) ).

fof(i_0_8010,plain,
    ! [X33228,X33229,X33230,X33231] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X33231,X33230,X33229,X33228,c_Lazy__Sequence_Olazy__sequence_OEmpty(X33230)) = X33229,
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Orecs_I1_J]) ).

fof(i_0_8011,plain,
    ! [X33106,X33107,X33108] :
      ( hAPP(c_Set_Oimage(X33108,X33107,X33106),c_Orderings_Otop__class_Otop(tc_fun(X33108,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X33107,tc_HOL_Obool))
      | c_Fun_Oinj__on(X33107,X33108,c_Hilbert__Choice_Oinv__into(X33108,X33107,c_Orderings_Otop__class_Otop(tc_fun(X33108,tc_HOL_Obool)),X33106),c_Orderings_Otop__class_Otop(tc_fun(X33107,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__imp__inj__inv])]) ).

fof(i_0_8012,plain,
    ! [X33256,X33257] : c_Fun_Obij__betw(X33257,X33257,c_Fun_Oid(X33257),X33256,X33256),
    inference(variable_rename,[status(thm)],[fact_bij__betw__id]) ).

fof(i_0_8013,plain,
    ! [X28173,X28174,X28175,X28176,X28177] : hAPP(c_Relation_ODomain(X28177,X28176),hAPP(hAPP(c_Set_Oinsert(tc_prod(X28177,X28176)),hAPP(hAPP(c_Product__Type_OPair(X28177,X28176),X28175),X28174)),X28173)) = hAPP(hAPP(c_Set_Oinsert(X28177),X28175),hAPP(c_Relation_ODomain(X28177,X28176),X28173)),
    inference(variable_rename,[status(thm)],[fact_Domain__insert]) ).

fof(i_0_8014,plain,
    ! [X27974,X27975,X27976,X27977,X27978] : hAPP(c_Relation_ORange(X27978,X27977),hAPP(hAPP(c_Set_Oinsert(tc_prod(X27978,X27977)),hAPP(hAPP(c_Product__Type_OPair(X27978,X27977),X27976),X27975)),X27974)) = hAPP(hAPP(c_Set_Oinsert(X27977),X27975),hAPP(c_Relation_ORange(X27978,X27977),X27974)),
    inference(variable_rename,[status(thm)],[fact_Range__insert]) ).

cnf(i_0_8015,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_5675]) ).

fof(i_0_8016,plain,
    ! [X17812,X17813,X17814,X17815] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17815,tc_HOL_Obool)),X17814),X17813))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17815,tc_HOL_Obool)),X17813),X17812))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17815,tc_HOL_Obool)),X17814),X17812)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__trans])]) ).

fof(i_0_8017,plain,
    ! [X17991,X17992,X17993,X17994] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17994,tc_HOL_Obool)),X17993),X17992))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17994,tc_HOL_Obool)),X17992),X17991))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17994,tc_HOL_Obool)),X17993),X17991)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__psubset__trans])]) ).

fof(i_0_8018,plain,
    ! [X17995,X17996,X17997,X17998] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17998,tc_HOL_Obool)),X17997),X17996))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17998,tc_HOL_Obool)),X17996),X17995))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17998,tc_HOL_Obool)),X17997),X17995)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__subset__trans])]) ).

fof(i_0_8019,plain,
    ! [X16912,X16913,X16914,X16915] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16915,tc_HOL_Obool)),X16914),X16913))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16915,tc_HOL_Obool)),X16913),X16912))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16915,tc_HOL_Obool)),X16914),X16912)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__trans])]) ).

fof(i_0_8020,plain,
    ! [X20150,X20151] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20151),X20150))
        | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20151)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20150))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20151)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20150)))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X20151),X20150)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I2_J])]) ).

fof(i_0_8021,plain,
    ! [X28508,X28509,X28510,X28511,X28512] : hAPP(hAPP(c_Product__Type_Oscomp(X28512,X28511,X28512,X28510),hAPP(c_Product__Type_OPair(X28511,X28512),X28509)),X28508) = hAPP(X28508,X28509),
    inference(variable_rename,[status(thm)],[fact_Pair__scomp]) ).

cnf(i_0_8022,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_5676]) ).

fof(i_0_8023,plain,
    ! [X20854,X20855,X20856] :
      ( ~ class_Divides_Osemiring__div(X20856)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20856),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20856),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20856),X20855),X20854)),X20854)),c_Divides_Odiv__class_Omod(X20856,X20855,X20854)) = X20855 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality])]) ).

fof(i_0_8024,plain,
    ! [X29099,X29100,X29101] :
      ( ~ class_Divides_Osemiring__div(X29101)
      | X29100 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X29101),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X29101),X29100),X29099)),X29099)),c_Divides_Odiv__class_Omod(X29101,X29100,X29099)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__decomp])]) ).

fof(i_0_8025,plain,
    ! [X31698,X31699,X31700,X31701] :
      ( ~ class_Orderings_Olinorder(X31701)
      | c_List_Olinorder__class_Osorted(X31701,hAPP(hAPP(c_List_Omap(X31700,X31701),X31699),c_List_Olinorder__class_Osort__key(X31700,X31701,X31699,X31698))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort__key])]) ).

cnf(i_0_8026,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_5677]) ).

cnf(i_0_8027,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_5678]) ).

fof(i_0_8028,plain,
    ! [X23876,X23877] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23877,tc_fun(X23877,tc_HOL_Obool)),X23876),hAPP(hAPP(c_COMBC(X23877,tc_fun(X23877,tc_HOL_Obool),tc_fun(X23877,tc_HOL_Obool)),c_Set_Oinsert(X23877)),c_Orderings_Obot__class_Obot(tc_fun(X23877,tc_HOL_Obool)))) = X23876,
    inference(variable_rename,[status(thm)],[fact_UN__singleton]) ).

fof(i_0_8029,plain,
    ! [X30224,X30225,X30226,X30227] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30227),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30226)),X30225)))
      | hAPP(hAPP(c_List_Olist__update(X30226,X30225),X30227),X30224) = hAPP(hAPP(c_List_Oappend(X30226),hAPP(hAPP(c_List_Otake(X30226),X30227),X30225)),hAPP(hAPP(c_List_Olist_OCons(X30226),X30224),hAPP(hAPP(c_List_Odrop(X30226),hAPP(c_Nat_OSuc,X30227)),X30225))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upd__conv__take__nth__drop])]) ).

fof(i_0_8030,plain,
    ! [X30543,X30544,X30545,X30546,X30547,X30548] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30548),hAPP(X30547,X30546)),hAPP(X30547,X30545)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30544,X30548,X30547),X30546),hAPP(hAPP(c_List_Olist_OCons(X30544),X30545),X30543)) = hAPP(hAPP(c_List_Olist_OCons(X30544),X30546),hAPP(hAPP(c_List_Olist_OCons(X30544),X30545),X30543))
        | ~ class_Orderings_Olinorder(X30548) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X30548),hAPP(X30547,X30546)),hAPP(X30547,X30545)))
        | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30544,X30548,X30547),X30546),hAPP(hAPP(c_List_Olist_OCons(X30544),X30545),X30543)) = hAPP(hAPP(c_List_Olist_OCons(X30544),X30545),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30544,X30548,X30547),X30546),X30543))
        | ~ class_Orderings_Olinorder(X30548) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5679])])]) ).

fof(i_0_8031,plain,
    ! [X31211,X31212] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31212),X31211))
      | hBOOL(hAPP(c_List_Odistinct(tc_fun(X31212,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31212),tc_fun(X31212,tc_HOL_Obool)),c_List_Oset(X31212)),c_Enum_Osublists(X31212,X31211)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists])]) ).

fof(i_0_8032,plain,
    ! [X29950,X29951] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29951)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29950)))
        | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29951),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29950)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29951)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29951)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29950))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29951)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29950)))
        | c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29951),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X29950)) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5680])]) ).

fof(i_0_8033,plain,
    ! [X23954,X23955,X23956] : hAPP(c_Set_OPow(X23956),hAPP(hAPP(c_Set_Oinsert(X23956),X23955),X23954)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X23956,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X23956),X23954)),hAPP(c_Set_Oimage(tc_fun(X23956,tc_HOL_Obool),tc_fun(X23956,tc_HOL_Obool),hAPP(c_Set_Oinsert(X23956),X23955)),hAPP(c_Set_OPow(X23956),X23954))),
    inference(variable_rename,[status(thm)],[fact_Pow__insert]) ).

fof(i_0_8034,plain,
    ! [X26901,X26902,X26903,X26904] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26904),hAPP(c_Set_Ovimage(X26904,X26903,X26902),X26901)))
      | hAPP(c_Set_Oimage(X26904,X26903,X26902),c_Orderings_Otop__class_Otop(tc_fun(X26904,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26903,tc_HOL_Obool))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26903),X26901)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageD])]) ).

fof(i_0_8035,plain,
    ! [X29390,X29391,X29392,X29393] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29393),X29392),X29390))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29393)),hAPP(hAPP(c_List_Olist_OCons(X29393),X29392),X29391)),c_List_Olists(X29393,X29390))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29393)),X29391),c_List_Olists(X29393,X29390)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29393)),hAPP(hAPP(c_List_Olist_OCons(X29393),X29392),X29391)),c_List_Olists(X29393,X29390))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29393),X29392),X29390))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29393)),X29391),c_List_Olists(X29393,X29390)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29393)),hAPP(hAPP(c_List_Olist_OCons(X29393),X29392),X29391)),c_List_Olists(X29393,X29390))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__in__lists__iff])])]) ).

fof(i_0_8036,plain,
    ! [X17079,X17080,X17081,X17082] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17082,tc_HOL_Obool)),X17080),hAPP(hAPP(c_Set_Oinsert(X17082),X17081),X17079)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17082,tc_HOL_Obool)),X17080),X17079))
        | hBOOL(hAPP(hAPP(c_member(X17082),X17081),X17080)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17082,tc_HOL_Obool)),X17080),X17079))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17082,tc_HOL_Obool)),X17080),hAPP(hAPP(c_Set_Oinsert(X17082),X17081),X17079)))
        | hBOOL(hAPP(hAPP(c_member(X17082),X17081),X17080)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5681])])]) ).

fof(i_0_8037,plain,
    ! [X28762,X28763] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X28763))
      | 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(X28763),X28762))),X28763)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range])]) ).

fof(i_0_8038,plain,
    ! [X25044,X25045,X25046,X25047] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25047),X25046),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25047,tc_HOL_Obool)),X25045),X25044)))
      | hBOOL(hAPP(hAPP(c_member(X25047),X25046),X25045)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD1])]) ).

fof(i_0_8039,plain,
    ! [X25040,X25041,X25042,X25043] :
      ( ( hBOOL(hAPP(hAPP(c_member(X25043),X25042),X25041))
        | ~ hBOOL(hAPP(hAPP(c_member(X25043),X25042),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25043,tc_HOL_Obool)),X25041),X25040))) )
      & ( hBOOL(hAPP(hAPP(c_member(X25043),X25042),X25040))
        | ~ hBOOL(hAPP(hAPP(c_member(X25043),X25042),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25043,tc_HOL_Obool)),X25041),X25040))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X25043),X25042),X25041))
        | ~ hBOOL(hAPP(hAPP(c_member(X25043),X25042),X25040))
        | hBOOL(hAPP(hAPP(c_member(X25043),X25042),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25043,tc_HOL_Obool)),X25041),X25040))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__iff])])]) ).

fof(i_0_8040,plain,
    ! [X24870,X24871,X24872,X24873] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24873),X24872),X24871))
        | ~ hBOOL(hAPP(hAPP(c_member(X24873),X24872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24873,tc_HOL_Obool)),X24871),X24870))) )
      & ( hBOOL(hAPP(hAPP(c_member(X24873),X24872),X24870))
        | ~ hBOOL(hAPP(hAPP(c_member(X24873),X24872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24873,tc_HOL_Obool)),X24871),X24870))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5682])])]) ).

fof(i_0_8041,plain,
    ! [X17361,X17362,X17363,X17364] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17364),X17363),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17364,tc_HOL_Obool)),X17362),X17361)))
      | hBOOL(hAPP(hAPP(c_member(X17364),X17363),X17362)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DiffD1])]) ).

fof(i_0_8042,plain,
    ! [X25048,X25049,X25050,X25051] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25051),X25050),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25051,tc_HOL_Obool)),X25049),X25048)))
      | hBOOL(hAPP(hAPP(c_member(X25051),X25050),X25048)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntD2])]) ).

fof(i_0_8043,plain,
    ! [X17418,X17419,X17420,X17421] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17421,tc_HOL_Obool)),X17420),hAPP(hAPP(c_Set_Oinsert(X17421),X17419),X17418)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17421,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17421,tc_HOL_Obool)),X17420),X17418)),hAPP(hAPP(c_Set_Oinsert(X17421),X17419),c_Orderings_Obot__class_Obot(tc_fun(X17421,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_Diff__insert]) ).

fof(i_0_8044,plain,
    ! [X29959,X29960] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29960),X29959))
        | c_List_Oupto(X29960,X29959) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X29960),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29960),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29959))
        | ~ 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),X29960),X29959))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29960),X29959))
        | c_List_Oupto(X29960,X29959) = 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),X29960),X29959))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5683])])]) ).

fof(i_0_8045,plain,
    ! [X25504,X25505,X25506] :
      ( ~ class_Groups_Oab__semigroup__mult(X25506)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25506),X25505))
      | X25505 = c_Orderings_Obot__class_Obot(tc_fun(X25506,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25506),X25504))
      | X25504 = c_Orderings_Obot__class_Obot(tc_fun(X25506,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25506,tc_HOL_Obool)),X25505),X25504) != c_Orderings_Obot__class_Obot(tc_fun(X25506,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ofold1(X25506,c_Groups_Otimes__class_Otimes(X25506)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25506,tc_HOL_Obool)),X25505),X25504)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25506),hAPP(c_Finite__Set_Ofold1(X25506,c_Groups_Otimes__class_Otimes(X25506)),X25505)),hAPP(c_Finite__Set_Ofold1(X25506,c_Groups_Otimes__class_Otimes(X25506)),X25504)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un])]) ).

fof(i_0_8046,plain,
    ! [X19830,X19831,X19832,X19833,X19834,X19835] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19835,X19834,X19833)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19835),X19832))
      | hBOOL(hAPP(hAPP(c_member(X19835),X19831),X19832))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19835,X19834,X19833),X19830),hAPP(hAPP(c_Set_Oinsert(X19835),X19831),X19832)) = hAPP(hAPP(X19833,X19831),hAPP(hAPP(c_Finite__Set_Ofold(X19835,X19834,X19833),X19830),X19832)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5684])]) ).

cnf(i_0_8047,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_5450]) ).

fof(i_0_8048,plain,
    ! [X19875,X19876,X19877,X19878,X19879,X19880] :
      ( ~ c_Finite__Set_Ofolding__idem(X19880,X19879,X19878,X19877)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19880),X19876))
      | hAPP(X19877,hAPP(hAPP(c_Set_Oinsert(X19880),X19875),X19876)) = hAPP(c_Fun_Ocomp(X19879,X19879,X19879,hAPP(X19877,X19876)),hAPP(X19878,X19875)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oinsert__idem])]) ).

fof(i_0_8049,plain,
    ! [X28504,X28505,X28506,X28507] : hAPP(hAPP(c_Product__Type_Oscomp(X28507,X28506,X28505,tc_prod(X28506,X28505)),X28504),c_Product__Type_OPair(X28506,X28505)) = X28504,
    inference(variable_rename,[status(thm)],[fact_scomp__Pair]) ).

fof(i_0_8050,plain,
    ! [X27726,X27727] : hAPP(c_Set_OPow(X27727),X27726) = hAPP(c_Set_OCollect(tc_fun(X27727,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(X27727,tc_HOL_Obool),tc_fun(X27727,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(X27727,tc_HOL_Obool))),X27726)),
    inference(variable_rename,[status(thm)],[fact_Pow__def]) ).

fof(i_0_8051,plain,
    ! [X31858,X31859] : hAPP(c_List_Orev(X31859),X31858) = hAPP(c_List_Ofoldl(tc_List_Olist(X31859),X31859,hAPP(c_COMBC(X31859,tc_List_Olist(X31859),tc_List_Olist(X31859)),c_List_Olist_OCons(X31859)),c_List_Olist_ONil(X31859)),X31858),
    inference(variable_rename,[status(thm)],[fact_rev__foldl__cons]) ).

fof(i_0_8052,plain,
    ! [X32650,X32651] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32651),X32650))
        | c_Lazy__Sequence_Osmall__lazy_H(X32651,X32650) = 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),X32651),X32650))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32651),X32650))
        | c_Lazy__Sequence_Osmall__lazy_H(X32651,X32650) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X32650),c_Lazy__Sequence_Osmall__lazy_H(X32651,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32650),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),X32651),X32650))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5685])])]) ).

cnf(i_0_8053,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_5643]) ).

fof(i_0_8054,plain,
    ! [X24666,X24667] :
      ( ~ class_Rings_Ocomm__semiring__1(X24667)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24667),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24667),c_Groups_Oone__class_Oone(X24667)),c_Groups_Oone__class_Oone(X24667))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24667),c_Nat_Osemiring__1__class_Oof__nat(X24667)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X24666))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24667),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24667),X24666)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24667),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24667),X24666)),c_Groups_Oone__class_Oone(X24667))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gauss__sum])]) ).

fof(i_0_8055,plain,
    ! [X31228,X31229,X31230,X31231] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31231)),X31230),hAPP(c_List_Oset(tc_List_Olist(X31231)),c_Enum_On__lists(X31231,X31229,X31228))))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31231)),X31230) = X31229 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem])]) ).

cnf(i_0_8056,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_5465]) ).

fof(i_0_8057,plain,
    ! [X32971,X32972,X32973] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X32973,X32973),tc_HOL_Obool)),X32972),X32971))
      | ~ c_Relation_Oantisym(X32973,X32971)
      | c_Relation_Oantisym(X32973,X32972) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__subset])]) ).

fof(i_0_8058,plain,
    ! [X28285,X28286,X28287] :
      ( ~ c_Wellfounded_Oacyclic(X28287,X28286)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28287,X28287),tc_HOL_Obool)),X28285),X28286))
      | c_Wellfounded_Oacyclic(X28287,X28285) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__subset])]) ).

fof(i_0_8059,plain,
    ! [X28077,X28078,X28079] :
      ( ~ c_Wellfounded_Owf(X28079,X28078)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X28079,X28079),tc_HOL_Obool)),X28077),X28078))
      | c_Wellfounded_Owf(X28079,X28077) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__subset])]) ).

fof(i_0_8060,plain,
    ! [X29905,X29906,X29907,X29908] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X29906),X29908),hAPP(c_List_Oset(X29906),c_List_Oremove1(X29906,X29907,X29905))))
        | hBOOL(hAPP(hAPP(c_member(X29906),X29908),hAPP(c_List_Oset(X29906),X29905)))
        | X29908 = X29907 )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29906),X29908),hAPP(c_List_Oset(X29906),X29905)))
        | hBOOL(hAPP(hAPP(c_member(X29906),X29908),hAPP(c_List_Oset(X29906),c_List_Oremove1(X29906,X29907,X29905))))
        | X29908 = X29907 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__remove1])])]) ).

fof(i_0_8061,plain,
    ! [X25119,X25120,X25121,X25122] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25122,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25122,tc_HOL_Obool)),X25121),X25120)),X25119) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25122,tc_HOL_Obool)),X25121),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25122,tc_HOL_Obool)),X25120),X25119)),
    inference(variable_rename,[status(thm)],[fact_Int__assoc]) ).

fof(i_0_8062,plain,
    ! [X23266,X23267,X23268,X23269] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23269,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23269,tc_HOL_Obool)),X23268),X23267)),X23266) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23269,tc_HOL_Obool)),X23268),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23269,tc_HOL_Obool)),X23267),X23266)),
    inference(variable_rename,[status(thm)],[fact_Un__assoc]) ).

fof(i_0_8063,plain,
    ! [X24895,X24896,X24897,X24898] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24898,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24898,tc_HOL_Obool)),X24897),X24896)),X24895) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24898,tc_HOL_Obool)),X24897),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24898,tc_HOL_Obool)),X24896),X24895)),
    inference(variable_rename,[status(thm)],[fact_Int__Diff]) ).

fof(i_0_8064,plain,
    ! [X18123,X18124,X18125] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18125),X18124))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18123),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18124),X18123)),X18125))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff])]) ).

fof(i_0_8065,plain,
    ! [X31904,X31905,X31906,X31907] :
      ( ( hBOOL(hAPP(hAPP(c_member(X31907),X31906),hAPP(c_List_Oset(X31907),X31904)))
        | ~ hBOOL(hAPP(hAPP(c_member(X31907),X31906),hAPP(c_List_Oset(X31907),c_List_OtakeWhile(X31907,X31905,X31904)))) )
      & ( hBOOL(hAPP(X31905,X31906))
        | ~ hBOOL(hAPP(hAPP(c_member(X31907),X31906),hAPP(c_List_Oset(X31907),c_List_OtakeWhile(X31907,X31905,X31904)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__takeWhileD])])]) ).

fof(i_0_8066,plain,
    ! [X29901,X29902,X29903,X29904] :
      ( hBOOL(hAPP(hAPP(c_member(X29904),X29903),hAPP(c_List_Oset(X29904),X29902)))
      | ~ hBOOL(hAPP(hAPP(c_member(X29904),X29903),hAPP(c_List_Oset(X29904),c_List_Oremove1(X29904,X29901,X29902)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5686])]) ).

fof(i_0_8067,plain,
    ! [X29485,X29486,X29487,X29488] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29488),X29487),hAPP(c_List_Oset(X29488),c_List_Osublist(X29488,X29486,X29485))))
      | hBOOL(hAPP(hAPP(c_member(X29488),X29487),hAPP(c_List_Oset(X29488),X29486))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__sublistD])]) ).

fof(i_0_8068,plain,
    ! [X29477,X29478,X29479,X29480] :
      ( hBOOL(hAPP(hAPP(c_member(X29480),X29479),hAPP(c_List_Oset(X29480),X29478)))
      | ~ hBOOL(hAPP(hAPP(c_member(X29480),X29479),hAPP(c_List_Oset(X29480),c_List_Osublist(X29480,X29478,X29477)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5687])]) ).

fof(i_0_8069,plain,
    ! [X31404,X31405,X31406] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31406,tc_HOL_Obool)),hAPP(c_List_Oset(X31406),hAPP(c_List_Ofilter(X31406,X31405),X31404))),hAPP(c_List_Oset(X31406),X31404))),
    inference(variable_rename,[status(thm)],[fact_filter__is__subset]) ).

fof(i_0_8070,plain,
    ! [X19095,X19096,X19097,X19098,X19099] :
      ( ( X19098 = X19097
        | X19096 = X19095
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19098),X19096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19097),X19095)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19098),X19095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19097),X19096))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19099) )
      & ( X19098 != X19097
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19098),X19096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19097),X19095)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19098),X19095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19097),X19096))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19099) )
      & ( X19096 != X19095
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19098),X19096)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19097),X19095)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19099),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19098),X19095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19099),X19097),X19096))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19099) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq])])]) ).

fof(i_0_8071,plain,
    ! [X19082,X19083,X19084,X19085,X19086] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19085),X19084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19083),X19082)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19085),X19082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19083),X19084))
        | X19085 = X19083
        | X19084 = X19082
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19086) )
      & ( X19085 != X19083
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19085),X19084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19083),X19082)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19085),X19082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19083),X19084))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19086) )
      & ( X19084 != X19082
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19085),X19084)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19083),X19082)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19085),X19082)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19086),X19083),X19084))
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19086) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_crossproduct__eq])])]) ).

cnf(i_0_8072,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_5688]) ).

fof(i_0_8073,plain,
    ! [X27778,X27779] :
      ( ( ~ c_Predicate_Oreflp(X27779,X27778)
        | c_Relation_Orefl__on(X27779,c_Orderings_Otop__class_Otop(tc_fun(X27779,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X27779,X27779)),hAPP(c_Product__Type_Oprod_Oprod__case(X27779,X27779,tc_HOL_Obool),X27778))) )
      & ( ~ c_Relation_Orefl__on(X27779,c_Orderings_Otop__class_Otop(tc_fun(X27779,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(X27779,X27779)),hAPP(c_Product__Type_Oprod_Oprod__case(X27779,X27779,tc_HOL_Obool),X27778)))
        | c_Predicate_Oreflp(X27779,X27778) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflp__def])]) ).

fof(i_0_8074,plain,
    ! [X18115,X18116,X18117] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18116),X18117)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18115),X18117)),X18116))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18117),X18116)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18115),X18117)),X18116))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18115),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18116),X18117)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18117),X18116)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv2])])]) ).

cnf(i_0_8075,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_5689]) ).

fof(i_0_8076,plain,
    ! [X32727,X32728,X32729,X32730,X32732,X32733,X32734,X32736] :
      ( ( hBOOL(hAPP(X32729,esk492_4(X32727,X32728,X32729,X32730)))
        | ~ hBOOL(hAPP(X32729,X32730))
        | c_FunDef_OTHE__default(X32728,X32727,X32729) = c_HOL_OThe(X32728,X32729) )
      & ( esk492_4(X32727,X32728,X32729,X32730) != X32730
        | ~ hBOOL(hAPP(X32729,X32730))
        | c_FunDef_OTHE__default(X32728,X32727,X32729) = c_HOL_OThe(X32728,X32729) )
      & ( hBOOL(hAPP(X32734,esk493_3(X32732,X32733,X32734)))
        | c_FunDef_OTHE__default(X32733,X32732,X32734) = X32732 )
      & ( ~ hBOOL(hAPP(X32734,X32736))
        | X32736 = esk493_3(X32732,X32733,X32734)
        | c_FunDef_OTHE__default(X32733,X32732,X32734) = X32732 ) ),
    inference(distribute,[status(thm)],[inference(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_8077,plain,
    ! [X26849,X26850,X26851,X26852,X26853] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26853),X26852),hAPP(c_Set_Ovimage(X26853,X26851,X26850),X26849)))
      | hBOOL(hAPP(hAPP(c_member(X26851),hAPP(X26850,X26852)),X26849)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageD])]) ).

fof(i_0_8078,plain,
    ! [X26844,X26845,X26846,X26847,X26848] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26848),X26847),hAPP(c_Set_Ovimage(X26848,X26846,X26845),X26844)))
        | hBOOL(hAPP(hAPP(c_member(X26846),hAPP(X26845,X26847)),X26844)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26846),hAPP(X26845,X26847)),X26844))
        | hBOOL(hAPP(hAPP(c_member(X26848),X26847),hAPP(c_Set_Ovimage(X26848,X26846,X26845),X26844))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__eq])]) ).

fof(i_0_8079,plain,
    ! [X17942,X17943,X17944,X17945] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17944,X17945)),X17943),X17942))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17944,X17945)),X17943),X17942))
        | ~ class_Orderings_Oord(X17945) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17944,X17945)),X17942),X17943))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17944,X17945)),X17943),X17942))
        | ~ class_Orderings_Oord(X17945) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17944,X17945)),X17943),X17942))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17944,X17945)),X17942),X17943))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17944,X17945)),X17943),X17942))
        | ~ class_Orderings_Oord(X17945) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5690])])]) ).

fof(i_0_8080,plain,
    ! [X30309,X30310,X30311,X30312] : hAPP(hAPP(c_List_Odrop(X30312),X30311),hAPP(hAPP(c_List_Olist_OCons(X30312),X30310),X30309)) = c_Nat_Onat_Onat__case(tc_List_Olist(X30312),hAPP(hAPP(c_List_Olist_OCons(X30312),X30310),X30309),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(X30312),tc_List_Olist(X30312)),c_List_Odrop(X30312)),X30309),X30311),
    inference(variable_rename,[status(thm)],[fact_drop__Cons]) ).

fof(i_0_8081,plain,
    ! [X18484,X18485,X18486] :
      ( ~ class_Rings_Olinordered__idom(X18486)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18486),c_Groups_Ozero__class_Ozero(X18486)),X18485))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18486),c_Groups_Ozero__class_Ozero(X18486)),X18484))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18486),X18484),c_Groups_Oone__class_Oone(X18486)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18486),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18486),X18485),X18484)),X18485)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le])]) ).

fof(i_0_8082,plain,
    ! [X18487,X18488,X18489] :
      ( ~ class_Rings_Olinordered__idom(X18489)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18489),c_Groups_Ozero__class_Ozero(X18489)),X18488))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18489),c_Groups_Ozero__class_Ozero(X18489)),X18487))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18489),X18487),c_Groups_Oone__class_Oone(X18489)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18489),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18489),X18487),X18488)),X18488)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le])]) ).

fof(i_0_8083,plain,
    ! [X29230,X29231,X29232,X29233] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X29233),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X29232),X29231)))
        | hAPP(c_Random_Opick(X29232,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X29232)),X29231),X29230)),X29233) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,X29232),X29231) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X29233),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X29232),X29231)))
        | hAPP(c_Random_Opick(X29232,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X29232)),X29231),X29230)),X29233) = hAPP(c_Random_Opick(X29232,X29230),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X29233),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,X29232),X29231))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5691])]) ).

cnf(i_0_8084,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_5621]) ).

cnf(i_0_8085,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_5623]) ).

cnf(i_0_8086,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_5622]) ).

cnf(i_0_8087,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_5624]) ).

fof(i_0_8088,plain,
    ! [X27027,X27028,X27029,X27030,X27031,X27032,X27033] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27029,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27029,tc_HOL_Obool),X27028)),X27027) != c_Orderings_Obot__class_Obot(tc_fun(X27029,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27029,tc_HOL_Obool)),X27030),X27028))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27029,tc_HOL_Obool)),X27030),X27027) = c_Orderings_Obot__class_Obot(tc_fun(X27029,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27033,tc_HOL_Obool)),esk248_3(X27031,X27032,X27033)),X27032))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27033,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27033,tc_HOL_Obool),X27032)),X27031) = c_Orderings_Obot__class_Obot(tc_fun(X27033,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27033,tc_HOL_Obool)),esk248_3(X27031,X27032,X27033)),X27031) != c_Orderings_Obot__class_Obot(tc_fun(X27033,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27033,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27033,tc_HOL_Obool),X27032)),X27031) = c_Orderings_Obot__class_Obot(tc_fun(X27033,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_8089,plain,
    ! [X20468,X20469,X20470] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20470))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20469))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20469),X20468))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20470),X20468)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20470),X20469))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2])]) ).

fof(i_0_8090,plain,
    ! [X28138,X28139,X28140,X28141] : hAPP(c_Relation_ODomain(X28141,X28140),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X28141,X28140),tc_HOL_Obool)),X28139),X28138)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28141,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X28141,X28140),X28139)),hAPP(c_Relation_ODomain(X28141,X28140),X28138)),
    inference(variable_rename,[status(thm)],[fact_Domain__Un__eq]) ).

fof(i_0_8091,plain,
    ! [X27954,X27955,X27956,X27957] : hAPP(c_Relation_ORange(X27957,X27956),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X27957,X27956),tc_HOL_Obool)),X27955),X27954)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27956,tc_HOL_Obool)),hAPP(c_Relation_ORange(X27957,X27956),X27955)),hAPP(c_Relation_ORange(X27957,X27956),X27954)),
    inference(variable_rename,[status(thm)],[fact_Range__Un__eq]) ).

fof(i_0_8092,plain,
    ! [X30733,X30734,X30735,X30736,X30737,X30738] : hAPP(hAPP(c_List_Omap(X30738,X30737),X30736),hAPP(hAPP(c_List_Olist__update(X30738,X30735),X30734),X30733)) = hAPP(hAPP(c_List_Olist__update(X30737,hAPP(hAPP(c_List_Omap(X30738,X30737),X30736),X30735)),X30734),hAPP(X30736,X30733)),
    inference(variable_rename,[status(thm)],[fact_map__update]) ).

fof(i_0_8093,plain,
    ! [X29489,X29490,X29491,X29492] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29492),X29491),hAPP(c_List_Oset(X29492),hAPP(hAPP(c_List_Olist_OCons(X29492),X29490),X29489))))
      | X29491 = X29490
      | hBOOL(hAPP(hAPP(c_member(X29492),X29491),hAPP(c_List_Oset(X29492),X29489))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__ConsD])]) ).

fof(i_0_8094,plain,
    ! [X31001] :
      ( X31001 = 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,X31001)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,X31001))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral__decr])]) ).

fof(i_0_8095,plain,
    ! [X30280,X30281,X30282,X30283] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X30283),X30282),hAPP(c_List_Oset(X30283),hAPP(hAPP(c_List_Odrop(X30283),X30281),X30280))))
      | hBOOL(hAPP(hAPP(c_member(X30283),X30282),hAPP(c_List_Oset(X30283),X30280))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__dropD])]) ).

fof(i_0_8096,plain,
    ! [X29481,X29482,X29483,X29484] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29484),X29483),hAPP(c_List_Oset(X29484),hAPP(hAPP(c_List_Otake(X29484),X29482),X29481))))
      | hBOOL(hAPP(hAPP(c_member(X29484),X29483),hAPP(c_List_Oset(X29484),X29481))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__takeD])]) ).

fof(i_0_8097,plain,
    ! [X20239,X20240,X20241] :
      ( ~ class_Rings_Olinordered__semidom(X20241)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20241),c_Groups_Ozero__class_Ozero(X20241)),X20240))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20241),X20240),c_Groups_Oone__class_Oone(X20241)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20241),hAPP(hAPP(c_Power_Opower__class_Opower(X20241),X20240),hAPP(c_Nat_OSuc,X20239))),c_Groups_Oone__class_Oone(X20241))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc__less__one])]) ).

fof(i_0_8098,plain,
    ! [X29123,X29124,X29125] :
      ( ( hBOOL(hAPP(hAPP(c_member(X29125),X29124),esk365_3(X29123,X29124,X29125)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29125),X29124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29125,tc_HOL_Obool),X29123))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(X29125,tc_HOL_Obool)),esk365_3(X29123,X29124,X29125)),X29123))
        | ~ hBOOL(hAPP(hAPP(c_member(X29125),X29124),c_Complete__Lattice_OSup__class_OSup(tc_fun(X29125,tc_HOL_Obool),X29123))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5692])])])]) ).

fof(i_0_8099,plain,
    ! [X20479,X20480,X20481] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20481),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)),X20480))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20480),X20479))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20481),X20480)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20481),X20479))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg])]) ).

fof(i_0_8100,plain,
    ! [X24852,X24853,X24854] :
      ( ( hBOOL(hAPP(hAPP(c_member(X24854),esk197_3(X24852,X24853,X24854)),X24852))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24854,X24854)),X24853),c_Relation_OId__on(X24854,X24852))) )
      & ( X24853 = hAPP(hAPP(c_Product__Type_OPair(X24854,X24854),esk197_3(X24852,X24853,X24854)),esk197_3(X24852,X24853,X24854))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X24854,X24854)),X24853),c_Relation_OId__on(X24854,X24852))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Id__onE])])])]) ).

fof(i_0_8101,plain,
    ! [X33174,X33175,X33176,X33177] :
      ( ~ c_Fun_Oinj__on(X33177,X33176,X33175,c_Orderings_Otop__class_Otop(tc_fun(X33177,tc_HOL_Obool)))
      | hAPP(c_Hilbert__Choice_Oinv__into(X33177,X33176,c_Orderings_Otop__class_Otop(tc_fun(X33177,tc_HOL_Obool)),X33175),hAPP(X33175,X33174)) = X33174 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__f])]) ).

fof(i_0_8102,plain,
    ! [X26203,X26204,X26205,X26206] :
      ( ~ c_Fun_Oinj__on(X26206,X26205,X26204,c_Orderings_Otop__class_Otop(tc_fun(X26206,tc_HOL_Obool)))
      | hAPP(c_Fun_Othe__inv__into(X26206,X26205,c_Orderings_Otop__class_Otop(tc_fun(X26206,tc_HOL_Obool)),X26204),hAPP(X26204,X26203)) = X26203 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__f__f])]) ).

fof(i_0_8103,plain,
    ! [X19801,X19802,X19803,X19804,X19805,X19806] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19806,X19805,X19804)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19806),X19803))
      | hAPP(hAPP(X19804,X19802),hAPP(hAPP(c_Finite__Set_Ofold(X19806,X19805,X19804),X19801),X19803)) = hAPP(hAPP(c_Finite__Set_Ofold(X19806,X19805,X19804),hAPP(hAPP(X19804,X19802),X19801)),X19803) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__fun__comm])]) ).

fof(i_0_8104,plain,
    ! [X33169,X33170,X33171,X33172,X33173] :
      ( ~ c_Fun_Oinj__on(X33173,X33172,X33171,c_Orderings_Otop__class_Otop(tc_fun(X33173,tc_HOL_Obool)))
      | hAPP(X33171,X33170) != X33169
      | hAPP(c_Hilbert__Choice_Oinv__into(X33173,X33172,c_Orderings_Otop__class_Otop(tc_fun(X33173,tc_HOL_Obool)),X33171),X33169) = X33170 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__f__eq])]) ).

fof(i_0_8105,plain,
    ! [X28258,X28259,X28260] :
      ( ~ c_Wellfounded_OwfP(X28260,X28259)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28260,tc_fun(X28260,tc_HOL_Obool))),X28258),X28259))
      | c_Wellfounded_OwfP(X28260,X28258) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__subset])]) ).

fof(i_0_8106,plain,
    ! [X17223,X17224,X17225] :
      ( ( hAPP(hAPP(c_COMBC(X17225,tc_fun(X17225,tc_HOL_Obool),tc_HOL_Obool),c_member(X17225)),X17224) != hAPP(hAPP(c_COMBC(X17225,tc_fun(X17225,tc_HOL_Obool),tc_HOL_Obool),c_member(X17225)),X17223)
        | X17224 = X17223 )
      & ( X17224 != X17223
        | hAPP(hAPP(c_COMBC(X17225,tc_fun(X17225,tc_HOL_Obool),tc_HOL_Obool),c_member(X17225)),X17224) = hAPP(hAPP(c_COMBC(X17225,tc_fun(X17225,tc_HOL_Obool),tc_HOL_Obool),c_member(X17225)),X17223) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pred__equals__eq])]) ).

fof(i_0_8107,plain,
    ! [X18397,X18398,X18399] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18399))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18399),X18398)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18399),X18397))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18398),X18397))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18399),X18398)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18399),X18397))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18399))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18398),X18397))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18399),X18398)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18399),X18397))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1])])]) ).

fof(i_0_8108,plain,
    ! [X18400,X18401,X18402] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18401))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18402),X18401)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18400),X18401))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18402),X18400))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18402),X18401)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18400),X18401))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18401))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18402),X18400))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18402),X18401)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18400),X18401))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2])])]) ).

fof(i_0_8109,plain,
    ! [X31359,X31360,X31361,X31362,X31363] :
      ( ~ class_Orderings_Olinorder(X31363)
      | c_List_Olinorder__class_Osort__key(X31362,X31363,X31361,hAPP(hAPP(c_List_Olist_OCons(X31362),X31360),X31359)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31362,X31363,X31361),X31360),c_List_Olinorder__class_Osort__key(X31362,X31363,X31361,X31359)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I2_J])]) ).

fof(i_0_8110,plain,
    ! [X22805,X22806,X22807,X22808] :
      ( ~ class_Fields_Olinordered__field(X22808)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22808),X22807),X22806))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22808),c_Groups_Ozero__class_Ozero(X22808)),X22805))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22808),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22808),X22807),X22805)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22808),X22806),X22805))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono])]) ).

fof(i_0_8111,plain,
    ! [X18220,X18221,X18222,X18223] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18223)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18223),X18222),X18221))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18223),c_Groups_Ozero__class_Ozero(X18223)),X18220))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18223),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18223),X18222),X18220)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18223),X18221),X18220))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono])]) ).

fof(i_0_8112,plain,
    ! [X18216,X18217,X18218,X18219] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18219)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18219),X18218),X18217))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18219),c_Groups_Ozero__class_Ozero(X18219)),X18216))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18219),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18219),X18216),X18218)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18219),X18216),X18217))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono])]) ).

fof(i_0_8113,plain,
    ! [X18212,X18213,X18214,X18215] :
      ( ~ class_Rings_Olinordered__comm__semiring__strict(X18215)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18215),X18214),X18213))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18215),c_Groups_Ozero__class_Ozero(X18215)),X18212))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18215),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18215),X18212),X18214)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18215),X18212),X18213))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__strict__left__mono])]) ).

fof(i_0_8114,plain,
    ! [X22793,X22794,X22795,X22796] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X22796)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22796),X22795),X22794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22796),c_Groups_Ozero__class_Ozero(X22796)),X22793))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22796),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22796),X22795),X22793)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22796),X22794),X22793))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono])]) ).

fof(i_0_8115,plain,
    ! [X20271,X20272,X20273,X20274] :
      ( ~ class_Rings_Olinordered__semidom(X20274)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20274),X20273),X20272))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20274),c_Groups_Ozero__class_Ozero(X20274)),X20273))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20274),hAPP(hAPP(c_Power_Opower__class_Opower(X20274),X20273),X20271)),hAPP(hAPP(c_Power_Opower__class_Opower(X20274),X20272),X20271))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mono])]) ).

fof(i_0_8116,plain,
    ! [X18286,X18287,X18288,X18289] :
      ( ~ class_Rings_Oordered__semiring(X18289)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18289),X18288),X18287))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18289),c_Groups_Ozero__class_Ozero(X18289)),X18286))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18289),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18289),X18288),X18286)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18289),X18287),X18286))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono])]) ).

fof(i_0_8117,plain,
    ! [X18294,X18295,X18296,X18297] :
      ( ~ class_Rings_Oordered__comm__semiring(X18297)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18297),X18296),X18295))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18297),c_Groups_Ozero__class_Ozero(X18297)),X18294))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18297),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18297),X18294),X18296)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18297),X18294),X18295))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__mult__left__mono])]) ).

fof(i_0_8118,plain,
    ! [X18290,X18291,X18292,X18293] :
      ( ~ class_Rings_Oordered__semiring(X18293)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18293),X18292),X18291))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18293),c_Groups_Ozero__class_Ozero(X18293)),X18290))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18293),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18293),X18290),X18292)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18293),X18290),X18291))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono])]) ).

fof(i_0_8119,plain,
    ! [X29587,X29588,X29589,X29590,X29591,X29592] : hAPP(hAPP(c_List_Ozip(X29592,X29591),hAPP(hAPP(c_List_Olist_OCons(X29592),X29590),X29589)),hAPP(hAPP(c_List_Olist_OCons(X29591),X29588),X29587)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(X29592,X29591)),hAPP(hAPP(c_Product__Type_OPair(X29592,X29591),X29590),X29588)),hAPP(hAPP(c_List_Ozip(X29592,X29591),X29589),X29587)),
    inference(variable_rename,[status(thm)],[fact_zip__Cons__Cons]) ).

fof(i_0_8120,plain,
    ! [X22821,X22822,X22823] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),X22822),c_Groups_Ozero__class_Ozero(X22823)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),c_Groups_Ozero__class_Ozero(X22823)),X22822))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22823),X22822),X22821)),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22823) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),c_Groups_Ozero__class_Ozero(X22823)),X22821))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),c_Groups_Ozero__class_Ozero(X22823)),X22822))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22823),X22822),X22821)),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22823) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),X22822),c_Groups_Ozero__class_Ozero(X22823)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),X22821),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22823),X22822),X22821)),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22823) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),c_Groups_Ozero__class_Ozero(X22823)),X22821))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),X22821),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22823),X22822),X22821)),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22823) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),c_Groups_Ozero__class_Ozero(X22823)),X22822))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),X22821),c_Groups_Ozero__class_Ozero(X22823)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22823),X22822),X22821)),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22823) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),X22822),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),c_Groups_Ozero__class_Ozero(X22823)),X22821))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22823),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22823),X22822),X22821)),c_Groups_Ozero__class_Ozero(X22823)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22823) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__less__0__iff])])]) ).

fof(i_0_8121,plain,
    ! [X22790,X22791,X22792] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),X22791),c_Groups_Ozero__class_Ozero(X22792)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),c_Groups_Ozero__class_Ozero(X22792)),X22791))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22792),X22791),X22790)),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22792) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),c_Groups_Ozero__class_Ozero(X22792)),X22790))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),c_Groups_Ozero__class_Ozero(X22792)),X22791))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22792),X22791),X22790)),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22792) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),X22791),c_Groups_Ozero__class_Ozero(X22792)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),X22790),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22792),X22791),X22790)),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22792) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),c_Groups_Ozero__class_Ozero(X22792)),X22790))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),X22790),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22792),X22791),X22790)),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22792) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),c_Groups_Ozero__class_Ozero(X22792)),X22791))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),X22790),c_Groups_Ozero__class_Ozero(X22792)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22792),X22791),X22790)),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22792) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),X22791),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),c_Groups_Ozero__class_Ozero(X22792)),X22790))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22792),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22792),X22791),X22790)),c_Groups_Ozero__class_Ozero(X22792)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22792) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__le__0__iff])])]) ).

fof(i_0_8122,plain,
    ! [X18268,X18269,X18270] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),X18269),c_Groups_Ozero__class_Ozero(X18270)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),c_Groups_Ozero__class_Ozero(X18270)),X18269))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18270),X18269),X18268)),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ class_Rings_Olinordered__ring__strict(X18270) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),c_Groups_Ozero__class_Ozero(X18270)),X18268))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),c_Groups_Ozero__class_Ozero(X18270)),X18269))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18270),X18269),X18268)),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ class_Rings_Olinordered__ring__strict(X18270) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),X18269),c_Groups_Ozero__class_Ozero(X18270)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),X18268),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18270),X18269),X18268)),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ class_Rings_Olinordered__ring__strict(X18270) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),c_Groups_Ozero__class_Ozero(X18270)),X18268))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),X18268),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18270),X18269),X18268)),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ class_Rings_Olinordered__ring__strict(X18270) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),c_Groups_Ozero__class_Ozero(X18270)),X18269))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),X18268),c_Groups_Ozero__class_Ozero(X18270)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18270),X18269),X18268)),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ class_Rings_Olinordered__ring__strict(X18270) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),X18269),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),c_Groups_Ozero__class_Ozero(X18270)),X18268))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18270),X18269),X18268)),c_Groups_Ozero__class_Ozero(X18270)))
        | ~ class_Rings_Olinordered__ring__strict(X18270) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__0__iff])])]) ).

fof(i_0_8123,plain,
    ! [X21740,X21741] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X21741),X21740))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X21741)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21740)))
        | ~ c_Nat__Transfer_Onat__set(X21740)
        | ~ c_Nat__Transfer_Ois__nat(X21741) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,X21741)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21740)))
        | hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X21741),X21740))
        | ~ c_Nat__Transfer_Onat__set(X21740)
        | ~ c_Nat__Transfer_Ois__nat(X21741) ) ),
    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_8124,plain,
    ! [X28450,X28451,X28452] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28452),esk327_3(X28450,X28451,X28452)),X28451))
        | ~ hBOOL(hAPP(hAPP(c_member(X28452),X28450),X28451))
        | c_Big__Operators_Olinorder__class_OMax(X28452,X28451) = X28450
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28452),X28451))
        | ~ class_Orderings_Olinorder(X28452) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28452),esk327_3(X28450,X28451,X28452)),X28450))
        | ~ hBOOL(hAPP(hAPP(c_member(X28452),X28450),X28451))
        | c_Big__Operators_Olinorder__class_OMax(X28452,X28451) = X28450
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28452),X28451))
        | ~ class_Orderings_Olinorder(X28452) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__eqI])])])]) ).

fof(i_0_8125,plain,
    ! [X33855,X33856,X33857] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33857),X33856)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33857),X33855)))
        | X33857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33856),X33855)) )
      & ( X33857 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33857),X33856)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33857),X33855))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33856),X33855))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33857),X33856)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33857),X33855))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel__disj])])]) ).

fof(i_0_8126,plain,
    ! [X32290,X32291,X32292,X32293,X32294,X32295,X32296] :
      ( ( ~ c_List_Olist__all(X32292,X32291,X32290)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32293),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32292)),X32290)))
        | hBOOL(hAPP(X32291,hAPP(hAPP(c_List_Onth(X32292),X32290),X32293))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_3(X32294,X32295,X32296)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32296)),X32294)))
        | c_List_Olist__all(X32296,X32295,X32294) )
      & ( ~ hBOOL(hAPP(X32295,hAPP(hAPP(c_List_Onth(X32296),X32294),esk474_3(X32294,X32295,X32296))))
        | c_List_Olist__all(X32296,X32295,X32294) ) ),
    inference(distribute,[status(thm)],[inference(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_8127,plain,
    ! [X22296] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22296)),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),X22296)) = 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),X22296))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__1__number__of])]) ).

fof(i_0_8128,plain,
    ! [X18409,X18410,X18411,X18412,X18413] :
      ( ~ c_Fun_Oinj__on(X18413,X18412,X18411,X18410)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18413,tc_HOL_Obool)),X18409),X18410))
      | c_Fun_Oinj__on(X18413,X18412,X18411,X18409) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__inj__on])]) ).

fof(i_0_8129,plain,
    ! [X31415,X31416,X31417] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31417)),hAPP(c_List_Ofilter(X31417,X31416),X31415))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31417)),X31415))),
    inference(variable_rename,[status(thm)],[fact_length__filter__le]) ).

fof(i_0_8130,plain,
    ! [X28599,X28600,X28601] : hBOOL(hAPP(hAPP(c_member(tc_prod(X28601,X28601)),hAPP(hAPP(c_Product__Type_OPair(X28601,X28601),X28600),X28600)),c_Transitive__Closure_Ortrancl(X28601,X28599))),
    inference(variable_rename,[status(thm)],[fact_rtrancl_Ortrancl__refl]) ).

cnf(i_0_8131,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_5693]) ).

cnf(i_0_8132,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_5694]) ).

fof(i_0_8133,plain,
    ! [X17984,X17985,X17986] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17986),X17985)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17986),X17984)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17985),X17984)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17985),X17984))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17986),X17985)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17986),X17984))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__less])]) ).

cnf(i_0_8134,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_5695]) ).

cnf(i_0_8135,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_5696]) ).

fof(i_0_8136,plain,
    ! [X18030,X18031,X18032] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18032),X18031)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18032),X18030)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18031),X18030)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18031),X18030))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18032),X18031)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18032),X18030))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel__le])]) ).

fof(i_0_8137,plain,
    ! [X33158,X33159,X33160,X33161,X33162] :
      ( ~ c_Fun_Oinj__on(X33162,X33161,X33160,X33159)
      | ~ hBOOL(hAPP(hAPP(c_member(X33162),X33158),X33159))
      | hAPP(c_Hilbert__Choice_Oinv__into(X33162,X33161,X33159,X33160),hAPP(X33160,X33158)) = X33158 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__f])]) ).

fof(i_0_8138,plain,
    ! [X19215,X19216,X19217,X19218,X19219] :
      ( ~ c_Fun_Oinj__on(X19219,X19218,X19217,X19216)
      | ~ hBOOL(hAPP(hAPP(c_member(X19219),X19215),X19216))
      | hAPP(c_Fun_Othe__inv__into(X19219,X19218,X19216,X19217),hAPP(X19217,X19215)) = X19215 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__f])]) ).

cnf(i_0_8139,plain,
    hAPP(c_List_OremoveAll(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5697]) ).

fof(i_0_8140,plain,
    ! [X22306] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X22306)),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),X22306)) = 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),X22306))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg__1__number__of])]) ).

fof(i_0_8141,plain,
    ! [X33163,X33164,X33165,X33166,X33167,X33168] :
      ( ~ c_Fun_Oinj__on(X33168,X33167,X33166,X33165)
      | ~ hBOOL(hAPP(hAPP(c_member(X33168),X33164),X33165))
      | hAPP(X33166,X33164) != X33163
      | hAPP(c_Hilbert__Choice_Oinv__into(X33168,X33167,X33165,X33166),X33163) = X33164 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inv__into__f__eq])]) ).

fof(i_0_8142,plain,
    ! [X19209,X19210,X19211,X19212,X19213,X19214] :
      ( ~ c_Fun_Oinj__on(X19214,X19213,X19212,X19211)
      | hAPP(X19212,X19210) != X19209
      | ~ hBOOL(hAPP(hAPP(c_member(X19214),X19210),X19211))
      | hAPP(c_Fun_Othe__inv__into(X19214,X19213,X19211,X19212),X19209) = X19210 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_the__inv__into__f__eq])]) ).

fof(i_0_8143,plain,
    ! [X26341,X26342,X26343,X26344,X26345] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26344),X26345),X26343))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26342),hAPP(X26341,X26345)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26342),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26344,tc_fun(X26342,tc_HOL_Obool)),X26343),X26341))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__INT])])]) ).

fof(i_0_8144,plain,
    ! [X20338,X20339,X20340,X20341] :
      ( ~ class_Rings_Olinordered__semidom(X20341)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20340),X20339))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20341),c_Groups_Oone__class_Oone(X20341)),X20338))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20341),hAPP(hAPP(c_Power_Opower__class_Opower(X20341),X20338),X20340)),hAPP(hAPP(c_Power_Opower__class_Opower(X20341),X20338),X20339))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__strict__increasing])]) ).

fof(i_0_8145,plain,
    ! [X20342,X20343,X20344,X20345] :
      ( ~ class_Rings_Olinordered__semidom(X20345)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20344),X20343))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20345),c_Groups_Oone__class_Oone(X20345)),X20342))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20345),hAPP(hAPP(c_Power_Opower__class_Opower(X20345),X20342),X20344)),hAPP(hAPP(c_Power_Opower__class_Opower(X20345),X20342),X20343))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__increasing])]) ).

fof(i_0_8146,plain,
    ! [X22801,X22802,X22803,X22804] :
      ( ~ class_Fields_Olinordered__field(X22804)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22804),X22803),X22802))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22804),X22801),c_Groups_Ozero__class_Ozero(X22804)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22804),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22804),X22802),X22801)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22804),X22803),X22801))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__strict__right__mono__neg])]) ).

fof(i_0_8147,plain,
    ! [X18208,X18209,X18210,X18211] :
      ( ~ class_Rings_Olinordered__ring__strict(X18211)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18211),X18210),X18209))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18211),X18208),c_Groups_Ozero__class_Ozero(X18211)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18211),X18209),X18208)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18211),X18210),X18208))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__right__mono__neg])]) ).

fof(i_0_8148,plain,
    ! [X18204,X18205,X18206,X18207] :
      ( ~ class_Rings_Olinordered__ring__strict(X18207)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18207),X18206),X18205))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18207),X18204),c_Groups_Ozero__class_Ozero(X18207)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18207),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18207),X18204),X18205)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18207),X18204),X18206))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__strict__left__mono__neg])]) ).

fof(i_0_8149,plain,
    ! [X22797,X22798,X22799,X22800] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X22800)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22800),X22799),X22798))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22800),X22797),c_Groups_Ozero__class_Ozero(X22800)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22800),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22800),X22798),X22797)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22800),X22799),X22797))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__right__mono__neg])]) ).

fof(i_0_8150,plain,
    ! [X18298,X18299,X18300,X18301] :
      ( ~ class_Rings_Oordered__ring(X18301)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18301),X18300),X18299))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18301),X18298),c_Groups_Ozero__class_Ozero(X18301)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18301),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18301),X18299),X18298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18301),X18300),X18298))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__right__mono__neg])]) ).

fof(i_0_8151,plain,
    ! [X18302,X18303,X18304,X18305] :
      ( ~ class_Rings_Oordered__ring(X18305)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18305),X18304),X18303))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18305),X18302),c_Groups_Ozero__class_Ozero(X18305)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18305),X18302),X18303)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18305),X18302),X18304))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__mono__neg])]) ).

cnf(i_0_8152,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_5648]) ).

fof(i_0_8153,plain,
    ! [X17510,X17511,X17512] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17512),X17511))
      | ~ hBOOL(hAPP(hAPP(c_member(X17512),X17510),X17511))
      | hAPP(c_Finite__Set_Ocard(X17512),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17512,tc_HOL_Obool)),X17511),hAPP(hAPP(c_Set_Oinsert(X17512),X17510),c_Orderings_Obot__class_Obot(tc_fun(X17512,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17512),X17511)),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_8154,plain,
    ! [X17513,X17514,X17515] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17515),X17513),X17514))
        | hAPP(c_Finite__Set_Ocard(X17515),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17515,tc_HOL_Obool)),X17514),hAPP(hAPP(c_Set_Oinsert(X17515),X17513),c_Orderings_Obot__class_Obot(tc_fun(X17515,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17515),X17514)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17515),X17514)) )
      & ( hBOOL(hAPP(hAPP(c_member(X17515),X17513),X17514))
        | hAPP(c_Finite__Set_Ocard(X17515),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17515,tc_HOL_Obool)),X17514),hAPP(hAPP(c_Set_Oinsert(X17515),X17513),c_Orderings_Obot__class_Obot(tc_fun(X17515,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(X17515),X17514)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17515),X17514)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5698])])]) ).

fof(i_0_8155,plain,
    ! [X17375,X17376,X17377] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17377,tc_HOL_Obool)),X17375),X17376)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17377),X17375))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17377),X17376)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17377),X17375))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17377),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17377,tc_HOL_Obool)),X17375),X17376)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17377),X17376)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff2])])]) ).

cnf(i_0_8156,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_5699]) ).

fof(i_0_8157,plain,
    ! [X19327,X19328,X19329] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19329),hAPP(c_Int_Onumber__class_Onumber__of(X19329),X19328)),hAPP(c_Int_Onumber__class_Onumber__of(X19329),X19327)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19329),hAPP(c_Int_Onumber__class_Onumber__of(X19329),X19327)),hAPP(c_Int_Onumber__class_Onumber__of(X19329),X19328)))
        | ~ class_Int_Onumber(X19329)
        | ~ class_Orderings_Olinorder(X19329) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19329),hAPP(c_Int_Onumber__class_Onumber__of(X19329),X19327)),hAPP(c_Int_Onumber__class_Onumber__of(X19329),X19328)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19329),hAPP(c_Int_Onumber__class_Onumber__of(X19329),X19328)),hAPP(c_Int_Onumber__class_Onumber__of(X19329),X19327)))
        | ~ class_Int_Onumber(X19329)
        | ~ class_Orderings_Olinorder(X19329) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5700])])]) ).

fof(i_0_8158,plain,
    ! [X22068,X22069,X22070,X22071] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X22071,tc_fun(X22070,tc_HOL_Obool))),X22069),X22068)),
    inference(variable_rename,[status(thm)],[i_0_5701]) ).

fof(i_0_8159,plain,
    ! [X29655,X29656,X29657] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29657),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X29656)))
      | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,X29656),X29657),X29655)) = 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),X29656)),X29655)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X29656),X29657)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__update__nat])]) ).

fof(i_0_8160,plain,
    ! [X19539,X19540,X19541,X19542,X19543,X19544] : hAPP(hAPP(c_Fun_Ocomp(X19544,X19543,X19542,X19541),X19540),X19539) = hAPP(X19541,hAPP(X19540,X19539)),
    inference(variable_rename,[status(thm)],[fact_o__def]) ).

fof(i_0_8161,plain,
    ! [X19526,X19527,X19528,X19529,X19530,X19531] : hAPP(hAPP(c_Fun_Ocomp(X19531,X19530,X19529,X19528),X19527),X19526) = hAPP(X19528,hAPP(X19527,X19526)),
    inference(variable_rename,[status(thm)],[fact_o__apply]) ).

fof(i_0_8162,plain,
    ! [X33897,X33898,X33899,X33900,X33901] :
      ( ~ class_Rings_Ocomm__semiring__1(X33901)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33901),X33900),X33899))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33901),X33898),X33897))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33901),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33901),X33900),X33898)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33901),X33899),X33897))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono])]) ).

fof(i_0_8163,plain,
    ! [X17921,X17922,X17923,X17924,X17925] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X17925)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17925),X17924),X17923))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17925),X17922),X17921))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17925),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17925),X17924),X17922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17925),X17923),X17921))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__mono])]) ).

fof(i_0_8164,plain,
    ! [X18081,X18082,X18083,X18084,X18085] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18085)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18085),X18084),X18083))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18085),X18082),X18081))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18085),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18085),X18084),X18082)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18085),X18083),X18081))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__less__mono])]) ).

fof(i_0_8165,plain,
    ! [X18076,X18077,X18078,X18079,X18080] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X18080)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18080),X18079),X18078))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18080),X18077),X18076))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18080),X18079),X18077)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18080),X18078),X18076))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__le__mono])]) ).

fof(i_0_8166,plain,
    ! [X25010,X25011,X25012,X25013,X25014] :
      ( ~ class_Lattices_Osemilattice__inf(X25014)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25014),X25013),X25012))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25014),X25011),X25010))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25014),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25014),X25013),X25011)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25014),X25012),X25010))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__mono])]) ).

fof(i_0_8167,plain,
    ! [X23296,X23297,X23298,X23299,X23300] :
      ( ~ class_Lattices_Osemilattice__sup(X23300)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23300),X23299),X23298))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23300),X23297),X23296))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23300),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23300),X23299),X23297)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23300),X23298),X23296))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__mono])]) ).

fof(i_0_8168,plain,
    ! [X22570,X22571,X22572,X22573,X22574] :
      ( ~ class_Orderings_Olinorder(X22574)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),X22573),X22572))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),X22571),X22570))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22574),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22574),X22573),X22571)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22574),X22572),X22570))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__mono])]) ).

fof(i_0_8169,plain,
    ! [X21561,X21562,X21563,X21564,X21565] :
      ( ~ class_Orderings_Olinorder(X21565)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21565),X21564),X21563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21565),X21562),X21561))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21565),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21565),X21564),X21562)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21565),X21563),X21561))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__mono])]) ).

fof(i_0_8170,plain,
    ! [X17892,X17893,X17894,X17895,X17896] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X17896)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17896),X17895),X17894))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17896),X17893),X17892))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17896),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17896),X17895),X17893)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17896),X17894),X17892))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__mono])]) ).

fof(i_0_8171,plain,
    ! [X19330,X19331,X19332,X19333] :
      ( ~ class_Int_Onumber(X19333)
      | ~ class_Rings_Osemiring(X19333)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19333),hAPP(c_Int_Onumber__class_Onumber__of(X19333),X19332)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19333),X19331),X19330)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19333),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19333),hAPP(c_Int_Onumber__class_Onumber__of(X19333),X19332)),X19331)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19333),hAPP(c_Int_Onumber__class_Onumber__of(X19333),X19332)),X19330)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__distrib__number__of])]) ).

fof(i_0_8172,plain,
    ! [X19346,X19347,X19348,X19349] :
      ( ~ class_Int_Onumber(X19349)
      | ~ class_Rings_Oring(X19349)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19349),hAPP(c_Int_Onumber__class_Onumber__of(X19349),X19348)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19349),X19347),X19346)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19349),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19349),hAPP(c_Int_Onumber__class_Onumber__of(X19349),X19348)),X19347)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19349),hAPP(c_Int_Onumber__class_Onumber__of(X19349),X19348)),X19346)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__diff__distrib__number__of])]) ).

fof(i_0_8173,plain,
    ! [X33858,X33859,X33860,X33861,X33862] :
      ( ~ class_Divides_Osemiring__div(X33862)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33862),X33861),X33860))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33862),X33859),X33858))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33862),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33862),X33860),X33861)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33862),X33858),X33859)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33862),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33862),X33860),X33858)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33862),X33861),X33859)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__div__if__dvd])]) ).

fof(i_0_8174,plain,
    ! [X25314,X25315,X25316,X25317] :
      ( ~ class_Lattices_Osemilattice__inf(X25317)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25317),X25316))
      | hAPP(hAPP(c_Finite__Set_Ofold(X25317,X25317,c_Lattices_Osemilattice__inf__class_Oinf(X25317)),X25315),hAPP(hAPP(c_Set_Oinsert(X25317),X25314),X25316)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25317),X25314),hAPP(hAPP(c_Finite__Set_Ofold(X25317,X25317,c_Lattices_Osemilattice__inf__class_Oinf(X25317)),X25315),X25316)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__inf__insert])]) ).

fof(i_0_8175,plain,
    ! [X23419,X23420,X23421,X23422] :
      ( ~ class_Lattices_Osemilattice__sup(X23422)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23422),X23421))
      | hAPP(hAPP(c_Finite__Set_Ofold(X23422,X23422,c_Lattices_Osemilattice__sup__class_Osup(X23422)),X23420),hAPP(hAPP(c_Set_Oinsert(X23422),X23419),X23421)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23422),X23419),hAPP(hAPP(c_Finite__Set_Ofold(X23422,X23422,c_Lattices_Osemilattice__sup__class_Osup(X23422)),X23420),X23421)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold__sup__insert])]) ).

fof(i_0_8176,plain,
    ! [X22700,X22701,X22702,X22703] :
      ( ~ class_Orderings_Olinorder(X22703)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22703),X22702))
      | hAPP(hAPP(c_Finite__Set_Ofold(X22703,X22703,c_Orderings_Oord__class_Omax(X22703)),X22701),hAPP(hAPP(c_Set_Oinsert(X22703),X22700),X22702)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22703),X22700),hAPP(hAPP(c_Finite__Set_Ofold(X22703,X22703,c_Orderings_Oord__class_Omax(X22703)),X22701),X22702)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__sup__insert])]) ).

fof(i_0_8177,plain,
    ! [X21710,X21711,X21712,X21713] :
      ( ~ class_Orderings_Olinorder(X21713)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21713),X21712))
      | hAPP(hAPP(c_Finite__Set_Ofold(X21713,X21713,c_Orderings_Oord__class_Omin(X21713)),X21711),hAPP(hAPP(c_Set_Oinsert(X21713),X21710),X21712)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21713),X21710),hAPP(hAPP(c_Finite__Set_Ofold(X21713,X21713,c_Orderings_Oord__class_Omin(X21713)),X21711),X21712)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold__inf__insert])]) ).

fof(i_0_8178,plain,
    ! [X26922,X26923,X26924,X26925] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26925),X26924))
      | ~ c_Fun_Oinj__on(X26923,X26925,X26922,c_Orderings_Otop__class_Otop(tc_fun(X26923,tc_HOL_Obool)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26923),hAPP(c_Set_Ovimage(X26923,X26925,X26922),X26924))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__vimageI])]) ).

fof(i_0_8179,plain,
    ! [X26607,X26608,X26609,X26610,X26611] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26611)
      | ~ hBOOL(hAPP(hAPP(c_member(X26610),X26609),X26608))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26611),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26610,X26611),X26608),X26607)),hAPP(X26607,X26609))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__leI])]) ).

fof(i_0_8180,plain,
    ! [X21382,X21383,X21384,X21385] :
      ( ~ class_Int_Onumber__ring(X21385)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21385),hAPP(c_Int_Onumber__class_Onumber__of(X21385),X21384)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21385),X21383),hAPP(c_Int_Onumber__class_Onumber__of(X21385),X21382))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21385),hAPP(c_Int_Onumber__class_Onumber__of(X21385),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21384),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21382)))),X21383) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff2])]) ).

fof(i_0_8181,plain,
    ! [X17314,X17315] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17315)),X17314))
        | hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17315),X17314)) )
      & ( ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17315),X17314))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17315)),X17314)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__nat_Osimps_I2_J])]) ).

fof(i_0_8182,plain,
    ! [X23641,X23642,X23643,X23644,X23645,X23646] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23646),X23645),X23644))
      | ~ hBOOL(hAPP(hAPP(X23643,X23645),X23642))
      | hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23646,tc_fun(X23641,tc_HOL_Obool)),X23644),X23643),X23642)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP1__I])]) ).

fof(i_0_8183,plain,
    ! [X27014,X27015,X27016,X27017] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27016),c_Complete__Lattice_OSup__class_OSup(X27016,X27015)),X27014))
        | ~ hBOOL(hAPP(hAPP(c_member(X27016),X27017),X27015))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27016),X27017),X27014))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X27016) )
      & ( hBOOL(hAPP(hAPP(c_member(X27016),esk247_3(X27014,X27015,X27016)),X27015))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27016),c_Complete__Lattice_OSup__class_OSup(X27016,X27015)),X27014))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X27016) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27016),esk247_3(X27014,X27015,X27016)),X27014))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27016),c_Complete__Lattice_OSup__class_OSup(X27016,X27015)),X27014))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X27016) ) ),
    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_8184,plain,
    ! [X19622,X19623,X19624,X19625,X19626,X19627] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X19627,X19626,X19625)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19627),X19624))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19627,X19626,X19625),X19623),hAPP(hAPP(c_Set_Oinsert(X19627),X19622),X19624)) = hAPP(hAPP(X19625,X19622),hAPP(hAPP(c_Finite__Set_Ofold(X19627,X19626,X19625),X19623),X19624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem])]) ).

fof(i_0_8185,plain,
    ! [X30487,X30488,X30489,X30490,X30491] :
      ( ( X30488 = 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),X30488),X30487) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30489),hAPP(c_List_Oset(tc_Nat_Onat),X30487)))
        | X30489 = 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),X30488),X30487) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk408_2(X30490,X30491)),hAPP(c_List_Oset(tc_Nat_Onat),X30490)))
        | X30491 != 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),X30491),X30490) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( esk408_2(X30490,X30491) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X30491 != 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),X30491),X30490) = 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_8186,plain,
    ! [X18507,X18508] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18508))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18507))
      | 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),X18507),X18508))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__mult])]) ).

fof(i_0_8187,plain,
    ! [X18509,X18510] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18510))
        | ~ 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),X18510),X18509))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18509))
        | ~ 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),X18510),X18509))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18510))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18509))
        | 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),X18510),X18509))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff])])]) ).

fof(i_0_8188,plain,
    ! [X21344,X21345,X21346] : 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),X21346),X21345)),X21344)),X21345) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21344),X21345),
    inference(variable_rename,[status(thm)],[fact_mod__mult__self4]) ).

fof(i_0_8189,plain,
    ! [X27053,X27054,X27055] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X27055,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X27055,tc_HOL_Obool),tc_HOL_Obool)),X27054),X27053)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27055,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27055,tc_HOL_Obool),X27054)),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27055,tc_HOL_Obool),X27053)),
    inference(variable_rename,[status(thm)],[fact_Union__Un__distrib]) ).

fof(i_0_8190,plain,
    ! [X26881,X26882,X26883] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X26883,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(X26883,tc_HOL_Obool),tc_HOL_Obool)),X26882),X26881)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26883,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26883,tc_HOL_Obool),X26882)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26883,tc_HOL_Obool),X26881)),
    inference(variable_rename,[status(thm)],[fact_Inter__Un__distrib]) ).

fof(i_0_8191,plain,
    ! [X21372,X21373,X21374,X21375,X21376,X21377,X21378,X21379] :
      ( ( X21372 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X21374,X21373))
        | ~ hBOOL(hAPP(X21374,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21373,X21372))) )
      & ( X21372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21376),X21372))
        | X21373 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21372),X21375)),X21376)
        | hBOOL(hAPP(X21374,X21376))
        | ~ hBOOL(hAPP(X21374,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21373,X21372))) )
      & ( X21377 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X21377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X21379,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21378,X21377))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk73_3(X21377,X21378,X21379)),X21377))
        | X21377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X21379,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21378,X21377))) )
      & ( X21378 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21377),esk72_3(X21377,X21378,X21379))),esk73_3(X21377,X21378,X21379))
        | X21377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X21379,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21378,X21377))) )
      & ( ~ hBOOL(hAPP(X21379,esk73_3(X21377,X21378,X21379)))
        | X21377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X21379,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21378,X21377))) )
      & ( X21377 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X21379,X21378))
        | hBOOL(hAPP(X21379,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21378,X21377))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk73_3(X21377,X21378,X21379)),X21377))
        | ~ hBOOL(hAPP(X21379,X21378))
        | hBOOL(hAPP(X21379,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21378,X21377))) )
      & ( X21378 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21377),esk72_3(X21377,X21378,X21379))),esk73_3(X21377,X21378,X21379))
        | ~ hBOOL(hAPP(X21379,X21378))
        | hBOOL(hAPP(X21379,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21378,X21377))) )
      & ( ~ hBOOL(hAPP(X21379,esk73_3(X21377,X21378,X21379)))
        | ~ hBOOL(hAPP(X21379,X21378))
        | hBOOL(hAPP(X21379,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21378,X21377))) ) ),
    inference(distribute,[status(thm)],[inference(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_8192,plain,
    ! [X29532,X29533,X29534,X29535,X29536,X29537,X29538] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29534)),X29533),c_List_Olists(X29534,X29532)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29534),X29535),hAPP(c_List_Oset(X29534),X29533)))
        | hBOOL(hAPP(hAPP(c_member(X29534),X29535),X29532)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29538),esk386_3(X29536,X29537,X29538)),hAPP(c_List_Oset(X29538),X29537)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29538)),X29537),c_List_Olists(X29538,X29536))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X29538),esk386_3(X29536,X29537,X29538)),X29536))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29538)),X29537),c_List_Olists(X29538,X29536))) ) ),
    inference(distribute,[status(thm)],[inference(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_8193,plain,
    ! [X29253,X29254,X29255,X29256] : c_List_Olist_Olist__size(X29256,X29255,hAPP(hAPP(c_List_Olist_OCons(X29256),X29254),X29253)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X29255,X29254)),c_List_Olist_Olist__size(X29256,X29255,X29253))),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_8194,plain,
    ! [X33639,X33640,X33641,X33642,X33643] :
      ( ~ class_Rings_Ocomm__semiring__1(X33643)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33643),X33642),X33641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33640),X33639))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33643),hAPP(hAPP(c_Power_Opower__class_Opower(X33643),X33642),X33640)),hAPP(hAPP(c_Power_Opower__class_Opower(X33643),X33641),X33639))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__le])]) ).

fof(i_0_8195,plain,
    ! [X29234,X29235,X29236] : c_Random_Oselect__weight(X29236,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,X29236)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X29236),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),X29235)),X29234)) = c_Random_Oselect__weight(X29236,X29234),
    inference(variable_rename,[status(thm)],[fact_select__weight__cons__zero]) ).

fof(i_0_8196,plain,
    ! [X21005,X21006,X21007,X21008] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21007))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21007))
        | X21007 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21008,X21007) = X21005
        | X21008 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21007),X21006)),X21005) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21007),X21005))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21005),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)),X21007))
        | X21007 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21008,X21007) = X21005
        | X21008 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21007),X21006)),X21005) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21007))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21005))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21005),X21007))
        | X21007 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21008,X21007) = X21005
        | X21008 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21007),X21006)),X21005) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21007),X21005))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21005),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)),X21005))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21005),X21007))
        | X21007 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21008,X21007) = X21005
        | X21008 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21007),X21006)),X21005) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5702])])]) ).

fof(i_0_8197,plain,
    ! [X31520,X31521] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31521)),c_List_Otranspose__rel(X31521)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31521)),c_List_Olist_ONil(X31521)),X31520)))
      | c_List_Otranspose(X31521,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31521)),c_List_Olist_ONil(X31521)),X31520)) = c_List_Otranspose(X31521,X31520) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I2_J])]) ).

cnf(i_0_8198,plain,
    c_List_Ofoldr(X1,X2,X3,c_List_Olist_ONil(X1),X4) = X4,
    inference(split_conjunct,[status(thm)],[i_0_5703]) ).

fof(i_0_8199,plain,
    ! [X25330,X25331,X25332] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25332,tc_HOL_Obool)),X25331),X25330) != c_Orderings_Obot__class_Obot(tc_fun(X25332,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25332,tc_HOL_Obool)),X25331),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25332,tc_HOL_Obool)),X25330))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25332,tc_HOL_Obool)),X25331),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25332,tc_HOL_Obool)),X25330)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25332,tc_HOL_Obool)),X25331),X25330) = c_Orderings_Obot__class_Obot(tc_fun(X25332,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_disjoint__eq__subset__Compl])]) ).

cnf(i_0_8200,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_5704]) ).

cnf(i_0_8201,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_5705]) ).

fof(i_0_8202,plain,
    ! [X17107,X17108,X17109] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17109),X17108))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17109,tc_HOL_Obool)),X17107),X17108))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17109),X17108)),hAPP(c_Finite__Set_Ocard(X17109),X17107)))
      | X17107 = X17108 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__seteq])]) ).

fof(i_0_8203,plain,
    ! [X26867,X26868,X26869] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26869,tc_HOL_Obool)),X26868),X26867))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26869,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26869,tc_HOL_Obool),X26867)),X26868)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inter__lower])]) ).

fof(i_0_8204,plain,
    ! [X28799,X28800,X28801,X28802,X28803] : hAPP(c_Relation_Oconverse(X28803,X28802),hAPP(hAPP(c_Relation_Orel__comp(X28803,X28801,X28802),X28800),X28799)) = hAPP(hAPP(c_Relation_Orel__comp(X28802,X28801,X28803),hAPP(c_Relation_Oconverse(X28801,X28802),X28799)),hAPP(c_Relation_Oconverse(X28803,X28801),X28800)),
    inference(variable_rename,[status(thm)],[fact_converse__rel__comp]) ).

fof(i_0_8205,plain,
    ! [X20555,X20556,X20557,X20558] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20557))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20557))
        | X20557 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20558),X20557) = X20556
        | X20558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20557),X20556)),X20555) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20557),X20555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20555),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)),X20557))
        | X20557 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20558),X20557) = X20556
        | X20558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20557),X20556)),X20555) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20557))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20555),X20557))
        | X20557 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20558),X20557) = X20556
        | X20558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20557),X20556)),X20555) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20557),X20555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20555),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)),X20555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20555),X20557))
        | X20557 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20558),X20557) = X20556
        | X20558 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20557),X20556)),X20555) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5706])])]) ).

fof(i_0_8206,plain,
    ! [X21586,X21587,X21588,X21589] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21589),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21589),X21588),X21587)),X21586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21589),X21588),X21586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21589),X21587),X21586))
        | ~ class_Orderings_Olinorder(X21589) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21589),X21588),X21586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21589),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21589),X21588),X21587)),X21586))
        | ~ class_Orderings_Olinorder(X21589) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21589),X21587),X21586))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21589),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21589),X21588),X21587)),X21586))
        | ~ class_Orderings_Olinorder(X21589) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__disj])])]) ).

fof(i_0_8207,plain,
    ! [X21570,X21571,X21572,X21573] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21573),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21573),X21572),X21571)),X21570))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21573),X21572),X21570))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21573),X21571),X21570))
        | ~ class_Orderings_Olinorder(X21573) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21573),X21572),X21570))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21573),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21573),X21572),X21571)),X21570))
        | ~ class_Orderings_Olinorder(X21573) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21573),X21571),X21570))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21573),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21573),X21572),X21571)),X21570))
        | ~ class_Orderings_Olinorder(X21573) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__le__iff__disj])])]) ).

fof(i_0_8208,plain,
    ! [X20929,X20930,X20931,X20932,X20933,X20934,X20935,X20936] :
      ( ( X20929 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X20931,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X20931,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20930),X20929))) )
      & ( X20929 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20933),X20929))
        | X20930 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20929),X20932)),X20933)
        | hBOOL(hAPP(X20931,X20932))
        | ~ hBOOL(hAPP(X20931,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20930),X20929))) )
      & ( X20934 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X20936,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20935),X20934))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk64_3(X20934,X20935,X20936)),X20934))
        | X20934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X20936,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20935),X20934))) )
      & ( X20935 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20934),esk63_3(X20934,X20935,X20936))),esk64_3(X20934,X20935,X20936))
        | X20934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X20936,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20935),X20934))) )
      & ( ~ hBOOL(hAPP(X20936,esk63_3(X20934,X20935,X20936)))
        | X20934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(X20936,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20935),X20934))) )
      & ( X20934 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(X20936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20936,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20935),X20934))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk64_3(X20934,X20935,X20936)),X20934))
        | ~ hBOOL(hAPP(X20936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20936,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20935),X20934))) )
      & ( X20935 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20934),esk63_3(X20934,X20935,X20936))),esk64_3(X20934,X20935,X20936))
        | ~ hBOOL(hAPP(X20936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20936,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20935),X20934))) )
      & ( ~ hBOOL(hAPP(X20936,esk63_3(X20934,X20935,X20936)))
        | ~ hBOOL(hAPP(X20936,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X20936,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20935),X20934))) ) ),
    inference(distribute,[status(thm)],[inference(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_8209,plain,
    ! [X23016,X23017,X23018] :
      ( ~ class_Orderings_Olinorder(X23018)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23018),X23017))
      | X23016 = c_Orderings_Obot__class_Obot(tc_fun(X23018,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23018,tc_HOL_Obool)),X23016),X23017))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X23018),c_Big__Operators_Olattice_OSup__fin(X23018,c_Orderings_Oord__class_Omax(X23018),X23016)),c_Big__Operators_Olattice_OSup__fin(X23018,c_Orderings_Oord__class_Omax(X23018),X23017)) = c_Big__Operators_Olattice_OSup__fin(X23018,c_Orderings_Oord__class_Omax(X23018),X23017) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osubset__idem])]) ).

fof(i_0_8210,plain,
    ! [X21790,X21791,X21792] :
      ( ~ class_Orderings_Olinorder(X21792)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21792),X21791))
      | X21790 = c_Orderings_Obot__class_Obot(tc_fun(X21792,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21792,tc_HOL_Obool)),X21790),X21791))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21792),c_Big__Operators_Olattice_OInf__fin(X21792,c_Orderings_Oord__class_Omin(X21792),X21790)),c_Big__Operators_Olattice_OInf__fin(X21792,c_Orderings_Oord__class_Omin(X21792),X21791)) = c_Big__Operators_Olattice_OInf__fin(X21792,c_Orderings_Oord__class_Omin(X21792),X21791) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osubset__idem])]) ).

cnf(i_0_8211,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_5707]) ).

fof(i_0_8212,plain,
    ! [X19824,X19825,X19826,X19827,X19828,X19829] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19829,X19828,X19827)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19829),X19826))
      | hBOOL(hAPP(hAPP(c_member(X19829),X19825),X19826))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19829,X19828,X19827),X19824),hAPP(hAPP(c_Set_Oinsert(X19829),X19825),X19826)) = hAPP(hAPP(c_Finite__Set_Ofold(X19829,X19828,X19827),hAPP(hAPP(X19827,X19825),X19824)),X19826) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5708])]) ).

cnf(i_0_8213,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_5709]) ).

fof(i_0_8214,plain,
    ! [X27050,X27051] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(X27051,tc_HOL_Obool),tc_HOL_Obool)),X27050),hAPP(c_Set_OPow(X27051),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27051,tc_HOL_Obool),X27050)))),
    inference(variable_rename,[status(thm)],[fact_subset__Pow__Union]) ).

fof(i_0_8215,plain,
    ! [X24874,X24875,X24876,X24877] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X24877),X24876),X24875))
      | ~ hBOOL(hAPP(hAPP(c_member(X24877),X24876),X24874))
      | hBOOL(hAPP(hAPP(c_member(X24877),X24876),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24877,tc_HOL_Obool)),X24875),X24874))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_IntI])]) ).

fof(i_0_8216,plain,
    ! [X24620,X24621,X24622,X24623] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24622),X24621))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24623),X24620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24621),hAPP(c_Nat_OSuc,X24622))) = c_Groups_Ozero__class_Ozero(X24623)
        | ~ class_Groups_Ocomm__monoid__add(X24623) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24622),X24621))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24623),X24620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24621),hAPP(c_Nat_OSuc,X24622))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24623),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24623),X24620),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24621),X24622))),hAPP(X24620,X24622))
        | ~ class_Groups_Ocomm__monoid__add(X24623) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5710])])]) ).

fof(i_0_8217,plain,
    ! [X22403,X22404,X22405,X22406,X22407,X22408] :
      ( ( hBOOL(hAPP(X22408,hAPP(c_Product__Type_Ofst(X22404,X22403),hAPP(hAPP(c_Product__Type_OPair(X22404,X22403),X22407),X22405))))
        | ~ hBOOL(hAPP(X22406,X22405))
        | ~ hBOOL(hAPP(X22408,X22407)) )
      & ( hBOOL(hAPP(X22406,hAPP(c_Product__Type_Osnd(X22404,X22403),hAPP(hAPP(c_Product__Type_OPair(X22404,X22403),X22407),X22405))))
        | ~ hBOOL(hAPP(X22406,X22405))
        | ~ hBOOL(hAPP(X22408,X22407)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conjI__realizer])])]) ).

fof(i_0_8218,plain,
    ! [X26457,X26458,X26459,X26460,X26461,X26462] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26462)
      | hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26461,tc_fun(X26460,X26462)),X26459),X26458),X26457) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26461,X26462),X26459),hAPP(hAPP(c_COMBC(X26461,X26460,X26462),X26458),X26457)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INFI__apply])]) ).

fof(i_0_8219,plain,
    ! [X23839,X23840,X23841,X23842,X23843,X23844] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X23844)
      | hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23843,tc_fun(X23842,X23844)),X23841),X23840),X23839) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23843,X23844),X23841),hAPP(hAPP(c_COMBC(X23843,X23842,X23844),X23840),X23839)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUPR__apply])]) ).

fof(i_0_8220,plain,
    ! [X23376,X23377,X23378] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23378),X23377))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23378,tc_HOL_Obool)),X23377),X23376))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X23378),X23376))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23378,tc_HOL_Obool)),X23377),X23376))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23378),X23377))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23378),X23376))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23378,tc_HOL_Obool)),X23377),X23376))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Un])])]) ).

fof(i_0_8221,plain,
    ! [X16833,X16834] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),esk2_2(X16833,X16834)),v_U))
        | v_P(X16833,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X16834)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
        | ~ v_wt(X16834) )
      & ( ~ v_P(X16833,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,esk2_2(X16833,X16834))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
        | v_P(X16833,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X16834)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
        | ~ v_wt(X16834) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_assms_I3_J])])])]) ).

fof(i_0_8222,plain,
    ! [X23126,X23127,X23128,X23129] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23129,tc_HOL_Obool)),X23128),X23127),X23126))
      | hBOOL(hAPP(X23128,X23126))
      | hBOOL(hAPP(X23127,X23126)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5711])]) ).

fof(i_0_8223,plain,
    ! [X25268,X25269,X25270] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25270,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25270,tc_HOL_Obool)),X25269),X25268)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25270,tc_HOL_Obool)),X25269),X25268)) = X25269,
    inference(variable_rename,[status(thm)],[fact_Un__Diff__Int]) ).

fof(i_0_8224,plain,
    ! [X31049,X31050,X31051] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X31051,tc_HOL_Obool)),X31050),X31049))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X31051),tc_HOL_Obool)),c_List_Olistsp(X31051,X31050)),c_List_Olistsp(X31051,X31049))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp__mono])]) ).

fof(i_0_8225,plain,
    ! [X29381,X29382,X29383] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29383,tc_HOL_Obool)),X29382),X29381))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(X29383),tc_HOL_Obool)),c_List_Olists(X29383,X29382)),c_List_Olists(X29383,X29381))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__mono])]) ).

fof(i_0_8226,plain,
    ! [X22887,X22888,X22889,X22890] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22890),X22888),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22890),X22887),X22889)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22890),X22887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22890),X22888),X22889)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22890),X22889),c_Groups_Ozero__class_Ozero(X22890)))
        | ~ class_Fields_Olinordered__field(X22890) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22890),X22887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22890),X22888),X22889)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22890),X22888),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22890),X22887),X22889)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22890),X22889),c_Groups_Ozero__class_Ozero(X22890)))
        | ~ class_Fields_Olinordered__field(X22890) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq])])]) ).

fof(i_0_8227,plain,
    ! [X22768,X22769,X22770,X22771] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22771),X22769),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22771),X22768),X22770)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22771),X22768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22771),X22769),X22770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22771),X22770),c_Groups_Ozero__class_Ozero(X22771)))
        | ~ class_Fields_Olinordered__field(X22771) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22771),X22768),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22771),X22769),X22770)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22771),X22769),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22771),X22768),X22770)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22771),X22770),c_Groups_Ozero__class_Ozero(X22771)))
        | ~ class_Fields_Olinordered__field(X22771) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq])])]) ).

fof(i_0_8228,plain,
    ! [X33050,X33051] :
      ( ( ~ c_Predicate_Osymp(X33051,X33050)
        | c_Relation_Osym(X33051,hAPP(c_Set_OCollect(tc_prod(X33051,X33051)),hAPP(c_Product__Type_Oprod_Oprod__case(X33051,X33051,tc_HOL_Obool),X33050))) )
      & ( ~ c_Relation_Osym(X33051,hAPP(c_Set_OCollect(tc_prod(X33051,X33051)),hAPP(c_Product__Type_Oprod_Oprod__case(X33051,X33051,tc_HOL_Obool),X33050)))
        | c_Predicate_Osymp(X33051,X33050) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_symp__def])]) ).

fof(i_0_8229,plain,
    ! [X32938,X32939] :
      ( ( ~ c_Predicate_Otransp(X32939,X32938)
        | c_Relation_Otrans(X32939,hAPP(c_Set_OCollect(tc_prod(X32939,X32939)),hAPP(c_Product__Type_Oprod_Oprod__case(X32939,X32939,tc_HOL_Obool),X32938))) )
      & ( ~ c_Relation_Otrans(X32939,hAPP(c_Set_OCollect(tc_prod(X32939,X32939)),hAPP(c_Product__Type_Oprod_Oprod__case(X32939,X32939,tc_HOL_Obool),X32938)))
        | c_Predicate_Otransp(X32939,X32938) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transp__def])]) ).

fof(i_0_8230,plain,
    ! [X28246,X28247] :
      ( ( ~ c_Wellfounded_OwfP(X28247,X28246)
        | c_Wellfounded_Owf(X28247,hAPP(c_Set_OCollect(tc_prod(X28247,X28247)),hAPP(c_Product__Type_Oprod_Oprod__case(X28247,X28247,tc_HOL_Obool),X28246))) )
      & ( ~ c_Wellfounded_Owf(X28247,hAPP(c_Set_OCollect(tc_prod(X28247,X28247)),hAPP(c_Product__Type_Oprod_Oprod__case(X28247,X28247,tc_HOL_Obool),X28246)))
        | c_Wellfounded_OwfP(X28247,X28246) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__def])]) ).

fof(i_0_8231,plain,
    ! [X20401,X20402] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20401),X20402)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20401),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)),X20402)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20401),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),X20401),X20402)),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)),X20402)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__neg__iff])])]) ).

cnf(i_0_8232,plain,
    ( c_List_OdropWhile(X3,X1,X2) = c_List_Olist_ONil(X3)
    | ~ hBOOL(hAPP(X1,esk435_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_5660]) ).

fof(i_0_8233,plain,
    ! [X27151,X27152,X27153,X27154,X27155,X27156] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(X27153,X27156),X27152),hAPP(c_COMBK(tc_fun(X27156,tc_HOL_Obool),X27153),X27154)) != hAPP(hAPP(c_Product__Type_OSigma(X27153,X27156),X27151),hAPP(c_COMBK(tc_fun(X27156,tc_HOL_Obool),X27153),X27154))
        | X27152 = X27151
        | ~ hBOOL(hAPP(hAPP(c_member(X27156),X27155),X27154)) )
      & ( X27152 != X27151
        | hAPP(hAPP(c_Product__Type_OSigma(X27153,X27156),X27152),hAPP(c_COMBK(tc_fun(X27156,tc_HOL_Obool),X27153),X27154)) = hAPP(hAPP(c_Product__Type_OSigma(X27153,X27156),X27151),hAPP(c_COMBK(tc_fun(X27156,tc_HOL_Obool),X27153),X27154))
        | ~ hBOOL(hAPP(hAPP(c_member(X27156),X27155),X27154)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__eq__cancel2])])]) ).

fof(i_0_8234,plain,
    ! [X20966,X20967] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20967))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20967),X20966)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X20967,X20966) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20967),X20966) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg__trivial])]) ).

fof(i_0_8235,plain,
    ! [X28398,X28399] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X28399,tc_HOL_Obool)),esk316_2(X28398,X28399)),hAPP(c_Relation_OImage(X28399,X28399,X28398),esk316_2(X28398,X28399))))
        | c_Wellfounded_Owf(X28399,X28398) )
      & ( esk316_2(X28398,X28399) != c_Orderings_Obot__class_Obot(tc_fun(X28399,tc_HOL_Obool))
        | c_Wellfounded_Owf(X28399,X28398) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfI__pf])])])]) ).

fof(i_0_8236,plain,
    ! [X22056,X22057,X22058,X22059,X22060] :
      ( ~ hBOOL(hAPP(hAPP(X22060,X22059),X22058))
      | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22057,X22056,tc_HOL_Obool),X22060),hAPP(hAPP(c_Product__Type_OPair(X22057,X22056),X22059),X22058))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_splitI])]) ).

fof(i_0_8237,plain,
    ! [X22051,X22052,X22053,X22054,X22055] :
      ( ~ hBOOL(hAPP(hAPP(X22055,X22054),X22053))
      | hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22052,X22051,tc_HOL_Obool),X22055),hAPP(hAPP(c_Product__Type_OPair(X22052,X22051),X22054),X22053))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__caseI])]) ).

fof(i_0_8238,plain,
    ! [X20403,X20404] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20403),X20404)),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)),X20403))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20404),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)),X20403))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20403),X20404)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20404),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_8239,plain,
    ! [X18096,X18097,X18098] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18098),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18097),X18096)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18098),X18096)),X18097)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18098),X18096)),X18097))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18098),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18097),X18096))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__diff__conv])]) ).

fof(i_0_8240,plain,
    ! [X18126,X18127,X18128] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18128),X18127)),X18126))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18126),X18127))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18126),X18127)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18128),X18127)),X18126)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__diff__conv])]) ).

fof(i_0_8241,plain,
    ! [X17477,X17478,X17479] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17479),X17478))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17479,tc_HOL_Obool)),X17478),X17477))
      | hAPP(c_Finite__Set_Ocard(X17479),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17479,tc_HOL_Obool)),X17477),X17478)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17479),X17477)),hAPP(c_Finite__Set_Ocard(X17479),X17478)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Diff__subset])]) ).

fof(i_0_8242,plain,
    ! [X19890,X19891,X19892,X19893,X19894] :
      ( ~ c_Finite__Set_Ofolding__idem(X19894,X19893,X19892,X19891)
      | hAPP(c_Fun_Ocomp(X19893,X19893,X19893,hAPP(X19892,X19890)),hAPP(X19892,X19890)) = hAPP(X19892,X19890) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__idem_Oidem__comp])]) ).

cnf(i_0_8243,plain,
    c_Int_Opred(c_Int_OBit1(X1)) = c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_5712]) ).

fof(i_0_8244,plain,
    ! [X19920,X19921,X19922] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19922)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19921)),X19920)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19921)),X19920) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19921)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19921)),X19920)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19922)),X19920)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19922))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19921)))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19922)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19921)),X19920)) = 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),X19922),X19921))),X19920)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19922))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5713])])]) ).

cnf(i_0_8245,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_5714]) ).

cnf(i_0_8246,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_5715]) ).

cnf(i_0_8247,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_5716]) ).

fof(i_0_8248,plain,
    ! [X23595,X23596,X23597] : hAPP(c_Relation_OField(X23597),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X23597,X23597),tc_HOL_Obool)),X23596),X23595)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23597,tc_HOL_Obool)),hAPP(c_Relation_OField(X23597),X23596)),hAPP(c_Relation_OField(X23597),X23595)),
    inference(variable_rename,[status(thm)],[fact_Field__Un]) ).

fof(i_0_8249,plain,
    ! [X31199,X31200,X31201,X31202] : hAPP(c_List_Oset(tc_prod(X31202,X31201)),c_Enum_Oproduct(X31202,X31201,X31200,X31199)) = hAPP(hAPP(c_Product__Type_OSigma(X31202,X31201),hAPP(c_List_Oset(X31202),X31200)),hAPP(c_COMBK(tc_fun(X31201,tc_HOL_Obool),X31202),hAPP(c_List_Oset(X31201),X31199))),
    inference(variable_rename,[status(thm)],[fact_product__list__set]) ).

fof(i_0_8250,plain,
    ! [X30945,X30946,X30947,X30948,X30949] :
      ( ( hAPP(hAPP(c_List_Omap(tc_prod(X30949,X30947),X30949),c_Product__Type_Ofst(X30949,X30947)),X30945) = X30948
        | hAPP(hAPP(c_List_Ozip(X30949,X30947),X30948),X30946) != X30945
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30949)),X30948) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30947)),X30946) )
      & ( hAPP(hAPP(c_List_Omap(tc_prod(X30949,X30947),X30947),c_Product__Type_Osnd(X30949,X30947)),X30945) = X30946
        | hAPP(hAPP(c_List_Ozip(X30949,X30947),X30948),X30946) != X30945
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30949)),X30948) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30947)),X30946) )
      & ( hAPP(hAPP(c_List_Omap(tc_prod(X30949,X30947),X30949),c_Product__Type_Ofst(X30949,X30947)),X30945) != X30948
        | hAPP(hAPP(c_List_Omap(tc_prod(X30949,X30947),X30947),c_Product__Type_Osnd(X30949,X30947)),X30945) != X30946
        | hAPP(hAPP(c_List_Ozip(X30949,X30947),X30948),X30946) = X30945
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30949)),X30948) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30947)),X30946) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__eq__conv])])]) ).

fof(i_0_8251,plain,
    ! [X24862,X24863,X24864,X24865] :
      ( ( hBOOL(hAPP(X24864,X24862))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24865,tc_HOL_Obool)),X24864),X24863),X24862)) )
      & ( hBOOL(hAPP(X24863,X24862))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24865,tc_HOL_Obool)),X24864),X24863),X24862)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5717])])]) ).

fof(i_0_8252,plain,
    ! [X25115,X25116,X25117,X25118] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25118,tc_HOL_Obool)),X25117),X25116),X25115))
      | hBOOL(hAPP(X25117,X25115)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D1])]) ).

fof(i_0_8253,plain,
    ! [X25111,X25112,X25113,X25114] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25114,tc_HOL_Obool)),X25113),X25112),X25111))
      | hBOOL(hAPP(X25112,X25111)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1D2])]) ).

cnf(i_0_8254,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_5718]) ).

fof(i_0_8255,plain,
    ! [X29364,X29365,X29366,X29367,X29368,X29369] :
      ( ( hBOOL(hAPP(hAPP(X29368,X29367),X29365))
        | ~ c_List_Olistrelp(X29369,X29368,hAPP(hAPP(c_List_Olist_OCons(X29369),X29367),X29366),hAPP(hAPP(c_List_Olist_OCons(X29369),X29365),X29364)) )
      & ( c_List_Olistrelp(X29369,X29368,X29366,X29364)
        | ~ c_List_Olistrelp(X29369,X29368,hAPP(hAPP(c_List_Olist_OCons(X29369),X29367),X29366),hAPP(hAPP(c_List_Olist_OCons(X29369),X29365),X29364)) )
      & ( ~ hBOOL(hAPP(hAPP(X29368,X29367),X29365))
        | ~ c_List_Olistrelp(X29369,X29368,X29366,X29364)
        | c_List_Olistrelp(X29369,X29368,hAPP(hAPP(c_List_Olist_OCons(X29369),X29367),X29366),hAPP(hAPP(c_List_Olist_OCons(X29369),X29365),X29364)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_Oequations_I2_J])])]) ).

fof(i_0_8256,plain,
    ! [X29358,X29359,X29360,X29361,X29362,X29363] :
      ( ~ hBOOL(hAPP(hAPP(X29363,X29362),X29361))
      | ~ c_List_Olistrelp(X29360,X29363,X29359,X29358)
      | c_List_Olistrelp(X29360,X29363,hAPP(hAPP(c_List_Olist_OCons(X29360),X29362),X29359),hAPP(hAPP(c_List_Olist_OCons(X29360),X29361),X29358)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrelp_OCons])]) ).

cnf(i_0_8257,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_5719]) ).

fof(i_0_8258,plain,
    ! [X27541] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X27541),c_Int_OInteg))
      | X27541 = hAPP(c_Int_ORep__Integ,esk275_1(X27541)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__cases])])]) ).

fof(i_0_8259,plain,
    ! [X28442,X28443,X28444] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X28444,tc_HOL_Obool)),esk325_3(X28442,X28443,X28444)),X28443))
        | hBOOL(hAPP(hAPP(c_member(X28444),X28442),c_Complete__Lattice_OInf__class_OInf(tc_fun(X28444,tc_HOL_Obool),X28443))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28444),X28442),esk325_3(X28442,X28443,X28444)))
        | hBOOL(hAPP(hAPP(c_member(X28444),X28442),c_Complete__Lattice_OInf__class_OInf(tc_fun(X28444,tc_HOL_Obool),X28443))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterI])])])]) ).

fof(i_0_8260,plain,
    ! [X30649,X30650,X30651,X30654,X30655,X30656,X30657,X30658] :
      ( ( X30650 = hAPP(hAPP(c_List_Olist_OCons(X30651),esk411_3(X30649,X30650,X30651)),esk412_3(X30649,X30650,X30651))
        | X30650 = c_List_Olist_ONil(X30651)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30651)),X30650),c_List_Olists(X30651,X30649))) )
      & ( hBOOL(hAPP(hAPP(c_member(X30651),esk411_3(X30649,X30650,X30651)),X30649))
        | X30650 = c_List_Olist_ONil(X30651)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30651)),X30650),c_List_Olists(X30651,X30649))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30651)),esk412_3(X30649,X30650,X30651)),c_List_Olists(X30651,X30649)))
        | X30650 = c_List_Olist_ONil(X30651)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30651)),X30650),c_List_Olists(X30651,X30649))) )
      & ( X30655 != c_List_Olist_ONil(X30656)
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30656)),X30655),c_List_Olists(X30656,X30654))) )
      & ( X30655 != hAPP(hAPP(c_List_Olist_OCons(X30656),X30657),X30658)
        | ~ hBOOL(hAPP(hAPP(c_member(X30656),X30657),X30654))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30656)),X30658),c_List_Olists(X30656,X30654)))
        | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X30656)),X30655),c_List_Olists(X30656,X30654))) ) ),
    inference(distribute,[status(thm)],[inference(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_8261,plain,
    ! [X32607,X32608,X32609,X32610] :
      ( ( X32609 = X32607
        | ~ hBOOL(hAPP(hAPP(c_member(X32610),X32609),hAPP(c_List_Oset(X32610),c_List_Oreplicate(X32610,X32608,X32607)))) )
      & ( X32608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X32610),X32609),hAPP(c_List_Oset(X32610),c_List_Oreplicate(X32610,X32608,X32607)))) )
      & ( X32609 != X32607
        | X32608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_member(X32610),X32609),hAPP(c_List_Oset(X32610),c_List_Oreplicate(X32610,X32608,X32607)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__replicate])])]) ).

fof(i_0_8262,plain,
    ! [X25458,X25459,X25460,X25461,X25462] :
      ( ~ c_Finite__Set_Ofolding__one(X25462,X25461,X25460)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25462),X25459))
      | X25459 = c_Orderings_Obot__class_Obot(tc_fun(X25462,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25462),X25458))
      | X25458 = c_Orderings_Obot__class_Obot(tc_fun(X25462,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25462,tc_HOL_Obool)),X25459),X25458) != c_Orderings_Obot__class_Obot(tc_fun(X25462,tc_HOL_Obool))
      | hAPP(X25460,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25462,tc_HOL_Obool)),X25459),X25458)) = hAPP(hAPP(X25461,hAPP(X25460,X25459)),hAPP(X25460,X25458)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Ounion__disjoint])]) ).

fof(i_0_8263,plain,
    ! [X20687,X20688,X20689,X20690] :
      ( ~ class_Divides_Osemiring__div(X20690)
      | c_Divides_Odiv__class_Omod(X20690,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20690),X20689),X20688),X20687) = c_Divides_Odiv__class_Omod(X20690,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20690),c_Divides_Odiv__class_Omod(X20690,X20689,X20687)),c_Divides_Odiv__class_Omod(X20690,X20688,X20687)),X20687) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__eq])]) ).

fof(i_0_8264,plain,
    ! [X20661,X20662,X20663,X20664] :
      ( ~ class_Divides_Osemiring__div(X20664)
      | c_Divides_Odiv__class_Omod(X20664,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20664),X20663),X20662),X20661) = c_Divides_Odiv__class_Omod(X20664,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20664),c_Divides_Odiv__class_Omod(X20664,X20663,X20661)),c_Divides_Odiv__class_Omod(X20664,X20662,X20661)),X20661) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__eq])]) ).

fof(i_0_8265,plain,
    ! [X20715,X20716,X20717,X20718] :
      ( ~ class_Divides_Oring__div(X20718)
      | c_Divides_Odiv__class_Omod(X20718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20718),X20717),X20716),X20715) = c_Divides_Odiv__class_Omod(X20718,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20718),c_Divides_Odiv__class_Omod(X20718,X20717,X20715)),c_Divides_Odiv__class_Omod(X20718,X20716,X20715)),X20715) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__eq])]) ).

fof(i_0_8266,plain,
    ! [X33803,X33804,X33805,X33806] :
      ( ~ class_Divides_Osemiring__div(X33806)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33806),X33805),X33804))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33806),X33805),X33803))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33806),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33806),X33804),X33803)),X33805) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33806),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33806),X33804),X33805)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33806),X33803),X33805)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add])]) ).

fof(i_0_8267,plain,
    ! [X20319,X20320,X20321] :
      ( ~ class_Rings_Olinordered__semidom(X20321)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20321),c_Groups_Oone__class_Oone(X20321)),X20320))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20321),c_Groups_Oone__class_Oone(X20321)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20321),X20320),hAPP(hAPP(c_Power_Opower__class_Opower(X20321),X20320),X20319)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1__lemma])]) ).

fof(i_0_8268,plain,
    ! [X18750,X18751] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18751),X18750),X18750)),c_Groups_Ozero__class_Ozero(X18751)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18751),X18750),c_Groups_Ozero__class_Ozero(X18751)))
        | ~ class_Groups_Olinordered__ab__group__add(X18751) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18751),X18750),c_Groups_Ozero__class_Ozero(X18751)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18751),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18751),X18750),X18750)),c_Groups_Ozero__class_Ozero(X18751)))
        | ~ class_Groups_Olinordered__ab__group__add(X18751) ) ),
    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_8269,plain,
    ! [X18983,X18984] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18984),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18984),X18983),X18983)),c_Groups_Ozero__class_Ozero(X18984)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18984),X18983),c_Groups_Ozero__class_Ozero(X18984)))
        | ~ class_Rings_Olinordered__idom(X18984) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18984),X18983),c_Groups_Ozero__class_Ozero(X18984)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18984),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18984),X18983),X18983)),c_Groups_Ozero__class_Ozero(X18984)))
        | ~ class_Rings_Olinordered__idom(X18984) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_even__less__0__iff])])]) ).

fof(i_0_8270,plain,
    ! [X18744,X18745] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18745),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18745),X18744),X18744)),c_Groups_Ozero__class_Ozero(X18745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18745),X18744),c_Groups_Ozero__class_Ozero(X18745)))
        | ~ class_Groups_Olinordered__ab__group__add(X18745) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18745),X18744),c_Groups_Ozero__class_Ozero(X18745)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18745),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18745),X18744),X18744)),c_Groups_Ozero__class_Ozero(X18745)))
        | ~ class_Groups_Olinordered__ab__group__add(X18745) ) ),
    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_8271,plain,
    ! [X19280,X19281] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_2(X19280,X19281)),X19281))
        | 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)),X19280),X19281) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19280),esk42_2(X19280,X19281)))
        | 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)),X19280),X19281) ) ),
    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_8272,plain,
    ! [X26766,X26767,X26768,X26769] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26769),X26768),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26769,tc_HOL_Obool),X26767)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26769,tc_HOL_Obool)),X26766),X26767))
      | hBOOL(hAPP(hAPP(c_member(X26769),X26768),X26766)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterD])]) ).

fof(i_0_8273,plain,
    ! [X26762,X26763,X26764,X26765] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26765),X26764),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26765,tc_HOL_Obool),X26763)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26765,tc_HOL_Obool)),X26762),X26763))
      | hBOOL(hAPP(hAPP(c_member(X26765),X26764),X26762)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_InterE])]) ).

fof(i_0_8274,plain,
    ! [X21055,X21056] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21056))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21056),X21055)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21056),X21055) = 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_8275,plain,
    ! [X26207,X26208] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X26208,X26207)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26208,X26207),tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(X26207),c_Orderings_Otop__class_Otop(tc_fun(X26207,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26208),c_Orderings_Otop__class_Otop(tc_fun(X26208,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD1])]) ).

fof(i_0_8276,plain,
    ! [X23453,X23454,X23455] :
      ( ~ class_Orderings_Olinorder(X23455)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23455),X23454))
      | X23454 = c_Orderings_Obot__class_Obot(tc_fun(X23455,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23455),X23453))
      | X23453 = c_Orderings_Obot__class_Obot(tc_fun(X23455,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X23455,c_Orderings_Oord__class_Omax(X23455),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23455,tc_HOL_Obool)),X23454),X23453)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X23455),c_Big__Operators_Olattice_OSup__fin(X23455,c_Orderings_Oord__class_Omax(X23455),X23454)),c_Big__Operators_Olattice_OSup__fin(X23455,c_Orderings_Oord__class_Omax(X23455),X23453)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Ounion__idem])]) ).

fof(i_0_8277,plain,
    ! [X23450,X23451,X23452] :
      ( ~ class_Orderings_Olinorder(X23452)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23452),X23451))
      | X23451 = c_Orderings_Obot__class_Obot(tc_fun(X23452,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23452),X23450))
      | X23450 = c_Orderings_Obot__class_Obot(tc_fun(X23452,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X23452,c_Orderings_Oord__class_Omin(X23452),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23452,tc_HOL_Obool)),X23451),X23450)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X23452),c_Big__Operators_Olattice_OInf__fin(X23452,c_Orderings_Oord__class_Omin(X23452),X23451)),c_Big__Operators_Olattice_OInf__fin(X23452,c_Orderings_Oord__class_Omin(X23452),X23450)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Ounion__idem])]) ).

fof(i_0_8278,plain,
    ! [X17336,X17337,X17338,X17339] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17339),X17338),X17337))
      | hBOOL(hAPP(hAPP(c_member(X17339),X17338),X17336))
      | hBOOL(hAPP(hAPP(c_member(X17339),X17338),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17339,tc_HOL_Obool)),X17337),X17336))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5720])]) ).

fof(i_0_8279,plain,
    ! [X19439,X19440,X19441] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19441),X19440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19439))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19439),X19441)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19439),X19440))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2])]) ).

fof(i_0_8280,plain,
    ! [X18403,X18404,X18405] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18405),X18404))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18403))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18405),X18403)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18404),X18403))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono1])]) ).

fof(i_0_8281,plain,
    ! [X18406,X18407,X18408] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18408),X18407))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18406))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18406),X18408)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18406),X18407))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__less__mono2])]) ).

fof(i_0_8282,plain,
    ! [X20484,X20485,X20486] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20486),X20485))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20484))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20486),X20484)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20485),X20484))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1])]) ).

fof(i_0_8283,plain,
    ! [X20863,X20864,X20865] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20865))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20865),X20864))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20863),X20864)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20863),X20865))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono2])]) ).

fof(i_0_8284,plain,
    ! [X30896,X30897,X30898] :
      ( ( ~ c_Fun_Oinj__on(tc_List_Olist(X30898),tc_List_Olist(X30897),hAPP(c_List_Omap(X30898,X30897),X30896),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30898),tc_HOL_Obool)))
        | c_Fun_Oinj__on(X30898,X30897,X30896,c_Orderings_Otop__class_Otop(tc_fun(X30898,tc_HOL_Obool))) )
      & ( ~ c_Fun_Oinj__on(X30898,X30897,X30896,c_Orderings_Otop__class_Otop(tc_fun(X30898,tc_HOL_Obool)))
        | c_Fun_Oinj__on(tc_List_Olist(X30898),tc_List_Olist(X30897),hAPP(c_List_Omap(X30898,X30897),X30896),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30898),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__map])]) ).

fof(i_0_8285,plain,
    ! [X30893,X30894,X30895] :
      ( ~ c_Fun_Oinj__on(tc_List_Olist(X30895),tc_List_Olist(X30894),hAPP(c_List_Omap(X30895,X30894),X30893),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30895),tc_HOL_Obool)))
      | c_Fun_Oinj__on(X30895,X30894,X30893,c_Orderings_Otop__class_Otop(tc_fun(X30895,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapD])]) ).

fof(i_0_8286,plain,
    ! [X17044,X17045,X17046,X17047] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17047,tc_HOL_Obool)),X17046),X17045))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17047,tc_HOL_Obool)),X17046),hAPP(hAPP(c_Set_Oinsert(X17047),X17044),X17045))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__insertI2])]) ).

fof(i_0_8287,plain,
    ! [X32521,X32522,X32523,X32524] : hAPP(hAPP(c_List_Oappend(X32524),c_List_Oreplicate(X32524,X32523,X32522)),hAPP(hAPP(c_List_Olist_OCons(X32524),X32522),X32521)) = hAPP(hAPP(c_List_Olist_OCons(X32524),X32522),hAPP(hAPP(c_List_Oappend(X32524),c_List_Oreplicate(X32524,X32523,X32522)),X32521)),
    inference(variable_rename,[status(thm)],[fact_replicate__app__Cons__same]) ).

fof(i_0_8288,plain,
    ! [X26548,X26549,X26550,X26551,X26552] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26552,tc_fun(X26551,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X26552),X26550),X26549)),X26548) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26551,tc_HOL_Obool)),hAPP(X26548,X26550)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26552,tc_fun(X26551,tc_HOL_Obool)),X26549),X26548)),
    inference(variable_rename,[status(thm)],[fact_INT__insert]) ).

fof(i_0_8289,plain,
    ! [X23917,X23918,X23919,X23920,X23921] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23921,tc_fun(X23920,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23921),X23919),X23918)),X23917) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23920,tc_HOL_Obool)),hAPP(X23917,X23919)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23921,tc_fun(X23920,tc_HOL_Obool)),X23918),X23917)),
    inference(variable_rename,[status(thm)],[fact_UN__insert]) ).

fof(i_0_8290,plain,
    ! [X25402,X25403,X25404,X25405] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25404),X25402),hAPP(c_Finite__Set_Ofold1(X25404,c_Lattices_Osemilattice__inf__class_Oinf(X25404)),X25403)))
        | ~ hBOOL(hAPP(hAPP(c_member(X25404),X25405),X25403))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25404),X25402),X25405))
        | X25403 = c_Orderings_Obot__class_Obot(tc_fun(X25404,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25404),X25403))
        | ~ class_Lattices_Osemilattice__inf(X25404) )
      & ( hBOOL(hAPP(hAPP(c_member(X25404),esk201_3(X25402,X25403,X25404)),X25403))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25404),X25402),hAPP(c_Finite__Set_Ofold1(X25404,c_Lattices_Osemilattice__inf__class_Oinf(X25404)),X25403)))
        | X25403 = c_Orderings_Obot__class_Obot(tc_fun(X25404,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25404),X25403))
        | ~ class_Lattices_Osemilattice__inf(X25404) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25404),X25402),esk201_3(X25402,X25403,X25404)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25404),X25402),hAPP(c_Finite__Set_Ofold1(X25404,c_Lattices_Osemilattice__inf__class_Oinf(X25404)),X25403)))
        | X25403 = c_Orderings_Obot__class_Obot(tc_fun(X25404,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25404),X25403))
        | ~ class_Lattices_Osemilattice__inf(X25404) ) ),
    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_8291,plain,
    ! [X21691,X21692,X21693,X21694] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21693),X21691),hAPP(c_Finite__Set_Ofold1(X21693,c_Orderings_Oord__class_Omin(X21693)),X21692)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21693),X21694),X21692))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21693),X21691),X21694))
        | X21692 = c_Orderings_Obot__class_Obot(tc_fun(X21693,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21693),X21692))
        | ~ class_Orderings_Olinorder(X21693) )
      & ( hBOOL(hAPP(hAPP(c_member(X21693),esk77_3(X21691,X21692,X21693)),X21692))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21693),X21691),hAPP(c_Finite__Set_Ofold1(X21693,c_Orderings_Oord__class_Omin(X21693)),X21692)))
        | X21692 = c_Orderings_Obot__class_Obot(tc_fun(X21693,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21693),X21692))
        | ~ class_Orderings_Olinorder(X21693) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21693),X21691),esk77_3(X21691,X21692,X21693)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21693),X21691),hAPP(c_Finite__Set_Ofold1(X21693,c_Orderings_Oord__class_Omin(X21693)),X21692)))
        | X21692 = c_Orderings_Obot__class_Obot(tc_fun(X21693,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21693),X21692))
        | ~ class_Orderings_Olinorder(X21693) ) ),
    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_8292,plain,
    ! [X21686,X21687,X21688,X21689] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21688),X21686),hAPP(c_Finite__Set_Ofold1(X21688,c_Orderings_Oord__class_Omin(X21688)),X21687)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21688),X21689),X21687))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21688),X21686),X21689))
        | X21687 = c_Orderings_Obot__class_Obot(tc_fun(X21688,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21688),X21687))
        | ~ class_Orderings_Olinorder(X21688) )
      & ( hBOOL(hAPP(hAPP(c_member(X21688),esk76_3(X21686,X21687,X21688)),X21687))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21688),X21686),hAPP(c_Finite__Set_Ofold1(X21688,c_Orderings_Oord__class_Omin(X21688)),X21687)))
        | X21687 = c_Orderings_Obot__class_Obot(tc_fun(X21688,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21688),X21687))
        | ~ class_Orderings_Olinorder(X21688) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21688),X21686),esk76_3(X21686,X21687,X21688)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21688),X21686),hAPP(c_Finite__Set_Ofold1(X21688,c_Orderings_Oord__class_Omin(X21688)),X21687)))
        | X21687 = c_Orderings_Obot__class_Obot(tc_fun(X21688,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21688),X21687))
        | ~ class_Orderings_Olinorder(X21688) ) ),
    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_8293,plain,
    ! [X32084,X32085,X32086,X32087,X32088] : c_List_Omaps(X32088,X32087,X32086,hAPP(hAPP(c_List_Olist_OCons(X32088),X32085),X32084)) = hAPP(hAPP(c_List_Oappend(X32087),hAPP(X32086,X32085)),c_List_Omaps(X32088,X32087,X32086,X32084)),
    inference(variable_rename,[status(thm)],[fact_maps__simps_I1_J]) ).

cnf(i_0_8294,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk420_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_5655]) ).

cnf(i_0_8295,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk421_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_5656]) ).

fof(i_0_8296,plain,
    ! [X18761,X18762,X18763] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18763),X18762),X18761))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18763),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18763),X18762),X18761)),c_Groups_Ozero__class_Ozero(X18763)))
        | ~ class_Groups_Oordered__ab__group__add(X18763) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18763),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18763),X18762),X18761)),c_Groups_Ozero__class_Ozero(X18763)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18763),X18762),X18761))
        | ~ class_Groups_Oordered__ab__group__add(X18763) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__iff__diff__less__0])])]) ).

fof(i_0_8297,plain,
    ! [X18758,X18759,X18760] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18760),X18759),X18758))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18760),X18759),X18758)),c_Groups_Ozero__class_Ozero(X18760)))
        | ~ class_Groups_Oordered__ab__group__add(X18760) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18760),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18760),X18759),X18758)),c_Groups_Ozero__class_Ozero(X18760)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18760),X18759),X18758))
        | ~ class_Groups_Oordered__ab__group__add(X18760) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__diff__le__0])])]) ).

fof(i_0_8298,plain,
    ! [X20487,X20488,X20489] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20489),X20488))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20487),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),X20488),X20487)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20489),X20487))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__mono1__neg])]) ).

cnf(i_0_8299,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_5721]) ).

cnf(i_0_8300,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_5722]) ).

fof(i_0_8301,plain,
    ! [X29543,X29544,X29545] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29545),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29544)),X29543)))
      | hBOOL(hAPP(hAPP(c_member(X29544),hAPP(hAPP(c_List_Onth(X29544),X29543),X29545)),hAPP(c_List_Oset(X29544),X29543))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__mem])]) ).

fof(i_0_8302,plain,
    ! [X18505,X18506] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18505))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18506),X18505))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m])]) ).

fof(i_0_8303,plain,
    ! [X18503,X18504] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18504))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X18503))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18504),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18503),X18504))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n])]) ).

fof(i_0_8304,plain,
    ! [X19254,X19255] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19255),X19254))
        | hAPP(c_Finite__Set_Ocard(X19255),X19254) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X19255,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X19255),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19254) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X19255),X19254))
        | hAPP(c_Finite__Set_Ocard(X19255),X19254) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5723])]) ).

fof(i_0_8305,plain,
    ! [X19252,X19253] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19253),X19252))
      | hAPP(c_Finite__Set_Ocard(X19253),X19252) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X19253,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X19253),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X19252) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oeq__fold__g])]) ).

fof(i_0_8306,plain,
    ! [X22927,X22928,X22929,X22930] :
      ( ~ class_Fields_Ofield(X22930)
      | X22929 = c_Groups_Ozero__class_Ozero(X22930)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22930),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22930),X22928),X22929)),X22927) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22930),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22930),X22928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22930),X22929),X22927))),X22929) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff])]) ).

fof(i_0_8307,plain,
    ! [X22923,X22924,X22925,X22926] :
      ( ~ class_Fields_Ofield__inverse__zero(X22926)
      | X22925 = c_Groups_Ozero__class_Ozero(X22926)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22926),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22926),X22924),X22925)),X22923) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22926),X22924),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22926),X22923),X22925))),X22925) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__frac__num])]) ).

fof(i_0_8308,plain,
    ! [X22941,X22942,X22943,X22944] :
      ( ~ class_Fields_Ofield(X22944)
      | X22943 = c_Groups_Ozero__class_Ozero(X22944)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22944),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22944),X22942),X22943)),X22941) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22944),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22944),X22942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22944),X22943),X22941))),X22943) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff])]) ).

fof(i_0_8309,plain,
    ! [X29546,X29547,X29548,X29550,X29551,X29552,X29553] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk387_3(X29546,X29547,X29548)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29548)),X29546)))
        | ~ hBOOL(hAPP(hAPP(c_member(X29548),X29547),hAPP(c_List_Oset(X29548),X29546))) )
      & ( hAPP(hAPP(c_List_Onth(X29548),X29546),esk387_3(X29546,X29547,X29548)) = X29547
        | ~ hBOOL(hAPP(hAPP(c_member(X29548),X29547),hAPP(c_List_Oset(X29548),X29546))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29553),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29552)),X29550)))
        | hAPP(hAPP(c_List_Onth(X29552),X29550),X29553) != X29551
        | hBOOL(hAPP(hAPP(c_member(X29552),X29551),hAPP(c_List_Oset(X29552),X29550))) ) ),
    inference(distribute,[status(thm)],[inference(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_8310,plain,
    ! [X19494,X19495,X19496,X19497] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19497),X19496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19495),X19494))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19497),X19495)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19496),X19494))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono])]) ).

fof(i_0_8311,plain,
    ! [X17971,X17972,X17973,X17974] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17974),X17973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17972),X17971))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17974),X17972)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17973),X17971))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono])]) ).

fof(i_0_8312,plain,
    ! [X17766,X17767,X17768] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17768),X17767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17766),X17768))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17768),X17766)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17767),X17766))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono])]) ).

fof(i_0_8313,plain,
    ! [X17744,X17745,X17746] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17746),X17745))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17746),X17744))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17744),X17745)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17744),X17746))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less__mono2])]) ).

fof(i_0_8314,plain,
    ! [X18548,X18549,X18550,X18551] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18551),X18550))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18549),X18548))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18551),X18549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18550),X18548))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono])]) ).

fof(i_0_8315,plain,
    ! [X18017,X18018,X18019,X18020] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18020),X18019))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18018),X18017))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18020),X18018)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18019),X18017))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono])]) ).

fof(i_0_8316,plain,
    ! [X19040,X19041,X19042,X19043,X19044] :
      ( ~ class_Rings_Ocomm__semiring__1(X19044)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19044),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19044),X19043),X19042)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19044),X19041),X19040)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19044),X19041),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19044),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19044),X19043),X19042)),X19040)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J])]) ).

fof(i_0_8317,plain,
    ! [X24369,X24370,X24371] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24371,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24371),X24370)),hAPP(c_SetInterval_Oord__class_OlessThan(X24371),X24369)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24371),X24370),X24369))
        | ~ class_Orderings_Olinorder(X24371) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24371),X24370),X24369))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X24371,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24371),X24370)),hAPP(c_SetInterval_Oord__class_OlessThan(X24371),X24369)))
        | ~ class_Orderings_Olinorder(X24371) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__strict__subset__iff])])]) ).

fof(i_0_8318,plain,
    ! [X25321,X25322,X25323] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25323,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25323),X25322)),hAPP(c_SetInterval_Oord__class_OatMost(X25323),X25321)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25323),X25322),X25321))
        | ~ class_Orderings_Oorder(X25323) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25323),X25322),X25321))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25323,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25323),X25322)),hAPP(c_SetInterval_Oord__class_OatMost(X25323),X25321)))
        | ~ class_Orderings_Oorder(X25323) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__subset__iff])])]) ).

fof(i_0_8319,plain,
    ! [X24366,X24367,X24368] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24368,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24368),X24367)),hAPP(c_SetInterval_Oord__class_OlessThan(X24368),X24366)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24368),X24367),X24366))
        | ~ class_Orderings_Olinorder(X24368) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24368),X24367),X24366))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X24368,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24368),X24367)),hAPP(c_SetInterval_Oord__class_OlessThan(X24368),X24366)))
        | ~ class_Orderings_Olinorder(X24368) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__subset__iff])])]) ).

fof(i_0_8320,plain,
    ! [X25737,X25738,X25739] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25739,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X25739),X25738)),hAPP(c_SetInterval_Oord__class_OatLeast(X25739),X25737)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25739),X25737),X25738))
        | ~ class_Orderings_Oorder(X25739) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25739),X25737),X25738))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25739,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X25739),X25738)),hAPP(c_SetInterval_Oord__class_OatLeast(X25739),X25737)))
        | ~ class_Orderings_Oorder(X25739) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__subset__iff])])]) ).

fof(i_0_8321,plain,
    ! [X25781,X25782,X25783] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25783,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25783),X25782)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25783),X25781)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25783),X25781),X25782))
        | ~ class_Orderings_Olinorder(X25783) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25783),X25781),X25782))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25783,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25783),X25782)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25783),X25781)))
        | ~ class_Orderings_Olinorder(X25783) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__subset__iff])])]) ).

cnf(i_0_8322,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X2),c_Relation_OId(X1)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5724]) ).

fof(i_0_8323,plain,
    ! [X22812,X22813,X22814] :
      ( ~ class_Fields_Olinordered__field(X22814)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22814),X22813),c_Groups_Ozero__class_Ozero(X22814)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22814),c_Groups_Ozero__class_Ozero(X22814)),X22812))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22814),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22814),X22813),X22812)),c_Groups_Ozero__class_Ozero(X22814))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__pos])]) ).

fof(i_0_8324,plain,
    ! [X22815,X22816,X22817] :
      ( ~ class_Fields_Olinordered__field(X22817)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22817),c_Groups_Ozero__class_Ozero(X22817)),X22816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22817),X22815),c_Groups_Ozero__class_Ozero(X22817)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22817),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22817),X22816),X22815)),c_Groups_Ozero__class_Ozero(X22817))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__neg])]) ).

fof(i_0_8325,plain,
    ! [X18227,X18228,X18229] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18229)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18229),X18228),c_Groups_Ozero__class_Ozero(X18229)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18229),c_Groups_Ozero__class_Ozero(X18229)),X18227))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18229),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18229),X18228),X18227)),c_Groups_Ozero__class_Ozero(X18229))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__pos])]) ).

fof(i_0_8326,plain,
    ! [X18243,X18244,X18245] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18245)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18245),c_Groups_Ozero__class_Ozero(X18245)),X18244))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18245),X18243),c_Groups_Ozero__class_Ozero(X18245)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18245),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18245),X18244),X18243)),c_Groups_Ozero__class_Ozero(X18245))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg])]) ).

fof(i_0_8327,plain,
    ! [X18240,X18241,X18242] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18242)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18242),c_Groups_Ozero__class_Ozero(X18242)),X18241))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18242),X18240),c_Groups_Ozero__class_Ozero(X18242)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18242),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18242),X18240),X18241)),c_Groups_Ozero__class_Ozero(X18242))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__neg2])]) ).

fof(i_0_8328,plain,
    ! [X22851,X22852,X22853] :
      ( ~ class_Fields_Olinordered__field(X22853)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22853),c_Groups_Ozero__class_Ozero(X22853)),X22852))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22853),X22851),c_Groups_Ozero__class_Ozero(X22853)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22853),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22853),X22852),X22851)),c_Groups_Ozero__class_Ozero(X22853))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__neg])]) ).

fof(i_0_8329,plain,
    ! [X22869,X22870,X22871] :
      ( ~ class_Fields_Olinordered__field(X22871)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22871),X22870),c_Groups_Ozero__class_Ozero(X22871)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22871),c_Groups_Ozero__class_Ozero(X22871)),X22869))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22871),X22870),X22869)),c_Groups_Ozero__class_Ozero(X22871))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__pos])]) ).

fof(i_0_8330,plain,
    ! [X18319,X18320,X18321] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18321),c_Groups_Ozero__class_Ozero(X18321)),X18320))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18321),X18319),c_Groups_Ozero__class_Ozero(X18321)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18321),X18320),X18319)),c_Groups_Ozero__class_Ozero(X18321)))
        | ~ class_Rings_Oordered__cancel__semiring(X18321) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18321),X18320),c_Groups_Ozero__class_Ozero(X18321)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18321),c_Groups_Ozero__class_Ozero(X18321)),X18319))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18321),X18320),X18319)),c_Groups_Ozero__class_Ozero(X18321)))
        | ~ class_Rings_Oordered__cancel__semiring(X18321) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__neg__le])])]) ).

fof(i_0_8331,plain,
    ! [X18280,X18281,X18282] :
      ( ~ class_Rings_Oordered__cancel__semiring(X18282)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18282),X18281),c_Groups_Ozero__class_Ozero(X18282)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18282),c_Groups_Ozero__class_Ozero(X18282)),X18280))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18282),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18282),X18281),X18280)),c_Groups_Ozero__class_Ozero(X18282))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonneg])]) ).

fof(i_0_8332,plain,
    ! [X18274,X18275,X18276] :
      ( ~ class_Rings_Oordered__cancel__semiring(X18276)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18276),c_Groups_Ozero__class_Ozero(X18276)),X18275))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18276),X18274),c_Groups_Ozero__class_Ozero(X18276)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18276),X18275),X18274)),c_Groups_Ozero__class_Ozero(X18276))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos])]) ).

fof(i_0_8333,plain,
    ! [X18277,X18278,X18279] :
      ( ~ class_Rings_Oordered__cancel__semiring(X18279)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18279),c_Groups_Ozero__class_Ozero(X18279)),X18278))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18279),X18277),c_Groups_Ozero__class_Ozero(X18279)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18279),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18279),X18277),X18278)),c_Groups_Ozero__class_Ozero(X18279))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonpos2])]) ).

fof(i_0_8334,plain,
    ! [X29457,X29458,X29459] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X29459,tc_HOL_Obool)),hAPP(c_List_Oset(X29459),X29458)),hAPP(c_List_Oset(X29459),hAPP(hAPP(c_List_Olist_OCons(X29459),X29457),X29458)))),
    inference(variable_rename,[status(thm)],[fact_set__subset__Cons]) ).

fof(i_0_8335,plain,
    ! [X33590,X33591,X33592,X33593,X33594] : c_Lazy__Sequence_Omap(X33594,X33593,X33592,c_Lazy__Sequence_Olazy__sequence_OInsert(X33594,X33591,X33590)) = c_Lazy__Sequence_Olazy__sequence_OInsert(X33593,hAPP(X33592,X33591),c_Lazy__Sequence_Omap(X33594,X33593,X33592,X33590)),
    inference(variable_rename,[status(thm)],[fact__06]) ).

fof(i_0_8336,plain,
    ! [X31488,X31489,X31490,X31491] : c_List_Otranspose(X31491,hAPP(hAPP(c_List_Omap(tc_List_Olist(X31490),tc_List_Olist(X31491)),hAPP(c_List_Omap(X31490,X31491),X31489)),X31488)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(X31490),tc_List_Olist(X31491)),hAPP(c_List_Omap(X31490,X31491),X31489)),c_List_Otranspose(X31490,X31488)),
    inference(variable_rename,[status(thm)],[fact_transpose__map__map]) ).

cnf(i_0_8337,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_5725]) ).

cnf(i_0_8338,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_5726]) ).

fof(i_0_8339,plain,
    ! [X33889,X33890,X33891,X33892] :
      ( ~ class_Rings_Ocomm__semiring__1(X33892)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33892),X33891),X33890)),X33889))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33892),X33891),X33889)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__left])]) ).

fof(i_0_8340,plain,
    ! [X33885,X33886,X33887,X33888] :
      ( ~ class_Rings_Ocomm__semiring__1(X33888)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33888),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33888),X33887),X33886)),X33885))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33888),X33886),X33885)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__right])]) ).

fof(i_0_8341,plain,
    ! [X22541,X22542,X22543,X22544] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22544),X22543),X22541))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22544),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22544),X22543),X22542)),X22541))
        | ~ class_Orderings_Olinorder(X22544) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22544),X22542),X22541))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22544),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22544),X22543),X22542)),X22541))
        | ~ class_Orderings_Olinorder(X22544) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22544),X22543),X22541))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22544),X22542),X22541))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22544),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22544),X22543),X22542)),X22541))
        | ~ class_Orderings_Olinorder(X22544) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__less__iff__conj])])]) ).

fof(i_0_8342,plain,
    ! [X23323,X23324,X23325,X23326] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23326),X23325),X23323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23326),X23325),X23324)),X23323))
        | ~ class_Lattices_Osemilattice__sup(X23326) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23326),X23324),X23323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23326),X23325),X23324)),X23323))
        | ~ class_Lattices_Osemilattice__sup(X23326) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23326),X23325),X23323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23326),X23324),X23323))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23326),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23326),X23325),X23324)),X23323))
        | ~ class_Lattices_Osemilattice__sup(X23326) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__sup__iff])])]) ).

fof(i_0_8343,plain,
    ! [X23292,X23293,X23294,X23295] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23295),X23294),X23292))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23295),X23294),X23293)),X23292))
        | ~ class_Lattices_Osemilattice__sup(X23295) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23295),X23293),X23292))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23295),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23295),X23294),X23293)),X23292))
        | ~ class_Lattices_Osemilattice__sup(X23295) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5727])])]) ).

fof(i_0_8344,plain,
    ! [X22597,X22598,X22599,X22600] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22600),X22599),X22597))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22600),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22600),X22599),X22598)),X22597))
        | ~ class_Orderings_Olinorder(X22600) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22600),X22598),X22597))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22600),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22600),X22599),X22598)),X22597))
        | ~ class_Orderings_Olinorder(X22600) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22600),X22599),X22597))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22600),X22598),X22597))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22600),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22600),X22599),X22598)),X22597))
        | ~ class_Orderings_Olinorder(X22600) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__sup__iff])])]) ).

fof(i_0_8345,plain,
    ! [X22566,X22567,X22568,X22569] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22569),X22568),X22566))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22569),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22569),X22568),X22567)),X22566))
        | ~ class_Orderings_Olinorder(X22569) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22569),X22567),X22566))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22569),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22569),X22568),X22567)),X22566))
        | ~ class_Orderings_Olinorder(X22569) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5728])])]) ).

fof(i_0_8346,plain,
    ! [X29798,X29799,X29800,X29801,X29802,X29803] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X29799),X29798))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29800),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29799)),X29798)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29801),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29799)),X29798)))
        | X29800 = X29801
        | hAPP(hAPP(c_List_Onth(X29799),X29798),X29800) != hAPP(hAPP(c_List_Onth(X29799),X29798),X29801) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk394_2(X29802,X29803)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29803)),X29802)))
        | hBOOL(hAPP(c_List_Odistinct(X29803),X29802)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk395_2(X29802,X29803)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29803)),X29802)))
        | hBOOL(hAPP(c_List_Odistinct(X29803),X29802)) )
      & ( esk394_2(X29802,X29803) != esk395_2(X29802,X29803)
        | hBOOL(hAPP(c_List_Odistinct(X29803),X29802)) )
      & ( hAPP(hAPP(c_List_Onth(X29803),X29802),esk394_2(X29802,X29803)) = hAPP(hAPP(c_List_Onth(X29803),X29802),esk395_2(X29802,X29803))
        | hBOOL(hAPP(c_List_Odistinct(X29803),X29802)) ) ),
    inference(distribute,[status(thm)],[inference(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_8347,plain,
    ! [X29794,X29795,X29796,X29797] :
      ( ( hAPP(hAPP(c_List_Onth(X29797),X29796),X29795) != hAPP(hAPP(c_List_Onth(X29797),X29796),X29794)
        | X29795 = X29794
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29794),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29797)),X29796)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29795),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29797)),X29796)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29797),X29796)) )
      & ( X29795 != X29794
        | hAPP(hAPP(c_List_Onth(X29797),X29796),X29795) = hAPP(hAPP(c_List_Onth(X29797),X29796),X29794)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29794),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29797)),X29796)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29795),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29797)),X29796)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29797),X29796)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__eq__iff__index__eq])])]) ).

fof(i_0_8348,plain,
    ! [X30879,X30880,X30881,X30882] :
      ( ( hBOOL(hAPP(c_List_Odistinct(X30881),X30879))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30882),hAPP(hAPP(c_List_Omap(X30881,X30882),X30880),X30879))) )
      & ( c_Fun_Oinj__on(X30881,X30882,X30880,hAPP(c_List_Oset(X30881),X30879))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30882),hAPP(hAPP(c_List_Omap(X30881,X30882),X30880),X30879))) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30881),X30879))
        | ~ c_Fun_Oinj__on(X30881,X30882,X30880,hAPP(c_List_Oset(X30881),X30879))
        | hBOOL(hAPP(c_List_Odistinct(X30882),hAPP(hAPP(c_List_Omap(X30881,X30882),X30880),X30879))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__map])])]) ).

fof(i_0_8349,plain,
    ! [X22985,X22986] :
      ( ~ class_Orderings_Olinorder(X22986)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22986),X22985))
      | X22985 = c_Orderings_Obot__class_Obot(tc_fun(X22986,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22986),c_Big__Operators_Olattice_OInf__fin(X22986,c_Orderings_Oord__class_Omin(X22986),X22985)),c_Big__Operators_Olattice_OSup__fin(X22986,c_Orderings_Oord__class_Omax(X22986),X22985))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__le__Sup])]) ).

fof(i_0_8350,plain,
    ! [X18414,X18415,X18416,X18417,X18418] :
      ( ~ c_Fun_Oinj__on(X18418,X18417,X18416,X18415)
      | c_Fun_Oinj__on(X18418,X18417,X18416,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X18418,tc_HOL_Obool)),X18415),X18414)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__diff])]) ).

fof(i_0_8351,plain,
    ! [X32664,X32665,X32666,X32667] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X32667,X32666),c_Lazy__Sequence_Olazy__sequence_OInsert(X32667,X32665,X32664)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(X32666,X32665)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X32667,X32666),X32664))),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_8352,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_5729]) ).

cnf(i_0_8353,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_5730]) ).

cnf(i_0_8354,plain,
    c_List_Omember(X1) = c_List_Oset(X1),
    inference(split_conjunct,[status(thm)],[i_0_5731]) ).

fof(i_0_8355,plain,
    ! [X19616,X19617,X19618,X19619,X19620,X19621] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X19621,X19620,X19619)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19621),X19618))
      | hAPP(hAPP(c_Finite__Set_Ofold(X19621,X19620,X19619),X19617),hAPP(hAPP(c_Set_Oinsert(X19621),X19616),X19618)) = hAPP(hAPP(c_Finite__Set_Ofold(X19621,X19620,X19619),hAPP(hAPP(X19619,X19616),X19617)),X19618) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofold__insert__idem2])]) ).

fof(i_0_8356,plain,
    ! [X17454,X17455,X17456] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17456),X17455),X17454))
      | hAPP(hAPP(c_Set_Oinsert(X17456),X17455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17456,tc_HOL_Obool)),X17454),hAPP(hAPP(c_Set_Oinsert(X17456),X17455),c_Orderings_Obot__class_Obot(tc_fun(X17456,tc_HOL_Obool))))) = X17454 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff])]) ).

fof(i_0_8357,plain,
    ! [X26125,X26126] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26126),c_Orderings_Otop__class_Otop(tc_fun(X26126,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26125),c_Orderings_Otop__class_Otop(tc_fun(X26125,tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X26126,X26125)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X26126,X26125),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Prod__UNIV])]) ).

fof(i_0_8358,plain,
    ! [X26130,X26131] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26131),c_Orderings_Otop__class_Otop(tc_fun(X26131,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X26131,X26130)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X26131,X26130),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X26130),c_Orderings_Otop__class_Otop(tc_fun(X26130,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X26131,X26130)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X26131,X26130),tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26131),c_Orderings_Otop__class_Otop(tc_fun(X26131,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26130),c_Orderings_Otop__class_Otop(tc_fun(X26130,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(X26131,X26130)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X26131,X26130),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_8359,plain,
    ! [X24603,X24604,X24605,X24606] :
      ( ~ class_Groups_Ocomm__monoid__add(X24606)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24605),X24604))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24606),X24603),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24605,X24604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24606),hAPP(X24603,X24605)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24606),X24603),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24605),X24604))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__Suc])]) ).

fof(i_0_8360,plain,
    ! [X26854,X26855,X26856,X26857,X26858] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26858),hAPP(X26857,X26856)),X26855))
      | hBOOL(hAPP(hAPP(c_member(X26854),X26856),hAPP(c_Set_Ovimage(X26854,X26858,X26857),X26855))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI2])]) ).

cnf(i_0_8361,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_5732]) ).

fof(i_0_8362,plain,
    ! [X31679,X31680,X31681] :
      ( ( ~ c_List_Olinorder__class_Osorted(X31681,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31681,X31681,c_COMBI(X31681)),X31680),X31679))
        | c_List_Olinorder__class_Osorted(X31681,X31679)
        | ~ class_Orderings_Olinorder(X31681) )
      & ( ~ c_List_Olinorder__class_Osorted(X31681,X31679)
        | c_List_Olinorder__class_Osorted(X31681,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31681,X31681,c_COMBI(X31681)),X31680),X31679))
        | ~ class_Orderings_Olinorder(X31681) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__insort])])]) ).

fof(i_0_8363,plain,
    ! [X24599,X24600,X24601,X24602] :
      ( ~ class_Groups_Ocomm__monoid__add(X24602)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24601),X24600))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24602),X24599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24601),X24600)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24602),hAPP(X24599,X24601)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24602),X24599),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24601)),X24600))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head__upt__Suc])]) ).

fof(i_0_8364,plain,
    ! [X16922,X16923,X16924] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16922,tc_HOL_Obool)),X16924),X16923))
        | X16924 != X16923 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16922,tc_HOL_Obool)),X16923),X16924))
        | X16924 != X16923 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16922,tc_HOL_Obool)),X16924),X16923))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16922,tc_HOL_Obool)),X16923),X16924))
        | X16924 = X16923 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__eq__subset])])]) ).

fof(i_0_8365,plain,
    ! [X16876,X16877,X16878] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16878,tc_HOL_Obool)),X16877),X16876))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16878,tc_HOL_Obool)),X16876),X16877))
      | X16877 = X16876 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityI])]) ).

fof(i_0_8366,plain,
    ! [X31869,X31870,X31871] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X31871),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31870)),X31869)))
      | hAPP(hAPP(c_List_Onth(X31870),hAPP(c_List_Orev(X31870),X31869)),X31871) = hAPP(hAPP(c_List_Onth(X31870),X31869),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31870)),X31869)),hAPP(c_Nat_OSuc,X31871))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__nth])]) ).

fof(i_0_8367,plain,
    ! [X26519,X26520,X26521,X26522,X26523] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X26523),X26522),X26521))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26520,tc_HOL_Obool)),hAPP(X26519,X26522)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26523,tc_fun(X26520,tc_HOL_Obool)),X26521),X26519)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26523,tc_fun(X26520,tc_HOL_Obool)),X26521),X26519) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__absorb])]) ).

fof(i_0_8368,plain,
    ! [X23866,X23867,X23868,X23869,X23870] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23870),X23869),X23868))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23867,tc_HOL_Obool)),hAPP(X23866,X23869)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23870,tc_fun(X23867,tc_HOL_Obool)),X23868),X23866)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23870,tc_fun(X23867,tc_HOL_Obool)),X23868),X23866) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__absorb])]) ).

fof(i_0_8369,plain,
    ! [X29694,X29695,X29696,X29697,X29698] : hAPP(hAPP(c_List_Olist__update(X29698,hAPP(hAPP(c_List_Olist__update(X29698,X29697),X29696),X29695)),X29696),X29694) = hAPP(hAPP(c_List_Olist__update(X29698,X29697),X29696),X29694),
    inference(variable_rename,[status(thm)],[fact_list__update__overwrite]) ).

fof(i_0_8370,plain,
    ! [X21095,X21096] : 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,X21096)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21095))),
    inference(variable_rename,[status(thm)],[fact_negative__zless]) ).

fof(i_0_8371,plain,
    ! [X18755,X18756,X18757] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18757)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18757),X18756),c_Groups_Ozero__class_Ozero(X18757)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18757),X18755),c_Groups_Ozero__class_Ozero(X18757)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18757),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18757),X18756),X18755)),c_Groups_Ozero__class_Ozero(X18757))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__neg])]) ).

fof(i_0_8372,plain,
    ! [X18831,X18832,X18833] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18833)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18833),X18832),c_Groups_Ozero__class_Ozero(X18833)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18833),X18831),c_Groups_Ozero__class_Ozero(X18833)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18833),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18833),X18832),X18831)),c_Groups_Ozero__class_Ozero(X18833))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__neg])]) ).

fof(i_0_8373,plain,
    ! [X18828,X18829,X18830] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18830)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18830),X18829),c_Groups_Ozero__class_Ozero(X18830)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18830),X18828),c_Groups_Ozero__class_Ozero(X18830)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18830),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18830),X18829),X18828)),c_Groups_Ozero__class_Ozero(X18830))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__neg__nonpos])]) ).

fof(i_0_8374,plain,
    ! [X20206,X20207,X20208] :
      ( ~ class_Rings_Osemiring__1(X20208)
      | ~ hBOOL(hAPP(hAPP(c_member(X20208),X20207),c_Nat_Osemiring__1__class_ONats(X20208)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20208),X20206),c_Nat_Osemiring__1__class_ONats(X20208)))
      | hBOOL(hAPP(hAPP(c_member(X20208),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20208),X20207),X20206)),c_Nat_Osemiring__1__class_ONats(X20208))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__mult])]) ).

fof(i_0_8375,plain,
    ! [X19202,X19203,X19204] :
      ( ~ class_Rings_Oring__1(X19204)
      | ~ hBOOL(hAPP(hAPP(c_member(X19204),X19203),c_Int_Oring__1__class_OInts(X19204)))
      | ~ hBOOL(hAPP(hAPP(c_member(X19204),X19202),c_Int_Oring__1__class_OInts(X19204)))
      | hBOOL(hAPP(hAPP(c_member(X19204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19204),X19203),X19202)),c_Int_Oring__1__class_OInts(X19204))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__mult])]) ).

fof(i_0_8376,plain,
    ! [X20203,X20204,X20205] :
      ( ~ class_Rings_Osemiring__1(X20205)
      | ~ hBOOL(hAPP(hAPP(c_member(X20205),X20204),c_Nat_Osemiring__1__class_ONats(X20205)))
      | ~ hBOOL(hAPP(hAPP(c_member(X20205),X20203),c_Nat_Osemiring__1__class_ONats(X20205)))
      | hBOOL(hAPP(hAPP(c_member(X20205),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20205),X20204),X20203)),c_Nat_Osemiring__1__class_ONats(X20205))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__add])]) ).

fof(i_0_8377,plain,
    ! [X19199,X19200,X19201] :
      ( ~ class_Rings_Oring__1(X19201)
      | ~ hBOOL(hAPP(hAPP(c_member(X19201),X19200),c_Int_Oring__1__class_OInts(X19201)))
      | ~ hBOOL(hAPP(hAPP(c_member(X19201),X19199),c_Int_Oring__1__class_OInts(X19201)))
      | hBOOL(hAPP(hAPP(c_member(X19201),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19201),X19200),X19199)),c_Int_Oring__1__class_OInts(X19201))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__add])]) ).

fof(i_0_8378,plain,
    ! [X19205,X19206,X19207] :
      ( ~ class_Rings_Oring__1(X19207)
      | ~ hBOOL(hAPP(hAPP(c_member(X19207),X19206),c_Int_Oring__1__class_OInts(X19207)))
      | ~ hBOOL(hAPP(hAPP(c_member(X19207),X19205),c_Int_Oring__1__class_OInts(X19207)))
      | hBOOL(hAPP(hAPP(c_member(X19207),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19207),X19206),X19205)),c_Int_Oring__1__class_OInts(X19207))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__diff])]) ).

fof(i_0_8379,plain,
    ! [X18727,X18728,X18729] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18729)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18729),X18728),c_Groups_Ozero__class_Ozero(X18729)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18729),X18727),c_Groups_Ozero__class_Ozero(X18729)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18729),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18729),X18728),X18727)),c_Groups_Ozero__class_Ozero(X18729))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonpos__nonpos])]) ).

fof(i_0_8380,plain,
    ! [X30950,X30951,X30952] : c_List_Olist_Olist__size(X30952,X30951,X30950) = 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(X30952,tc_Nat_Onat),X30951),X30950))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30952)),X30950)),
    inference(variable_rename,[status(thm)],[fact_list__size__conv__listsum]) ).

fof(i_0_8381,plain,
    ! [X26236,X26237] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26237),c_Orderings_Otop__class_Otop(tc_fun(X26237,tc_HOL_Obool))))
      | ~ c_Fun_Oinj__on(X26237,X26237,X26236,c_Orderings_Otop__class_Otop(tc_fun(X26237,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(X26237,X26237,X26236),c_Orderings_Otop__class_Otop(tc_fun(X26237,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26237,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__inj__surj])]) ).

fof(i_0_8382,plain,
    ! [X30903,X30904,X30905,X30906] :
      ( ~ class_Rings_Osemiring__1(X30906)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30906),hAPP(hAPP(c_List_Omap(X30905,X30906),hAPP(c_COMBK(X30906,X30905),X30904)),X30903)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X30906),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X30906),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30905)),X30903))),X30904) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__triv])]) ).

fof(i_0_8383,plain,
    ! [X21339,X21340,X21341] :
      ( ~ class_Rings_Oring__1(X21341)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X21341),hAPP(c_Groups_Ouminus__class_Ouminus(X21341),X21340)),X21339) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21341),hAPP(hAPP(c_Power_Opower__class_Opower(X21341),hAPP(c_Groups_Ouminus__class_Ouminus(X21341),c_Groups_Oone__class_Oone(X21341))),X21339)),hAPP(hAPP(c_Power_Opower__class_Opower(X21341),X21340),X21339)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__minus])]) ).

fof(i_0_8384,plain,
    ! [X26156,X26157,X26158,X26159] : hBOOL(hAPP(hAPP(c_member(X26159),hAPP(X26158,X26157)),hAPP(c_Set_Oimage(X26156,X26159,X26158),c_Orderings_Otop__class_Otop(tc_fun(X26156,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[fact_rangeI]) ).

fof(i_0_8385,plain,
    ! [X19334,X19335,X19336,X19337] :
      ( ~ class_Int_Onumber(X19337)
      | ~ class_Rings_Osemiring(X19337)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19337),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19337),X19336),X19335)),hAPP(c_Int_Onumber__class_Onumber__of(X19337),X19334)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19337),X19336),hAPP(c_Int_Onumber__class_Onumber__of(X19337),X19334))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19337),X19335),hAPP(c_Int_Onumber__class_Onumber__of(X19337),X19334))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__distrib__number__of])]) ).

fof(i_0_8386,plain,
    ! [X19342,X19343,X19344,X19345] :
      ( ~ class_Int_Onumber(X19345)
      | ~ class_Rings_Oring(X19345)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19345),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19345),X19344),X19343)),hAPP(c_Int_Onumber__class_Onumber__of(X19345),X19342)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19345),X19344),hAPP(c_Int_Onumber__class_Onumber__of(X19345),X19342))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19345),X19343),hAPP(c_Int_Onumber__class_Onumber__of(X19345),X19342))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__diff__distrib__number__of])]) ).

fof(i_0_8387,plain,
    ! [X25677,X25678,X25679] :
      ( ~ class_Lattices_Olattice(X25679)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25679),X25678))
      | X25678 = c_Orderings_Obot__class_Obot(tc_fun(X25679,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25679),X25677))
      | X25677 = c_Orderings_Obot__class_Obot(tc_fun(X25679,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25679,tc_HOL_Obool)),X25678),X25677) != c_Orderings_Obot__class_Obot(tc_fun(X25679,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X25679,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25679,tc_HOL_Obool)),X25678),X25677)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25679),c_Big__Operators_Olattice__class_OInf__fin(X25679,X25678)),c_Big__Operators_Olattice__class_OInf__fin(X25679,X25677)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__disjoint])]) ).

fof(i_0_8388,plain,
    ! [X25507,X25508,X25509] :
      ( ~ class_Lattices_Olattice(X25509)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25509),X25508))
      | X25508 = c_Orderings_Obot__class_Obot(tc_fun(X25509,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25509),X25507))
      | X25507 = c_Orderings_Obot__class_Obot(tc_fun(X25509,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25509,tc_HOL_Obool)),X25508),X25507) != c_Orderings_Obot__class_Obot(tc_fun(X25509,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X25509,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25509,tc_HOL_Obool)),X25508),X25507)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25509),c_Big__Operators_Olattice__class_OSup__fin(X25509,X25508)),c_Big__Operators_Olattice__class_OSup__fin(X25509,X25507)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__disjoint])]) ).

fof(i_0_8389,plain,
    ! [X25522,X25523,X25524] :
      ( ~ class_Orderings_Olinorder(X25524)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25524),X25523))
      | X25523 = c_Orderings_Obot__class_Obot(tc_fun(X25524,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25524),X25522))
      | X25522 = c_Orderings_Obot__class_Obot(tc_fun(X25524,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25524,tc_HOL_Obool)),X25523),X25522) != c_Orderings_Obot__class_Obot(tc_fun(X25524,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X25524,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25524,tc_HOL_Obool)),X25523),X25522)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X25524),c_Big__Operators_Olinorder__class_OMax(X25524,X25523)),c_Big__Operators_Olinorder__class_OMax(X25524,X25522)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Ounion__disjoint])]) ).

fof(i_0_8390,plain,
    ! [X25516,X25517,X25518] :
      ( ~ class_Orderings_Olinorder(X25518)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25518),X25517))
      | X25517 = c_Orderings_Obot__class_Obot(tc_fun(X25518,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25518),X25516))
      | X25516 = c_Orderings_Obot__class_Obot(tc_fun(X25518,tc_HOL_Obool))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25518,tc_HOL_Obool)),X25517),X25516) != c_Orderings_Obot__class_Obot(tc_fun(X25518,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X25518,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25518,tc_HOL_Obool)),X25517),X25516)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X25518),c_Big__Operators_Olinorder__class_OMin(X25518,X25517)),c_Big__Operators_Olinorder__class_OMin(X25518,X25516)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Ounion__disjoint])]) ).

fof(i_0_8391,plain,
    ! [X33756,X33757,X33758,X33759] :
      ( ~ class_Rings_Ocomm__semiring__1(X33759)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33759),X33758),X33757))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33759),hAPP(hAPP(c_Power_Opower__class_Opower(X33759),X33758),X33756)),hAPP(hAPP(c_Power_Opower__class_Opower(X33759),X33757),X33756))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power__same])]) ).

fof(i_0_8392,plain,
    ! [X17930,X17931,X17932,X17933] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X17933)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17933),X17932),X17931))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17933),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17933),X17932),X17930)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17933),X17931),X17930))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__right__mono])]) ).

fof(i_0_8393,plain,
    ! [X17926,X17927,X17928,X17929] :
      ( ~ class_Groups_Oordered__cancel__ab__semigroup__add(X17929)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17929),X17928),X17927))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17929),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17929),X17926),X17928)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17929),X17926),X17927))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__left__mono])]) ).

fof(i_0_8394,plain,
    ! [X17901,X17902,X17903,X17904] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X17904)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17904),X17903),X17902))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17904),X17903),X17901)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17904),X17902),X17901))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__mono])]) ).

fof(i_0_8395,plain,
    ! [X17897,X17898,X17899,X17900] :
      ( ~ class_Groups_Oordered__ab__semigroup__add(X17900)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17900),X17899),X17898))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17900),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17900),X17897),X17899)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17900),X17897),X17898))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__mono])]) ).

fof(i_0_8396,plain,
    ! [X23441,X23442,X23443] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X23443)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23443),X23442))
      | X23442 = c_Orderings_Obot__class_Obot(tc_fun(X23443,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23443),X23441))
      | X23441 = c_Orderings_Obot__class_Obot(tc_fun(X23443,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ofold1(X23443,c_Groups_Otimes__class_Otimes(X23443)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23443,tc_HOL_Obool)),X23442),X23441)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23443),hAPP(c_Finite__Set_Ofold1(X23443,c_Groups_Otimes__class_Otimes(X23443)),X23442)),hAPP(c_Finite__Set_Ofold1(X23443,c_Groups_Otimes__class_Otimes(X23443)),X23441)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__Un2])]) ).

fof(i_0_8397,plain,
    ! [X31860,X31861,X31862] : hAPP(c_List_Orev(X31862),hAPP(hAPP(c_List_Odrop(X31862),X31861),X31860)) = hAPP(hAPP(c_List_Otake(X31862),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31862)),X31860)),X31861)),hAPP(c_List_Orev(X31862),X31860)),
    inference(variable_rename,[status(thm)],[fact_rev__drop]) ).

fof(i_0_8398,plain,
    ! [X31863,X31864,X31865] : hAPP(c_List_Orev(X31865),hAPP(hAPP(c_List_Otake(X31865),X31864),X31863)) = hAPP(hAPP(c_List_Odrop(X31865),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31865)),X31863)),X31864)),hAPP(c_List_Orev(X31865),X31863)),
    inference(variable_rename,[status(thm)],[fact_rev__take]) ).

fof(i_0_8399,plain,
    ! [X24209,X24210,X24211] :
      ( ~ class_Orderings_Olinorder(X24211)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24211),X24210),X24209))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24211,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24211),X24210),c_Orderings_Obot__class_Obot(tc_fun(X24211,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(X24211,X24210,X24209)) = c_SetInterval_Oord__class_OatLeastAtMost(X24211,X24210,X24209) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I5_J])]) ).

fof(i_0_8400,plain,
    ! [X21460,X21461] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21461,tc_HOL_Obool)),X21460),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21461,tc_HOL_Obool)),X21460)))
        | X21460 = c_Orderings_Obot__class_Obot(tc_fun(X21461,tc_HOL_Obool)) )
      & ( X21460 != c_Orderings_Obot__class_Obot(tc_fun(X21461,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21461,tc_HOL_Obool)),X21460),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21461,tc_HOL_Obool)),X21460))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Compl__self__eq])]) ).

fof(i_0_8401,plain,
    ! [X19944,X19945,X19946] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19946),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19945)),X19944)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19946),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19945)),X19944)) = 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),X19946),X19945))),X19944) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5733])]) ).

fof(i_0_8402,plain,
    ! [X26024,X26025] : c_Divides_Opdivmod(X26025,X26024) = 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),X26025)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26024))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26025),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26024))),
    inference(variable_rename,[status(thm)],[fact_pdivmod__def]) ).

fof(i_0_8403,plain,
    ! [X27035,X27036,X27037] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X27037,tc_HOL_Obool)),X27036),X27035))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X27037,tc_HOL_Obool)),X27036),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27037,tc_HOL_Obool),X27035))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__upper])]) ).

fof(i_0_8404,plain,
    ! [X19589,X19590,X19591,X19592] : hAPP(c_Finite__Set_Ofold__image(X19592,X19591,X19590),X19589) = c_Finite__Set_Ofold(X19591,X19592,hAPP(hAPP(c_COMBB(X19592,tc_fun(X19592,X19592),X19591),X19590),X19589)),
    inference(variable_rename,[status(thm)],[fact_fold__image__def]) ).

fof(i_0_8405,plain,
    ! [X22689,X22690] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22690)),X22689) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,X22690),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),X22690)),X22689),
    inference(variable_rename,[status(thm)],[fact_max__Suc1]) ).

fof(i_0_8406,plain,
    ! [X27005,X27006] : hAPP(c_Relation_OField(X27006),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X27006,X27006),tc_HOL_Obool),X27005)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X27006,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(X27006,X27006),tc_HOL_Obool),tc_fun(X27006,tc_HOL_Obool),c_Relation_OField(X27006)),X27005)),
    inference(variable_rename,[status(thm)],[fact_Field__Union]) ).

fof(i_0_8407,plain,
    ! [X33933,X33934] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33933),X33934)),X33934))
        | X33933 = 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)),X33934)) )
      & ( X33933 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33933),X33934)),X33934))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33934)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2])])]) ).

fof(i_0_8408,plain,
    ! [X33931,X33932] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33932),X33931)),X33932))
        | X33931 = 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)),X33932)) )
      & ( X33931 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X33932),X33931)),X33932))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33932)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1])])]) ).

fof(i_0_8409,plain,
    ! [X23398,X23399,X23400] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23400,tc_HOL_Obool)),X23399),X23398))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23400,tc_HOL_Obool)),X23399),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23400,tc_HOL_Obool)),X23398),X23399)) = X23398 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__partition])]) ).

fof(i_0_8410,plain,
    ! [X30661,X30662,X30663] :
      ( ~ c_Fun_Oinj__on(X30663,X30662,X30661,c_Orderings_Otop__class_Otop(tc_fun(X30663,tc_HOL_Obool)))
      | c_Fun_Oinj__on(tc_List_Olist(X30663),tc_List_Olist(X30662),hAPP(c_List_Omap(X30663,X30662),X30661),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X30663),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__mapI])]) ).

fof(i_0_8411,plain,
    ! [X25286,X25287,X25288] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25288,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25288,tc_HOL_Obool)),X25287),X25286)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25288,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25288,tc_HOL_Obool)),X25287)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25288,tc_HOL_Obool)),X25286)),
    inference(variable_rename,[status(thm)],[fact_Compl__Int]) ).

fof(i_0_8412,plain,
    ! [X25289,X25290,X25291] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25291,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25291,tc_HOL_Obool)),X25290),X25289)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25291,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25291,tc_HOL_Obool)),X25290)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25291,tc_HOL_Obool)),X25289)),
    inference(variable_rename,[status(thm)],[fact_Compl__Un]) ).

fof(i_0_8413,plain,
    ! [X32485,X32486,X32487,X32488,X32489] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32489,X32488,X32487),X32486),X32485))
        | hBOOL(hAPP(hAPP(X32487,X32485),X32486)) )
      & ( ~ hBOOL(hAPP(hAPP(X32487,X32485),X32486))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32489,X32488,X32487),X32486),X32485)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep__iff])]) ).

fof(i_0_8414,plain,
    ! [X32480,X32481,X32482,X32483,X32484] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32484,X32483,X32482),X32481),X32480))
        | hBOOL(hAPP(hAPP(X32482,X32480),X32481)) )
      & ( ~ hBOOL(hAPP(hAPP(X32482,X32480),X32481))
        | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32484,X32483,X32482),X32481),X32480)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Oequations])]) ).

fof(i_0_8415,plain,
    ! [X32470,X32471,X32472,X32473,X32474] :
      ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32474,X32473,X32472),X32471),X32470))
      | hBOOL(hAPP(hAPP(X32472,X32470),X32471)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversepD])]) ).

fof(i_0_8416,plain,
    ! [X26821,X26822,X26823,X26824,X26825] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(X26825,X26824,X26823),X26822),X26821))
        | hBOOL(hAPP(X26822,hAPP(X26823,X26821))) )
      & ( ~ hBOOL(hAPP(X26822,hAPP(X26823,X26821)))
        | hBOOL(hAPP(hAPP(c_Set_Ovimage(X26825,X26824,X26823),X26822),X26821)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimage__code])]) ).

fof(i_0_8417,plain,
    ! [X26795,X26796,X26797,X26799] :
      ( ( hBOOL(hAPP(hAPP(c_member(X26797),esk244_3(X26795,X26796,X26797)),X26796))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26797),c_Complete__Lattice_OInf__class_OInf(X26797,X26796)),X26795))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26797)
        | ~ class_Orderings_Olinorder(X26797) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26797),esk244_3(X26795,X26796,X26797)),X26795))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26797),c_Complete__Lattice_OInf__class_OInf(X26797,X26796)),X26795))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26797)
        | ~ class_Orderings_Olinorder(X26797) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X26797),X26799),X26796))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26797),X26799),X26795))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X26797),c_Complete__Lattice_OInf__class_OInf(X26797,X26796)),X26795))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26797)
        | ~ class_Orderings_Olinorder(X26797) ) ),
    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_8418,plain,
    ! [X19315,X19316,X19317,X19318] :
      ( ~ class_Int_Onumber__ring(X19318)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19318),hAPP(c_Int_Onumber__class_Onumber__of(X19318),X19317)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19318),hAPP(c_Int_Onumber__class_Onumber__of(X19318),X19316)),X19315)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19318),hAPP(c_Int_Onumber__class_Onumber__of(X19318),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19317),X19316))),X19315) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__number__of__left])]) ).

fof(i_0_8419,plain,
    ! [X19305,X19306,X19307,X19308] :
      ( ~ class_Int_Onumber__ring(X19308)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19308),hAPP(c_Int_Onumber__class_Onumber__of(X19308),X19307)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19308),hAPP(c_Int_Onumber__class_Onumber__of(X19308),X19306)),X19305)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19308),hAPP(c_Int_Onumber__class_Onumber__of(X19308),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19307),X19306))),X19305) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__left])]) ).

fof(i_0_8420,plain,
    ! [X19338,X19339,X19340,X19341] :
      ( ~ class_Int_Onumber__ring(X19341)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19341),hAPP(c_Int_Onumber__class_Onumber__of(X19341),X19340)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19341),hAPP(c_Int_Onumber__class_Onumber__of(X19341),X19339)),X19338)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19341),hAPP(c_Int_Onumber__class_Onumber__of(X19341),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19340),X19339))),X19338) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__diff1])]) ).

fof(i_0_8421,plain,
    ! [X23992,X23993,X23994] :
      ( ~ class_Orderings_Olinorder(X23994)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23994),X23993),X23992))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23994,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23994),X23993),c_Orderings_Obot__class_Obot(tc_fun(X23994,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(X23994,X23993,X23992)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X23994,X23993),X23992) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I3_J])]) ).

fof(i_0_8422,plain,
    ! [X30868,X30869,X30870,X30871,X30872] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30872),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30871)),X30870)))
      | hAPP(hAPP(c_List_Onth(X30869),hAPP(hAPP(c_List_Omap(X30871,X30869),X30868),X30870)),X30872) = hAPP(X30868,hAPP(hAPP(c_List_Onth(X30871),X30870),X30872)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__map])]) ).

fof(i_0_8423,plain,
    ! [X33635,X33636,X33637,X33638] :
      ( ~ class_Rings_Ocomm__semiring__1(X33638)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33637),X33636))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33638),hAPP(hAPP(c_Power_Opower__class_Opower(X33638),X33635),X33637)),hAPP(hAPP(c_Power_Opower__class_Opower(X33638),X33635),X33636))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd])]) ).

fof(i_0_8424,plain,
    ! [X26028,X26029] :
      ( ( X26028 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X26029,X26028) = X26029
        | ~ 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),X26029),X26028))) )
      & ( X26028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X26029,X26028) = c_Nitpick_Onat__gcd(X26028,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26029,X26028))
        | ~ 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),X26029),X26028))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Opsimps])])]) ).

fof(i_0_8425,plain,
    ! [X26977,X26978,X26979,X26980] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26980,tc_HOL_Obool)),X26979),X26978))
      | ~ hBOOL(hAPP(hAPP(c_member(X26980),X26977),X26979))
      | hBOOL(hAPP(hAPP(c_member(X26980),X26977),c_Complete__Lattice_OSup__class_OSup(tc_fun(X26980,tc_HOL_Obool),X26978))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnionI])]) ).

fof(i_0_8426,plain,
    ! [X18234,X18235,X18236] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18236)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18236),c_Groups_Ozero__class_Ozero(X18236)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18236),X18235),X18234)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18236),c_Groups_Ozero__class_Ozero(X18236)),X18234))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18236),c_Groups_Ozero__class_Ozero(X18236)),X18235)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos2])]) ).

fof(i_0_8427,plain,
    ! [X18237,X18238,X18239] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18239)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18239),c_Groups_Ozero__class_Ozero(X18239)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18239),X18238),X18237)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18239),c_Groups_Ozero__class_Ozero(X18239)),X18238))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18239),c_Groups_Ozero__class_Ozero(X18239)),X18237)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__mult__pos])]) ).

fof(i_0_8428,plain,
    ! [X32239,X32240,X32241,X32244,X32245,X32246,X32247,X32248] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32241),X32240),hAPP(c_List_Oset(X32241),X32239)))
        | X32239 = hAPP(hAPP(c_List_Oappend(X32241),esk467_3(X32239,X32240,X32241)),hAPP(hAPP(c_List_Olist_OCons(X32241),X32240),esk468_3(X32239,X32240,X32241))) )
      & ( X32244 != hAPP(hAPP(c_List_Oappend(X32246),X32247),hAPP(hAPP(c_List_Olist_OCons(X32246),X32245),X32248))
        | hBOOL(hAPP(hAPP(c_member(X32246),X32245),hAPP(c_List_Oset(X32246),X32244))) ) ),
    inference(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_8429,plain,
    ! [X33039,X33040] : c_Relation_Osym(X33040,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X33040,X33040),tc_HOL_Obool)),X33039),hAPP(c_Relation_Oconverse(X33040,X33040),X33039))),
    inference(variable_rename,[status(thm)],[fact_sym__Int__converse]) ).

fof(i_0_8430,plain,
    ! [X33018,X33019] : c_Relation_Osym(X33019,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33019,X33019),tc_HOL_Obool)),X33018),hAPP(c_Relation_Oconverse(X33019,X33019),X33018))),
    inference(variable_rename,[status(thm)],[fact_sym__Un__converse]) ).

fof(i_0_8431,plain,
    ! [X25491,X25492,X25493] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25493),X25492))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25493),X25491))
      | 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))
      | hAPP(c_Finite__Set_Ocard(X25493),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25493,tc_HOL_Obool)),X25492),X25491)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X25493),X25492)),hAPP(c_Finite__Set_Ocard(X25493),X25491)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Un__disjoint])]) ).

fof(i_0_8432,plain,
    ! [X21659,X21660] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21660)),X21659) = 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),X21660)),X21659),
    inference(variable_rename,[status(thm)],[fact_min__Suc1]) ).

fof(i_0_8433,plain,
    ! [X29988,X29989,X29990] :
      ( ~ class_Orderings_Olinorder(X29990)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X29990),X29989))
      | c_List_Olinorder__class_Osorted__list__of__set(X29990,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29990,tc_HOL_Obool)),X29989),hAPP(hAPP(c_Set_Oinsert(X29990),X29988),c_Orderings_Obot__class_Obot(tc_fun(X29990,tc_HOL_Obool))))) = c_List_Oremove1(X29990,X29988,c_List_Olinorder__class_Osorted__list__of__set(X29990,X29989)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__remove])]) ).

fof(i_0_8434,plain,
    ! [X26128,X26129] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X26129,X26128)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26129,X26128),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26128),c_Orderings_Otop__class_Otop(tc_fun(X26128,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__fun__UNIVD2])]) ).

fof(i_0_8435,plain,
    ! [X31393,X31394,X31395,X31396,X31397] :
      ( ~ class_Orderings_Olinorder(X31397)
      | hAPP(c_List_Ofilter(X31396,X31395),c_List_Olinorder__class_Osort__key(X31396,X31397,X31394,X31393)) = c_List_Olinorder__class_Osort__key(X31396,X31397,X31394,hAPP(c_List_Ofilter(X31396,X31395),X31393)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_filter__sort])]) ).

fof(i_0_8436,plain,
    ! [X23960,X23961,X23962] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X23962,tc_HOL_Obool)),X23961),hAPP(c_Set_OPow(X23962),X23960)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23962,tc_HOL_Obool)),X23961),X23960)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowD])]) ).

fof(i_0_8437,plain,
    ! [X23957,X23958,X23959] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X23959,tc_HOL_Obool)),X23958),hAPP(c_Set_OPow(X23959),X23957)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23959,tc_HOL_Obool)),X23958),X23957)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23959,tc_HOL_Obool)),X23958),X23957))
        | hBOOL(hAPP(hAPP(c_member(tc_fun(X23959,tc_HOL_Obool)),X23958),hAPP(c_Set_OPow(X23959),X23957))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pow__iff])]) ).

fof(i_0_8438,plain,
    ! [X25978,X25979] :
      ( ( ~ 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),X25979)),X25978)))
        | X25979 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X25978 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X25979 = 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),X25979)),X25978))) )
      & ( X25978 != 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),X25979)),X25978))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff])])]) ).

fof(i_0_8439,plain,
    ! [X24172,X24173,X24174,X24175] :
      ( ~ class_Orderings_Olinorder(X24175)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24175),X24174),X24173))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24175),X24173),X24172))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24175,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24175,X24174,X24173)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24175,X24173,X24172)) = c_SetInterval_Oord__class_OatLeastAtMost(X24175,X24174,X24172) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I22_J])]) ).

fof(i_0_8440,plain,
    ! [X23498,X23499,X23500,X23501] :
      ( ~ class_Orderings_Olinorder(X23501)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23500),X23499))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23501),X23499),X23498))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23501,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23501,X23500,X23499)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23501,X23499,X23498)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23501,X23500,X23498) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I20_J])]) ).

fof(i_0_8441,plain,
    ! [X23529,X23530,X23531,X23532] :
      ( ~ class_Orderings_Olinorder(X23532)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23532),X23531),X23530))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23532),X23530),X23529))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23532,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X23532,X23531,X23530)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23532,X23530,X23529)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X23532,X23531,X23529) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I16_J])]) ).

fof(i_0_8442,plain,
    ! [X23986,X23987,X23988,X23989] :
      ( ~ class_Orderings_Olinorder(X23989)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23989),X23988),X23987))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23989),X23987),X23986))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23989,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23989,X23988,X23987)),c_SetInterval_Oord__class_OatLeastAtMost(X23989,X23987,X23986)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23989,X23988,X23986) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I19_J])]) ).

fof(i_0_8443,plain,
    ! [X23342,X23343,X23344] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23344,tc_HOL_Obool)),X23343),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23344,tc_HOL_Obool)),X23343),X23342))),
    inference(variable_rename,[status(thm)],[fact_Un__upper1]) ).

fof(i_0_8444,plain,
    ! [X23345,X23346,X23347] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23347,tc_HOL_Obool)),X23346),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23347,tc_HOL_Obool)),X23345),X23346))),
    inference(variable_rename,[status(thm)],[fact_Un__upper2]) ).

fof(i_0_8445,plain,
    ! [X28596,X28597,X28598] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X28598,X28598)),X28597),X28596))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(X28598,X28598)),X28597),c_Transitive__Closure_Ortrancl(X28598,X28596))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__into__rtrancl])]) ).

fof(i_0_8446,plain,
    ! [X18681,X18682,X18683,X18684] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18684),X18683))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18682),X18681))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X18684,X18682)),c_Sum__Type_OPlus(X18684,X18682,X18683,X18681)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18684),X18683)),hAPP(c_Finite__Set_Ocard(X18682),X18681)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X18684),X18683))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X18684,X18682)),c_Sum__Type_OPlus(X18684,X18682,X18683,X18681)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X18682),X18681))
        | hAPP(c_Finite__Set_Ocard(tc_sum(X18684,X18682)),c_Sum__Type_OPlus(X18684,X18682,X18683,X18681)) = 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_8447,plain,
    ! [X18183,X18184,X18185,X18186] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18186),X18185))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18184),X18183))
      | hAPP(c_Finite__Set_Ocard(tc_sum(X18186,X18184)),c_Sum__Type_OPlus(X18186,X18184,X18185,X18183)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18186),X18185)),hAPP(c_Finite__Set_Ocard(X18184),X18183)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Plus])]) ).

fof(i_0_8448,plain,
    ! [X23305,X23306,X23307,X23308] :
      ( ~ class_Lattices_Osemilattice__sup(X23308)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23308),X23307),X23306))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23308),X23305),X23306))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23308),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23308),X23307),X23305)),X23306)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI])]) ).

fof(i_0_8449,plain,
    ! [X23301,X23302,X23303,X23304] :
      ( ~ class_Lattices_Osemilattice__sup(X23304)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23304),X23303),X23302))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23304),X23301),X23302))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23304),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23304),X23303),X23301)),X23302)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__least])]) ).

fof(i_0_8450,plain,
    ! [X22579,X22580,X22581,X22582] :
      ( ~ class_Orderings_Olinorder(X22582)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22582),X22581),X22580))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22582),X22579),X22580))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22582),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22582),X22581),X22579)),X22580)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI])]) ).

fof(i_0_8451,plain,
    ! [X22575,X22576,X22577,X22578] :
      ( ~ class_Orderings_Olinorder(X22578)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22578),X22577),X22576))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22578),X22575),X22576))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22578),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22578),X22577),X22575)),X22576)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__least])]) ).

fof(i_0_8452,plain,
    ! [X25123,X25124,X25125,X25126] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25126,tc_HOL_Obool)),X25125),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25126,tc_HOL_Obool)),X25124),X25123)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25126,tc_HOL_Obool)),X25124),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25126,tc_HOL_Obool)),X25125),X25123)),
    inference(variable_rename,[status(thm)],[fact_Int__left__commute]) ).

fof(i_0_8453,plain,
    ! [X23270,X23271,X23272,X23273] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23273,tc_HOL_Obool)),X23272),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23273,tc_HOL_Obool)),X23271),X23270)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23273,tc_HOL_Obool)),X23271),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23273,tc_HOL_Obool)),X23272),X23270)),
    inference(variable_rename,[status(thm)],[fact_Un__left__commute]) ).

fof(i_0_8454,plain,
    ! [X23162,X23163,X23164] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23164,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23164,tc_HOL_Obool)),X23163),X23162)),X23162) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23164,tc_HOL_Obool)),X23163),X23162),
    inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel2]) ).

fof(i_0_8455,plain,
    ! [X17343,X17344,X17345] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17345,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17345,tc_HOL_Obool)),X17344),X17343)),X17343) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17345,tc_HOL_Obool)),X17344),X17343),
    inference(variable_rename,[status(thm)],[fact_Diff__idemp]) ).

cnf(i_0_8456,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_5734]) ).

fof(i_0_8457,plain,
    ! [X16986,X16987,X16988,X16989,X16990] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X16990),X16989),X16988))
      | hBOOL(hAPP(hAPP(c_member(X16987),hAPP(X16986,X16989)),hAPP(c_Set_Oimage(X16990,X16987,X16986),X16988))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_imageI])]) ).

fof(i_0_8458,plain,
    ! [X19724,X19725,X19726,X19727,X19728] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19728,X19727,X19726)
      | c_Finite__Set_Ofun__left__comm(X19725,X19727,hAPP(hAPP(c_COMBB(X19728,tc_fun(X19727,X19727),X19725),X19726),X19724)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm__apply])]) ).

fof(i_0_8459,plain,
    ! [X17871,X17872,X17873,X17874,X17875] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X17875,X17874,X17873)
      | c_Finite__Set_Ofun__left__comm__idem(X17872,X17874,hAPP(hAPP(c_COMBB(X17875,tc_fun(X17874,X17874),X17872),X17873),X17871)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__comm__idem__apply])]) ).

fof(i_0_8460,plain,
    ! [X25237,X25238,X25239,X25240] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X25240),X25239),X25238))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25240,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25240),X25239),X25237)),X25238) = hAPP(hAPP(c_Set_Oinsert(X25240),X25239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25240,tc_HOL_Obool)),X25237),X25238)) )
      & ( hBOOL(hAPP(hAPP(c_member(X25240),X25239),X25238))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25240,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25240),X25239),X25237)),X25238) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25240,tc_HOL_Obool)),X25237),X25238) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5735])]) ).

fof(i_0_8461,plain,
    ! [X25221,X25222,X25223,X25224] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25224),X25223),X25222))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25224,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25224),X25223),X25221)),X25222) = hAPP(hAPP(c_Set_Oinsert(X25224),X25223),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25224,tc_HOL_Obool)),X25221),X25222)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__left__if1])]) ).

fof(i_0_8462,plain,
    ! [X26174,X26175,X26176,X26177,X26178] :
      ( ( hAPP(c_Set_Oimage(X26178,X26177,X26176),X26175) != hAPP(c_Set_Oimage(X26178,X26177,X26176),X26174)
        | X26175 = X26174
        | ~ c_Fun_Oinj__on(X26178,X26177,X26176,c_Orderings_Otop__class_Otop(tc_fun(X26178,tc_HOL_Obool))) )
      & ( X26175 != X26174
        | hAPP(c_Set_Oimage(X26178,X26177,X26176),X26175) = hAPP(c_Set_Oimage(X26178,X26177,X26176),X26174)
        | ~ c_Fun_Oinj__on(X26178,X26177,X26176,c_Orderings_Otop__class_Otop(tc_fun(X26178,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_8463,plain,
    ! [X26652,X26653,X26654,X26655,X26656,X26657,X26658] :
      ( hAPP(c_Fun_Ocomp(X26658,X26657,X26656,X26655),X26654) != X26653
      | hAPP(X26655,hAPP(X26654,X26652)) = hAPP(X26653,X26652) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_o__eq__dest__lhs])]) ).

fof(i_0_8464,plain,
    ! [X21395] : 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,X21395)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negative__zless__0]) ).

fof(i_0_8465,plain,
    ! [X30326,X30327,X30328] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30328),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30327)),X30326)))
      | hAPP(hAPP(c_List_Olist_OCons(X30327),hAPP(hAPP(c_List_Onth(X30327),X30326),X30328)),hAPP(hAPP(c_List_Odrop(X30327),hAPP(c_Nat_OSuc,X30328)),X30326)) = hAPP(hAPP(c_List_Odrop(X30327),X30328),X30326) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__drop_H])]) ).

fof(i_0_8466,plain,
    ! [X26918,X26919,X26920,X26921] : hAPP(c_Set_Oimage(X26921,X26920,X26919),hAPP(c_Set_Ovimage(X26921,X26920,X26919),X26918)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26920,tc_HOL_Obool)),X26918),hAPP(c_Set_Oimage(X26921,X26920,X26919),c_Orderings_Otop__class_Otop(tc_fun(X26921,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_image__vimage__eq]) ).

fof(i_0_8467,plain,
    ! [X19500,X19501] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19501),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19500))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19501),X19500)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19501),X19500))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19501),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19500)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add1__zle__eq])]) ).

fof(i_0_8468,plain,
    ! [X24073,X24074,X24075,X24076] :
      ( ~ class_Orderings_Olinorder(X24076)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24076),X24075),X24074))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24076),X24074),X24073))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24076,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X24076,X24075,X24074)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24076,X24074,X24073)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24076,X24075),X24073) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I18_J])]) ).

fof(i_0_8469,plain,
    ! [X19977] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X19977))
        | 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)),X19977))) )
      & ( ~ 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)),X19977)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X19977)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I1_J])]) ).

fof(i_0_8470,plain,
    ! [X18141,X18142,X18143] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18143),X18142))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18143,tc_HOL_Obool)),X18141),X18142))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X18143),X18141)),hAPP(c_Finite__Set_Ocard(X18143),X18142))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__card__mono])]) ).

fof(i_0_8471,plain,
    ! [X17110,X17111,X17112] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17112),X17111))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17112,tc_HOL_Obool)),X17110),X17111))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17112),X17110)),hAPP(c_Finite__Set_Ocard(X17112),X17111))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__mono])]) ).

fof(i_0_8472,plain,
    ! [X23142,X23143,X23144,X23145] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23145),X23144),X23143))
      | hBOOL(hAPP(hAPP(c_member(X23145),X23144),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23145,tc_HOL_Obool)),X23143),X23142))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI1])]) ).

fof(i_0_8473,plain,
    ! [X23130,X23131,X23132,X23133] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X23133),X23132),X23131))
        | hBOOL(hAPP(hAPP(c_member(X23133),X23132),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23133,tc_HOL_Obool)),X23130),X23131))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X23133),X23132),X23130))
        | hBOOL(hAPP(hAPP(c_member(X23133),X23132),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23133,tc_HOL_Obool)),X23130),X23131))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5736])])]) ).

fof(i_0_8474,plain,
    ! [X23138,X23139,X23140,X23141] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X23141),X23140),X23139))
      | hBOOL(hAPP(hAPP(c_member(X23141),X23140),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23141,tc_HOL_Obool)),X23138),X23139))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UnI2])]) ).

fof(i_0_8475,plain,
    ! [X26238,X26239] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26239),c_Orderings_Otop__class_Otop(tc_fun(X26239,tc_HOL_Obool))))
      | hAPP(c_Set_Oimage(X26239,X26239,X26238),c_Orderings_Otop__class_Otop(tc_fun(X26239,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26239,tc_HOL_Obool))
      | c_Fun_Oinj__on(X26239,X26239,X26238,c_Orderings_Otop__class_Otop(tc_fun(X26239,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__surj__inj])]) ).

fof(i_0_8476,plain,
    ! [X25924,X25925,X25926] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25926),X25925),X25924))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25926),hAPP(c_Groups_Oabs__class_Oabs(X25926),X25925)),X25924))
        | ~ class_Rings_Olinordered__idom(X25926) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25926),hAPP(c_Groups_Ouminus__class_Ouminus(X25926),X25925)),X25924))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25926),hAPP(c_Groups_Oabs__class_Oabs(X25926),X25925)),X25924))
        | ~ class_Rings_Olinordered__idom(X25926) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25926),X25925),X25924))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25926),hAPP(c_Groups_Ouminus__class_Ouminus(X25926),X25925)),X25924))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25926),hAPP(c_Groups_Oabs__class_Oabs(X25926),X25925)),X25924))
        | ~ class_Rings_Olinordered__idom(X25926) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__less__iff])])]) ).

fof(i_0_8477,plain,
    ! [X25918,X25919,X25920] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25920)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25920),X25919),X25918))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25920),hAPP(c_Groups_Ouminus__class_Ouminus(X25920),X25919)),X25918))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25920),hAPP(c_Groups_Oabs__class_Oabs(X25920),X25919)),X25918)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__leI])]) ).

fof(i_0_8478,plain,
    ! [X25915,X25916,X25917] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25917),X25916),X25915))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25917),hAPP(c_Groups_Oabs__class_Oabs(X25917),X25916)),X25915))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25917) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25917),hAPP(c_Groups_Ouminus__class_Ouminus(X25917),X25916)),X25915))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25917),hAPP(c_Groups_Oabs__class_Oabs(X25917),X25916)),X25915))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25917) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25917),X25916),X25915))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25917),hAPP(c_Groups_Ouminus__class_Ouminus(X25917),X25916)),X25915))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25917),hAPP(c_Groups_Oabs__class_Oabs(X25917),X25916)),X25915))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25917) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__iff])])]) ).

fof(i_0_8479,plain,
    ! [X29394,X29395,X29396] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29396)),X29395),c_Wellfounded_Oacc(tc_List_Olist(X29396),c_List_Olistrel1(X29396,X29394))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29396)),X29395),c_List_Olists(X29396,c_Wellfounded_Oacc(X29396,X29394)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accI])]) ).

fof(i_0_8480,plain,
    ! [X18261,X18262] :
      ( ~ class_Rings_Olinordered__ring(X18262)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18262),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18262),X18261),X18261)),c_Groups_Ozero__class_Ozero(X18262))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5737])]) ).

fof(i_0_8481,plain,
    ! [X26926,X26927,X26928,X26929] :
      ( ~ c_Fun_Oinj__on(X26929,X26928,X26927,c_Orderings_Otop__class_Otop(tc_fun(X26929,tc_HOL_Obool)))
      | hAPP(c_Set_Ovimage(X26929,X26928,X26927),hAPP(c_Set_Oimage(X26929,X26928,X26927),X26926)) = X26926 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__vimage__image__eq])]) ).

fof(i_0_8482,plain,
    ! [X24195,X24196,X24197,X24198] :
      ( ~ class_Orderings_Olinorder(X24198)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24198),X24197),X24196))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24198),X24196),X24195))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24198,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24198,X24197,X24196)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24198,X24196),X24195)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X24198,X24197,X24195) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I15_J])]) ).

fof(i_0_8483,plain,
    ! [X20516,X20517,X20518,X20519] :
      ( ~ class_Divides_Osemiring__div(X20519)
      | X20518 = c_Groups_Ozero__class_Ozero(X20519)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20519),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20519),X20517),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20519),X20518),X20516))),X20518) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20519),X20516),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20519),X20517),X20518)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2])]) ).

fof(i_0_8484,plain,
    ! [X20520,X20521,X20522,X20523] :
      ( ~ class_Divides_Osemiring__div(X20523)
      | X20522 = c_Groups_Ozero__class_Ozero(X20523)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20523),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20523),X20521),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20523),X20520),X20522))),X20522) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20523),X20520),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20523),X20521),X20522)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1])]) ).

fof(i_0_8485,plain,
    ! [X22915,X22916,X22917,X22918] :
      ( ~ class_Fields_Ofield__inverse__zero(X22918)
      | X22917 = c_Groups_Ozero__class_Ozero(X22918)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22918),X22916),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22918),X22915),X22917)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22918),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22918),X22915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22918),X22916),X22917))),X22917) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__num__frac])]) ).

fof(i_0_8486,plain,
    ! [X27843,X27844,X27845,X27846] :
      ( ~ class_Groups_Ocomm__monoid__add(X27846)
      | ~ c_Fun_Oinj__on(X27845,X27846,X27844,X27843)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27845,X27846),X27844),X27843) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X27846,X27846),c_Fun_Oid(X27846)),hAPP(c_Set_Oimage(X27845,X27846,X27844),X27843)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__reindex__id])]) ).

fof(i_0_8487,plain,
    ! [X27847,X27848,X27849,X27850] :
      ( ~ class_Groups_Ocomm__monoid__mult(X27850)
      | ~ c_Fun_Oinj__on(X27849,X27850,X27848,X27847)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27849,X27850),X27848),X27847) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X27850,X27850),c_Fun_Oid(X27850)),hAPP(c_Set_Oimage(X27849,X27850,X27848),X27847)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__reindex__id])]) ).

fof(i_0_8488,plain,
    ! [X28075,X28076] :
      ( ( ~ c_Wellfounded_Owf(X28076,X28075)
        | c_Wellfounded_Owf(X28076,hAPP(hAPP(c_Relation_Orel__comp(X28076,X28076,X28076),X28075),X28075)) )
      & ( ~ c_Wellfounded_Owf(X28076,hAPP(hAPP(c_Relation_Orel__comp(X28076,X28076,X28076),X28075),X28075))
        | c_Wellfounded_Owf(X28076,X28075) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__comp__self])]) ).

fof(i_0_8489,plain,
    ! [X22082,X22083,X22084] :
      ( X22084 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X22083,X22083),tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X22083,X22083),tc_HOL_Obool)),X22084),X22082)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__by__empty])]) ).

fof(i_0_8490,plain,
    ! [X30168,X30169,X30170] :
      ( ( hBOOL(hAPP(c_List_Odistinct(X30170),X30169))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30170),hAPP(hAPP(c_List_Oappend(X30170),X30169),X30168))) )
      & ( hBOOL(hAPP(c_List_Odistinct(X30170),X30168))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30170),hAPP(hAPP(c_List_Oappend(X30170),X30169),X30168))) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30170,tc_HOL_Obool)),hAPP(c_List_Oset(X30170),X30169)),hAPP(c_List_Oset(X30170),X30168)) = c_Orderings_Obot__class_Obot(tc_fun(X30170,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30170),hAPP(hAPP(c_List_Oappend(X30170),X30169),X30168))) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30170),X30169))
        | ~ hBOOL(hAPP(c_List_Odistinct(X30170),X30168))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X30170,tc_HOL_Obool)),hAPP(c_List_Oset(X30170),X30169)),hAPP(c_List_Oset(X30170),X30168)) != c_Orderings_Obot__class_Obot(tc_fun(X30170,tc_HOL_Obool))
        | hBOOL(hAPP(c_List_Odistinct(X30170),hAPP(hAPP(c_List_Oappend(X30170),X30169),X30168))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__append])])]) ).

fof(i_0_8491,plain,
    ! [X30517,X30518,X30519] :
      ( ~ class_Orderings_Olinorder(X30519)
      | c_Big__Operators_Olattice_OSup__fin(X30519,c_Orderings_Oord__class_Omax(X30519),hAPP(c_List_Oset(X30519),hAPP(hAPP(c_List_Olist_OCons(X30519),X30518),X30517))) = hAPP(c_List_Ofoldl(X30519,X30519,c_Orderings_Oord__class_Omax(X30519),X30518),X30517) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin__set__fold])]) ).

fof(i_0_8492,plain,
    ! [X30514,X30515,X30516] :
      ( ~ class_Orderings_Olinorder(X30516)
      | c_Big__Operators_Olattice_OInf__fin(X30516,c_Orderings_Oord__class_Omin(X30516),hAPP(c_List_Oset(X30516),hAPP(hAPP(c_List_Olist_OCons(X30516),X30515),X30514))) = hAPP(c_List_Ofoldl(X30516,X30516,c_Orderings_Oord__class_Omin(X30516),X30515),X30514) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin__set__fold])]) ).

fof(i_0_8493,plain,
    ! [X24628,X24629,X24630,X24631] :
      ( ~ class_Groups_Ocomm__monoid__add(X24631)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24630),X24629))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24631),X24628),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24630,X24629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24631),hAPP(X24628,X24630)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24631),X24628),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X24630,X24629))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__head])]) ).

fof(i_0_8494,plain,
    ! [X29001,X29002,X29003] : hAPP(hAPP(c_Nat_Ocompow(X29003,X29003),hAPP(c_Nat_OSuc,X29002)),X29001) = hAPP(c_Fun_Ocomp(X29003,X29003,X29003,X29001),hAPP(hAPP(c_Nat_Ocompow(X29003,X29003),X29002),X29001)),
    inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I2_J]) ).

fof(i_0_8495,plain,
    ! [X29522,X29523,X29524,X29525,X29526] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29526),X29525),hAPP(c_List_Oset(X29526),X29524)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29523),hAPP(X29522,X29525)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29523),c_List_Olist_Olist__size(X29526,X29522,X29524))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation])]) ).

fof(i_0_8496,plain,
    ! [X29527,X29528,X29529,X29530,X29531] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29531),X29530),hAPP(c_List_Oset(X29531),X29529)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29528),hAPP(X29527,X29530)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29528),c_List_Olist_Olist__size(X29531,X29527,X29529))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__size__estimation_H])]) ).

fof(i_0_8497,plain,
    ! [X29640,X29641] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29641),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),X29640)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),X29640),X29641)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29640))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_elem__le__listsum__nat])]) ).

fof(i_0_8498,plain,
    ! [X20980,X20981] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20981))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20981),X20980))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20980),X20981) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20980),X20981)),X20981)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__div__geq])]) ).

fof(i_0_8499,plain,
    ! [X29397,X29398,X29399] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29399)),X29398),c_List_Olists(X29399,c_Wellfounded_Oacc(X29399,X29397))))
      | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29399)),X29398),c_Wellfounded_Oacc(tc_List_Olist(X29399),c_List_Olistrel1(X29399,X29397)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lists__accD])]) ).

cnf(i_0_8500,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_5738]) ).

cnf(i_0_8501,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_5739]) ).

fof(i_0_8502,plain,
    ! [X33656,X33657,X33658] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33658),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33657),X33656)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33658),X33656))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33656),X33657))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33658),X33657)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD])]) ).

fof(i_0_8503,plain,
    ! [X33653,X33654,X33655] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33655),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33654),X33653)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33655),X33654))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33653),X33654))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33655),X33653)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diffD1])]) ).

fof(i_0_8504,plain,
    ! [X20128,X20129] :
      ( ~ class_Rings_Osemiring__1(X20129)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20129),X20128) = c_Nat_Osemiring__1__class_Oof__nat__aux(X20129,hAPP(hAPP(c_COMBC(X20129,X20129,X20129),c_Groups_Oplus__class_Oplus(X20129)),c_Groups_Oone__class_Oone(X20129)),X20128,c_Groups_Ozero__class_Ozero(X20129)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__1__class_Oof__nat__code])]) ).

fof(i_0_8505,plain,
    ! [X29203,X29204,X29205,X29206] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29206)),X29205)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29206)),X29204)))
      | X29205 != hAPP(hAPP(c_List_Olist_OCons(X29206),X29203),X29204) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_impossible__Cons])]) ).

fof(i_0_8506,plain,
    ! [X23937,X23938,X23939] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23939,tc_HOL_Obool)),X23938),X23937))
      | hBOOL(hAPP(hAPP(c_member(tc_fun(X23939,tc_HOL_Obool)),X23938),hAPP(c_Set_OPow(X23939),X23937))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_PowI])]) ).

fof(i_0_8507,plain,
    ! [X20509,X20510,X20511,X20512,X20513] : hAPP(hAPP(c_Power_Opower_Opower(X20513,X20512,X20511),X20510),hAPP(c_Nat_OSuc,X20509)) = hAPP(hAPP(X20511,X20510),hAPP(hAPP(c_Power_Opower_Opower(X20513,X20512,X20511),X20510),X20509)),
    inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__Suc]) ).

fof(i_0_8508,plain,
    ! [X23026,X23027,X23028] :
      ( ~ class_Orderings_Olinorder(X23028)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23028,tc_HOL_Obool)),X23027),X23026))
      | X23027 = c_Orderings_Obot__class_Obot(tc_fun(X23028,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23028),X23026))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23028),c_Big__Operators_Olinorder__class_OMax(X23028,X23027)),c_Big__Operators_Olinorder__class_OMax(X23028,X23026))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__mono])]) ).

fof(i_0_8509,plain,
    ! [X21793,X21794,X21795] :
      ( ~ class_Orderings_Olinorder(X21795)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21795,tc_HOL_Obool)),X21794),X21793))
      | X21794 = c_Orderings_Obot__class_Obot(tc_fun(X21795,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21795),X21793))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21795),c_Big__Operators_Olinorder__class_OMin(X21795,X21793)),c_Big__Operators_Olinorder__class_OMin(X21795,X21794))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__antimono])]) ).

fof(i_0_8510,plain,
    ! [X19437,X19438] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19438),X19437))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19438),X19437)),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),X19438),X19437)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19438),X19437)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__bin__lemma])]) ).

fof(i_0_8511,plain,
    ! [X17076,X17077,X17078] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17078),X17077),hAPP(hAPP(c_Set_Oinsert(X17078),X17076),c_Orderings_Obot__class_Obot(tc_fun(X17078,tc_HOL_Obool)))))
        | X17077 = X17076 )
      & ( X17077 != X17076
        | hBOOL(hAPP(hAPP(c_member(X17078),X17077),hAPP(hAPP(c_Set_Oinsert(X17078),X17076),c_Orderings_Obot__class_Obot(tc_fun(X17078,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__iff])]) ).

fof(i_0_8512,plain,
    ! [X17073,X17074,X17075] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17075),X17074),hAPP(hAPP(c_Set_Oinsert(X17075),X17073),c_Orderings_Obot__class_Obot(tc_fun(X17075,tc_HOL_Obool)))))
      | X17074 = X17073 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singletonE])]) ).

fof(i_0_8513,plain,
    ! [X26160,X26161,X26162,X26163,X26164] :
      ( X26164 != hAPP(X26163,X26162)
      | hBOOL(hAPP(hAPP(c_member(X26161),X26164),hAPP(c_Set_Oimage(X26160,X26161,X26163),c_Orderings_Otop__class_Otop(tc_fun(X26160,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_range__eqI])]) ).

fof(i_0_8514,plain,
    ! [X27290,X27291,X27292,X27293] :
      ( ( X27293 != c_Orderings_Obot__class_Obot(tc_fun(X27292,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27292,X27291),X27291,c_Product__Type_Osnd(X27292,X27291)),hAPP(hAPP(c_Product__Type_OSigma(X27292,X27291),X27293),hAPP(c_COMBK(tc_fun(X27291,tc_HOL_Obool),X27292),X27290))) = c_Orderings_Obot__class_Obot(tc_fun(X27291,tc_HOL_Obool)) )
      & ( X27293 = c_Orderings_Obot__class_Obot(tc_fun(X27292,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27292,X27291),X27291,c_Product__Type_Osnd(X27292,X27291)),hAPP(hAPP(c_Product__Type_OSigma(X27292,X27291),X27293),hAPP(c_COMBK(tc_fun(X27291,tc_HOL_Obool),X27292),X27290))) = X27290 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__image__times])]) ).

fof(i_0_8515,plain,
    ! [X27286,X27287,X27288,X27289] :
      ( ( X27289 != c_Orderings_Obot__class_Obot(tc_fun(X27288,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27287,X27288),X27287,c_Product__Type_Ofst(X27287,X27288)),hAPP(hAPP(c_Product__Type_OSigma(X27287,X27288),X27286),hAPP(c_COMBK(tc_fun(X27288,tc_HOL_Obool),X27287),X27289))) = c_Orderings_Obot__class_Obot(tc_fun(X27287,tc_HOL_Obool)) )
      & ( X27289 = c_Orderings_Obot__class_Obot(tc_fun(X27288,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(tc_prod(X27287,X27288),X27287,c_Product__Type_Ofst(X27287,X27288)),hAPP(hAPP(c_Product__Type_OSigma(X27287,X27288),X27286),hAPP(c_COMBK(tc_fun(X27288,tc_HOL_Obool),X27287),X27289))) = X27286 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__image__times])]) ).

fof(i_0_8516,plain,
    ! [X17007,X17008,X17009,X17010,X17011] :
      ( ( X17010 = X17007
        | X17010 = X17008
        | hAPP(hAPP(c_Set_Oinsert(X17011),X17010),hAPP(hAPP(c_Set_Oinsert(X17011),X17009),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17011),X17008),hAPP(hAPP(c_Set_Oinsert(X17011),X17007),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) )
      & ( X17009 = X17008
        | X17010 = X17008
        | hAPP(hAPP(c_Set_Oinsert(X17011),X17010),hAPP(hAPP(c_Set_Oinsert(X17011),X17009),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17011),X17008),hAPP(hAPP(c_Set_Oinsert(X17011),X17007),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) )
      & ( X17010 = X17007
        | X17009 = X17007
        | hAPP(hAPP(c_Set_Oinsert(X17011),X17010),hAPP(hAPP(c_Set_Oinsert(X17011),X17009),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17011),X17008),hAPP(hAPP(c_Set_Oinsert(X17011),X17007),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) )
      & ( X17009 = X17008
        | X17009 = X17007
        | hAPP(hAPP(c_Set_Oinsert(X17011),X17010),hAPP(hAPP(c_Set_Oinsert(X17011),X17009),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X17011),X17008),hAPP(hAPP(c_Set_Oinsert(X17011),X17007),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) )
      & ( X17010 != X17008
        | X17009 != X17007
        | hAPP(hAPP(c_Set_Oinsert(X17011),X17010),hAPP(hAPP(c_Set_Oinsert(X17011),X17009),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X17011),X17008),hAPP(hAPP(c_Set_Oinsert(X17011),X17007),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) )
      & ( X17010 != X17007
        | X17009 != X17008
        | hAPP(hAPP(c_Set_Oinsert(X17011),X17010),hAPP(hAPP(c_Set_Oinsert(X17011),X17009),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X17011),X17008),hAPP(hAPP(c_Set_Oinsert(X17011),X17007),c_Orderings_Obot__class_Obot(tc_fun(X17011,tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_doubleton__eq__iff])])]) ).

fof(i_0_8517,plain,
    ! [X33923,X33924,X33925,X33926,X33927] :
      ( ~ class_Rings_Ocomm__semiring__1(X33927)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X33926),X33925))
      | ~ hBOOL(hAPP(hAPP(c_member(X33926),X33924),X33925))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33927),hAPP(X33923,X33924)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X33926,X33927),X33923),X33925))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__setprod])]) ).

fof(i_0_8518,plain,
    ! [X29739,X29740,X29741,X29742,X29743] :
      ( ( X29743 != X29740
        | hAPP(hAPP(c_List_Onth(X29742),hAPP(hAPP(c_List_Olist__update(X29742,X29741),X29743),X29739)),X29740) = X29739
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29743),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29742)),X29741))) )
      & ( X29743 = X29740
        | hAPP(hAPP(c_List_Onth(X29742),hAPP(hAPP(c_List_Olist__update(X29742,X29741),X29743),X29739)),X29740) = hAPP(hAPP(c_List_Onth(X29742),X29741),X29740)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29743),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29742)),X29741))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update])])]) ).

fof(i_0_8519,plain,
    ! [X17964,X17965,X17966] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17966),X17965)),X17964))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17966),X17964)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__lessD1])]) ).

fof(i_0_8520,plain,
    ! [X18008,X18009,X18010] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18010),X18008))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18010),X18009)),X18008)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18009),X18008))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18010),X18009)),X18008)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5740])])]) ).

fof(i_0_8521,plain,
    ! [X18011,X18012,X18013] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18013),X18012)),X18011))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18013),X18011)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD1])]) ).

fof(i_0_8522,plain,
    ! [X18014,X18015,X18016] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18016),X18015)),X18014))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18015),X18014)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__leD2])]) ).

fof(i_0_8523,plain,
    ! [X18852,X18853] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18853))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18853),hAPP(c_Nat_OSuc,X18852))),X18853)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__less])]) ).

fof(i_0_8524,plain,
    ! [X24008,X24009,X24010,X24011] :
      ( ~ class_Orderings_Olinorder(X24011)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24011),X24010),X24009))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24011),X24009),X24008))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24011,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24011,X24010),X24009)),c_SetInterval_Oord__class_OatLeastAtMost(X24011,X24009,X24008)) = c_SetInterval_Oord__class_OatLeastAtMost(X24011,X24010,X24008) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I21_J])]) ).

fof(i_0_8525,plain,
    ! [X24169,X24170,X24171] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24171),X24170))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24171),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24170),X24169)) = 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,X24171),X24170)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24170),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24170),X24169))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__add__Un])]) ).

fof(i_0_8526,plain,
    ! [X17411,X17412,X17413] : hAPP(hAPP(c_Set_Oinsert(X17413),X17412),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17413,tc_HOL_Obool)),X17411),hAPP(hAPP(c_Set_Oinsert(X17413),X17412),c_Orderings_Obot__class_Obot(tc_fun(X17413,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(X17413),X17412),X17411),
    inference(variable_rename,[status(thm)],[fact_insert__Diff__single]) ).

cnf(i_0_8527,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_5741]) ).

cnf(i_0_8528,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5742]) ).

cnf(i_0_8529,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_5743]) ).

cnf(i_0_8530,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_5744]) ).

cnf(i_0_8531,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_5745]) ).

cnf(i_0_8532,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_5567]) ).

fof(i_0_8533,plain,
    ! [X17104,X17105,X17106] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17106),X17105))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X17106),X17105)),hAPP(c_Finite__Set_Ocard(X17106),hAPP(hAPP(c_Set_Oinsert(X17106),X17104),X17105)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__insert__le])]) ).

fof(i_0_8534,plain,
    ! [X20023,X20024,X20025] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20025)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20024)),X20023)) = 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),X20025),X20024))),X20023),
    inference(variable_rename,[status(thm)],[fact_zadd__int__left]) ).

fof(i_0_8535,plain,
    ! [X27009,X27010,X27011,X27013] :
      ( ( hBOOL(hAPP(hAPP(c_member(X27011),esk246_3(X27009,X27010,X27011)),X27009))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27011),X27010),c_Complete__Lattice_OSup__class_OSup(X27011,X27009)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X27011)
        | ~ class_Orderings_Olinorder(X27011) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27011),X27010),esk246_3(X27009,X27010,X27011)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27011),X27010),c_Complete__Lattice_OSup__class_OSup(X27011,X27009)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X27011)
        | ~ class_Orderings_Olinorder(X27011) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X27011),X27013),X27009))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27011),X27010),X27013))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X27011),X27010),c_Complete__Lattice_OSup__class_OSup(X27011,X27009)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X27011)
        | ~ class_Orderings_Olinorder(X27011) ) ),
    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_8536,plain,
    ! [X21676] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X21676))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21676)))
        | ~ c_Nat__Transfer_Onat__set(X21676) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21676)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X21676))
        | ~ c_Nat__Transfer_Onat__set(X21676) ) ),
    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_8537,plain,
    hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_5746]) ).

fof(i_0_8538,plain,
    ! [X20940,X20941] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20941)),hAPP(c_Int_Onat,X20940)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20941),X20940))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20940))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20941)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20941),X20940))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20941)),hAPP(c_Int_Onat,X20940)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20940))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20941)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I2_J])])]) ).

fof(i_0_8539,plain,
    ! [X20881,X20882] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X20882)),hAPP(c_Int_Onat,X20881)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20882),X20881))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20881))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20882)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20882),X20881))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X20882)),hAPP(c_Int_Onat,X20881)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20881))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20882)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I3_J])])]) ).

fof(i_0_8540,plain,
    ! [X23466,X23467,X23468] :
      ( ~ class_Orderings_Olinorder(X23468)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23468),X23467),X23466))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23468,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X23468,X23467,X23466)),hAPP(hAPP(c_Set_Oinsert(X23468),X23466),c_Orderings_Obot__class_Obot(tc_fun(X23468,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23468,X23467,X23466) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I4_J])]) ).

fof(i_0_8541,plain,
    ! [X17407,X17408,X17409,X17410] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17410),X17409),X17408))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17410,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17410),X17409),X17407)),X17408) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17410,tc_HOL_Obool)),X17407),X17408) )
      & ( hBOOL(hAPP(hAPP(c_member(X17410),X17409),X17408))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17410,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17410),X17409),X17407)),X17408) = hAPP(hAPP(c_Set_Oinsert(X17410),X17409),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17410,tc_HOL_Obool)),X17407),X17408)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5747])]) ).

fof(i_0_8542,plain,
    ! [X28446,X28447,X28448] :
      ( ( hBOOL(hAPP(hAPP(c_member(X28448),esk326_3(X28446,X28447,X28448)),X28447))
        | ~ hBOOL(hAPP(hAPP(c_member(X28448),X28446),X28447))
        | c_Big__Operators_Olinorder__class_OMin(X28448,X28447) = X28446
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28448),X28447))
        | ~ class_Orderings_Olinorder(X28448) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X28448),X28446),esk326_3(X28446,X28447,X28448)))
        | ~ hBOOL(hAPP(hAPP(c_member(X28448),X28446),X28447))
        | c_Big__Operators_Olinorder__class_OMin(X28448,X28447) = X28446
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X28448),X28447))
        | ~ class_Orderings_Olinorder(X28448) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__eqI])])])]) ).

fof(i_0_8543,plain,
    ! [X30815,X30816,X30817,X30818,X30819] : hAPP(hAPP(c_List_Omap(X30819,X30818),X30817),hAPP(hAPP(c_List_Oappend(X30819),X30816),X30815)) = hAPP(hAPP(c_List_Oappend(X30818),hAPP(hAPP(c_List_Omap(X30819,X30818),X30817),X30816)),hAPP(hAPP(c_List_Omap(X30819,X30818),X30817),X30815)),
    inference(variable_rename,[status(thm)],[fact_map__append]) ).

fof(i_0_8544,plain,
    ! [X27101,X27102] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X27102,tc_HOL_Obool)),esk249_2(X27101,X27102)),X27101))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27102),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27102,tc_HOL_Obool),X27101)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27102,tc_HOL_Obool)),X27101)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27102),esk249_2(X27101,X27102)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X27102),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27102,tc_HOL_Obool),X27101)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27102,tc_HOL_Obool)),X27101)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Union])])])]) ).

fof(i_0_8545,plain,
    ! [X33796,X33797,X33798,X33799] :
      ( ~ class_Divides_Osemiring__div(X33799)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33799),X33798),X33797))
      | hAPP(hAPP(c_Power_Opower__class_Opower(X33799),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33799),X33797),X33798)),X33796) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33799),hAPP(hAPP(c_Power_Opower__class_Opower(X33799),X33797),X33796)),hAPP(hAPP(c_Power_Opower__class_Opower(X33799),X33798),X33796)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__power])]) ).

fof(i_0_8546,plain,
    ! [X20490,X20491] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20491))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X20490))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20491),X20490)),X20491)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__div__less__self])]) ).

fof(i_0_8547,plain,
    ! [X20873,X20874] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X20874))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20873))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20873),X20874)),X20873)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less__dividend])]) ).

fof(i_0_8548,plain,
    ! [X18784,X18785] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18785))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18784))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18784),X18785)),X18784)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__less])]) ).

cnf(i_0_8549,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_5748]) ).

cnf(i_0_8550,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_5749]) ).

fof(i_0_8551,plain,
    ! [X25160,X25161,X25162,X25163] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25163,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25163),X25162),X25161)),hAPP(hAPP(c_Set_Oinsert(X25163),X25162),X25160)) = hAPP(hAPP(c_Set_Oinsert(X25163),X25162),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25163,tc_HOL_Obool)),X25161),X25160)),
    inference(variable_rename,[status(thm)],[fact_insert__inter__insert]) ).

fof(i_0_8552,plain,
    ! [X20405,X20406] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20406),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)),X20405))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20406),X20405)),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_8553,plain,
    ! [X20471,X20472] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20472))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20471),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),X20472),X20471)),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_8554,plain,
    ! [X20477,X20478] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20478),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)),X20477))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20478),X20477)),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_8555,plain,
    ! [X33772,X33773,X33774,X33775] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33775),X33774),c_Divides_Odiv__class_Omod(X33775,X33772,X33773)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33775),X33774),X33772))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33775),X33774),X33773))
        | ~ class_Divides_Osemiring__div(X33775) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33775),X33774),X33772))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33775),X33774),c_Divides_Odiv__class_Omod(X33775,X33772,X33773)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33775),X33774),X33773))
        | ~ class_Divides_Osemiring__div(X33775) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__iff])])]) ).

fof(i_0_8556,plain,
    ! [X33760,X33761,X33762,X33763] :
      ( ~ class_Divides_Osemiring__div(X33763)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33763),X33762),c_Divides_Odiv__class_Omod(X33763,X33761,X33760)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33763),X33762),X33760))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33763),X33762),X33761)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod__imp__dvd])]) ).

fof(i_0_8557,plain,
    ! [X20860,X20861,X20862] :
      ( ~ class_Divides_Osemiring__div(X20862)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20862),c_Divides_Odiv__class_Omod(X20862,X20861,X20860)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20862),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20862),X20861),X20860)),X20860)) = X20861 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__div__class_Omod__div__equality_H])]) ).

fof(i_0_8558,plain,
    ! [X22824,X22825,X22826] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),X22825),c_Groups_Ozero__class_Ozero(X22826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),X22825))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22826),X22825),X22824)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22826) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),X22824),c_Groups_Ozero__class_Ozero(X22826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),X22825))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22826),X22825),X22824)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22826) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),X22825),c_Groups_Ozero__class_Ozero(X22826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),X22824))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22826),X22825),X22824)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22826) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),X22824),c_Groups_Ozero__class_Ozero(X22826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),X22824))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22826),X22825),X22824)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22826) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),X22825))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),X22824))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22826),X22825),X22824)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22826) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),X22825),c_Groups_Ozero__class_Ozero(X22826)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),X22824),c_Groups_Ozero__class_Ozero(X22826)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22826),c_Groups_Ozero__class_Ozero(X22826)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22826),X22825),X22824)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22826) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__divide__iff])])]) ).

fof(i_0_8559,plain,
    ! [X22787,X22788,X22789] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),X22788),c_Groups_Ozero__class_Ozero(X22789)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),X22788))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22789),X22788),X22787)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22789) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),X22787),c_Groups_Ozero__class_Ozero(X22789)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),X22788))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22789),X22788),X22787)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22789) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),X22788),c_Groups_Ozero__class_Ozero(X22789)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),X22787))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22789),X22788),X22787)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22789) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),X22787),c_Groups_Ozero__class_Ozero(X22789)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),X22787))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22789),X22788),X22787)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22789) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),X22788))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),X22787))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22789),X22788),X22787)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22789) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),X22788),c_Groups_Ozero__class_Ozero(X22789)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),X22787),c_Groups_Ozero__class_Ozero(X22789)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22789),c_Groups_Ozero__class_Ozero(X22789)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22789),X22788),X22787)))
        | ~ class_Fields_Olinordered__field__inverse__zero(X22789) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__divide__iff])])]) ).

fof(i_0_8560,plain,
    ! [X18265,X18266,X18267] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),X18266),c_Groups_Ozero__class_Ozero(X18267)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),X18266))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18267),X18266),X18265)))
        | ~ class_Rings_Olinordered__ring__strict(X18267) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),X18265),c_Groups_Ozero__class_Ozero(X18267)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),X18266))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18267),X18266),X18265)))
        | ~ class_Rings_Olinordered__ring__strict(X18267) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),X18266),c_Groups_Ozero__class_Ozero(X18267)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),X18265))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18267),X18266),X18265)))
        | ~ class_Rings_Olinordered__ring__strict(X18267) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),X18265),c_Groups_Ozero__class_Ozero(X18267)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),X18265))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18267),X18266),X18265)))
        | ~ class_Rings_Olinordered__ring__strict(X18267) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),X18266))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),X18265))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18267),X18266),X18265)))
        | ~ class_Rings_Olinordered__ring__strict(X18267) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),X18266),c_Groups_Ozero__class_Ozero(X18267)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),X18265),c_Groups_Ozero__class_Ozero(X18267)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18267),c_Groups_Ozero__class_Ozero(X18267)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18267),X18266),X18265)))
        | ~ class_Rings_Olinordered__ring__strict(X18267) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__mult__iff])])]) ).

fof(i_0_8561,plain,
    ! [X32778,X32779,X32780,X32781,X32782,X32783,X32784] :
      ( ( ~ c_List_Oall__interval__int(X32780,X32779,X32778)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X32781),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X32779,X32778)))
        | hBOOL(hAPP(X32780,X32781)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk497_3(X32782,X32783,X32784)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X32783,X32782)))
        | c_List_Oall__interval__int(X32784,X32783,X32782) )
      & ( ~ hBOOL(hAPP(X32784,esk497_3(X32782,X32783,X32784)))
        | c_List_Oall__interval__int(X32784,X32783,X32782) ) ),
    inference(distribute,[status(thm)],[inference(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_8562,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_5693]) ).

cnf(i_0_8563,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_5694]) ).

fof(i_0_8564,plain,
    ! [X19491,X19492,X19493] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19493),X19492))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19493),X19491)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19492),X19491))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__strict__right__mono])]) ).

fof(i_0_8565,plain,
    ! [X17975,X17976,X17977] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17977),X17976))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17977),X17975)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17976),X17975))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__less__mono1])]) ).

cnf(i_0_8566,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_5695]) ).

cnf(i_0_8567,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_5696]) ).

fof(i_0_8568,plain,
    ! [X19475,X19476,X19477] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19477),X19476))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19475),X19477)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19475),X19476))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zadd__left__mono])]) ).

fof(i_0_8569,plain,
    ! [X20727,X20728,X20729] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20729),X20728))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20729),X20727)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20728),X20727))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__le__mono])]) ).

fof(i_0_8570,plain,
    ! [X18542,X18543,X18544] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18544),X18543))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18544),X18542)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18543),X18542))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono1])]) ).

fof(i_0_8571,plain,
    ! [X18545,X18546,X18547] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18547),X18546))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18545),X18547)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18545),X18546))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__le__mono2])]) ).

fof(i_0_8572,plain,
    ! [X18021,X18022,X18023] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18023),X18022))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18023),X18021)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18022),X18021))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__le__mono1])]) ).

fof(i_0_8573,plain,
    ! [X17270,X17271,X17272] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17272),X17271))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17272),X17270)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17271),X17270))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono])]) ).

fof(i_0_8574,plain,
    ! [X17267,X17268,X17269] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17269),X17268))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17267),X17268)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17267),X17269))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__le__mono2])]) ).

fof(i_0_8575,plain,
    ! [X30505,X30506,X30507] :
      ( ~ class_Lattices_Olattice(X30507)
      | c_Big__Operators_Olattice__class_OInf__fin(X30507,hAPP(c_List_Oset(X30507),hAPP(hAPP(c_List_Olist_OCons(X30507),X30506),X30505))) = hAPP(c_List_Ofoldl(X30507,X30507,c_Lattices_Osemilattice__inf__class_Oinf(X30507),X30506),X30505) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__set__fold])]) ).

fof(i_0_8576,plain,
    ! [X30502,X30503,X30504] :
      ( ~ class_Lattices_Olattice(X30504)
      | c_Big__Operators_Olattice__class_OSup__fin(X30504,hAPP(c_List_Oset(X30504),hAPP(hAPP(c_List_Olist_OCons(X30504),X30503),X30502))) = hAPP(c_List_Ofoldl(X30504,X30504,c_Lattices_Osemilattice__sup__class_Osup(X30504),X30503),X30502) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__set__fold])]) ).

fof(i_0_8577,plain,
    ! [X30511,X30512,X30513] :
      ( ~ class_Orderings_Olinorder(X30513)
      | c_Big__Operators_Olinorder__class_OMax(X30513,hAPP(c_List_Oset(X30513),hAPP(hAPP(c_List_Olist_OCons(X30513),X30512),X30511))) = hAPP(c_List_Ofoldl(X30513,X30513,c_Orderings_Oord__class_Omax(X30513),X30512),X30511) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__fin__set__fold])]) ).

fof(i_0_8578,plain,
    ! [X30508,X30509,X30510] :
      ( ~ class_Orderings_Olinorder(X30510)
      | c_Big__Operators_Olinorder__class_OMin(X30510,hAPP(c_List_Oset(X30510),hAPP(hAPP(c_List_Olist_OCons(X30510),X30509),X30508))) = hAPP(c_List_Ofoldl(X30510,X30510,c_Orderings_Oord__class_Omin(X30510),X30509),X30508) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__fin__set__fold])]) ).

fof(i_0_8579,plain,
    ! [X18144,X18145,X18146] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18146),X18145))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18145),X18146))),X18144) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18145)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18146),X18144)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq2])]) ).

fof(i_0_8580,plain,
    ! [X20857,X20858,X20859] :
      ( ~ class_Divides_Osemiring__div(X20859)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20859),X20858),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20859),X20857),X20858))),c_Divides_Odiv__class_Omod(X20859,X20857,X20858)) = X20857 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__equality2])]) ).

cnf(i_0_8581,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_5750]) ).

fof(i_0_8582,plain,
    ! [X29709,X29710,X29711,X29712,X29713] : hAPP(hAPP(c_List_Olist__update(X29713,hAPP(hAPP(c_List_Olist_OCons(X29713),X29712),X29711)),hAPP(c_Nat_OSuc,X29710)),X29709) = hAPP(hAPP(c_List_Olist_OCons(X29713),X29712),hAPP(hAPP(c_List_Olist__update(X29713,X29711),X29710),X29709)),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I3_J]) ).

fof(i_0_8583,plain,
    ! [X19556,X19557,X19558,X19559,X19560,X19561] :
      ( ( X19559 = X19557
        | c_Nitpick_Opair__box_OPairBox(X19561,X19560,X19559,X19558) != c_Nitpick_Opair__box_OPairBox(X19561,X19560,X19557,X19556) )
      & ( X19558 = X19556
        | c_Nitpick_Opair__box_OPairBox(X19561,X19560,X19559,X19558) != c_Nitpick_Opair__box_OPairBox(X19561,X19560,X19557,X19556) )
      & ( X19559 != X19557
        | X19558 != X19556
        | c_Nitpick_Opair__box_OPairBox(X19561,X19560,X19559,X19558) = c_Nitpick_Opair__box_OPairBox(X19561,X19560,X19557,X19556) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pair__box_Oinject])])]) ).

fof(i_0_8584,plain,
    ! [X26770,X26771,X26772,X26773,X26774,X26775] :
      ( hAPP(X26775,X26774) != X26773
      | ~ hBOOL(hAPP(hAPP(c_member(X26772),X26773),X26771))
      | hBOOL(hAPP(hAPP(c_member(X26770),X26774),hAPP(c_Set_Ovimage(X26770,X26772,X26775),X26771))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_vimageI])]) ).

fof(i_0_8585,plain,
    ! [X16852,X16853,X16854,X16855,X16856,X16857] :
      ( X16857 != hAPP(X16856,X16855)
      | ~ hBOOL(hAPP(hAPP(c_member(X16854),X16855),X16853))
      | hBOOL(hAPP(hAPP(c_member(X16852),X16857),hAPP(c_Set_Oimage(X16854,X16852,X16856),X16853))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__eqI])]) ).

fof(i_0_8586,plain,
    ! [X16980,X16981,X16982,X16983,X16984,X16985] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X16985),X16984),X16983))
      | X16982 != hAPP(X16981,X16984)
      | hBOOL(hAPP(hAPP(c_member(X16980),X16982),hAPP(c_Set_Oimage(X16985,X16980,X16981),X16983))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__image__eqI])]) ).

fof(i_0_8587,plain,
    ! [X18378,X18379,X18380,X18381,X18382,X18383] :
      ( ( hAPP(X18381,X18379) != hAPP(X18381,X18378)
        | X18379 = X18378
        | ~ hBOOL(hAPP(hAPP(c_member(X18383),X18378),X18380))
        | ~ hBOOL(hAPP(hAPP(c_member(X18383),X18379),X18380))
        | ~ c_Fun_Oinj__on(X18383,X18382,X18381,X18380) )
      & ( X18379 != X18378
        | hAPP(X18381,X18379) = hAPP(X18381,X18378)
        | ~ hBOOL(hAPP(hAPP(c_member(X18383),X18378),X18380))
        | ~ hBOOL(hAPP(hAPP(c_member(X18383),X18379),X18380))
        | ~ c_Fun_Oinj__on(X18383,X18382,X18381,X18380) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff])])]) ).

fof(i_0_8588,plain,
    ! [X18384,X18385,X18386,X18387,X18388,X18389] :
      ( ~ c_Fun_Oinj__on(X18389,X18388,X18387,X18386)
      | hAPP(X18387,X18385) != hAPP(X18387,X18384)
      | ~ hBOOL(hAPP(hAPP(c_member(X18389),X18385),X18386))
      | ~ hBOOL(hAPP(hAPP(c_member(X18389),X18384),X18386))
      | X18385 = X18384 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__onD])]) ).

fof(i_0_8589,plain,
    ! [X18372,X18373,X18374,X18375,X18376,X18377] :
      ( ~ c_Fun_Oinj__on(X18377,X18376,X18375,X18374)
      | X18373 = X18372
      | ~ hBOOL(hAPP(hAPP(c_member(X18377),X18373),X18374))
      | ~ hBOOL(hAPP(hAPP(c_member(X18377),X18372),X18374))
      | hAPP(X18375,X18373) != hAPP(X18375,X18372) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__contraD])]) ).

fof(i_0_8590,plain,
    ! [X20927,X20928] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20927),X20928))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20927),X20928) = 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)),X20928)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20927),X20928))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20927),X20928) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20927),X20928)),X20928))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20928)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5751])])]) ).

fof(i_0_8591,plain,
    ! [X20925,X20926] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20926))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20925),X20926))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20925),X20926) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20925),X20926)),X20926)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5752])]) ).

fof(i_0_8592,plain,
    ! [X20466,X20467] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20466),X20467))
        | ~ 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),X20467),X20466)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20467)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20466))
        | ~ 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),X20467),X20466)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20467)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20466),X20467))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20466))
        | 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),X20467),X20466)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20467)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonneg1__imp__zdiv__pos__iff])])]) ).

fof(i_0_8593,plain,
    ! [X32231,X32232,X32233,X32235,X32236,X32237,X32238] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk466_3(X32231,X32232,X32233)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32233)),X32231)))
        | ~ c_List_Olist__ex(X32233,X32232,X32231) )
      & ( hBOOL(hAPP(X32232,hAPP(hAPP(c_List_Onth(X32233),X32231),esk466_3(X32231,X32232,X32233))))
        | ~ c_List_Olist__ex(X32233,X32232,X32231) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32238),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32237)),X32235)))
        | ~ hBOOL(hAPP(X32236,hAPP(hAPP(c_List_Onth(X32237),X32235),X32238)))
        | c_List_Olist__ex(X32237,X32236,X32235) ) ),
    inference(distribute,[status(thm)],[inference(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_8594,plain,
    ! [X17285,X17286,X17287,X17288,X17289] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17289,X17288,X17287)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17289),X17286))
      | X17285 = c_Orderings_Obot__class_Obot(tc_fun(X17289,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17289,tc_HOL_Obool)),X17285),X17286))
      | hAPP(hAPP(X17288,hAPP(X17287,X17285)),hAPP(X17287,X17286)) = hAPP(X17287,X17286) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Osubset__idem])]) ).

fof(i_0_8595,plain,
    ! [X33063,X33064,X33066,X33067,X33068,X33069,X33070,X33071,X33074] :
      ( ( hBOOL(hAPP(hAPP(X33063,esk516_1(X33063)),esk516_1(X33063)))
        | ~ c_Equiv__Relations_Opart__equivp(X33064,X33063) )
      & ( hBOOL(hAPP(hAPP(X33063,X33066),X33066))
        | ~ hBOOL(hAPP(hAPP(X33063,X33066),X33067))
        | ~ c_Equiv__Relations_Opart__equivp(X33064,X33063) )
      & ( hBOOL(hAPP(hAPP(X33063,X33067),X33067))
        | ~ hBOOL(hAPP(hAPP(X33063,X33066),X33067))
        | ~ c_Equiv__Relations_Opart__equivp(X33064,X33063) )
      & ( hAPP(X33063,X33066) = hAPP(X33063,X33067)
        | ~ hBOOL(hAPP(hAPP(X33063,X33066),X33067))
        | ~ c_Equiv__Relations_Opart__equivp(X33064,X33063) )
      & ( ~ hBOOL(hAPP(hAPP(X33063,X33068),X33068))
        | ~ hBOOL(hAPP(hAPP(X33063,X33069),X33069))
        | hAPP(X33063,X33068) != hAPP(X33063,X33069)
        | hBOOL(hAPP(hAPP(X33063,X33068),X33069))
        | ~ c_Equiv__Relations_Opart__equivp(X33064,X33063) )
      & ( ~ hBOOL(hAPP(hAPP(X33070,esk517_1(X33070)),esk518_1(X33070)))
        | ~ hBOOL(hAPP(hAPP(X33070,esk517_1(X33070)),esk517_1(X33070)))
        | ~ hBOOL(hAPP(hAPP(X33070,esk518_1(X33070)),esk518_1(X33070)))
        | hAPP(X33070,esk517_1(X33070)) != hAPP(X33070,esk518_1(X33070))
        | ~ hBOOL(hAPP(hAPP(X33070,X33071),X33071))
        | c_Equiv__Relations_Opart__equivp(X33074,X33070) )
      & ( hBOOL(hAPP(hAPP(X33070,esk517_1(X33070)),esk517_1(X33070)))
        | hBOOL(hAPP(hAPP(X33070,esk517_1(X33070)),esk518_1(X33070)))
        | ~ hBOOL(hAPP(hAPP(X33070,X33071),X33071))
        | c_Equiv__Relations_Opart__equivp(X33074,X33070) )
      & ( hBOOL(hAPP(hAPP(X33070,esk518_1(X33070)),esk518_1(X33070)))
        | hBOOL(hAPP(hAPP(X33070,esk517_1(X33070)),esk518_1(X33070)))
        | ~ hBOOL(hAPP(hAPP(X33070,X33071),X33071))
        | c_Equiv__Relations_Opart__equivp(X33074,X33070) )
      & ( hAPP(X33070,esk517_1(X33070)) = hAPP(X33070,esk518_1(X33070))
        | hBOOL(hAPP(hAPP(X33070,esk517_1(X33070)),esk518_1(X33070)))
        | ~ hBOOL(hAPP(hAPP(X33070,X33071),X33071))
        | c_Equiv__Relations_Opart__equivp(X33074,X33070) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__def])])])])])]) ).

fof(i_0_8596,plain,
    ! [X28867,X28868,X28869] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X28869,X28869,X28869),hAPP(c_Relation_Oconverse(X28869,X28869),X28868)),X28868) != X28868
      | hAPP(c_Relation_ODomain(X28869,X28869),X28868) != X28867
      | c_Equiv__Relations_Oequiv(X28869,X28867,X28868) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comp__equivI])]) ).

fof(i_0_8597,plain,
    ! [X32545,X32546,X32547,X32548,X32549,X32550] : hAPP(hAPP(c_List_Ozip(X32550,X32549),c_List_Oreplicate(X32550,X32548,X32547)),c_List_Oreplicate(X32549,X32546,X32545)) = c_List_Oreplicate(tc_prod(X32550,X32549),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X32548),X32546),hAPP(hAPP(c_Product__Type_OPair(X32550,X32549),X32547),X32545)),
    inference(variable_rename,[status(thm)],[fact_zip__replicate]) ).

fof(i_0_8598,plain,
    ! [X17239,X17240,X17241,X17242,X17243] :
      ( ~ class_Orderings_Oord(X17243)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17242,X17243)),X17241),X17240))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17243),hAPP(X17241,X17239)),hAPP(X17240,X17239))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funE])]) ).

fof(i_0_8599,plain,
    ! [X17234,X17235,X17236,X17237,X17238] :
      ( ~ class_Orderings_Oord(X17238)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17237,X17238)),X17236),X17235))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17238),hAPP(X17236,X17234)),hAPP(X17235,X17234))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__funD])]) ).

fof(i_0_8600,plain,
    ! [X30790,X30791,X30792,X30793,X30794] :
      ( hAPP(hAPP(c_List_Omap(X30794,X30793),X30792),X30791) != hAPP(hAPP(c_List_Omap(X30794,X30793),X30792),X30790)
      | ~ c_Fun_Oinj__on(X30794,X30793,X30792,c_Orderings_Otop__class_Otop(tc_fun(X30794,tc_HOL_Obool)))
      | X30791 = X30790 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__injective])]) ).

fof(i_0_8601,plain,
    ! [X30785,X30786,X30787,X30788,X30789] :
      ( ( hAPP(hAPP(c_List_Omap(X30789,X30788),X30787),X30786) != hAPP(hAPP(c_List_Omap(X30789,X30788),X30787),X30785)
        | X30786 = X30785
        | ~ c_Fun_Oinj__on(X30789,X30788,X30787,c_Orderings_Otop__class_Otop(tc_fun(X30789,tc_HOL_Obool))) )
      & ( X30786 != X30785
        | hAPP(hAPP(c_List_Omap(X30789,X30788),X30787),X30786) = hAPP(hAPP(c_List_Omap(X30789,X30788),X30787),X30785)
        | ~ c_Fun_Oinj__on(X30789,X30788,X30787,c_Orderings_Otop__class_Otop(tc_fun(X30789,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_8602,plain,
    ! [X29731,X29732,X29733,X29734] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29734),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29733)),X29732)))
      | hAPP(hAPP(c_List_Onth(X29733),hAPP(hAPP(c_List_Olist__update(X29733,X29732),X29734),X29731)),X29734) = X29731 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__eq])]) ).

fof(i_0_8603,plain,
    ! [X25436,X25437,X25438] :
      ( ~ class_Groups_Ocomm__monoid__add(X25438)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X25438),X25437),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25436))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25438),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X25438),X25437),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25436))),hAPP(X25437,hAPP(c_Nat_OSuc,X25436))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__atMost__Suc])]) ).

fof(i_0_8604,plain,
    ! [X33020,X33021,X33022] :
      ( ~ c_Relation_Osym(X33022,X33021)
      | ~ c_Relation_Osym(X33022,X33020)
      | c_Relation_Osym(X33022,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X33022,X33022),tc_HOL_Obool)),X33021),X33020)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__Int])]) ).

fof(i_0_8605,plain,
    ! [X33030,X33031,X33032] :
      ( ~ c_Relation_Osym(X33032,X33031)
      | ~ c_Relation_Osym(X33032,X33030)
      | c_Relation_Osym(X33032,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X33032,X33032),tc_HOL_Obool)),X33031),X33030)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__Un])]) ).

fof(i_0_8606,plain,
    ! [X32856,X32857,X32858] :
      ( ~ c_Relation_Otrans(X32858,X32857)
      | ~ c_Relation_Otrans(X32858,X32856)
      | c_Relation_Otrans(X32858,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X32858,X32858),tc_HOL_Obool)),X32857),X32856)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__Int])]) ).

fof(i_0_8607,plain,
    ! [X24114,X24115,X24116,X24117] :
      ( ~ class_Orderings_Olinorder(X24117)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24117),X24116),X24115))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24117),X24115),X24114))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24117,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24117,X24116),X24115)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24117,X24115),X24114)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24117,X24116),X24114) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I17_J])]) ).

fof(i_0_8608,plain,
    ! [X29753,X29754] : c_List_Obutlast(X29754,X29753) = hAPP(hAPP(c_List_Otake(X29754),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29754)),X29753)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29753),
    inference(variable_rename,[status(thm)],[fact_butlast__conv__take]) ).

fof(i_0_8609,plain,
    ! [X25399,X25400,X25401] :
      ( ~ class_Lattices_Osemilattice__inf(X25401)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25401),X25400))
      | ~ hBOOL(hAPP(hAPP(c_member(X25401),X25399),X25400))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25401),hAPP(c_Finite__Set_Ofold1(X25401,c_Lattices_Osemilattice__inf__class_Oinf(X25401)),X25400)),X25399)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__belowI])]) ).

fof(i_0_8610,plain,
    ! [X21701,X21702,X21703] :
      ( ~ class_Orderings_Olinorder(X21703)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21703),X21702))
      | ~ hBOOL(hAPP(hAPP(c_member(X21703),X21701),X21702))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21703),hAPP(c_Finite__Set_Ofold1(X21703,c_Orderings_Oord__class_Omin(X21703)),X21702)),X21701)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofold1__belowI])]) ).

fof(i_0_8611,plain,
    ! [X21394] : ~ 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,X21394))))),
    inference(variable_rename,[status(thm)],[i_0_5753]) ).

fof(i_0_8612,plain,
    ! [X32227,X32228,X32229] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32229),esk465_3(X32227,X32228,X32229)),hAPP(c_List_Oset(X32229),X32228)))
        | ~ c_List_Olinorder__class_Osorted(X32229,X32228)
        | c_List_Olinorder__class_Osorted(X32229,hAPP(hAPP(c_List_Olist_OCons(X32229),X32227),X32228))
        | ~ class_Orderings_Olinorder(X32229) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X32229),X32227),esk465_3(X32227,X32228,X32229)))
        | ~ c_List_Olinorder__class_Osorted(X32229,X32228)
        | c_List_Olinorder__class_Osorted(X32229,hAPP(hAPP(c_List_Olist_OCons(X32229),X32227),X32228))
        | ~ class_Orderings_Olinorder(X32229) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_OCons])])])]) ).

fof(i_0_8613,plain,
    ! [X31748,X31749,X31750,X31751] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31750),X31751),hAPP(c_List_Oset(X31750),X31748)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31750),X31749),X31751))
        | ~ c_List_Olinorder__class_Osorted(X31750,hAPP(hAPP(c_List_Olist_OCons(X31750),X31749),X31748))
        | ~ class_Orderings_Olinorder(X31750) )
      & ( c_List_Olinorder__class_Osorted(X31750,X31748)
        | ~ c_List_Olinorder__class_Osorted(X31750,hAPP(hAPP(c_List_Olist_OCons(X31750),X31749),X31748))
        | ~ class_Orderings_Olinorder(X31750) )
      & ( hBOOL(hAPP(hAPP(c_member(X31750),esk431_3(X31748,X31749,X31750)),hAPP(c_List_Oset(X31750),X31748)))
        | ~ c_List_Olinorder__class_Osorted(X31750,X31748)
        | c_List_Olinorder__class_Osorted(X31750,hAPP(hAPP(c_List_Olist_OCons(X31750),X31749),X31748))
        | ~ class_Orderings_Olinorder(X31750) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31750),X31749),esk431_3(X31748,X31749,X31750)))
        | ~ c_List_Olinorder__class_Osorted(X31750,X31748)
        | c_List_Olinorder__class_Osorted(X31750,hAPP(hAPP(c_List_Olist_OCons(X31750),X31749),X31748))
        | ~ class_Orderings_Olinorder(X31750) ) ),
    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_8614,plain,
    ! [X31730,X31731,X31732,X31733] :
      ( ( c_List_Olinorder__class_Osorted(X31732,X31730)
        | ~ c_List_Olinorder__class_Osorted(X31732,hAPP(hAPP(c_List_Olist_OCons(X31732),X31731),X31730))
        | ~ class_Orderings_Olinorder(X31732) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31732),X31733),hAPP(c_List_Oset(X31732),X31730)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31732),X31731),X31733))
        | ~ c_List_Olinorder__class_Osorted(X31732,hAPP(hAPP(c_List_Olist_OCons(X31732),X31731),X31730))
        | ~ class_Orderings_Olinorder(X31732) )
      & ( hBOOL(hAPP(hAPP(c_member(X31732),esk428_3(X31730,X31731,X31732)),hAPP(c_List_Oset(X31732),X31730)))
        | ~ c_List_Olinorder__class_Osorted(X31732,X31730)
        | c_List_Olinorder__class_Osorted(X31732,hAPP(hAPP(c_List_Olist_OCons(X31732),X31731),X31730))
        | ~ class_Orderings_Olinorder(X31732) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31732),X31731),esk428_3(X31730,X31731,X31732)))
        | ~ c_List_Olinorder__class_Osorted(X31732,X31730)
        | c_List_Olinorder__class_Osorted(X31732,hAPP(hAPP(c_List_Olist_OCons(X31732),X31731),X31730))
        | ~ class_Orderings_Olinorder(X31732) ) ),
    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_8615,plain,
    ! [X20365,X20366] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20366))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20365))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20365),X20366)),X20365) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20365),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20366),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_8616,plain,
    ! [X22818,X22819,X22820] :
      ( ~ class_Fields_Olinordered__field(X22820)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22820),c_Groups_Ozero__class_Ozero(X22820)),X22819))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22820),c_Groups_Ozero__class_Ozero(X22820)),X22818))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22820),c_Groups_Ozero__class_Ozero(X22820)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22820),X22819),X22818))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__pos__pos])]) ).

fof(i_0_8617,plain,
    ! [X18246,X18247,X18248] :
      ( ~ class_Rings_Olinordered__semiring__strict(X18248)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18248),c_Groups_Ozero__class_Ozero(X18248)),X18247))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18248),c_Groups_Ozero__class_Ozero(X18248)),X18246))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18248),c_Groups_Ozero__class_Ozero(X18248)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18248),X18247),X18246))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__pos__pos])]) ).

fof(i_0_8618,plain,
    ! [X18752,X18753,X18754] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18754)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18754),c_Groups_Ozero__class_Ozero(X18754)),X18753))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18754),c_Groups_Ozero__class_Ozero(X18754)),X18752))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18754),c_Groups_Ozero__class_Ozero(X18754)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18754),X18753),X18752))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__pos])]) ).

fof(i_0_8619,plain,
    ! [X18817,X18818,X18819] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18819)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18819),c_Groups_Ozero__class_Ozero(X18819)),X18818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18819),c_Groups_Ozero__class_Ozero(X18819)),X18817))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18819),c_Groups_Ozero__class_Ozero(X18819)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18819),X18818),X18817))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__pos])]) ).

fof(i_0_8620,plain,
    ! [X18814,X18815,X18816] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18816)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18816),c_Groups_Ozero__class_Ozero(X18816)),X18815))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18816),c_Groups_Ozero__class_Ozero(X18816)),X18814))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18816),c_Groups_Ozero__class_Ozero(X18816)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18816),X18815),X18814))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__pos__nonneg])]) ).

fof(i_0_8621,plain,
    ! [X18609,X18610,X18611] :
      ( ~ class_Rings_Olinordered__semidom(X18611)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18611),c_Groups_Oone__class_Oone(X18611)),X18610))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18611),c_Groups_Oone__class_Oone(X18611)),X18609))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18611),c_Groups_Oone__class_Oone(X18611)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18611),X18610),X18609))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__1__mult])]) ).

fof(i_0_8622,plain,
    ! [X22848,X22849,X22850] :
      ( ~ class_Fields_Olinordered__field(X22850)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22850),c_Groups_Ozero__class_Ozero(X22850)),X22849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22850),c_Groups_Ozero__class_Ozero(X22850)),X22848))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22850),c_Groups_Ozero__class_Ozero(X22850)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22850),X22849),X22848))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonneg__pos])]) ).

fof(i_0_8623,plain,
    ! [X18316,X18317,X18318] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18318),c_Groups_Ozero__class_Ozero(X18318)),X18317))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18318),c_Groups_Ozero__class_Ozero(X18318)),X18316))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18318),c_Groups_Ozero__class_Ozero(X18318)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18318),X18317),X18316)))
        | ~ class_Rings_Oordered__ring(X18318) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18318),X18317),c_Groups_Ozero__class_Ozero(X18318)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18318),X18316),c_Groups_Ozero__class_Ozero(X18318)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18318),c_Groups_Ozero__class_Ozero(X18318)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18318),X18317),X18316)))
        | ~ class_Rings_Oordered__ring(X18318) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_split__mult__pos__le])])]) ).

fof(i_0_8624,plain,
    ! [X18271,X18272,X18273] :
      ( ~ class_Rings_Oordered__cancel__semiring(X18273)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18273),c_Groups_Ozero__class_Ozero(X18273)),X18272))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18273),c_Groups_Ozero__class_Ozero(X18273)),X18271))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18273),c_Groups_Ozero__class_Ozero(X18273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18273),X18272),X18271))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonneg__nonneg])]) ).

fof(i_0_8625,plain,
    ! [X18741,X18742,X18743] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18743)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18743),c_Groups_Ozero__class_Ozero(X18743)),X18742))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18743),c_Groups_Ozero__class_Ozero(X18743)),X18741))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18743),c_Groups_Ozero__class_Ozero(X18743)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18743),X18742),X18741))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__nonneg])]) ).

fof(i_0_8626,plain,
    ! [X18806,X18807,X18808,X18809] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18809),X18808))
      | hAPP(c_Finite__Set_Ocard(X18807),hAPP(c_Set_Oimage(X18809,X18807,X18806),X18808)) != hAPP(c_Finite__Set_Ocard(X18809),X18808)
      | c_Fun_Oinj__on(X18809,X18807,X18806,X18808) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__card__imp__inj__on])]) ).

fof(i_0_8627,plain,
    ! [X18802,X18803,X18804,X18805] :
      ( ( ~ c_Fun_Oinj__on(X18805,X18803,X18802,X18804)
        | hAPP(c_Finite__Set_Ocard(X18803),hAPP(c_Set_Oimage(X18805,X18803,X18802),X18804)) = hAPP(c_Finite__Set_Ocard(X18805),X18804)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18805),X18804)) )
      & ( hAPP(c_Finite__Set_Ocard(X18803),hAPP(c_Set_Oimage(X18805,X18803,X18802),X18804)) != hAPP(c_Finite__Set_Ocard(X18805),X18804)
        | c_Fun_Oinj__on(X18805,X18803,X18802,X18804)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18805),X18804)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__on__iff__eq__card])])]) ).

fof(i_0_8628,plain,
    ! [X23406,X23407,X23408] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23408,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23408,tc_HOL_Obool)),X23407),X23406)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23408,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X23408,tc_HOL_Obool)),X23407)),X23406),
    inference(variable_rename,[status(thm)],[fact_Compl__Diff__eq]) ).

cnf(i_0_8629,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_5754]) ).

fof(i_0_8630,plain,
    ! [X20349,X20350,X20351,X20352] :
      ( ~ class_Rings_Olinordered__semidom(X20352)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20352),X20351),X20350) != hAPP(hAPP(c_Power_Opower__class_Opower(X20352),X20349),X20350)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20352),c_Groups_Ozero__class_Ozero(X20352)),X20351))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20352),c_Groups_Ozero__class_Ozero(X20352)),X20349))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20350))
      | X20351 = X20349 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__imp__eq__base])]) ).

cnf(i_0_8631,plain,
    ( c_List_Oupt(X1,hAPP(c_Nat_OSuc,X2)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(X1,X2)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5755]) ).

cnf(i_0_8632,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_5756]) ).

fof(i_0_8633,plain,
    ! [X27164,X27165,X27166,X27167] : hAPP(c_Finite__Set_Ocard(tc_prod(X27167,X27166)),hAPP(hAPP(c_Product__Type_OSigma(X27167,X27166),X27165),hAPP(c_COMBK(tc_fun(X27166,tc_HOL_Obool),X27167),X27164))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X27167),X27165)),hAPP(c_Finite__Set_Ocard(X27166),X27164)),
    inference(variable_rename,[status(thm)],[fact_card__cartesian__product]) ).

fof(i_0_8634,plain,
    ! [X25241,X25242,X25243,X25244] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X25244),X25243),X25242))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25244,tc_HOL_Obool)),X25242),hAPP(hAPP(c_Set_Oinsert(X25244),X25243),X25241)) = hAPP(hAPP(c_Set_Oinsert(X25244),X25243),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25244,tc_HOL_Obool)),X25242),X25241)) )
      & ( hBOOL(hAPP(hAPP(c_member(X25244),X25243),X25242))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25244,tc_HOL_Obool)),X25242),hAPP(hAPP(c_Set_Oinsert(X25244),X25243),X25241)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25244,tc_HOL_Obool)),X25242),X25241) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5757])]) ).

fof(i_0_8635,plain,
    ! [X25225,X25226,X25227,X25228] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X25228),X25227),X25226))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25228,tc_HOL_Obool)),X25226),hAPP(hAPP(c_Set_Oinsert(X25228),X25227),X25225)) = hAPP(hAPP(c_Set_Oinsert(X25228),X25227),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25228,tc_HOL_Obool)),X25226),X25225)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__insert__right__if1])]) ).

fof(i_0_8636,plain,
    ! [X29415,X29416,X29417,X29418,X29419,X29420,X29421] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29415)),X29417) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29415)),X29416)
        | X29417 != X29416 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29418),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29415)),X29417)))
        | hAPP(hAPP(c_List_Onth(X29415),X29417),X29418) = hAPP(hAPP(c_List_Onth(X29415),X29416),X29418)
        | X29417 != X29416 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk382_3(X29419,X29420,X29421)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29419)),X29421)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29419)),X29421) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29419)),X29420)
        | X29421 = X29420 )
      & ( hAPP(hAPP(c_List_Onth(X29419),X29421),esk382_3(X29419,X29420,X29421)) != hAPP(hAPP(c_List_Onth(X29419),X29420),esk382_3(X29419,X29420,X29421))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29419)),X29421) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29419)),X29420)
        | X29421 = X29420 ) ),
    inference(distribute,[status(thm)],[inference(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_8637,plain,
    ! [X19795,X19796,X19797,X19798,X19799,X19800] :
      ( ~ c_Finite__Set_Ofolding(X19800,X19799,X19798,X19797)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19800),X19796))
      | hAPP(hAPP(X19797,X19796),X19795) = hAPP(hAPP(c_Finite__Set_Ofold(X19800,X19799,X19798),X19795),X19796) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oeq__fold])]) ).

fof(i_0_8638,plain,
    ! [X23682,X23683,X23684,X23685,X23686] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X23686)
      | ~ hBOOL(hAPP(hAPP(c_member(X23685),X23684),X23683))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23686),hAPP(X23682,X23684)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23685,X23686),X23683),X23682))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SUPI])]) ).

fof(i_0_8639,plain,
    ! [X20699,X20700,X20701,X20702] :
      ( ~ class_Divides_Osemiring__div(X20702)
      | c_Divides_Odiv__class_Omod(X20702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20702),c_Divides_Odiv__class_Omod(X20702,X20701,X20700)),X20699),X20700) = c_Divides_Odiv__class_Omod(X20702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20702),X20701),X20699),X20700) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I4_J])]) ).

fof(i_0_8640,plain,
    ! [X20669,X20670,X20671,X20672] :
      ( ~ class_Divides_Osemiring__div(X20672)
      | c_Divides_Odiv__class_Omod(X20672,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20672),c_Divides_Odiv__class_Omod(X20672,X20671,X20670)),X20669),X20670) = c_Divides_Odiv__class_Omod(X20672,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20672),X20671),X20669),X20670) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I1_J])]) ).

fof(i_0_8641,plain,
    ! [X20683,X20684,X20685,X20686] :
      ( ~ class_Divides_Osemiring__div(X20686)
      | c_Divides_Odiv__class_Omod(X20686,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20686),X20685),X20684),X20683) = c_Divides_Odiv__class_Omod(X20686,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20686),c_Divides_Odiv__class_Omod(X20686,X20685,X20683)),X20684),X20683) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__left__eq])]) ).

fof(i_0_8642,plain,
    ! [X20657,X20658,X20659,X20660] :
      ( ~ class_Divides_Osemiring__div(X20660)
      | c_Divides_Odiv__class_Omod(X20660,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20660),X20659),X20658),X20657) = c_Divides_Odiv__class_Omod(X20660,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20660),c_Divides_Odiv__class_Omod(X20660,X20659,X20657)),X20658),X20657) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__left__eq])]) ).

fof(i_0_8643,plain,
    ! [X20719,X20720,X20721,X20722] :
      ( ~ class_Divides_Oring__div(X20722)
      | c_Divides_Odiv__class_Omod(X20722,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20722),X20721),X20720),X20719) = c_Divides_Odiv__class_Omod(X20722,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20722),c_Divides_Odiv__class_Omod(X20722,X20721,X20719)),X20720),X20719) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__left__eq])]) ).

fof(i_0_8644,plain,
    ! [X18005,X18006,X18007] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18007,tc_HOL_Obool)),X18006),X18005))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18007,tc_HOL_Obool)),X18006),X18005)) )
      & ( X18006 != X18005
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18007,tc_HOL_Obool)),X18006),X18005)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18007,tc_HOL_Obool)),X18006),X18005))
        | X18006 = X18005
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18007,tc_HOL_Obool)),X18006),X18005)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__eq])])]) ).

fof(i_0_8645,plain,
    ! [X18002,X18003,X18004] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18004,tc_HOL_Obool)),X18003),X18002))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18004,tc_HOL_Obool)),X18003),X18002))
        | X18003 = X18002 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18004,tc_HOL_Obool)),X18003),X18002))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18004,tc_HOL_Obool)),X18003),X18002)) )
      & ( X18003 != X18002
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18004,tc_HOL_Obool)),X18003),X18002)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__iff__psubset__eq])])]) ).

fof(i_0_8646,plain,
    ! [X23373,X23374,X23375] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23375),X23374))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23375),X23373))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23375),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23375,tc_HOL_Obool)),X23374),X23373))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnI])]) ).

fof(i_0_8647,plain,
    ! [X25149,X25150,X25151] : hAPP(c_Set_OPow(X25151),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25151,tc_HOL_Obool)),X25150),X25149)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(X25151,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(X25151),X25150)),hAPP(c_Set_OPow(X25151),X25149)),
    inference(variable_rename,[status(thm)],[fact_Pow__Int__eq]) ).

fof(i_0_8648,plain,
    ! [X32753,X32754,X32756] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X32754)),X32753))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X32754)),X32756),X32753))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32754)),X32756)),esk496_2(X32753,X32754))) ),
    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_8649,plain,
    ! [X24580,X24581,X24582,X24583] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24582),X24581))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24582,X24583),X24580),X24581) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24583,X24582,c_Groups_Oplus__class_Oplus(X24583)),X24580),c_Groups_Ozero__class_Ozero(X24583)),X24581)
        | ~ class_Groups_Ocomm__monoid__add(X24583) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X24582),X24581))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24582,X24583),X24580),X24581) = c_Groups_Ozero__class_Ozero(X24583)
        | ~ class_Groups_Ocomm__monoid__add(X24583) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5758])])]) ).

fof(i_0_8650,plain,
    ! [X24584,X24585,X24586,X24587] :
      ( ~ class_Groups_Ocomm__monoid__add(X24587)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24586),X24585))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24586,X24587),X24584),X24585) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X24587,X24586,c_Groups_Oplus__class_Oplus(X24587)),X24584),c_Groups_Ozero__class_Ozero(X24587)),X24585) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oeq__fold])]) ).

fof(i_0_8651,plain,
    ! [X21998,X21999,X22000,X22001] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22000),X21999))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22000,X22001),X21998),X21999) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X22001,X22000,c_Groups_Otimes__class_Otimes(X22001)),X21998),c_Groups_Oone__class_Oone(X22001)),X21999)
        | ~ class_Groups_Ocomm__monoid__mult(X22001) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X22000),X21999))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22000,X22001),X21998),X21999) = c_Groups_Oone__class_Oone(X22001)
        | ~ class_Groups_Ocomm__monoid__mult(X22001) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5759])])]) ).

fof(i_0_8652,plain,
    ! [X22002,X22003,X22004,X22005] :
      ( ~ class_Groups_Ocomm__monoid__mult(X22005)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22004),X22003))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X22004,X22005),X22002),X22003) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X22005,X22004,c_Groups_Otimes__class_Otimes(X22005)),X22002),c_Groups_Oone__class_Oone(X22005)),X22003) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oeq__fold])]) ).

fof(i_0_8653,plain,
    ! [X17999,X18000,X18001] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X18001,tc_HOL_Obool)),X18000),X17999))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X18001,tc_HOL_Obool)),X18000),X17999)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubset__imp__subset])]) ).

fof(i_0_8654,plain,
    ! [X32584,X32585,X32586,X32587] : hAPP(hAPP(c_List_Oappend(X32587),c_List_Oreplicate(X32587,X32586,X32585)),c_List_Oreplicate(X32587,X32584,X32585)) = hAPP(hAPP(c_List_Oappend(X32587),c_List_Oreplicate(X32587,X32584,X32585)),c_List_Oreplicate(X32587,X32586,X32585)),
    inference(variable_rename,[status(thm)],[fact_append__replicate__commute]) ).

fof(i_0_8655,plain,
    ! [X22394,X22395] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22394),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22395,X22394) = 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),X22395),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22394)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__neg])]) ).

fof(i_0_8656,plain,
    ! [X30171,X30172,X30173,X30174] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30174),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30173)),X30172)))
        | hAPP(hAPP(c_List_Onth(X30173),hAPP(hAPP(c_List_Oappend(X30173),X30172),X30171)),X30174) = hAPP(hAPP(c_List_Onth(X30173),X30172),X30174) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30174),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30173)),X30172)))
        | hAPP(hAPP(c_List_Onth(X30173),hAPP(hAPP(c_List_Oappend(X30173),X30172),X30171)),X30174) = hAPP(hAPP(c_List_Onth(X30173),X30171),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30174),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30173)),X30172))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5760])]) ).

fof(i_0_8657,plain,
    ! [X21447,X21448,X21449] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X21449),X21448),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21449,tc_HOL_Obool)),X21447)))
        | ~ hBOOL(hAPP(hAPP(c_member(X21449),X21448),X21447)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21449),X21448),X21447))
        | hBOOL(hAPP(hAPP(c_member(X21449),X21448),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21449,tc_HOL_Obool)),X21447))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5761])]) ).

fof(i_0_8658,plain,
    ! [X21444,X21445,X21446] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21446),X21445),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21446,tc_HOL_Obool)),X21444)))
      | ~ hBOOL(hAPP(hAPP(c_member(X21446),X21445),X21444)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5762])]) ).

fof(i_0_8659,plain,
    ! [X21441,X21442,X21443] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X21443),X21442),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21443,tc_HOL_Obool)),X21441)))
      | ~ hBOOL(hAPP(hAPP(c_member(X21443),X21442),X21441)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5763])]) ).

fof(i_0_8660,plain,
    ! [X24238,X24239,X24240,X24242,X24243,X24244] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk142_2(X24238,X24239)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24239)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24240),X24239))
        | ~ hBOOL(hAPP(X24238,X24240)) )
      & ( hBOOL(hAPP(X24238,esk142_2(X24238,X24239)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24240),X24239))
        | ~ hBOOL(hAPP(X24238,X24240)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk143_2(X24242,X24243)),X24243))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24244),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24243)))
        | ~ hBOOL(hAPP(X24242,X24244)) )
      & ( hBOOL(hAPP(X24242,esk143_2(X24242,X24243)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24244),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24243)))
        | ~ hBOOL(hAPP(X24242,X24244)) ) ),
    inference(distribute,[status(thm)],[inference(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_8661,plain,
    ! [X30333,X30334,X30335,X30336] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30336) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X30335),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30336)),hAPP(hAPP(c_List_Olist_OCons(X30335),X30334),X30333)) = hAPP(hAPP(c_List_Olist_OCons(X30335),X30334),X30333) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30336) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X30335),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30336)),hAPP(hAPP(c_List_Olist_OCons(X30335),X30334),X30333)) = hAPP(hAPP(c_List_Odrop(X30335),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30336)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30333) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons__number__of])]) ).

fof(i_0_8662,plain,
    ! [X28277,X28278] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk301_2(X28277,X28278)),c_Int_OInteg))
        | hBOOL(hAPP(X28278,X28277)) )
      & ( ~ hBOOL(hAPP(X28278,hAPP(c_Int_OAbs__Integ,esk301_2(X28277,X28278))))
        | hBOOL(hAPP(X28278,X28277)) ) ),
    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_8663,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_5764]) ).

fof(i_0_8664,plain,
    ! [X28086,X28087,X28088] :
      ( ~ c_Wellfounded_Owf(X28088,X28087)
      | c_Wellfounded_Owf(X28088,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28088,X28088),tc_HOL_Obool)),X28087),X28086)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int1])]) ).

fof(i_0_8665,plain,
    ! [X28083,X28084,X28085] :
      ( ~ c_Wellfounded_Owf(X28085,X28084)
      | c_Wellfounded_Owf(X28085,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X28085,X28085),tc_HOL_Obool)),X28083),X28084)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__Int2])]) ).

fof(i_0_8666,plain,
    ! [X22392,X22393] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22393))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22392),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22393),X22392) = 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),X22393),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22392)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__neg])]) ).

fof(i_0_8667,plain,
    ! [X30452,X30453] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X30453)
      | X30452 = c_List_Olist_ONil(X30453)
      | hAPP(c_Finite__Set_Ofold1(X30453,c_Groups_Otimes__class_Otimes(X30453)),hAPP(c_List_Oset(X30453),X30452)) = hAPP(c_List_Ofoldl(X30453,X30453,c_Groups_Otimes__class_Otimes(X30453),hAPP(c_List_Ohd(X30453),X30452)),hAPP(c_List_Otl(X30453),X30452)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__set])]) ).

fof(i_0_8668,plain,
    ! [X30268,X30269,X30270,X30271,X30272] : hAPP(hAPP(c_List_Odrop(tc_prod(X30272,X30271)),X30270),hAPP(hAPP(c_List_Ozip(X30272,X30271),X30269),X30268)) = hAPP(hAPP(c_List_Ozip(X30272,X30271),hAPP(hAPP(c_List_Odrop(X30272),X30270),X30269)),hAPP(hAPP(c_List_Odrop(X30271),X30270),X30268)),
    inference(variable_rename,[status(thm)],[fact_drop__zip]) ).

fof(i_0_8669,plain,
    ! [X29578,X29579,X29580,X29581,X29582] : hAPP(hAPP(c_List_Otake(tc_prod(X29582,X29581)),X29580),hAPP(hAPP(c_List_Ozip(X29582,X29581),X29579),X29578)) = hAPP(hAPP(c_List_Ozip(X29582,X29581),hAPP(hAPP(c_List_Otake(X29582),X29580),X29579)),hAPP(hAPP(c_List_Otake(X29581),X29580),X29578)),
    inference(variable_rename,[status(thm)],[fact_take__zip]) ).

fof(i_0_8670,plain,
    ! [X24055,X24056,X24057] :
      ( ~ class_Orderings_Olinorder(X24057)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24057),X24056),X24055))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24057,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24057,X24056),X24055)),hAPP(hAPP(c_Set_Oinsert(X24057),X24055),c_Orderings_Obot__class_Obot(tc_fun(X24057,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(X24057,X24056,X24055) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I6_J])]) ).

fof(i_0_8671,plain,
    ! [X22307,X22308] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22308),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22308,X22307) = 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),X22308),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22307)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg])]) ).

fof(i_0_8672,plain,
    ! [X28887,X28888,X28889,X28890,X28891] :
      ( ~ c_Relation_Osingle__valued(X28891,X28890,X28889)
      | ~ c_Relation_Osingle__valued(X28890,X28888,X28887)
      | c_Relation_Osingle__valued(X28891,X28888,hAPP(hAPP(c_Relation_Orel__comp(X28891,X28890,X28888),X28889),X28887)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__comp])]) ).

fof(i_0_8673,plain,
    ! [X31856,X31857] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X31857),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X31857))),c_List_Otranspose(X31857,X31856)))),
    inference(variable_rename,[status(thm)],[fact_sorted__transpose]) ).

fof(i_0_8674,plain,
    ! [X25342,X25343,X25344,X25345,X25346] :
      ( ~ class_Orderings_Olinorder(X25346)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25346,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25346,X25345),X25344)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25346,X25343),X25342)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25346,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25346),X25345),X25343)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25346),X25344),X25342)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastLessThan])]) ).

fof(i_0_8675,plain,
    ! [X25337,X25338,X25339,X25340,X25341] :
      ( ~ class_Orderings_Olinorder(X25341)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25341,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25341,X25340,X25339)),c_SetInterval_Oord__class_OatLeastAtMost(X25341,X25338,X25337)) = c_SetInterval_Oord__class_OatLeastAtMost(X25341,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25341),X25340),X25338),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25341),X25339),X25337)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMost])]) ).

fof(i_0_8676,plain,
    ! [X25369,X25370,X25371,X25372,X25373] :
      ( ~ class_Orderings_Olinorder(X25373)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25373,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25373,X25372,X25371)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25373,X25370,X25369)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X25373,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25373),X25372),X25370),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25373),X25371),X25369)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanAtMost])]) ).

fof(i_0_8677,plain,
    ! [X25378,X25379,X25380,X25381,X25382] :
      ( ~ class_Orderings_Olinorder(X25382)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25382,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25382,X25381,X25380)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25382,X25379,X25378)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X25382,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25382),X25381),X25379),hAPP(hAPP(c_Orderings_Oord__class_Omin(X25382),X25380),X25378)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__greaterThanLessThan])]) ).

fof(i_0_8678,plain,
    ! [X16972,X16973,X16974,X16975] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X16975),X16974),X16973))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16975,tc_HOL_Obool)),X16973),X16972))
      | hBOOL(hAPP(hAPP(c_member(X16975),X16974),X16972)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__rev__mp])]) ).

fof(i_0_8679,plain,
    ! [X17952,X17953,X17954,X17955] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17955,tc_HOL_Obool)),X17954),X17953))
      | ~ hBOOL(hAPP(hAPP(c_member(X17955),X17952),X17954))
      | hBOOL(hAPP(hAPP(c_member(X17955),X17952),X17953)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_psubsetD])]) ).

fof(i_0_8680,plain,
    ! [X16976,X16977,X16978,X16979] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16979,tc_HOL_Obool)),X16978),X16977))
      | ~ hBOOL(hAPP(hAPP(c_member(X16979),X16976),X16978))
      | hBOOL(hAPP(hAPP(c_member(X16979),X16976),X16977)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__mono])]) ).

fof(i_0_8681,plain,
    ! [X16968,X16969,X16970,X16971] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16971,tc_HOL_Obool)),X16970),X16969))
      | ~ hBOOL(hAPP(hAPP(c_member(X16971),X16968),X16970))
      | hBOOL(hAPP(hAPP(c_member(X16971),X16968),X16969)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__mp])]) ).

fof(i_0_8682,plain,
    ! [X16858,X16859,X16860,X16861] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16861,tc_HOL_Obool)),X16860),X16859))
      | ~ hBOOL(hAPP(hAPP(c_member(X16861),X16858),X16860))
      | hBOOL(hAPP(hAPP(c_member(X16861),X16858),X16859)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subsetD])]) ).

fof(i_0_8683,plain,
    ! [X30124,X30125,X30126,X30127] : hAPP(hAPP(c_List_Onth(X30127),hAPP(hAPP(c_List_Oappend(X30127),X30126),hAPP(hAPP(c_List_Olist_OCons(X30127),X30125),X30124))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30127)),X30126)) = X30125,
    inference(variable_rename,[status(thm)],[fact_nth__append__length]) ).

fof(i_0_8684,plain,
    ! [X22634,X22635,X22636] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22636),hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22635)),hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22634)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22636),hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22635)),hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22634)) = hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22634)
        | ~ class_Int_Onumber(X22636)
        | ~ class_Orderings_Oord(X22636) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22636),hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22635)),hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22634)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22636),hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22635)),hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22634)) = hAPP(c_Int_Onumber__class_Onumber__of(X22636),X22635)
        | ~ class_Int_Onumber(X22636)
        | ~ class_Orderings_Oord(X22636) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5765])])]) ).

fof(i_0_8685,plain,
    ! [X21610,X21611,X21612] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21611)),hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21610)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21611)),hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21610)) = hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21611)
        | ~ class_Int_Onumber(X21612)
        | ~ class_Orderings_Oord(X21612) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21611)),hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21610)))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21612),hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21611)),hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21610)) = hAPP(c_Int_Onumber__class_Onumber__of(X21612),X21610)
        | ~ class_Int_Onumber(X21612)
        | ~ class_Orderings_Oord(X21612) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5766])])]) ).

fof(i_0_8686,plain,
    ! [X22396,X22397] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22397),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X22396),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22397),X22396) = 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),X22397),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22396)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__neg])]) ).

fof(i_0_8687,plain,
    ! [X18629,X18630] : 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)),X18630),X18629),
    inference(variable_rename,[status(thm)],[fact_inj__on__add__nat]) ).

fof(i_0_8688,plain,
    ! [X20462,X20463] :
      ( ( ~ 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),X20462),X20463)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20462))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20463)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20462))
        | 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),X20462),X20463)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20463)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__nonneg__iff])])]) ).

fof(i_0_8689,plain,
    ! [X22776,X22777,X22778,X22779,X22780] :
      ( ~ class_Fields_Ofield__inverse__zero(X22780)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22780),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22780),X22779),X22778)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22780),X22777),X22776)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22780),X22779),X22777)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22780),X22778),X22776)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__times__eq])]) ).

fof(i_0_8690,plain,
    ! [X19035,X19036,X19037,X19038,X19039] :
      ( ~ class_Rings_Ocomm__semiring__1(X19039)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19039),X19038),X19037)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19039),X19036),X19035)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19039),X19038),X19036)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19039),X19037),X19035)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J])]) ).

fof(i_0_8691,plain,
    ! [X19011,X19012,X19013,X19014,X19015] :
      ( ~ class_Rings_Ocomm__semiring__1(X19015)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19015),X19014),X19013)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19015),X19012),X19011)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19015),X19014),X19012)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19015),X19013),X19011)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J])]) ).

fof(i_0_8692,plain,
    ! [X19045,X19046,X19047,X19048,X19049] :
      ( ~ class_Rings_Ocomm__semiring__1(X19049)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19049),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19049),X19048),X19047)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19049),X19046),X19045)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19049),X19048),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19049),X19047),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19049),X19046),X19045))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J])]) ).

fof(i_0_8693,plain,
    ! [X31707,X31708,X31709,X31710,X31711] :
      ( ~ class_Orderings_Olinorder(X31711)
      | ~ c_List_Olinorder__class_Osorted(X31711,hAPP(hAPP(c_List_Omap(X31710,X31711),X31709),X31708))
      | c_List_Olinorder__class_Osorted(X31711,hAPP(hAPP(c_List_Omap(X31710,X31711),X31709),c_List_Oremove1(X31710,X31707,X31708))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__map__remove1])]) ).

fof(i_0_8694,plain,
    ! [X28198,X28199,X28200] : hAPP(c_Relation_ODomain(X28200,X28199),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X28200,X28199),tc_HOL_Obool),X28198)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X28200,X28199),tc_HOL_Obool),tc_fun(X28200,tc_HOL_Obool)),X28198),c_Relation_ODomain(X28200,X28199)),
    inference(variable_rename,[status(thm)],[fact_Domain__Union]) ).

fof(i_0_8695,plain,
    ! [X27938,X27939,X27940] : hAPP(c_Relation_ORange(X27940,X27939),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(X27940,X27939),tc_HOL_Obool),X27938)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(X27940,X27939),tc_HOL_Obool),tc_fun(X27939,tc_HOL_Obool)),X27938),c_Relation_ORange(X27940,X27939)),
    inference(variable_rename,[status(thm)],[fact_Range__Union]) ).

fof(i_0_8696,plain,
    ! [X24246,X24247,X24249,X24250,X24251,X24253] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk144_2(X24246,X24247)),X24247))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24249),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24247)))
        | hBOOL(hAPP(X24246,X24249)) )
      & ( ~ hBOOL(hAPP(X24246,esk144_2(X24246,X24247)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24249),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24247)))
        | hBOOL(hAPP(X24246,X24249)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk145_2(X24250,X24251)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24251)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24253),X24251))
        | hBOOL(hAPP(X24250,X24253)) )
      & ( ~ hBOOL(hAPP(X24250,esk145_2(X24250,X24251)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24253),X24251))
        | hBOOL(hAPP(X24250,X24253)) ) ),
    inference(distribute,[status(thm)],[inference(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_8697,plain,
    ! [X20192,X20193,X20194] :
      ( ~ class_Rings_Oring__1(X20194)
      | ~ hBOOL(hAPP(hAPP(c_member(X20194),X20193),c_Int_Oring__1__class_OInts(X20194)))
      | hBOOL(hAPP(hAPP(c_member(X20194),hAPP(hAPP(c_Power_Opower__class_Opower(X20194),X20193),X20192)),c_Int_Oring__1__class_OInts(X20194))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__power])]) ).

fof(i_0_8698,plain,
    ! [X27580,X27581] : hAPP(c_Set_OCollect(X27581),hAPP(hAPP(c_COMBC(X27581,tc_fun(X27581,tc_HOL_Obool),tc_HOL_Obool),c_member(X27581)),X27580)) = X27580,
    inference(variable_rename,[status(thm)],[fact_Collect__mem__eq]) ).

fof(i_0_8699,plain,
    ! [X20299,X20300] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20300))
      | 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),X20300),X20299))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__one__le__power])]) ).

fof(i_0_8700,plain,
    ! [X33566,X33567,X33568,X33569,X33570,X33571,X33572] :
      ( ( ~ c_List_Oall__interval__nat(X33568,X33567,X33566)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33569),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X33567),X33566)))
        | hBOOL(hAPP(X33568,X33569)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk560_3(X33570,X33571,X33572)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X33571),X33570)))
        | c_List_Oall__interval__nat(X33572,X33571,X33570) )
      & ( ~ hBOOL(hAPP(X33572,esk560_3(X33570,X33571,X33572)))
        | c_List_Oall__interval__nat(X33572,X33571,X33570) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_all__interval__nat__def])])])])])]) ).

fof(i_0_8701,plain,
    ! [X20220,X20221,X20222] :
      ( ~ class_Rings_Olinordered__semidom(X20222)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20222),c_Groups_Oone__class_Oone(X20222)),X20221))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20220))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20222),c_Groups_Oone__class_Oone(X20222)),hAPP(hAPP(c_Power_Opower__class_Opower(X20222),X20221),X20220))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__power])]) ).

fof(i_0_8702,plain,
    ! [X22809,X22810,X22811] :
      ( ~ class_Fields_Olinordered__field(X22811)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22811),X22810),c_Groups_Ozero__class_Ozero(X22811)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22811),X22809),c_Groups_Ozero__class_Ozero(X22811)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22811),c_Groups_Ozero__class_Ozero(X22811)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22811),X22810),X22809))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__neg__neg])]) ).

fof(i_0_8703,plain,
    ! [X18224,X18225,X18226] :
      ( ~ class_Rings_Olinordered__ring__strict(X18226)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18226),X18225),c_Groups_Ozero__class_Ozero(X18226)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18226),X18224),c_Groups_Ozero__class_Ozero(X18226)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18226),c_Groups_Ozero__class_Ozero(X18226)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18226),X18225),X18224))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__neg__neg])]) ).

fof(i_0_8704,plain,
    ! [X22872,X22873,X22874] :
      ( ~ class_Fields_Olinordered__field(X22874)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22874),X22873),c_Groups_Ozero__class_Ozero(X22874)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22874),X22872),c_Groups_Ozero__class_Ozero(X22874)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22874),c_Groups_Ozero__class_Ozero(X22874)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22874),X22873),X22872))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__nonpos__neg])]) ).

fof(i_0_8705,plain,
    ! [X18283,X18284,X18285] :
      ( ~ class_Rings_Oordered__ring(X18285)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18285),X18284),c_Groups_Ozero__class_Ozero(X18285)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18285),X18283),c_Groups_Ozero__class_Ozero(X18285)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18285),c_Groups_Ozero__class_Ozero(X18285)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18285),X18284),X18283))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__nonpos__nonpos])]) ).

fof(i_0_8706,plain,
    ! [X24557,X24558,X24559] :
      ( ~ class_Groups_Ocomm__monoid__add(X24559)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24559),X24558),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24557))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24559),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24559),X24558),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24557))),hAPP(X24558,X24557)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__lessThan__Suc])]) ).

fof(i_0_8707,plain,
    ! [X17989,X17990] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17990),X17989)),X17990)),
    inference(variable_rename,[status(thm)],[i_0_5767]) ).

fof(i_0_8708,plain,
    ! [X17987,X17988] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17988),X17987)),X17987)),
    inference(variable_rename,[status(thm)],[i_0_5768]) ).

fof(i_0_8709,plain,
    ! [X22193,X22194] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22194))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22193))
      | c_Divides_OposDivAlg(X22194,X22193) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22194),X22193)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22194,X22193)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__div__mod])]) ).

fof(i_0_8710,plain,
    ! [X20464,X20465] :
      ( ( ~ 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),X20464),X20465)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20465),X20464))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20465)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20465),X20464))
        | 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),X20464),X20465)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20465)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__imp__zdiv__pos__iff])])]) ).

fof(i_0_8711,plain,
    ! [X28232,X28233] : c_List_Olex(X28233,X28232) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(X28233),tc_List_Olist(X28233)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(X28233,X28232)),
    inference(variable_rename,[status(thm)],[fact_lex__def]) ).

fof(i_0_8712,plain,
    ! [X30146,X30147,X30148,X30149] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X30149),X30148),hAPP(c_List_Oset(X30149),X30147)))
        | c_List_Oremove1(X30149,X30148,hAPP(hAPP(c_List_Oappend(X30149),X30147),X30146)) = hAPP(hAPP(c_List_Oappend(X30149),c_List_Oremove1(X30149,X30148,X30147)),X30146) )
      & ( hBOOL(hAPP(hAPP(c_member(X30149),X30148),hAPP(c_List_Oset(X30149),X30147)))
        | c_List_Oremove1(X30149,X30148,hAPP(hAPP(c_List_Oappend(X30149),X30147),X30146)) = hAPP(hAPP(c_List_Oappend(X30149),X30147),c_List_Oremove1(X30149,X30148,X30146)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5769])]) ).

cnf(i_0_8713,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_5770]) ).

fof(i_0_8714,plain,
    ! [X22537,X22538,X22539,X22540] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22540),X22539),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22540),X22538),X22537)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22540),X22539),X22538))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22540),X22539),X22537))
        | ~ class_Orderings_Olinorder(X22540) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22540),X22539),X22538))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22540),X22539),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22540),X22538),X22537)))
        | ~ class_Orderings_Olinorder(X22540) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22540),X22539),X22537))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22540),X22539),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22540),X22538),X22537)))
        | ~ class_Orderings_Olinorder(X22540) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__max__iff__disj])])]) ).

fof(i_0_8715,plain,
    ! [X22562,X22563,X22564,X22565] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22565),X22564),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22565),X22563),X22562)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22565),X22564),X22563))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22565),X22564),X22562))
        | ~ class_Orderings_Olinorder(X22565) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22565),X22564),X22563))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22565),X22564),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22565),X22563),X22562)))
        | ~ class_Orderings_Olinorder(X22565) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22565),X22564),X22562))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22565),X22564),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22565),X22563),X22562)))
        | ~ class_Orderings_Olinorder(X22565) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__max__iff__disj])])]) ).

fof(i_0_8716,plain,
    ! [X18709,X18710,X18711] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18711,X18710,c_Orderings_Obot__class_Obot(tc_fun(X18711,tc_HOL_Obool))),X18709)),
    inference(variable_rename,[status(thm)],[i_0_5771]) ).

fof(i_0_8717,plain,
    ! [X20475,X20476] :
      ( ( ~ 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),X20475),X20476)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20475),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20476),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20475),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),X20475),X20476)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20476),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_8718,plain,
    ! [X30659,X30660] :
      ( X30660 = c_List_Olist_ONil(X30659)
      | c_Random_Oselect__weight(X30659,hAPP(hAPP(c_List_Omap(X30659,tc_prod(tc_Code__Numeral_Ocode__numeral,X30659)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,X30659),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),X30660)) = c_Random_Oselect(X30659,X30660) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_select__weigth__select])]) ).

fof(i_0_8719,plain,
    ! [X26759,X26760,X26761] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X26760,tc_HOL_Obool)),X26761),X26759))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26760),X26761))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26760),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26760,tc_HOL_Obool),X26759))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Inter])])]) ).

fof(i_0_8720,plain,
    ! [X25942,X25943,X25944] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25944),c_Groups_Ozero__class_Ozero(X25944)),X25942))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25944),c_Groups_Ozero__class_Ozero(X25944)),X25943))
        | hAPP(c_Groups_Oabs__class_Oabs(X25944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25944),X25943),X25942)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25944),hAPP(c_Groups_Oabs__class_Oabs(X25944),X25943)),hAPP(c_Groups_Oabs__class_Oabs(X25944),X25942))
        | ~ class_Rings_Oordered__ring__abs(X25944) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25944),X25942),c_Groups_Ozero__class_Ozero(X25944)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25944),c_Groups_Ozero__class_Ozero(X25944)),X25943))
        | hAPP(c_Groups_Oabs__class_Oabs(X25944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25944),X25943),X25942)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25944),hAPP(c_Groups_Oabs__class_Oabs(X25944),X25943)),hAPP(c_Groups_Oabs__class_Oabs(X25944),X25942))
        | ~ class_Rings_Oordered__ring__abs(X25944) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25944),c_Groups_Ozero__class_Ozero(X25944)),X25942))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25944),X25943),c_Groups_Ozero__class_Ozero(X25944)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25944),X25943),X25942)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25944),hAPP(c_Groups_Oabs__class_Oabs(X25944),X25943)),hAPP(c_Groups_Oabs__class_Oabs(X25944),X25942))
        | ~ class_Rings_Oordered__ring__abs(X25944) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25944),X25942),c_Groups_Ozero__class_Ozero(X25944)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25944),X25943),c_Groups_Ozero__class_Ozero(X25944)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25944),X25943),X25942)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25944),hAPP(c_Groups_Oabs__class_Oabs(X25944),X25943)),hAPP(c_Groups_Oabs__class_Oabs(X25944),X25942))
        | ~ class_Rings_Oordered__ring__abs(X25944) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__mult])])]) ).

cnf(i_0_8721,plain,
    ( X1 = X2
    | c_Int_OBit1(X1) != c_Int_OBit1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5772]) ).

fof(i_0_8722,plain,
    ! [X29658,X29659,X29660] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X29660),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29659)),X29658)))
      | c_List_Obutlast(X29659,hAPP(hAPP(c_List_Otake(X29659),X29660),X29658)) = hAPP(hAPP(c_List_Otake(X29659),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29660),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29658) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__take])]) ).

fof(i_0_8723,plain,
    ! [X24373,X24374] :
      ( ~ class_Orderings_Oorder(X24374)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24374,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X24374),X24373),c_Orderings_Obot__class_Obot(tc_fun(X24374,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(X24374),X24373)) = hAPP(hAPP(c_Set_Oinsert(X24374),X24373),c_Orderings_Obot__class_Obot(tc_fun(X24374,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__Diff__lessThan])]) ).

fof(i_0_8724,plain,
    ! [X24952,X24953,X24954,X24955,X24956,X24957,X24958,X24959] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24954,tc_HOL_Obool)),X24953),X24952) != c_Orderings_Obot__class_Obot(tc_fun(X24954,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X24954),X24955),X24953))
        | ~ hBOOL(hAPP(hAPP(c_member(X24954),X24956),X24952))
        | X24955 != X24956 )
      & ( hBOOL(hAPP(hAPP(c_member(X24959),esk199_3(X24957,X24958,X24959)),X24958))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24959,tc_HOL_Obool)),X24958),X24957) = c_Orderings_Obot__class_Obot(tc_fun(X24959,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24959),esk200_3(X24957,X24958,X24959)),X24957))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24959,tc_HOL_Obool)),X24958),X24957) = c_Orderings_Obot__class_Obot(tc_fun(X24959,tc_HOL_Obool)) )
      & ( esk199_3(X24957,X24958,X24959) = esk200_3(X24957,X24958,X24959)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24959,tc_HOL_Obool)),X24958),X24957) = c_Orderings_Obot__class_Obot(tc_fun(X24959,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_8725,plain,
    ! [X31755,X31756,X31757] :
      ( ~ class_Orderings_Olinorder(X31757)
      | ~ hBOOL(hAPP(hAPP(c_member(X31757),X31756),hAPP(c_List_Oset(X31757),X31755)))
      | ~ c_List_Olinorder__class_Osorted(X31757,X31755)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31757,X31757,c_COMBI(X31757)),X31756),c_List_Oremove1(X31757,X31756,X31755)) = X31755 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__remove1])]) ).

fof(i_0_8726,plain,
    ! [X22154,X22155] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22155),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)),X22154))
      | c_Divides_OnegDivAlg(X22155,X22154) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22155),X22154)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22155,X22154)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__div__mod])]) ).

fof(i_0_8727,plain,
    ! [X25660,X25661,X25662] :
      ( ~ class_Lattices_Olattice(X25662)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25662),X25661))
      | X25660 = c_Orderings_Obot__class_Obot(tc_fun(X25662,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25662,tc_HOL_Obool)),X25660),X25661))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25662),c_Big__Operators_Olattice__class_OInf__fin(X25662,X25660)),c_Big__Operators_Olattice__class_OInf__fin(X25662,X25661)) = c_Big__Operators_Olattice__class_OInf__fin(X25662,X25661) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osubset__idem])]) ).

fof(i_0_8728,plain,
    ! [X23518,X23519,X23520] :
      ( ~ class_Lattices_Olattice(X23520)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23520),X23519))
      | X23518 = c_Orderings_Obot__class_Obot(tc_fun(X23520,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23520,tc_HOL_Obool)),X23518),X23519))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23520),c_Big__Operators_Olattice__class_OSup__fin(X23520,X23518)),c_Big__Operators_Olattice__class_OSup__fin(X23520,X23519)) = c_Big__Operators_Olattice__class_OSup__fin(X23520,X23519) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osubset__idem])]) ).

fof(i_0_8729,plain,
    ! [X23035,X23036,X23037] :
      ( ~ class_Orderings_Olinorder(X23037)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23037),X23036))
      | X23035 = c_Orderings_Obot__class_Obot(tc_fun(X23037,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23037,tc_HOL_Obool)),X23035),X23036))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X23037),c_Big__Operators_Olinorder__class_OMax(X23037,X23035)),c_Big__Operators_Olinorder__class_OMax(X23037,X23036)) = c_Big__Operators_Olinorder__class_OMax(X23037,X23036) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osubset__idem])]) ).

fof(i_0_8730,plain,
    ! [X21802,X21803,X21804] :
      ( ~ class_Orderings_Olinorder(X21804)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21804),X21803))
      | X21802 = c_Orderings_Obot__class_Obot(tc_fun(X21804,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X21804,tc_HOL_Obool)),X21802),X21803))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21804),c_Big__Operators_Olinorder__class_OMin(X21804,X21802)),c_Big__Operators_Olinorder__class_OMin(X21804,X21803)) = c_Big__Operators_Olinorder__class_OMin(X21804,X21803) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osubset__idem])]) ).

fof(i_0_8731,plain,
    ! [X20754,X20755,X20756] : 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,X20756,X20755)),X20754),X20755) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20756),X20754),X20755),
    inference(variable_rename,[status(thm)],[fact_zpower__zmod]) ).

fof(i_0_8732,plain,
    ! [X20748,X20749,X20750] : 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,X20750,X20749)),X20748),X20749) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20750),X20748),X20749),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmod__left]) ).

fof(i_0_8733,plain,
    ! [X26790,X26791,X26792,X26793] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26792),X26791),c_Complete__Lattice_OInf__class_OInf(X26792,X26790)))
        | ~ hBOOL(hAPP(hAPP(c_member(X26792),X26793),X26790))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26792),X26791),X26793))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26792) )
      & ( hBOOL(hAPP(hAPP(c_member(X26792),esk243_3(X26790,X26791,X26792)),X26790))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26792),X26791),c_Complete__Lattice_OInf__class_OInf(X26792,X26790)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26792) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26792),X26791),esk243_3(X26790,X26791,X26792)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26792),X26791),c_Complete__Lattice_OInf__class_OInf(X26792,X26790)))
        | ~ class_Complete__Lattice_Ocomplete__lattice(X26792) ) ),
    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_8734,plain,
    ! [X29946,X29947,X29948,X29949] :
      ( ( X29949 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X29948),X29949),hAPP(hAPP(c_List_Olist_OCons(X29948),X29947),X29946)) = c_List_Olist_ONil(X29948) )
      & ( X29949 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X29948),X29949),hAPP(hAPP(c_List_Olist_OCons(X29948),X29947),X29946)) = hAPP(hAPP(c_List_Olist_OCons(X29948),X29947),hAPP(hAPP(c_List_Otake(X29948),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29949),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X29946)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Cons_H])]) ).

fof(i_0_8735,plain,
    ! [X24866,X24867,X24868,X24869] :
      ( ~ hBOOL(hAPP(X24869,X24868))
      | ~ hBOOL(hAPP(X24867,X24868))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24866,tc_HOL_Obool)),X24869),X24867),X24868)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf1I])]) ).

fof(i_0_8736,plain,
    ! [X32900,X32901,X32902,X32904,X32905,X32906,X32907] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32902),esk507_3(X32900,X32901,X32902)),hAPP(c_List_Oset(X32902),X32900)))
        | ~ c_List_Olist__ex(X32902,X32901,X32900) )
      & ( hBOOL(hAPP(X32901,esk507_3(X32900,X32901,X32902)))
        | ~ c_List_Olist__ex(X32902,X32901,X32900) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32906),X32907),hAPP(c_List_Oset(X32906),X32904)))
        | ~ hBOOL(hAPP(X32905,X32907))
        | c_List_Olist__ex(X32906,X32905,X32904) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__iff__raw])])])])])]) ).

fof(i_0_8737,plain,
    ! [X32892,X32893,X32894,X32895,X32896,X32897,X32898] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32894),X32895),hAPP(c_List_Oset(X32894),X32893)))
        | ~ hBOOL(hAPP(X32892,X32895))
        | c_List_Olist__ex(X32894,X32892,X32893) )
      & ( hBOOL(hAPP(hAPP(c_member(X32898),esk506_3(X32896,X32897,X32898)),hAPP(c_List_Oset(X32898),X32897)))
        | ~ c_List_Olist__ex(X32898,X32896,X32897) )
      & ( hBOOL(hAPP(X32896,esk506_3(X32896,X32897,X32898)))
        | ~ c_List_Olist__ex(X32898,X32896,X32897) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Bex__set__list__ex])])])])])]) ).

fof(i_0_8738,plain,
    ! [X32255,X32256,X32257,X32259,X32260,X32261,X32262] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32257),esk469_3(X32255,X32256,X32257)),hAPP(c_List_Oset(X32257),X32255)))
        | ~ c_List_Olist__ex(X32257,X32256,X32255) )
      & ( hBOOL(hAPP(X32256,esk469_3(X32255,X32256,X32257)))
        | ~ c_List_Olist__ex(X32257,X32256,X32255) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X32261),X32262),hAPP(c_List_Oset(X32261),X32259)))
        | ~ hBOOL(hAPP(X32260,X32262))
        | c_List_Olist__ex(X32261,X32260,X32259) ) ),
    inference(distribute,[status(thm)],[inference(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_8739,plain,
    ! [X26651] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X26651)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[fact_Rep__Integ]) ).

fof(i_0_8740,plain,
    ! [X23423,X23424,X23425,X23426,X23427] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X23427,X23426,X23425)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23427),X23424))
      | X23424 = c_Orderings_Obot__class_Obot(tc_fun(X23427,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23427),X23423))
      | X23423 = c_Orderings_Obot__class_Obot(tc_fun(X23427,tc_HOL_Obool))
      | hAPP(X23425,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23427,tc_HOL_Obool)),X23424),X23423)) = hAPP(hAPP(X23426,hAPP(X23425,X23424)),hAPP(X23425,X23423)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Ounion__idem])]) ).

fof(i_0_8741,plain,
    ! [X31022,X31023,X31024,X31025,X31026,X31027,X31028] :
      ( ( ~ hBOOL(hAPP(c_List_Olistsp(X31024,X31023),X31022))
        | ~ hBOOL(hAPP(hAPP(c_member(X31024),X31025),hAPP(c_List_Oset(X31024),X31022)))
        | hBOOL(hAPP(X31023,X31025)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31028),esk415_3(X31026,X31027,X31028)),hAPP(c_List_Oset(X31028),X31026)))
        | hBOOL(hAPP(c_List_Olistsp(X31028,X31027),X31026)) )
      & ( ~ hBOOL(hAPP(X31027,esk415_3(X31026,X31027,X31028)))
        | hBOOL(hAPP(c_List_Olistsp(X31028,X31027),X31026)) ) ),
    inference(distribute,[status(thm)],[inference(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_8742,plain,
    ! [X18824,X18825,X18826,X18827] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18827)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18827),c_Groups_Ozero__class_Ozero(X18827)),X18826))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18827),X18825),X18824))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18827),X18825),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18827),X18826),X18824))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing2])]) ).

fof(i_0_8743,plain,
    ! [X18820,X18821,X18822,X18823] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18823)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18823),c_Groups_Ozero__class_Ozero(X18823)),X18822))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18823),X18821),X18820))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18823),X18821),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18823),X18822),X18820))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__strict__increasing])]) ).

fof(i_0_8744,plain,
    ! [X18631,X18632,X18633,X18634] :
      ( ~ class_Rings_Olinordered__semidom(X18634)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18634),c_Groups_Ozero__class_Ozero(X18634)),X18633))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18634),X18632),X18631))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18634),X18632),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18634),X18633),X18631))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__add__strict])]) ).

fof(i_0_8745,plain,
    ! [X18734,X18735,X18736,X18737] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18737)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18737),c_Groups_Ozero__class_Ozero(X18737)),X18736))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18737),X18735),X18734))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18737),X18735),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18737),X18736),X18734))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing])]) ).

fof(i_0_8746,plain,
    ! [X18730,X18731,X18732,X18733] :
      ( ~ class_Groups_Oordered__comm__monoid__add(X18733)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18733),c_Groups_Ozero__class_Ozero(X18733)),X18732))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18733),X18731),X18730))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18733),X18731),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18733),X18730),X18732))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__increasing2])]) ).

fof(i_0_8747,plain,
    ! [X20912,X20913] : X20913 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20912),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20913),X20912))),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20913,X20912)),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality]) ).

cnf(i_0_8748,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_5773]) ).

fof(i_0_8749,plain,
    ! [X25142,X25143,X25144,X25145] :
      ( ~ class_Lattices_Osemilattice__inf(X25145)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25145),X25144),X25143))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25145),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25145),X25144),X25142)),X25143)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI1])]) ).

fof(i_0_8750,plain,
    ! [X25138,X25139,X25140,X25141] :
      ( ~ class_Lattices_Osemilattice__inf(X25141)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25141),X25140),X25139))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25141),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25141),X25138),X25140)),X25139)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__infI2])]) ).

fof(i_0_8751,plain,
    ! [X21578,X21579,X21580,X21581] :
      ( ~ class_Orderings_Olinorder(X21581)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21581),X21580),X21579))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21581),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21581),X21580),X21578)),X21579)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI1])]) ).

fof(i_0_8752,plain,
    ! [X21574,X21575,X21576,X21577] :
      ( ~ class_Orderings_Olinorder(X21577)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21577),X21576),X21575))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21577),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21577),X21574),X21576)),X21575)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__infI2])]) ).

fof(i_0_8753,plain,
    ! [X24988,X24989,X24990,X24991] :
      ( ~ class_Lattices_Osemilattice__inf(X24991)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24991),X24990),X24989))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24991),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24991),X24990),X24988)),X24989)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI1])]) ).

fof(i_0_8754,plain,
    ! [X24992,X24993,X24994,X24995] :
      ( ~ class_Lattices_Osemilattice__inf(X24995)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24995),X24994),X24993))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24995),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24995),X24992),X24994)),X24993)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI2])]) ).

fof(i_0_8755,plain,
    ! [X21539,X21540,X21541,X21542] :
      ( ~ class_Orderings_Olinorder(X21542)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21542),X21541),X21540))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21542),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21542),X21541),X21539)),X21540)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI1])]) ).

fof(i_0_8756,plain,
    ! [X21543,X21544,X21545,X21546] :
      ( ~ class_Orderings_Olinorder(X21546)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21546),X21545),X21544))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21546),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21546),X21543),X21545)),X21544)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI2])]) ).

fof(i_0_8757,plain,
    ! [X29952,X29953] : hAPP(c_Relation_OImage(tc_List_Olist(X29953),tc_List_Olist(X29953),c_List_Olistrel(X29953,X29952)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29953)),c_List_Olist_ONil(X29953)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29953),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29953)),c_List_Olist_ONil(X29953)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29953),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_listrel__Nil]) ).

fof(i_0_8758,plain,
    ! [X24481,X24482,X24483,X24484] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24483,tc_Nat_Onat),X24481),X24482) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X24483),X24484),X24482))
        | hAPP(X24481,X24484) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24483),X24482)) )
      & ( hBOOL(hAPP(hAPP(c_member(X24483),esk180_3(X24481,X24482,X24483)),X24482))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24483,tc_Nat_Onat),X24481),X24482) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24483),X24482)) )
      & ( hAPP(X24481,esk180_3(X24481,X24482,X24483)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24483,tc_Nat_Onat),X24481),X24482) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24483),X24482)) ) ),
    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_8759,plain,
    ! [X21910,X21911,X21912,X21913] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21912,tc_Nat_Onat),X21910),X21911) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(X21912),X21913),X21911))
        | hAPP(X21910,X21913) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21912),X21911)) )
      & ( hBOOL(hAPP(hAPP(c_member(X21912),esk84_3(X21910,X21911,X21912)),X21911))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21912,tc_Nat_Onat),X21910),X21911) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21912),X21911)) )
      & ( hAPP(X21910,esk84_3(X21910,X21911,X21912)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21912,tc_Nat_Onat),X21910),X21911) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21912),X21911)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__eq__1__iff])])])])]) ).

fof(i_0_8760,plain,
    ! [X33486,X33487,X33488,X33489,X33490] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X33490),X33489),X33488))
      | hAPP(c_Quotient_OBabs(X33490,X33487,X33488,X33486),X33489) = hAPP(X33486,X33489) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Babs__def])]) ).

fof(i_0_8761,plain,
    ! [X18862,X18863,X18864,X18865,X18866,X18867,X18868] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18863),X18862))
        | hBOOL(hAPP(X18864,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X18864,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18863),X18862))) )
      & ( X18863 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18862),X18865)
        | hBOOL(hAPP(X18864,X18865))
        | ~ hBOOL(hAPP(X18864,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18863),X18862))) )
      & ( X18867 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18866),esk27_3(X18866,X18867,X18868))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18867),X18866))
        | hBOOL(hAPP(X18868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18867),X18866))) )
      & ( ~ hBOOL(hAPP(X18868,esk27_3(X18866,X18867,X18868)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18867),X18866))
        | hBOOL(hAPP(X18868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18867),X18866))) )
      & ( X18867 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18866),esk27_3(X18866,X18867,X18868))
        | ~ hBOOL(hAPP(X18868,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X18868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18867),X18866))) )
      & ( ~ hBOOL(hAPP(X18868,esk27_3(X18866,X18867,X18868)))
        | ~ hBOOL(hAPP(X18868,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X18868,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18867),X18866))) ) ),
    inference(distribute,[status(thm)],[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_5774])])])])])]) ).

fof(i_0_8762,plain,
    ! [X18854,X18855,X18856,X18857,X18858,X18859,X18860] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18855),X18854))
        | hBOOL(hAPP(X18856,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X18856,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18855),X18854))) )
      & ( X18855 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18854),X18857)
        | hBOOL(hAPP(X18856,X18857))
        | ~ hBOOL(hAPP(X18856,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18855),X18854))) )
      & ( X18859 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18858),esk26_3(X18858,X18859,X18860))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18859),X18858))
        | hBOOL(hAPP(X18860,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18859),X18858))) )
      & ( ~ hBOOL(hAPP(X18860,esk26_3(X18858,X18859,X18860)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18859),X18858))
        | hBOOL(hAPP(X18860,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18859),X18858))) )
      & ( X18859 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18858),esk26_3(X18858,X18859,X18860))
        | ~ hBOOL(hAPP(X18860,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X18860,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18859),X18858))) )
      & ( ~ hBOOL(hAPP(X18860,esk26_3(X18858,X18859,X18860)))
        | ~ hBOOL(hAPP(X18860,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | hBOOL(hAPP(X18860,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18859),X18858))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__split])])])])])]) ).

fof(i_0_8763,plain,
    ! [X33863,X33864,X33865,X33866] :
      ( ~ class_Divides_Osemiring__div(X33866)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33866),X33865),X33864))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33866),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33866),X33864),X33865)),X33863) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33866),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33866),X33864),X33863)),X33865) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult])]) ).

fof(i_0_8764,plain,
    ! [X26186,X26187] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26187),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26187,tc_HOL_Obool)),X26186)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X26187),c_Orderings_Otop__class_Otop(tc_fun(X26187,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26187),X26186)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26187),c_Orderings_Otop__class_Otop(tc_fun(X26187,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X26187),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26187,tc_HOL_Obool)),X26186)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26187),X26186)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__compl])])]) ).

fof(i_0_8765,plain,
    ! [X20098,X20099] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20099),X20098))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20098))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20099)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20098))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20099),X20098))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20099)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20098))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20099),X20098))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20099),X20098))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20099)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20098))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20098))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20099),X20098))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20099)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20098))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__nat__number__of])])]) ).

fof(i_0_8766,plain,
    ! [X23150,X23151,X23152,X23153] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23153,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23153),X23152),X23151)),X23150) = hAPP(hAPP(c_Set_Oinsert(X23153),X23152),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23153,tc_HOL_Obool)),X23151),X23150)),
    inference(variable_rename,[status(thm)],[fact_Un__insert__left]) ).

fof(i_0_8767,plain,
    ! [X19585,X19586,X19587,X19588] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X19588,X19587,X19586)
      | hAPP(c_Fun_Ocomp(X19587,X19587,X19587,hAPP(X19586,X19585)),hAPP(X19586,X19585)) = hAPP(X19586,X19585) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__comp__idem])]) ).

cnf(i_0_8768,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_5730]) ).

fof(i_0_8769,plain,
    ! [X21975,X21976,X21977,X21978] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21978,X21977),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21976),X21975)))
      | X21977 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21978,X21977) = X21975 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__mod])]) ).

fof(i_0_8770,plain,
    ! [X22375,X22376,X22377] : hAPP(c_Product__Type_Osnd(X22377,X22376),X22375) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22377,X22376,X22376),hAPP(c_COMBK(tc_fun(X22376,X22376),X22377),c_COMBI(X22376))),X22375),
    inference(variable_rename,[status(thm)],[fact_snd__def]) ).

fof(i_0_8771,plain,
    ! [X19246,X19247] :
      ( ~ class_Int_Oring__char__0(X19247)
      | ~ hBOOL(hAPP(hAPP(c_member(X19247),X19246),c_Int_Oring__1__class_OInts(X19247)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19247),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19247),c_Groups_Oone__class_Oone(X19247)),X19246)),X19246) != c_Groups_Ozero__class_Ozero(X19247) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__odd__nonzero])]) ).

fof(i_0_8772,plain,
    ! [X24878,X24879,X24880] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24880),X24879))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X24880),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24880,tc_HOL_Obool)),X24879),X24878))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24880),X24878))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X24880),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24880,tc_HOL_Obool)),X24879),X24878))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Int])])]) ).

fof(i_0_8773,plain,
    ! [X17340,X17341,X17342] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17342),X17341))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17342),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17342,tc_HOL_Obool)),X17341),X17340))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Diff])]) ).

fof(i_0_8774,plain,
    ! [X31689,X31690,X31691,X31692] :
      ( ~ class_Orderings_Olinorder(X31692)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31692),X31691),X31690))
      | ~ c_List_Olinorder__class_Osorted(X31692,hAPP(hAPP(c_List_Olist_OCons(X31692),X31690),X31689))
      | c_List_Olinorder__class_Osorted(X31692,hAPP(hAPP(c_List_Olist_OCons(X31692),X31691),hAPP(hAPP(c_List_Olist_OCons(X31692),X31690),X31689))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many])]) ).

fof(i_0_8775,plain,
    ! [X31685,X31686,X31687,X31688] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31688),X31687),X31686))
        | ~ c_List_Olinorder__class_Osorted(X31688,hAPP(hAPP(c_List_Olist_OCons(X31688),X31687),hAPP(hAPP(c_List_Olist_OCons(X31688),X31686),X31685)))
        | ~ class_Orderings_Olinorder(X31688) )
      & ( c_List_Olinorder__class_Osorted(X31688,hAPP(hAPP(c_List_Olist_OCons(X31688),X31686),X31685))
        | ~ c_List_Olinorder__class_Osorted(X31688,hAPP(hAPP(c_List_Olist_OCons(X31688),X31687),hAPP(hAPP(c_List_Olist_OCons(X31688),X31686),X31685)))
        | ~ class_Orderings_Olinorder(X31688) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X31688),X31687),X31686))
        | ~ c_List_Olinorder__class_Osorted(X31688,hAPP(hAPP(c_List_Olist_OCons(X31688),X31686),X31685))
        | c_List_Olinorder__class_Osorted(X31688,hAPP(hAPP(c_List_Olist_OCons(X31688),X31687),hAPP(hAPP(c_List_Olist_OCons(X31688),X31686),X31685)))
        | ~ class_Orderings_Olinorder(X31688) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__many__eq])])]) ).

fof(i_0_8776,plain,
    ! [X22279,X22280,X22281,X22282] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22282,X22281),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22280),X22279)))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22282,X22281) = X22279 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__eq])]) ).

fof(i_0_8777,plain,
    ! [X20897,X20898] :
      ( ( 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,X20897,X20898)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20898)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20897,X20898)),X20898))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20898)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__conj])])]) ).

fof(i_0_8778,plain,
    ! [X20808,X20809] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20809))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20808,X20809)),X20809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__bound])]) ).

fof(i_0_8779,plain,
    ! [X21282,X21283] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21283))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21282,X21283)),X21283)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less__divisor])]) ).

fof(i_0_8780,plain,
    ! [X20802,X20803] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20803))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20803,X20802)),X20803)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__le__nonneg__dividend])]) ).

fof(i_0_8781,plain,
    ! [X21342,X21343] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21343))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21342,X21343)),X21343)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__le__divisor])]) ).

fof(i_0_8782,plain,
    ! [X31255,X31256] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31256)),c_List_Oremdups(X31256,X31255))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31256)),X31255))),
    inference(variable_rename,[status(thm)],[fact_length__remdups__leq]) ).

fof(i_0_8783,plain,
    ! [X29510,X29511] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X29511),hAPP(c_List_Oset(X29511),X29510))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29511)),X29510))),
    inference(variable_rename,[status(thm)],[fact_card__length]) ).

fof(i_0_8784,plain,
    ! [X33623,X33624,X33625] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33625),hAPP(c_Int_Onumber__class_Onumber__of(X33625),X33624)),hAPP(c_Int_Onumber__class_Onumber__of(X33625),X33623)))
        | c_Divides_Odiv__class_Omod(X33625,hAPP(c_Int_Onumber__class_Onumber__of(X33625),X33623),hAPP(c_Int_Onumber__class_Onumber__of(X33625),X33624)) = c_Groups_Ozero__class_Ozero(X33625)
        | ~ class_Divides_Osemiring__div(X33625)
        | ~ class_Int_Onumber(X33625) )
      & ( c_Divides_Odiv__class_Omod(X33625,hAPP(c_Int_Onumber__class_Onumber__of(X33625),X33623),hAPP(c_Int_Onumber__class_Onumber__of(X33625),X33624)) != c_Groups_Ozero__class_Ozero(X33625)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33625),hAPP(c_Int_Onumber__class_Onumber__of(X33625),X33624)),hAPP(c_Int_Onumber__class_Onumber__of(X33625),X33623)))
        | ~ class_Divides_Osemiring__div(X33625)
        | ~ class_Int_Onumber(X33625) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0__number__of])])]) ).

fof(i_0_8785,plain,
    ! [X23966,X23967,X23968,X23969,X23970] :
      ( hAPP(c_Set_Oimage(X23970,X23969,X23968),X23967) != X23966
      | hAPP(c_Set_Oimage(tc_fun(X23970,tc_HOL_Obool),tc_fun(X23969,tc_HOL_Obool),c_Set_Oimage(X23970,X23969,X23968)),hAPP(c_Set_OPow(X23970),X23967)) = hAPP(c_Set_OPow(X23969),X23966) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__Pow__surj])]) ).

fof(i_0_8786,plain,
    ! [X29787,X29788,X29789] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X29789),X29788),hAPP(c_List_Oset(X29789),X29787)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29789),hAPP(hAPP(c_List_Olist_OCons(X29789),X29788),X29787))) )
      & ( hBOOL(hAPP(c_List_Odistinct(X29789),X29787))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29789),hAPP(hAPP(c_List_Olist_OCons(X29789),X29788),X29787))) )
      & ( hBOOL(hAPP(hAPP(c_member(X29789),X29788),hAPP(c_List_Oset(X29789),X29787)))
        | ~ hBOOL(hAPP(c_List_Odistinct(X29789),X29787))
        | hBOOL(hAPP(c_List_Odistinct(X29789),hAPP(hAPP(c_List_Olist_OCons(X29789),X29788),X29787))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5775])])]) ).

fof(i_0_8787,plain,
    ! [X26863,X26864,X26865,X26866] :
      ( hAPP(c_Set_Oimage(X26866,X26865,X26864),c_Orderings_Otop__class_Otop(tc_fun(X26866,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X26865,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(X26866,X26865,X26864),hAPP(c_Set_Ovimage(X26866,X26865,X26864),X26863)) = X26863 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_surj__image__vimage__eq])]) ).

cnf(i_0_8788,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_5709]) ).

fof(i_0_8789,plain,
    ! [X21979,X21980,X21981,X21982] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21982,X21981),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21980),X21979)))
      | X21981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21982),X21981) = X21980 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__div])]) ).

fof(i_0_8790,plain,
    ! [X21159,X21160,X21161] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21161),hAPP(c_Groups_Ouminus__class_Ouminus(X21161),X21160)),X21159))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21161),hAPP(c_Groups_Ouminus__class_Ouminus(X21161),X21159)),X21160))
        | ~ class_Groups_Oordered__ab__group__add(X21161) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21161),hAPP(c_Groups_Ouminus__class_Ouminus(X21161),X21159)),X21160))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21161),hAPP(c_Groups_Ouminus__class_Ouminus(X21161),X21160)),X21159))
        | ~ class_Groups_Oordered__ab__group__add(X21161) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__less__iff])])]) ).

fof(i_0_8791,plain,
    ! [X25921,X25922,X25923] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25923)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25923),hAPP(c_Groups_Oabs__class_Oabs(X25923),X25922)),X25921))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25923),hAPP(c_Groups_Ouminus__class_Ouminus(X25923),X25922)),X25921)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D2])]) ).

fof(i_0_8792,plain,
    ! [X21138,X21139,X21140] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21140),hAPP(c_Groups_Ouminus__class_Ouminus(X21140),X21139)),X21138))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21140),hAPP(c_Groups_Ouminus__class_Ouminus(X21140),X21138)),X21139))
        | ~ class_Groups_Oordered__ab__group__add(X21140) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21140),hAPP(c_Groups_Ouminus__class_Ouminus(X21140),X21138)),X21139))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21140),hAPP(c_Groups_Ouminus__class_Ouminus(X21140),X21139)),X21138))
        | ~ class_Groups_Oordered__ab__group__add(X21140) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__iff])])]) ).

fof(i_0_8793,plain,
    ! [X20891,X20892] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20891,X20892)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20892),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20892),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20891,X20892)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20892),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_8794,plain,
    ! [X20893,X20894] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20894),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,X20893,X20894)),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_8795,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_5776]) ).

fof(i_0_8796,plain,
    ! [X27612,X27613,X27614,X27615] : hAPP(c_Set_Ovimage(X27615,X27614,X27613),hAPP(c_Set_OCollect(X27614),X27612)) = hAPP(c_Set_OCollect(X27615),hAPP(hAPP(c_COMBB(X27614,tc_HOL_Obool,X27615),X27612),X27613)),
    inference(variable_rename,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(i_0_8797,plain,
    ! [X22283,X22284,X22285,X22286] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22286,X22285),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),X22284),X22283)))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X22286),X22285) = X22284 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__eq])]) ).

fof(i_0_8798,plain,
    ! [X18655,X18656,X18657,X18658] :
      ( ~ c_Fun_Oinj__on(X18658,X18657,X18656,X18655)
      | hAPP(c_Finite__Set_Ocard(X18657),hAPP(c_Set_Oimage(X18658,X18657,X18656),X18655)) = hAPP(c_Finite__Set_Ocard(X18658),X18655) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__image])]) ).

fof(i_0_8799,plain,
    ! [X30254,X30255,X30256,X30257] : hAPP(hAPP(c_List_Otake(X30257),X30256),hAPP(hAPP(c_List_Odrop(X30257),X30255),X30254)) = hAPP(hAPP(c_List_Odrop(X30257),X30255),hAPP(hAPP(c_List_Otake(X30257),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30256),X30255)),X30254)),
    inference(variable_rename,[status(thm)],[fact_take__drop]) ).

fof(i_0_8800,plain,
    ! [X31722,X31723,X31724,X31725,X31726] :
      ( ~ class_Orderings_Olinorder(X31726)
      | ~ c_List_Olinorder__class_Osorted(X31726,hAPP(hAPP(c_List_Omap(X31725,X31726),X31724),X31723))
      | c_List_Olinorder__class_Osorted(X31726,hAPP(hAPP(c_List_Omap(X31725,X31726),X31724),hAPP(c_List_Ofilter(X31725,X31722),X31723))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__filter])]) ).

fof(i_0_8801,plain,
    ! [X28364,X28365,X28366] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X28366,X28365) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X28364,X28365)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X28364),X28366))
      | X28366 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X28364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28365),esk314_3(X28364,X28365,X28366))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__eq__lemma])])]) ).

fof(i_0_8802,plain,
    ! [X31896,X31897,X31898,X31899,X31900,X31901,X31902] :
      ( ( c_List_OtakeWhile(X31898,X31897,X31896) != X31896
        | ~ hBOOL(hAPP(hAPP(c_member(X31898),X31899),hAPP(c_List_Oset(X31898),X31896)))
        | hBOOL(hAPP(X31897,X31899)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31902),esk434_3(X31900,X31901,X31902)),hAPP(c_List_Oset(X31902),X31900)))
        | c_List_OtakeWhile(X31902,X31901,X31900) = X31900 )
      & ( ~ hBOOL(hAPP(X31901,esk434_3(X31900,X31901,X31902)))
        | c_List_OtakeWhile(X31902,X31901,X31900) = X31900 ) ),
    inference(distribute,[status(thm)],[inference(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_8803,plain,
    ! [X18748,X18749] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18749),c_Groups_Ozero__class_Ozero(X18749)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18749),X18748),X18748)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18749),c_Groups_Ozero__class_Ozero(X18749)),X18748))
        | ~ class_Groups_Olinordered__ab__group__add(X18749) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18749),c_Groups_Ozero__class_Ozero(X18749)),X18748))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18749),c_Groups_Ozero__class_Ozero(X18749)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18749),X18748),X18748)))
        | ~ class_Groups_Olinordered__ab__group__add(X18749) ) ),
    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_8804,plain,
    ! [X18746,X18747] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18747),c_Groups_Ozero__class_Ozero(X18747)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18747),X18746),X18746)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18747),c_Groups_Ozero__class_Ozero(X18747)),X18746))
        | ~ class_Groups_Olinordered__ab__group__add(X18747) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18747),c_Groups_Ozero__class_Ozero(X18747)),X18746))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18747),c_Groups_Ozero__class_Ozero(X18747)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18747),X18746),X18746)))
        | ~ class_Groups_Olinordered__ab__group__add(X18747) ) ),
    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_8805,plain,
    ! [X32332,X32333,X32334,X32336,X32337,X32338,X32339] :
      ( ( hBOOL(hAPP(hAPP(c_member(X32334),esk476_3(X32332,X32333,X32334)),hAPP(c_List_Oset(X32334),X32333)))
        | c_List_Olist__all(X32334,X32332,X32333) )
      & ( ~ hBOOL(hAPP(X32332,esk476_3(X32332,X32333,X32334)))
        | c_List_Olist__all(X32334,X32332,X32333) )
      & ( ~ c_List_Olist__all(X32338,X32336,X32337)
        | ~ hBOOL(hAPP(hAPP(c_member(X32338),X32339),hAPP(c_List_Oset(X32338),X32337)))
        | hBOOL(hAPP(X32336,X32339)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ball__set__list__all])])])])])]) ).

fof(i_0_8806,plain,
    ! [X32340,X32341,X32342,X32343,X32344,X32345,X32346] :
      ( ( ~ c_List_Olist__all(X32342,X32341,X32340)
        | ~ hBOOL(hAPP(hAPP(c_member(X32342),X32343),hAPP(c_List_Oset(X32342),X32340)))
        | hBOOL(hAPP(X32341,X32343)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32346),esk477_3(X32344,X32345,X32346)),hAPP(c_List_Oset(X32346),X32344)))
        | c_List_Olist__all(X32346,X32345,X32344) )
      & ( ~ hBOOL(hAPP(X32345,esk477_3(X32344,X32345,X32346)))
        | c_List_Olist__all(X32346,X32345,X32344) ) ),
    inference(distribute,[status(thm)],[inference(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_8807,plain,
    ! [X32311,X32312,X32313,X32314,X32315,X32316,X32317] :
      ( ( ~ c_List_Olist__all(X32313,X32312,X32311)
        | ~ hBOOL(hAPP(hAPP(c_member(X32313),X32314),hAPP(c_List_Oset(X32313),X32311)))
        | hBOOL(hAPP(X32312,X32314)) )
      & ( hBOOL(hAPP(hAPP(c_member(X32317),esk475_3(X32315,X32316,X32317)),hAPP(c_List_Oset(X32317),X32315)))
        | c_List_Olist__all(X32317,X32316,X32315) )
      & ( ~ hBOOL(hAPP(X32316,esk475_3(X32315,X32316,X32317)))
        | c_List_Olist__all(X32317,X32316,X32315) ) ),
    inference(distribute,[status(thm)],[inference(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_8808,plain,
    ! [X18779,X18780] :
      ( ( ~ 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),X18780),X18779)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18780))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18779)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18780))
        | 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),X18780),X18779))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18779))
        | 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),X18780),X18779))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__gr__0])])]) ).

cnf(i_0_8809,plain,
    c_List_OdropWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_5777]) ).

fof(i_0_8810,plain,
    ! [X20703,X20704,X20705,X20706,X20707,X20708] :
      ( ~ class_Divides_Osemiring__div(X20708)
      | c_Divides_Odiv__class_Omod(X20708,X20707,X20706) != c_Divides_Odiv__class_Omod(X20708,X20705,X20706)
      | c_Divides_Odiv__class_Omod(X20708,X20704,X20706) != c_Divides_Odiv__class_Omod(X20708,X20703,X20706)
      | c_Divides_Odiv__class_Omod(X20708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20708),X20707),X20704),X20706) = c_Divides_Odiv__class_Omod(X20708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20708),X20705),X20703),X20706) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__cong])]) ).

fof(i_0_8811,plain,
    ! [X20673,X20674,X20675,X20676,X20677,X20678] :
      ( ~ class_Divides_Osemiring__div(X20678)
      | c_Divides_Odiv__class_Omod(X20678,X20677,X20676) != c_Divides_Odiv__class_Omod(X20678,X20675,X20676)
      | c_Divides_Odiv__class_Omod(X20678,X20674,X20676) != c_Divides_Odiv__class_Omod(X20678,X20673,X20676)
      | c_Divides_Odiv__class_Omod(X20678,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20678),X20677),X20674),X20676) = c_Divides_Odiv__class_Omod(X20678,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20678),X20675),X20673),X20676) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__cong])]) ).

fof(i_0_8812,plain,
    ! [X20709,X20710,X20711,X20712,X20713,X20714] :
      ( ~ class_Divides_Oring__div(X20714)
      | c_Divides_Odiv__class_Omod(X20714,X20713,X20712) != c_Divides_Odiv__class_Omod(X20714,X20711,X20712)
      | c_Divides_Odiv__class_Omod(X20714,X20710,X20712) != c_Divides_Odiv__class_Omod(X20714,X20709,X20712)
      | c_Divides_Odiv__class_Omod(X20714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20714),X20713),X20710),X20712) = c_Divides_Odiv__class_Omod(X20714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20714),X20711),X20709),X20712) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__cong])]) ).

fof(i_0_8813,plain,
    ! [X33764,X33765,X33766,X33767] :
      ( ~ class_Divides_Osemiring__div(X33767)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33767),X33766),X33765))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33767),X33766),X33764))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33767),X33766),c_Divides_Odiv__class_Omod(X33767,X33765,X33764))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mod])]) ).

fof(i_0_8814,plain,
    ! [X22721,X22722,X22723,X22724] :
      ( ~ class_Fields_Ofield(X22724)
      | X22723 = c_Groups_Ozero__class_Ozero(X22724)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X22722),X22721))
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22724),X22723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22721),X22722)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22724),hAPP(hAPP(c_Power_Opower__class_Opower(X22724),X22723),X22721)),hAPP(hAPP(c_Power_Opower__class_Opower(X22724),X22723),X22722)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__diff])]) ).

fof(i_0_8815,plain,
    ! [X17457,X17458,X17459] :
      ( hBOOL(hAPP(hAPP(c_member(X17459),X17458),X17457))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17459,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17459),X17458),X17457)),hAPP(hAPP(c_Set_Oinsert(X17459),X17458),c_Orderings_Obot__class_Obot(tc_fun(X17459,tc_HOL_Obool)))) = X17457 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5778])]) ).

fof(i_0_8816,plain,
    ! [X24565,X24566,X24567,X24568,X24569] :
      ( ~ class_Groups_Ocomm__monoid__add(X24569)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24568),X24567))
      | hBOOL(hAPP(hAPP(c_member(X24568),X24566),X24567))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24568,X24569),X24565),hAPP(hAPP(c_Set_Oinsert(X24568),X24566),X24567)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24569),hAPP(X24565,X24566)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24568,X24569),X24565),X24567)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5779])]) ).

fof(i_0_8817,plain,
    ! [X24560,X24561,X24562,X24563,X24564] :
      ( ~ class_Groups_Ocomm__monoid__add(X24564)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X24563),X24562))
      | hBOOL(hAPP(hAPP(c_member(X24563),X24561),X24562))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24563,X24564),X24560),hAPP(hAPP(c_Set_Oinsert(X24563),X24561),X24562)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X24564),hAPP(X24560,X24561)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24563,X24564),X24560),X24562)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5780])]) ).

fof(i_0_8818,plain,
    ! [X21988,X21989,X21990,X21991,X21992] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21992)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21991),X21990))
      | hBOOL(hAPP(hAPP(c_member(X21991),X21989),X21990))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21991,X21992),X21988),hAPP(hAPP(c_Set_Oinsert(X21991),X21989),X21990)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21992),hAPP(X21988,X21989)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21991,X21992),X21988),X21990)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5781])]) ).

fof(i_0_8819,plain,
    ! [X21983,X21984,X21985,X21986,X21987] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21987)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21986),X21985))
      | hBOOL(hAPP(hAPP(c_member(X21986),X21984),X21985))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21986,X21987),X21983),hAPP(hAPP(c_Set_Oinsert(X21986),X21984),X21985)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21987),hAPP(X21983,X21984)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21986,X21987),X21983),X21985)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5782])]) ).

fof(i_0_8820,plain,
    ! [X22241,X22242,X22243] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22243),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22242)),X22241))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22243,X22242),hAPP(c_Divides_OnegateSnd,X22241))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__rel__neg])]) ).

fof(i_0_8821,plain,
    ! [X17403,X17404,X17405,X17406] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17406),X17405),X17404))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17406,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X17406),X17405),X17403)),X17404) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17406,tc_HOL_Obool)),X17403),X17404) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__Diff1])]) ).

fof(i_0_8822,plain,
    ! [X17142,X17143,X17144] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17144),X17143))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17144),X17142))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17143),X17144)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17142),X17144)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17143),X17142) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat_Odiff__diff__eq])]) ).

fof(i_0_8823,plain,
    ! [X31934,X31935,X31936] : c_List_OtakeWhile(X31936,X31935,X31934) = hAPP(hAPP(c_List_Otake(X31936),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31936)),c_List_OtakeWhile(X31936,X31935,X31934))),X31934),
    inference(variable_rename,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(i_0_8824,plain,
    ! [X24262,X24263,X24264,X24266,X24267,X24268] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk148_2(X24262,X24263)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24263)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24264),X24263))
        | ~ hBOOL(hAPP(X24262,X24264)) )
      & ( hBOOL(hAPP(X24262,esk148_2(X24262,X24263)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24264),X24263))
        | ~ hBOOL(hAPP(X24262,X24264)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk149_2(X24266,X24267)),X24267))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24268),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24267)))
        | ~ hBOOL(hAPP(X24266,X24268)) )
      & ( hBOOL(hAPP(X24266,esk149_2(X24266,X24267)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24268),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24267)))
        | ~ hBOOL(hAPP(X24266,X24268)) ) ),
    inference(distribute,[status(thm)],[inference(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_8825,plain,
    ! [X17262,X17263,X17264] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17264)),X17263)),hAPP(c_Nat_OSuc,X17262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17264),X17263)),X17262),
    inference(variable_rename,[status(thm)],[fact_Suc__diff__diff]) ).

fof(i_0_8826,plain,
    ! [X20311,X20312,X20313,X20314] :
      ( ~ class_Rings_Olinordered__semidom(X20314)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20314),X20313),hAPP(c_Nat_OSuc,X20312)) != hAPP(hAPP(c_Power_Opower__class_Opower(X20314),X20311),hAPP(c_Nat_OSuc,X20312))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20314),c_Groups_Ozero__class_Ozero(X20314)),X20313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20314),c_Groups_Ozero__class_Ozero(X20314)),X20311))
      | X20313 = X20311 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__base])]) ).

cnf(i_0_8827,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_5783]) ).

fof(i_0_8828,plain,
    ! [X33462,X33463,X33464,X33465,X33467] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33464),X33465),c_Quotient_ORespects(X33464,X33463)))
        | ~ hBOOL(hAPP(X33462,X33465))
        | hBOOL(hAPP(X33462,esk536_3(X33462,X33463,X33464)))
        | ~ c_Equiv__Relations_Oequivp(X33464,X33463) )
      & ( hBOOL(hAPP(hAPP(c_member(X33464),esk537_3(X33462,X33463,X33464)),c_Quotient_ORespects(X33464,X33463)))
        | ~ hBOOL(hAPP(X33462,X33467))
        | ~ c_Equiv__Relations_Oequivp(X33464,X33463) )
      & ( hBOOL(hAPP(X33462,esk537_3(X33462,X33463,X33464)))
        | ~ hBOOL(hAPP(X33462,X33467))
        | ~ c_Equiv__Relations_Oequivp(X33464,X33463) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__reg__eqv])])])])]) ).

fof(i_0_8829,plain,
    ! [X21356,X21357] :
      ( ( X21357 = 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),X21357)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21356)))) )
      & ( X21356 = 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),X21357)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21356)))) )
      & ( X21357 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X21356 != 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),X21357)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21356)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__zle__neg])])]) ).

fof(i_0_8830,plain,
    ! [X28172] :
      ( ~ class_Orderings_Owellorder(X28172)
      | c_Wellfounded_Owf(X28172,hAPP(c_Set_OCollect(tc_prod(X28172,X28172)),hAPP(c_Product__Type_Oprod_Oprod__case(X28172,X28172,tc_HOL_Obool),c_Orderings_Oord__class_Oless(X28172)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf])]) ).

fof(i_0_8831,plain,
    ! [X31461,X31462,X31463,X31464,X31465,X31466,X31467] :
      ( ( hAPP(c_List_Ofilter(X31463,X31462),X31461) != c_List_Olist_ONil(X31463)
        | ~ hBOOL(hAPP(hAPP(c_member(X31463),X31464),hAPP(c_List_Oset(X31463),X31461)))
        | ~ hBOOL(hAPP(X31462,X31464)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31467),esk425_3(X31465,X31466,X31467)),hAPP(c_List_Oset(X31467),X31465)))
        | hAPP(c_List_Ofilter(X31467,X31466),X31465) = c_List_Olist_ONil(X31467) )
      & ( hBOOL(hAPP(X31466,esk425_3(X31465,X31466,X31467)))
        | hAPP(c_List_Ofilter(X31467,X31466),X31465) = c_List_Olist_ONil(X31467) ) ),
    inference(distribute,[status(thm)],[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_5784])])])])])]) ).

fof(i_0_8832,plain,
    ! [X33809,X33810,X33811,X33812] :
      ( ~ class_Rings_Ocomm__semiring__1(X33812)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33812),X33811),X33810))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33812),X33811),X33809))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33812),X33811),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X33812),X33810),X33809))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__add])]) ).

fof(i_0_8833,plain,
    ! [X33786,X33787,X33788,X33789] :
      ( ~ class_Rings_Ocomm__ring__1(X33789)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33789),X33788),X33787))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33789),X33788),X33786))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33789),X33788),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X33789),X33787),X33786))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff])]) ).

fof(i_0_8834,plain,
    ! [X21582,X21583,X21584,X21585] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21585),X21584),X21583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21585),X21584),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21585),X21583),X21582)))
        | ~ class_Orderings_Olinorder(X21585) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21585),X21584),X21582))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21585),X21584),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21585),X21583),X21582)))
        | ~ class_Orderings_Olinorder(X21585) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21585),X21584),X21583))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21585),X21584),X21582))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21585),X21584),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21585),X21583),X21582)))
        | ~ class_Orderings_Olinorder(X21585) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__less__iff__conj])])]) ).

fof(i_0_8835,plain,
    ! [X25006,X25007,X25008,X25009] :
      ( ~ class_Lattices_Osemilattice__inf(X25009)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25009),X25008),X25007))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25009),X25008),X25006))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25009),X25008),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25009),X25007),X25006))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__greatest])]) ).

fof(i_0_8836,plain,
    ! [X25002,X25003,X25004,X25005] :
      ( ~ class_Lattices_Osemilattice__inf(X25005)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25005),X25004),X25003))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25005),X25004),X25002))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25005),X25004),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25005),X25003),X25002))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__infI])]) ).

fof(i_0_8837,plain,
    ! [X24984,X24985,X24986,X24987] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24987),X24986),X24985))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24987),X24986),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24987),X24985),X24984)))
        | ~ class_Lattices_Osemilattice__inf(X24987) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24987),X24986),X24984))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24987),X24986),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24987),X24985),X24984)))
        | ~ class_Lattices_Osemilattice__inf(X24987) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24987),X24986),X24985))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24987),X24986),X24984))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24987),X24986),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24987),X24985),X24984)))
        | ~ class_Lattices_Osemilattice__inf(X24987) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__inf__iff])])]) ).

fof(i_0_8838,plain,
    ! [X21557,X21558,X21559,X21560] :
      ( ~ class_Orderings_Olinorder(X21560)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21560),X21559),X21558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21560),X21559),X21557))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21560),X21559),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21560),X21558),X21557))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__greatest])]) ).

fof(i_0_8839,plain,
    ! [X21553,X21554,X21555,X21556] :
      ( ~ class_Orderings_Olinorder(X21556)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21556),X21555),X21554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21556),X21555),X21553))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21556),X21555),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21556),X21554),X21553))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__infI])]) ).

fof(i_0_8840,plain,
    ! [X21535,X21536,X21537,X21538] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21538),X21537),X21536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21538),X21537),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21538),X21536),X21535)))
        | ~ class_Orderings_Olinorder(X21538) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21538),X21537),X21535))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21538),X21537),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21538),X21536),X21535)))
        | ~ class_Orderings_Olinorder(X21538) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21538),X21537),X21536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21538),X21537),X21535))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21538),X21537),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21538),X21536),X21535)))
        | ~ class_Orderings_Olinorder(X21538) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__inf__iff])])]) ).

fof(i_0_8841,plain,
    ! [X21325,X21326] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21326)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21325)))),
    inference(variable_rename,[status(thm)],[i_0_5785]) ).

fof(i_0_8842,plain,
    ! [X19682,X19683,X19684] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19684))
      | X19684 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19684),X19682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19683))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19682),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_8843,plain,
    ! [X31407,X31408,X31409,X31410,X31411,X31412,X31413] :
      ( ( hAPP(c_List_Ofilter(X31409,X31408),X31407) != X31407
        | ~ hBOOL(hAPP(hAPP(c_member(X31409),X31410),hAPP(c_List_Oset(X31409),X31407)))
        | hBOOL(hAPP(X31408,X31410)) )
      & ( hBOOL(hAPP(hAPP(c_member(X31413),esk424_3(X31411,X31412,X31413)),hAPP(c_List_Oset(X31413),X31411)))
        | hAPP(c_List_Ofilter(X31413,X31412),X31411) = X31411 )
      & ( ~ hBOOL(hAPP(X31412,esk424_3(X31411,X31412,X31413)))
        | hAPP(c_List_Ofilter(X31413,X31412),X31411) = X31411 ) ),
    inference(distribute,[status(thm)],[inference(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_8844,plain,
    ! [X20804,X20805] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20805))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20804))
      | 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,X20805,X20804))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_8845,plain,
    ! [X30128,X30129,X30130,X30131] : hAPP(hAPP(c_List_Onth(X30131),hAPP(hAPP(c_List_Oappend(X30131),X30130),X30129)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30131)),X30130)),X30128)) = hAPP(hAPP(c_List_Onth(X30131),X30129),X30128),
    inference(variable_rename,[status(thm)],[fact_nth__append__length__plus]) ).

cnf(i_0_8846,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_5786]) ).

fof(i_0_8847,plain,
    ! [X29970,X29971,X29972,X29973,X29974,X29975] : hAPP(c_List_Olist_Olist__case(X29975,X29974,X29973,X29972),hAPP(hAPP(c_List_Olist_OCons(X29974),X29971),X29970)) = hAPP(hAPP(X29972,X29971),X29970),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I5_J]) ).

fof(i_0_8848,plain,
    ! [X23234,X23235,X23236,X23237] :
      ( ~ hBOOL(hAPP(X23237,X23236))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23235,tc_HOL_Obool)),X23237),X23234),X23236)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I1])]) ).

fof(i_0_8849,plain,
    ! [X23122,X23123,X23124,X23125] :
      ( ( ~ hBOOL(hAPP(X23125,X23124))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23122,tc_HOL_Obool)),X23123),X23125),X23124)) )
      & ( ~ hBOOL(hAPP(X23123,X23124))
        | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23122,tc_HOL_Obool)),X23123),X23125),X23124)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5787])])]) ).

fof(i_0_8850,plain,
    ! [X23230,X23231,X23232,X23233] :
      ( ~ hBOOL(hAPP(X23233,X23232))
      | hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23231,tc_HOL_Obool)),X23230),X23233),X23232)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup1I2])]) ).

fof(i_0_8851,plain,
    ! [X25961,X25962,X25963] :
      ( ~ class_Rings_Olinordered__idom(X25963)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25963),c_Groups_Ozero__class_Ozero(X25963)),hAPP(hAPP(c_Power_Opower__class_Opower(X25963),hAPP(c_Groups_Oabs__class_Oabs(X25963),X25962)),X25961))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power__abs])]) ).

fof(i_0_8852,plain,
    ! [X18147,X18148,X18149] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18149),X18148))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18147),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18148),X18149))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18147),X18149)),hAPP(c_Nat_OSuc,X18148)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__Suc__diff__eq1])]) ).

fof(i_0_8853,plain,
    ! [X17021,X17022] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17022,tc_HOL_Obool)),X17021),c_Orderings_Obot__class_Obot(tc_fun(X17022,tc_HOL_Obool))))
        | X17021 = c_Orderings_Obot__class_Obot(tc_fun(X17022,tc_HOL_Obool)) )
      & ( X17021 != c_Orderings_Obot__class_Obot(tc_fun(X17022,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17022,tc_HOL_Obool)),X17021),c_Orderings_Obot__class_Obot(tc_fun(X17022,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__empty])]) ).

fof(i_0_8854,plain,
    ! [X28265,X28266] :
      ( ~ c_Wellfounded_OwfP(X28266,X28265)
      | c_Wellfounded_Oacyclic(X28266,hAPP(c_Set_OCollect(tc_prod(X28266,X28266)),hAPP(c_Product__Type_Oprod_Oprod__case(X28266,X28266,tc_HOL_Obool),X28265))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wfP__acyclicP])]) ).

fof(i_0_8855,plain,
    ! [X27893,X27894,X27895,X27896] : hAPP(hAPP(c_Relation_Orel__comp(X27896,X27895,X27894),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27896,X27895),tc_HOL_Obool))),X27893) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27896,X27894),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__empty1]) ).

fof(i_0_8856,plain,
    ! [X21407,X21408] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21407,X21408) != 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),X21407)),X21408) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21407),X21408))
        | X21408 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21407,X21408) = 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),X21407)),X21408) = 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),X21407),X21408))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X21408 = 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_8857,plain,
    ! [X31052,X31053,X31054,X31055,X31056,X31057,X31058] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31056),X31057),hAPP(c_List_Oset(X31056),X31053)))
        | hBOOL(hAPP(X31055,X31057))
        | c_List_Opartition(X31056,X31055,X31054) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31056),tc_List_Olist(X31056)),X31053),X31052) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X31056),X31058),hAPP(c_List_Oset(X31056),X31052)))
        | ~ hBOOL(hAPP(X31055,X31058))
        | c_List_Opartition(X31056,X31055,X31054) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31056),tc_List_Olist(X31056)),X31053),X31052) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5788])])])]) ).

fof(i_0_8858,plain,
    ! [X21162,X21163,X21164] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21164),hAPP(c_Groups_Ouminus__class_Ouminus(X21164),X21163)),hAPP(c_Groups_Ouminus__class_Ouminus(X21164),X21162)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21164),X21162),X21163))
        | ~ class_Groups_Oordered__ab__group__add(X21164) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21164),X21162),X21163))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21164),hAPP(c_Groups_Ouminus__class_Ouminus(X21164),X21163)),hAPP(c_Groups_Ouminus__class_Ouminus(X21164),X21162)))
        | ~ class_Groups_Oordered__ab__group__add(X21164) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less])])]) ).

fof(i_0_8859,plain,
    ! [X21129,X21130,X21131] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21131),hAPP(c_Groups_Ouminus__class_Ouminus(X21131),X21130)),hAPP(c_Groups_Ouminus__class_Ouminus(X21131),X21129)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21131),X21129),X21130))
        | ~ class_Lattices_Oboolean__algebra(X21131) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21131),X21129),X21130))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21131),hAPP(c_Groups_Ouminus__class_Ouminus(X21131),X21130)),hAPP(c_Groups_Ouminus__class_Ouminus(X21131),X21129)))
        | ~ class_Lattices_Oboolean__algebra(X21131) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff])])]) ).

fof(i_0_8860,plain,
    ! [X21141,X21142,X21143] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21143),hAPP(c_Groups_Ouminus__class_Ouminus(X21143),X21142)),hAPP(c_Groups_Ouminus__class_Ouminus(X21143),X21141)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21143),X21141),X21142))
        | ~ class_Groups_Oordered__ab__group__add(X21143) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21143),X21141),X21142))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21143),hAPP(c_Groups_Ouminus__class_Ouminus(X21143),X21142)),hAPP(c_Groups_Ouminus__class_Ouminus(X21143),X21141)))
        | ~ class_Groups_Oordered__ab__group__add(X21143) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le])])]) ).

fof(i_0_8861,plain,
    ! [X24254,X24255,X24257,X24258,X24259,X24261] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk146_2(X24254,X24255)),X24255))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24257),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24255)))
        | hBOOL(hAPP(X24254,X24257)) )
      & ( ~ hBOOL(hAPP(X24254,esk146_2(X24254,X24255)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X24257),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24255)))
        | hBOOL(hAPP(X24254,X24257)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk147_2(X24258,X24259)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24259)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24261),X24259))
        | hBOOL(hAPP(X24258,X24261)) )
      & ( ~ hBOOL(hAPP(X24258,esk147_2(X24258,X24259)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24261),X24259))
        | hBOOL(hAPP(X24258,X24261)) ) ),
    inference(distribute,[status(thm)],[inference(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_8862,plain,
    ! [X20327,X20328,X20329] :
      ( ~ class_Rings_Olinordered__semidom(X20329)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20329),c_Groups_Oone__class_Oone(X20329)),X20328))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20329),c_Groups_Oone__class_Oone(X20329)),hAPP(hAPP(c_Power_Opower__class_Opower(X20329),X20328),hAPP(c_Nat_OSuc,X20327)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__gt1])]) ).

fof(i_0_8863,plain,
    ! [X33577,X33578,X33579,X33580] : hAPP(c_Lazy__Sequence_Obind(X33580,X33579,X33578),X33577) = c_Lazy__Sequence_Oflat(X33579,c_Lazy__Sequence_Omap(X33580,tc_Lazy__Sequence_Olazy__sequence(X33579),X33577,X33578)),
    inference(variable_rename,[status(thm)],[fact__05]) ).

fof(i_0_8864,plain,
    ! [X19679,X19680,X19681] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19681))
      | X19681 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19681),X19679))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19680),X19681))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19679)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1])]) ).

fof(i_0_8865,plain,
    ! [X32475,X32476,X32477,X32478,X32479] :
      ( ~ hBOOL(hAPP(hAPP(X32479,X32478),X32477))
      | hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X32476,X32475,X32479),X32477),X32478)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_conversep_Ointros])]) ).

cnf(i_0_8866,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_5789]) ).

cnf(i_0_8867,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_5790]) ).

fof(i_0_8868,plain,
    ! [X20103,X20104] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20104)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20103)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20104),X20103))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20104),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20104),X20103))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20104)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20103))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20104),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),X20104)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20103))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5791])])]) ).

fof(i_0_8869,plain,
    ! [X19296,X19297,X19298] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19298),hAPP(c_Int_Onumber__class_Onumber__of(X19298),X19297)),hAPP(c_Int_Onumber__class_Onumber__of(X19298),X19296)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19297),X19296))
        | ~ class_Int_Onumber__ring(X19298)
        | ~ class_Rings_Olinordered__idom(X19298) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19297),X19296))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X19298),hAPP(c_Int_Onumber__class_Onumber__of(X19298),X19297)),hAPP(c_Int_Onumber__class_Onumber__of(X19298),X19296)))
        | ~ class_Int_Onumber__ring(X19298)
        | ~ class_Rings_Olinordered__idom(X19298) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of])])]) ).

fof(i_0_8870,plain,
    ! [X19293,X19294,X19295] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19295),hAPP(c_Int_Onumber__class_Onumber__of(X19295),X19294)),hAPP(c_Int_Onumber__class_Onumber__of(X19295),X19293)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19294),X19293))
        | ~ class_Int_Onumber__ring(X19295)
        | ~ class_Rings_Olinordered__idom(X19295) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19294),X19293))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X19295),hAPP(c_Int_Onumber__class_Onumber__of(X19295),X19294)),hAPP(c_Int_Onumber__class_Onumber__of(X19295),X19293)))
        | ~ class_Int_Onumber__ring(X19295)
        | ~ class_Rings_Olinordered__idom(X19295) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__number__of])])]) ).

fof(i_0_8871,plain,
    ! [X33946,X33947] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33947))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33946))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X33947),X33946))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X33946),X33947))
      | X33947 = X33946 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg])]) ).

fof(i_0_8872,plain,
    ! [X33739,X33740,X33741] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33741),X33739))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33740),X33739))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33739),X33740))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33741),X33740))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33740),X33741)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33739),X33741))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33740),X33739))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33739),X33740))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33741),X33740))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33740),X33741)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5792])])]) ).

fof(i_0_8873,plain,
    ! [X29661,X29662,X29663,X29664] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29664)),X29663)),X29662))
      | hAPP(hAPP(c_List_Olist__update(X29664,X29663),X29662),X29661) = X29663 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__beyond])]) ).

fof(i_0_8874,plain,
    ! [X18541] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18541),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18541),X18541)))),
    inference(variable_rename,[status(thm)],[fact_le__cube]) ).

fof(i_0_8875,plain,
    ! [X29719,X29720,X29721] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29721),X29720),hAPP(c_List_Oset(X29721),c_List_Obutlast(X29721,X29719))))
      | hBOOL(hAPP(hAPP(c_member(X29721),X29720),hAPP(c_List_Oset(X29721),X29719))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__butlastD])]) ).

fof(i_0_8876,plain,
    ! [X17087,X17088,X17089,X17090,X17091] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17091),X17090),X17089))
      | hAPP(hAPP(c_Set_Oinsert(X17088),hAPP(X17087,X17090)),hAPP(c_Set_Oimage(X17091,X17088,X17087),X17089)) = hAPP(c_Set_Oimage(X17091,X17088,X17087),X17089) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__image])]) ).

cnf(i_0_8877,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5793]) ).

cnf(i_0_8878,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit0(X2)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5794]) ).

fof(i_0_8879,plain,
    ! [X21972,X21973,X21974] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21974,X21974),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21973),X21972)))
      | X21974 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X21973 = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__quotient])]) ).

fof(i_0_8880,plain,
    ! [X21935,X21936,X21937] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21937,X21937),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X21936),X21935)))
      | X21937 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | X21935 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__remainder])]) ).

fof(i_0_8881,plain,
    ! [X19646,X19647,X19648,X19649,X19650] :
      ( ~ c_Finite__Set_Ofolding__one(X19650,X19649,X19648)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19650),X19647))
      | hBOOL(hAPP(hAPP(c_member(X19650),X19646),X19647))
      | hAPP(X19648,hAPP(hAPP(c_Set_Oinsert(X19650),X19646),X19647)) = hAPP(hAPP(c_Finite__Set_Ofold(X19650,X19650,X19649),X19646),X19647) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5795])]) ).

fof(i_0_8882,plain,
    ! [X28953,X28954,X28955] :
      ( ~ c_Wellfounded_Owf(X28955,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28955,X28955),tc_HOL_Obool),X28954),X28953))
      | c_Wellfounded_Owf(X28955,X28953) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__exp])]) ).

fof(i_0_8883,plain,
    ! [X21621,X21622,X21623] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21623),hAPP(c_Int_Oring__1__class_Oof__int(X21623),X21622)),hAPP(c_Int_Oring__1__class_Oof__int(X21623),X21621)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21622),X21621))
        | ~ class_Rings_Olinordered__idom(X21623) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21622),X21621))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21623),hAPP(c_Int_Oring__1__class_Oof__int(X21623),X21622)),hAPP(c_Int_Oring__1__class_Oof__int(X21623),X21621)))
        | ~ class_Rings_Olinordered__idom(X21623) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__iff])])]) ).

fof(i_0_8884,plain,
    ! [X20058,X20059,X20060] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20060),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20060),X20059)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20060),X20058)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20059),X20058))
        | ~ class_Rings_Olinordered__semidom(X20060) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20059),X20058))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20060),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20060),X20059)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20060),X20058)))
        | ~ class_Rings_Olinordered__semidom(X20060) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__iff])])]) ).

fof(i_0_8885,plain,
    ! [X20052,X20053,X20054] :
      ( ~ class_Rings_Olinordered__semidom(X20054)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20054),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20054),X20053)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20054),X20052)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20053),X20052)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__less__imp__less])]) ).

fof(i_0_8886,plain,
    ! [X21618,X21619,X21620] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21620),hAPP(c_Int_Oring__1__class_Oof__int(X21620),X21619)),hAPP(c_Int_Oring__1__class_Oof__int(X21620),X21618)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21619),X21618))
        | ~ class_Rings_Olinordered__idom(X21620) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21619),X21618))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21620),hAPP(c_Int_Oring__1__class_Oof__int(X21620),X21619)),hAPP(c_Int_Oring__1__class_Oof__int(X21620),X21618)))
        | ~ class_Rings_Olinordered__idom(X21620) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__iff])])]) ).

fof(i_0_8887,plain,
    ! [X20061,X20062,X20063] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20063),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20063),X20062)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20063),X20061)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20062),X20061))
        | ~ class_Rings_Olinordered__semidom(X20063) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20062),X20061))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20063),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20063),X20062)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20063),X20061)))
        | ~ class_Rings_Olinordered__semidom(X20063) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__le__iff])])]) ).

fof(i_0_8888,plain,
    ! [X28325] :
      ( X28325 = hAPP(c_Int_OAbs__Integ,esk304_1(X28325))
      & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk304_1(X28325)),c_Int_OInteg)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5796])])]) ).

cnf(i_0_8889,plain,
    ( c_List_Oupt(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5797]) ).

cnf(i_0_8890,plain,
    ( c_List_Oupt(X1,X2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5798]) ).

fof(i_0_8891,plain,
    ! [X22643,X22644,X22645,X22646] :
      ( ~ class_Fields_Ofield(X22646)
      | X22645 = c_Groups_Ozero__class_Ozero(X22646)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22646),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22646),X22644),X22645)),X22643) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22646),hAPP(hAPP(c_Power_Opower__class_Opower(X22646),X22644),X22643)),hAPP(hAPP(c_Power_Opower__class_Opower(X22646),X22645),X22643)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__power__divide])]) ).

fof(i_0_8892,plain,
    ! [X19498,X19499] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19499),X19498))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19499),c_Groups_Oone__class_Oone(tc_Int_Oint))),X19498)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle])]) ).

fof(i_0_8893,plain,
    ! [X25663,X25664,X25665] :
      ( ~ class_Lattices_Olattice(X25665)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25665),X25664))
      | X25664 = c_Orderings_Obot__class_Obot(tc_fun(X25665,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25665),X25663))
      | X25663 = c_Orderings_Obot__class_Obot(tc_fun(X25665,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X25665,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25665,tc_HOL_Obool)),X25664),X25663)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25665),c_Big__Operators_Olattice__class_OInf__fin(X25665,X25664)),c_Big__Operators_Olattice__class_OInf__fin(X25665,X25663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Ounion__idem])]) ).

fof(i_0_8894,plain,
    ! [X23523,X23524,X23525] :
      ( ~ class_Lattices_Olattice(X23525)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23525),X23524))
      | X23524 = c_Orderings_Obot__class_Obot(tc_fun(X23525,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23525),X23523))
      | X23523 = c_Orderings_Obot__class_Obot(tc_fun(X23525,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X23525,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23525,tc_HOL_Obool)),X23524),X23523)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23525),c_Big__Operators_Olattice__class_OSup__fin(X23525,X23524)),c_Big__Operators_Olattice__class_OSup__fin(X23525,X23523)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Ounion__idem])]) ).

fof(i_0_8895,plain,
    ! [X23447,X23448,X23449] :
      ( ~ class_Orderings_Olinorder(X23449)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23449),X23448))
      | X23448 = c_Orderings_Obot__class_Obot(tc_fun(X23449,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23449),X23447))
      | X23447 = c_Orderings_Obot__class_Obot(tc_fun(X23449,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X23449,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23449,tc_HOL_Obool)),X23448),X23447)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X23449),c_Big__Operators_Olinorder__class_OMax(X23449,X23448)),c_Big__Operators_Olinorder__class_OMax(X23449,X23447)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__Un])]) ).

fof(i_0_8896,plain,
    ! [X23444,X23445,X23446] :
      ( ~ class_Orderings_Olinorder(X23446)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23446),X23445))
      | X23445 = c_Orderings_Obot__class_Obot(tc_fun(X23446,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23446),X23444))
      | X23444 = c_Orderings_Obot__class_Obot(tc_fun(X23446,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X23446,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23446,tc_HOL_Obool)),X23445),X23444)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X23446),c_Big__Operators_Olinorder__class_OMin(X23446,X23445)),c_Big__Operators_Olinorder__class_OMin(X23446,X23444)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__Un])]) ).

fof(i_0_8897,plain,
    ! [X32442,X32443,X32444,X32445,X32446] : c_List_Osplice(X32446,hAPP(hAPP(c_List_Olist_OCons(X32446),X32445),X32444),hAPP(hAPP(c_List_Olist_OCons(X32446),X32443),X32442)) = hAPP(hAPP(c_List_Olist_OCons(X32446),X32445),hAPP(hAPP(c_List_Olist_OCons(X32446),X32443),c_List_Osplice(X32446,X32444,X32442))),
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I3_J]) ).

fof(i_0_8898,plain,
    ! [X30925,X30926] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,X30926) != hAPP(c_Code__Numeral_Oof__nat,X30925)
        | X30926 = X30925
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30925),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30926),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) )
      & ( X30926 != X30925
        | hAPP(c_Code__Numeral_Oof__nat,X30926) = hAPP(c_Code__Numeral_Oof__nat,X30925)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30925),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30926),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Oof__nat__inject])])]) ).

fof(i_0_8899,plain,
    ! [X20879,X20880] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20879)),hAPP(c_Int_Onat,X20880)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20879),X20880))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20880)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20879),X20880))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20879)),hAPP(c_Int_Onat,X20880)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20880)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mono__iff])])]) ).

fof(i_0_8900,plain,
    ! [X20942,X20943] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20943)),hAPP(c_Int_Onat,X20942)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20943),X20942))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20943)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20943),X20942))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20943)),hAPP(c_Int_Onat,X20942)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20943)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__eq__zless])])]) ).

fof(i_0_8901,plain,
    ! [X20948,X20949] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X20949)),hAPP(c_Int_Onat,X20948)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20949),X20948))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20949)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20949),X20948))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X20949)),hAPP(c_Int_Onat,X20948)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20949)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X20949)),hAPP(c_Int_Onat,X20948)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20949),X20948))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20948)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20949),X20948))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X20949)),hAPP(c_Int_Onat,X20948)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20948)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__le__eq__zle])])]) ).

fof(i_0_8902,plain,
    ! [X28941,X28942,X28943,X28944] : hAPP(X28944,hAPP(hAPP(hAPP(c_Nat_Ocompow(X28943,X28943),X28942),X28944),X28941)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X28943,X28943),X28942),X28944),hAPP(X28944,X28941)),
    inference(variable_rename,[status(thm)],[fact_funpow__swap1]) ).

fof(i_0_8903,plain,
    ! [X31439,X31440,X31441,X31442,X31443,X31444] :
      ( ~ class_Orderings_Olinorder(X31444)
      | hBOOL(hAPP(X31443,X31442))
      | hAPP(c_List_Ofilter(X31441,X31443),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X31441,X31444,X31440),X31442),X31439)) = hAPP(c_List_Ofilter(X31441,X31443),X31439) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5799])]) ).

fof(i_0_8904,plain,
    ! [X19087,X19088,X19089,X19090] :
      ( ~ class_Rings_Ocomm__semiring__1(X19090)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19090),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19090),X19089),X19088)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19090),X19087),X19088)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19090),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19090),X19089),X19087)),X19088) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J])]) ).

fof(i_0_8905,plain,
    ! [X24907,X24908,X24909,X24910] :
      ( ~ class_Lattices_Odistrib__lattice(X24910)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24910),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24910),X24909),X24908)),X24907) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24910),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24910),X24909),X24907)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24910),X24908),X24907)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib2])]) ).

fof(i_0_8906,plain,
    ! [X24903,X24904,X24905,X24906] :
      ( ~ class_Lattices_Odistrib__lattice(X24906)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24906),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24906),X24905),X24904)),X24903) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24906),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24906),X24905),X24903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24906),X24904),X24903)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib2])]) ).

fof(i_0_8907,plain,
    ! [X22469,X22470,X22471,X22472] :
      ( ~ class_Orderings_Olinorder(X22472)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22472),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22472),X22471),X22470)),X22469) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22472),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22472),X22471),X22469)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22472),X22470),X22469)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib2])]) ).

fof(i_0_8908,plain,
    ! [X22525,X22526,X22527,X22528] :
      ( ~ class_Rings_Odivision__ring(X22528)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22528),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22528),X22527),X22526)),X22525) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22528),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22528),X22527),X22525)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22528),X22526),X22525)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__divide__distrib])]) ).

fof(i_0_8909,plain,
    ! [X22481,X22482,X22483,X22484] :
      ( ~ class_Rings_Odivision__ring(X22484)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22484),X22483),X22482)),X22481) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22484),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22484),X22483),X22481)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22484),X22482),X22481)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__divide__distrib])]) ).

fof(i_0_8910,plain,
    ! [X22473,X22474,X22475,X22476] :
      ( ~ class_Orderings_Olinorder(X22476)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22476),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22476),X22475),X22474)),X22473) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22476),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22476),X22475),X22473)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22476),X22474),X22473)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib2])]) ).

fof(i_0_8911,plain,
    ! [X22551,X22552,X22553,X22554] :
      ( ~ class_Fields_Ofield__inverse__zero(X22554)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X22554),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22554),X22553),X22552)),X22551) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22554),hAPP(hAPP(c_Power_Opower__class_Opower(X22554),X22553),X22551)),hAPP(hAPP(c_Power_Opower__class_Opower(X22554),X22552),X22551)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__divide])]) ).

fof(i_0_8912,plain,
    ! [X20159,X20160,X20161,X20162] :
      ( ~ class_Rings_Ocomm__semiring__1(X20162)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20162),X20161),X20160)),X20159) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20162),hAPP(hAPP(c_Power_Opower__class_Opower(X20162),X20161),X20159)),hAPP(hAPP(c_Power_Opower__class_Opower(X20162),X20160),X20159)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J])]) ).

fof(i_0_8913,plain,
    ! [X20256,X20257,X20258,X20259] :
      ( ~ class_Groups_Ocomm__monoid__mult(X20259)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20259),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20259),X20258),X20257)),X20256) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20259),hAPP(hAPP(c_Power_Opower__class_Opower(X20259),X20258),X20256)),hAPP(hAPP(c_Power_Opower__class_Opower(X20259),X20257),X20256)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult__distrib])]) ).

fof(i_0_8914,plain,
    ! [X19091,X19092,X19093,X19094] :
      ( ~ class_Rings_Ocomm__semiring__1(X19094)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19094),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19094),X19093),X19092)),X19091) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19094),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19094),X19093),X19091)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19094),X19092),X19091)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J])]) ).

fof(i_0_8915,plain,
    ! [X18426,X18427,X18428,X18429] :
      ( ~ class_Rings_Ocomm__semiring(X18429)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18429),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18429),X18428),X18427)),X18426) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18429),X18428),X18426)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18429),X18427),X18426)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__class_Odistrib])]) ).

fof(i_0_8916,plain,
    ! [X22477,X22478,X22479,X22480] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X22480)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22480),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22480),X22479),X22478)),X22477) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22480),X22479),X22477)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X22480),X22478),X22477)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__add__distrib__left])]) ).

fof(i_0_8917,plain,
    ! [X21590,X21591,X21592,X21593] :
      ( ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X21593)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21593),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21593),X21592),X21591)),X21590) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21593),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21593),X21592),X21590)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21593),X21591),X21590)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__add__distrib__left])]) ).

fof(i_0_8918,plain,
    ! [X22487,X22488,X22489,X22490] :
      ( ~ class_Groups_Oordered__ab__group__add(X22490)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22490),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22490),X22489),X22488)),X22487) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22490),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22490),X22489),X22487)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X22490),X22488),X22487)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__diff__distrib__left])]) ).

fof(i_0_8919,plain,
    ! [X21594,X21595,X21596,X21597] :
      ( ~ class_Groups_Oordered__ab__group__add(X21597)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21597),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21597),X21596),X21595)),X21594) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21597),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21597),X21596),X21594)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21597),X21595),X21594)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__diff__distrib__left])]) ).

fof(i_0_8920,plain,
    ! [X30553,X30554,X30555,X30556,X30557] :
      ( ~ class_Orderings_Olinorder(X30557)
      | hAPP(c_List_Oset(X30556),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30556,X30557,X30555),X30554),X30553)) = hAPP(hAPP(c_Set_Oinsert(X30556),X30554),hAPP(c_List_Oset(X30556),X30553)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__insort])]) ).

fof(i_0_8921,plain,
    ! [X18395,X18396] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18396))
        | ~ 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),X18396),X18395))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18395))
        | ~ 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),X18396),X18395))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18396))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18395))
        | 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),X18396),X18395))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff])])]) ).

fof(i_0_8922,plain,
    ! [X20399,X20400] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20399))
      | 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),X20400),X20399))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_8923,plain,
    ! [X19686,X19687] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19686))
      | 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),X19687),X19686))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J])]) ).

fof(i_0_8924,plain,
    ! [X19688,X19689] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19688))
      | 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),X19689),X19688))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J])]) ).

fof(i_0_8925,plain,
    ! [X33630,X33631,X33632,X33633,X33634] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33634),X33631),X33633) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33634),X33630),X33632)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33634),X33631),X33632) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33634),X33633),X33630)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33634),X33632),X33630))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33634),X33633),X33631))
        | X33632 = c_Groups_Ozero__class_Ozero(X33634)
        | X33633 = c_Groups_Ozero__class_Ozero(X33634)
        | ~ class_Divides_Osemiring__div(X33634) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33634),X33631),X33632) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33634),X33633),X33630)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33634),X33631),X33633) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33634),X33630),X33632)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33634),X33632),X33630))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33634),X33633),X33631))
        | X33632 = c_Groups_Ozero__class_Ozero(X33634)
        | X33633 = c_Groups_Ozero__class_Ozero(X33634)
        | ~ class_Divides_Osemiring__div(X33634) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__div__eq__mult])])]) ).

fof(i_0_8926,plain,
    ! [X23047,X23048,X23049] :
      ( ~ class_Orderings_Olinorder(X23049)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23049),X23048))
      | hBOOL(hAPP(hAPP(c_member(X23049),X23047),X23048))
      | c_Big__Operators_Olattice_OSup__fin(X23049,c_Orderings_Oord__class_Omax(X23049),hAPP(hAPP(c_Set_Oinsert(X23049),X23047),X23048)) = hAPP(hAPP(c_Finite__Set_Ofold(X23049,X23049,c_Orderings_Oord__class_Omax(X23049)),X23047),X23048) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5800])]) ).

fof(i_0_8927,plain,
    ! [X21814,X21815,X21816] :
      ( ~ class_Orderings_Olinorder(X21816)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21816),X21815))
      | hBOOL(hAPP(hAPP(c_member(X21816),X21814),X21815))
      | c_Big__Operators_Olattice_OInf__fin(X21816,c_Orderings_Oord__class_Omin(X21816),hAPP(hAPP(c_Set_Oinsert(X21816),X21814),X21815)) = hAPP(hAPP(c_Finite__Set_Ofold(X21816,X21816,c_Orderings_Oord__class_Omin(X21816)),X21814),X21815) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5801])]) ).

fof(i_0_8928,plain,
    ! [X25772,X25773] :
      ( ~ class_Orderings_Olinorder(X25773)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25773,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25773),X25772),c_Orderings_Obot__class_Obot(tc_fun(X25773,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25773),X25772)) = hAPP(c_SetInterval_Oord__class_OatLeast(X25773),X25772) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I1_J])]) ).

fof(i_0_8929,plain,
    ! [X28793,X28794,X28795] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28795,X28794)),hAPP(c_Relation_Oconverse(X28794,X28795),X28793)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28794,X28795)),X28793)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28794,X28795)),X28793))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28795,X28794)),hAPP(c_Relation_Oconverse(X28794,X28795),X28793))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__converse])]) ).

fof(i_0_8930,plain,
    ! [X26274] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26274),c_Orderings_Otop__class_Otop(tc_fun(X26274,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(X26274),c_Orderings_Otop__class_Otop(tc_fun(X26274,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV__card__ge__0])]) ).

fof(i_0_8931,plain,
    ! [X29815,X29816,X29817] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29817),X29816))
      | hAPP(c_List_Oset(X29817),c_List_Oremove1(X29817,X29815,X29816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X29817,tc_HOL_Obool)),hAPP(c_List_Oset(X29817),X29816)),hAPP(hAPP(c_Set_Oinsert(X29817),X29815),c_Orderings_Obot__class_Obot(tc_fun(X29817,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__remove1__eq])]) ).

fof(i_0_8932,plain,
    ! [X26999,X27000,X27001] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27001,tc_HOL_Obool)),X27000),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27001,tc_HOL_Obool),X26999)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X27001,tc_HOL_Obool),tc_fun(X27001,tc_HOL_Obool)),X26999),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27001,tc_HOL_Obool)),X27000)),
    inference(variable_rename,[status(thm)],[fact_Int__Union]) ).

fof(i_0_8933,plain,
    ! [X26776,X26777,X26778] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26778,tc_HOL_Obool)),X26777),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26778,tc_HOL_Obool),X26776)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X26778,tc_HOL_Obool),tc_fun(X26778,tc_HOL_Obool)),X26776),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26778,tc_HOL_Obool)),X26777)),
    inference(variable_rename,[status(thm)],[fact_Un__Inter]) ).

fof(i_0_8934,plain,
    ! [X30558,X30559,X30560,X30561,X30562] :
      ( ~ class_Orderings_Olinorder(X30562)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30561)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30561,X30562,X30560),X30559),X30558)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30561)),X30558)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__insort])]) ).

fof(i_0_8935,plain,
    ! [X21002,X21003] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X21003)),X21002))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21003),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21002)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21003)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21003),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21002)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X21003)),X21002))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21003)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__iff])])]) ).

cnf(i_0_8936,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_5738]) ).

fof(i_0_8937,plain,
    ! [X17956,X17957] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X17957,tc_HOL_Obool)),X17956),c_Orderings_Obot__class_Obot(tc_fun(X17957,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5802]) ).

fof(i_0_8938,plain,
    ! [X30574,X30575,X30576] :
      ( ~ class_Orderings_Olinorder(X30576)
      | c_List_Oremove1(X30576,X30575,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30576,X30576,c_COMBI(X30576)),X30575),X30574)) = X30574 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__insort])]) ).

fof(i_0_8939,plain,
    ! [X28288,X28289,X28290,X28291,X28292,X28293,X28294] :
      ( ( ~ hBOOL(hAPP(c_Predicate_OPowp(X28290,X28289),X28288))
        | ~ hBOOL(hAPP(hAPP(c_member(X28290),X28291),X28288))
        | hBOOL(hAPP(X28289,X28291)) )
      & ( hBOOL(hAPP(hAPP(c_member(X28294),esk302_3(X28292,X28293,X28294)),X28292))
        | hBOOL(hAPP(c_Predicate_OPowp(X28294,X28293),X28292)) )
      & ( ~ hBOOL(hAPP(X28293,esk302_3(X28292,X28293,X28294)))
        | hBOOL(hAPP(c_Predicate_OPowp(X28294,X28293),X28292)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Powp__def])])])])])]) ).

fof(i_0_8940,plain,
    ! [X33421,X33422,X33423,X33424] : hAPP(c_Product__Type_Oprod_Oprod__case(X33424,X33423,X33422),c_Product__Type_Ocurry(X33424,X33423,X33422,X33421)) = X33421,
    inference(variable_rename,[status(thm)],[fact_split__curry]) ).

fof(i_0_8941,plain,
    ! [X21469,X21470,X21471] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X21471),X21470) != hAPP(c_Int_Onumber__class_Onumber__of(X21471),X21469)
        | c_Int_Oiszero(X21471,hAPP(c_Int_Onumber__class_Onumber__of(X21471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21469))))
        | ~ class_Int_Onumber__ring(X21471) )
      & ( ~ c_Int_Oiszero(X21471,hAPP(c_Int_Onumber__class_Onumber__of(X21471),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21470),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21469))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X21471),X21470) = hAPP(c_Int_Onumber__class_Onumber__of(X21471),X21469)
        | ~ class_Int_Onumber__ring(X21471) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of__eq])])]) ).

fof(i_0_8942,plain,
    ! [X30305,X30306,X30307,X30308] :
      ( ( X30307 = hAPP(hAPP(c_List_Otake(X30308),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30308)),X30307)),X30305)
        | hAPP(hAPP(c_List_Oappend(X30308),X30307),X30306) != X30305 )
      & ( X30306 = hAPP(hAPP(c_List_Odrop(X30308),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30308)),X30307)),X30305)
        | hAPP(hAPP(c_List_Oappend(X30308),X30307),X30306) != X30305 )
      & ( X30307 != hAPP(hAPP(c_List_Otake(X30308),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30308)),X30307)),X30305)
        | X30306 != hAPP(hAPP(c_List_Odrop(X30308),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30308)),X30307)),X30305)
        | hAPP(hAPP(c_List_Oappend(X30308),X30307),X30306) = X30305 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__conv__conj])])]) ).

fof(i_0_8943,plain,
    ! [X19408,X19409,X19410] :
      ( ~ class_Groups_Oab__semigroup__mult(X19410)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19410),X19409))
      | hBOOL(hAPP(hAPP(c_member(X19410),X19408),X19409))
      | hAPP(c_Finite__Set_Ofold1(X19410,c_Groups_Otimes__class_Otimes(X19410)),hAPP(hAPP(c_Set_Oinsert(X19410),X19408),X19409)) = hAPP(hAPP(c_Finite__Set_Ofold(X19410,X19410,c_Groups_Otimes__class_Otimes(X19410)),X19408),X19409) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5803])]) ).

cnf(i_0_8944,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit0(X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5804]) ).

fof(i_0_8945,plain,
    ! [X21409,X21410] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21409,X21410) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21409),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21410)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21409),X21410))
        | X21410 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21409,X21410) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21409),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21410)) = 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),X21409),X21410))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X21410 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zminus2__eq__if])])]) ).

fof(i_0_8946,plain,
    ! [X27642,X27643] : hAPP(c_Set_OCollect(X27643),hAPP(hAPP(c_COMBC(X27643,X27643,tc_HOL_Obool),c_fequal),X27642)) = hAPP(hAPP(c_Set_Oinsert(X27643),X27642),c_Orderings_Obot__class_Obot(tc_fun(X27643,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__conv]) ).

cnf(i_0_8947,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X1)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5575]) ).

fof(i_0_8948,plain,
    ! [X23391,X23392,X23393] : hAPP(hAPP(c_Set_Oinsert(X23393),X23392),X23391) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23393,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X23393),X23392),c_Orderings_Obot__class_Obot(tc_fun(X23393,tc_HOL_Obool)))),X23391),
    inference(variable_rename,[status(thm)],[fact_insert__is__Un]) ).

fof(i_0_8949,plain,
    ! [X33218,X33219] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33219),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(X33218,hAPP(c_Code__Numeral_Onat__of,esk526_2(X33218,X33219))))
      | hBOOL(hAPP(X33218,X33219)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__induct])])]) ).

cnf(i_0_8950,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) = X2,
    inference(split_conjunct,[status(thm)],[i_0_5805]) ).

fof(i_0_8951,plain,
    ! [X17741,X17742,X17743] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17743),X17742))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17743),X17741)),X17742)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__diff__less])]) ).

fof(i_0_8952,plain,
    ! [X25015,X25016,X25017,X25018] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25018),X25017),X25016))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25018),X25017),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25018),X25016),X25015)))
        | ~ class_Lattices_Osemilattice__inf(X25018) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25018),X25017),X25015))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25018),X25017),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25018),X25016),X25015)))
        | ~ class_Lattices_Osemilattice__inf(X25018) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5806])])]) ).

fof(i_0_8953,plain,
    ! [X21566,X21567,X21568,X21569] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21569),X21568),X21567))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21569),X21568),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21569),X21567),X21566)))
        | ~ class_Orderings_Olinorder(X21569) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21569),X21568),X21566))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21569),X21568),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21569),X21567),X21566)))
        | ~ class_Orderings_Olinorder(X21569) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5807])])]) ).

fof(i_0_8954,plain,
    ! [X29956,X29957,X29958] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X29958),X29957),hAPP(c_List_Oset(X29958),X29956)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29958)),c_List_Oremove1(X29958,X29957,X29956)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29958)),X29956)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( hBOOL(hAPP(hAPP(c_member(X29958),X29957),hAPP(c_List_Oset(X29958),X29956)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29958)),c_List_Oremove1(X29958,X29957,X29956)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29958)),X29956) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5808])]) ).

fof(i_0_8955,plain,
    ! [X18104,X18105,X18106] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18106),X18105))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18105),X18106)),X18104) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18105),X18104)),X18106) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc2])]) ).

fof(i_0_8956,plain,
    ! [X18101,X18102,X18103] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18103),X18102))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18102),X18101)),X18103) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18102),X18103)),X18101) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc2])]) ).

fof(i_0_8957,plain,
    ! [X25031,X25032,X25033] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25033,tc_HOL_Obool)),X25032),X25031))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25033,tc_HOL_Obool)),X25032),X25031) = X25032 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb2])]) ).

fof(i_0_8958,plain,
    ! [X25028,X25029,X25030] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X25030,tc_HOL_Obool)),X25029),X25028))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25030,tc_HOL_Obool)),X25028),X25029) = X25029 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__absorb1])]) ).

fof(i_0_8959,plain,
    ! [X23351,X23352,X23353] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23353,tc_HOL_Obool)),X23352),X23351))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23353,tc_HOL_Obool)),X23352),X23351) = X23351 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb1])]) ).

fof(i_0_8960,plain,
    ! [X23348,X23349,X23350] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23350,tc_HOL_Obool)),X23349),X23348))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23350,tc_HOL_Obool)),X23349),X23348) = X23348 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23350,tc_HOL_Obool)),X23349),X23348) != X23348
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23350,tc_HOL_Obool)),X23349),X23348)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_subset__Un__eq])]) ).

fof(i_0_8961,plain,
    ! [X23354,X23355,X23356] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X23356,tc_HOL_Obool)),X23355),X23354))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23356,tc_HOL_Obool)),X23354),X23355) = X23354 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__absorb2])]) ).

fof(i_0_8962,plain,
    ! [X25229,X25230,X25231,X25232] :
      ( hBOOL(hAPP(hAPP(c_member(X25232),X25231),X25230))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25232,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X25232),X25231),X25229)),X25230) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25232,tc_HOL_Obool)),X25229),X25230) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5809])]) ).

fof(i_0_8963,plain,
    ! [X27610,X27611] : hAPP(c_Set_OCollect(X27611),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X27611),c_fNot),X27610)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X27611,tc_HOL_Obool)),hAPP(c_Set_OCollect(X27611),X27610)),
    inference(variable_rename,[status(thm)],[fact_Collect__neg__eq]) ).

fof(i_0_8964,plain,
    ! [X30298,X30299,X30300] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30300)),X30299)),X30298))
      | hAPP(hAPP(c_List_Odrop(X30300),X30298),X30299) = c_List_Olist_ONil(X30300) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__all])]) ).

fof(i_0_8965,plain,
    ! [X30295,X30296,X30297] :
      ( ( hAPP(hAPP(c_List_Odrop(X30297),X30296),X30295) != c_List_Olist_ONil(X30297)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30297)),X30295)),X30296)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30297)),X30295)),X30296))
        | hAPP(hAPP(c_List_Odrop(X30297),X30296),X30295) = c_List_Olist_ONil(X30297) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__eq__Nil])]) ).

fof(i_0_8966,plain,
    ! [X16961,X16962,X16963,X16964] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X16964),X16963),hAPP(hAPP(c_Set_Oinsert(X16964),X16962),X16961)))
        | X16963 = X16962
        | hBOOL(hAPP(hAPP(c_member(X16964),X16963),X16961)) )
      & ( X16963 != X16962
        | hBOOL(hAPP(hAPP(c_member(X16964),X16963),hAPP(hAPP(c_Set_Oinsert(X16964),X16962),X16961))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X16964),X16963),X16961))
        | hBOOL(hAPP(hAPP(c_member(X16964),X16963),hAPP(hAPP(c_Set_Oinsert(X16964),X16962),X16961))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__iff])])]) ).

fof(i_0_8967,plain,
    ! [X16862,X16863,X16864,X16865] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X16865),X16864),hAPP(hAPP(c_Set_Oinsert(X16865),X16863),X16862)))
      | X16864 = X16863
      | hBOOL(hAPP(hAPP(c_member(X16865),X16864),X16862)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertE])]) ).

cnf(i_0_8968,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5742]) ).

cnf(i_0_8969,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5741]) ).

cnf(i_0_8970,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(split_conjunct,[status(thm)],[i_0_5743]) ).

cnf(i_0_8971,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(split_conjunct,[status(thm)],[i_0_5744]) ).

cnf(i_0_8972,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X1))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5745]) ).

fof(i_0_8973,plain,
    ! [X29460,X29461,X29462] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29462)),X29461)),X29460))
      | hAPP(hAPP(c_List_Otake(X29462),X29460),X29461) = X29461 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__all])]) ).

cnf(i_0_8974,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | c_Code__Numeral_Onat__of__aux(X1,X2) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5810]) ).

cnf(i_0_8975,plain,
    c_Code__Numeral_Onat__of__aux(X1,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2),
    inference(split_conjunct,[status(thm)],[i_0_5811]) ).

cnf(i_0_8976,plain,
    ( c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5812]) ).

cnf(i_0_8977,plain,
    ( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5813]) ).

fof(i_0_8978,plain,
    ! [X24121,X24122,X24123,X24124] :
      ( ~ class_Orderings_Olinorder(X24124)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24124),X24123),X24122))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X24124,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24124,X24123),X24121)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24124,X24123),X24122)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24124,X24122),X24121) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__diff])]) ).

fof(i_0_8979,plain,
    ! [X22223,X22224,X22225,X22226,X22227,X22228,X22229] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22225,X22224),X22223))
        | ~ hBOOL(hAPP(hAPP(X22224,X22226),X22223))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22225,X22224),X22226)) )
      & ( hBOOL(hAPP(hAPP(X22228,esk92_3(X22227,X22228,X22229)),X22227))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22229,X22228),X22227)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22229,X22228),esk92_3(X22227,X22228,X22229)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22229,X22228),X22227)) ) ),
    inference(distribute,[status(thm)],[inference(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_8980,plain,
    ! [X22215,X22216,X22217,X22218,X22219,X22220,X22221] :
      ( ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22217,X22216),X22215))
        | ~ hBOOL(hAPP(hAPP(X22216,X22218),X22215))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22217,X22216),X22218)) )
      & ( hBOOL(hAPP(hAPP(X22220,esk91_3(X22219,X22220,X22221)),X22219))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22221,X22220),X22219)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22221,X22220),esk91_3(X22219,X22220,X22221)))
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X22221,X22220),X22219)) ) ),
    inference(distribute,[status(thm)],[inference(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_8981,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Relation_OId(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_5814]) ).

fof(i_0_8982,plain,
    ! [X27177,X27178,X27179,X27180] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(X27180,X27179),X27178),hAPP(c_COMBK(tc_fun(X27179,tc_HOL_Obool),X27180),X27177)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27180,X27179),tc_HOL_Obool))
        | X27178 = c_Orderings_Obot__class_Obot(tc_fun(X27180,tc_HOL_Obool))
        | X27177 = c_Orderings_Obot__class_Obot(tc_fun(X27179,tc_HOL_Obool)) )
      & ( X27178 != c_Orderings_Obot__class_Obot(tc_fun(X27180,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(X27180,X27179),X27178),hAPP(c_COMBK(tc_fun(X27179,tc_HOL_Obool),X27180),X27177)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27180,X27179),tc_HOL_Obool)) )
      & ( X27177 != c_Orderings_Obot__class_Obot(tc_fun(X27179,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(X27180,X27179),X27178),hAPP(c_COMBK(tc_fun(X27179,tc_HOL_Obool),X27180),X27177)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27180,X27179),tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Times__empty])])]) ).

cnf(i_0_8983,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5748]) ).

fof(i_0_8984,plain,
    ! [X25769,X25770,X25771] :
      ( ~ class_Orderings_Olinorder(X25771)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25771),X25770),X25769))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25771,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25771,X25770,X25769)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25771),X25769)) = hAPP(c_SetInterval_Oord__class_OatLeast(X25771),X25770) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I13_J])]) ).

fof(i_0_8985,plain,
    ! [X25791,X25792,X25793] :
      ( ~ class_Orderings_Olinorder(X25793)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25793),X25792),X25791))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25793,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25793,X25792,X25791)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25793),X25791)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X25793),X25792) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I11_J])]) ).

fof(i_0_8986,plain,
    ! [X25766,X25767,X25768] :
      ( ~ class_Orderings_Olinorder(X25768)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25768),X25767),X25766))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25768,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25768,X25767,X25766)),hAPP(c_SetInterval_Oord__class_OatLeast(X25768),X25766)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X25768),X25767) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I12_J])]) ).

fof(i_0_8987,plain,
    ! [X30498,X30499] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30499)
      | c_Complete__Lattice_OSup__class_OSup(X30499,hAPP(c_List_Oset(X30499),X30498)) = hAPP(c_List_Ofoldl(X30499,X30499,c_Lattices_Osemilattice__sup__class_Osup(X30499),c_Orderings_Obot__class_Obot(X30499)),X30498) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__set__fold])]) ).

fof(i_0_8988,plain,
    ! [X30500,X30501] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X30501)
      | c_Complete__Lattice_OInf__class_OInf(X30501,hAPP(c_List_Oset(X30501),X30500)) = hAPP(c_List_Ofoldl(X30501,X30501,c_Lattices_Osemilattice__inf__class_Oinf(X30501),c_Orderings_Otop__class_Otop(X30501)),X30500) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__set__fold])]) ).

fof(i_0_8989,plain,
    ! [X24204,X24205] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24205,X24204)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24204),X24205)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost__int]) ).

fof(i_0_8990,plain,
    ! [X16836,X16837,X16838,X16839] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16839),X16838))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X16837),hAPP(c_Set_Oimage(X16839,X16837,X16836),X16838))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__imageI])]) ).

cnf(i_0_8991,plain,
    ( c_List_Oconcat(X2,X1) = c_List_Olist_ONil(X2)
    | esk420_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5655]) ).

cnf(i_0_8992,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oconcat(X2,X1)
    | esk421_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5656]) ).

fof(i_0_8993,plain,
    ! [X33661,X33662] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33662),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33661)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33662),X33661)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33662),X33661))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33662),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33661))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatMost__iff])]) ).

fof(i_0_8994,plain,
    ! [X33659,X33660] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33660),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33659)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33659),X33660)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33659),X33660))
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33660),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33659))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeast__iff])]) ).

fof(i_0_8995,plain,
    ! [X27085,X27086,X27087] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X27087)
      | c_Complete__Lattice_OSup__class_OSup(X27087,hAPP(hAPP(c_Set_Oinsert(X27087),X27086),hAPP(hAPP(c_Set_Oinsert(X27087),X27085),c_Orderings_Obot__class_Obot(tc_fun(X27087,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27087),X27086),X27085) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__binary])]) ).

fof(i_0_8996,plain,
    ! [X26954,X26955,X26956] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26956)
      | c_Complete__Lattice_OInf__class_OInf(X26956,hAPP(hAPP(c_Set_Oinsert(X26956),X26955),hAPP(hAPP(c_Set_Oinsert(X26956),X26954),c_Orderings_Obot__class_Obot(tc_fun(X26956,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26956),X26955),X26954) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__binary])]) ).

fof(i_0_8997,plain,
    ! [X33870,X33871,X33872,X33873] :
      ( ~ class_Divides_Osemiring__div(X33873)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33873),X33872),X33871))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33873),X33870),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33873),X33871),X33872)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33873),X33870),X33871)),X33872) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__swap])]) ).

fof(i_0_8998,plain,
    ! [X19116,X19117,X19118,X19119] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19119),X19118),c_SetInterval_Oord_OlessThan(X19119,X19117,X19116)))
        | hBOOL(hAPP(hAPP(X19117,X19118),X19116)) )
      & ( ~ hBOOL(hAPP(hAPP(X19117,X19118),X19116))
        | hBOOL(hAPP(hAPP(c_member(X19119),X19118),c_SetInterval_Oord_OlessThan(X19119,X19117,X19116))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OlessThan__iff])]) ).

fof(i_0_8999,plain,
    ! [X19108,X19109,X19110,X19111] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19111),X19110),c_SetInterval_Oord_OatMost(X19111,X19109,X19108)))
        | hBOOL(hAPP(hAPP(X19109,X19110),X19108)) )
      & ( ~ hBOOL(hAPP(hAPP(X19109,X19110),X19108))
        | hBOOL(hAPP(hAPP(c_member(X19111),X19110),c_SetInterval_Oord_OatMost(X19111,X19109,X19108))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatMost__iff])]) ).

fof(i_0_9000,plain,
    ! [X19120,X19121,X19122,X19123] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19123),X19122),c_SetInterval_Oord_OgreaterThan(X19123,X19121,X19120)))
        | hBOOL(hAPP(hAPP(X19121,X19120),X19122)) )
      & ( ~ hBOOL(hAPP(hAPP(X19121,X19120),X19122))
        | hBOOL(hAPP(hAPP(c_member(X19123),X19122),c_SetInterval_Oord_OgreaterThan(X19123,X19121,X19120))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OgreaterThan__iff])]) ).

fof(i_0_9001,plain,
    ! [X19112,X19113,X19114,X19115] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X19115),X19114),c_SetInterval_Oord_OatLeast(X19115,X19113,X19112)))
        | hBOOL(hAPP(hAPP(X19113,X19112),X19114)) )
      & ( ~ hBOOL(hAPP(hAPP(X19113,X19112),X19114))
        | hBOOL(hAPP(hAPP(c_member(X19115),X19114),c_SetInterval_Oord_OatLeast(X19115,X19113,X19112))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ord_OatLeast__iff])]) ).

fof(i_0_9002,plain,
    ! [X31010,X31011,X31012,X31013,X31014] :
      ( c_List_Opartition(X31014,X31013,X31012) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31014),tc_List_Olist(X31014)),X31011),X31010)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X31014,tc_HOL_Obool)),hAPP(c_List_Oset(X31014),X31011)),hAPP(c_List_Oset(X31014),X31010)) = hAPP(c_List_Oset(X31014),X31012) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_partition__set])]) ).

fof(i_0_9003,plain,
    ! [X29438,X29439,X29440,X29441] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29441) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X29440),hAPP(hAPP(c_List_Olist_OCons(X29440),X29439),X29438)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29441)) = X29439 )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29441) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X29440),hAPP(hAPP(c_List_Olist_OCons(X29440),X29439),X29438)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29441)) = hAPP(hAPP(c_List_Onth(X29440),X29438),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X29441)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__Cons__number__of])]) ).

fof(i_0_9004,plain,
    ! [X28626,X28627] : hAPP(hAPP(c_Relation_Orel__comp(X28627,X28627,X28627),X28626),c_Transitive__Closure_Ortrancl(X28627,X28626)) = hAPP(hAPP(c_Relation_Orel__comp(X28627,X28627,X28627),c_Transitive__Closure_Ortrancl(X28627,X28626)),X28626),
    inference(variable_rename,[status(thm)],[fact_r__comp__rtrancl__eq]) ).

cnf(i_0_9005,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_5815]) ).

fof(i_0_9006,plain,
    ! [X34024,X34025,X34026,X34027,X34028,X34029] : hAPP(hAPP(hAPP(c_COMBS(X34029,X34028,X34027),X34026),X34025),X34024) = hAPP(hAPP(X34026,X34024),hAPP(X34025,X34024)),
    inference(variable_rename,[status(thm)],[help_c__COMBS__1]) ).

cnf(i_0_9007,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_5816]) ).

fof(i_0_9008,plain,
    ! [X25953,X25954] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25954)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25954),hAPP(c_Groups_Ouminus__class_Ouminus(X25954),hAPP(c_Groups_Oabs__class_Oabs(X25954),X25953))),c_Groups_Ozero__class_Ozero(X25954))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero])]) ).

fof(i_0_9009,plain,
    ! [X23154,X23155,X23156,X23157] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23157,tc_HOL_Obool)),X23156),hAPP(hAPP(c_Set_Oinsert(X23157),X23155),X23154)) = hAPP(hAPP(c_Set_Oinsert(X23157),X23155),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23157,tc_HOL_Obool)),X23156),X23154)),
    inference(variable_rename,[status(thm)],[fact_Un__insert__right]) ).

fof(i_0_9010,plain,
    ! [X18390,X18391,X18392] :
      ( ( X18391 = c_Groups_Ozero__class_Ozero(X18392)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18392),X18391),X18391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18392),X18390),X18390)) != c_Groups_Ozero__class_Ozero(X18392)
        | ~ class_Rings_Olinordered__ring__strict(X18392) )
      & ( X18390 = c_Groups_Ozero__class_Ozero(X18392)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18392),X18391),X18391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18392),X18390),X18390)) != c_Groups_Ozero__class_Ozero(X18392)
        | ~ class_Rings_Olinordered__ring__strict(X18392) )
      & ( X18391 != c_Groups_Ozero__class_Ozero(X18392)
        | X18390 != c_Groups_Ozero__class_Ozero(X18392)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18392),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18392),X18391),X18391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18392),X18390),X18390)) = c_Groups_Ozero__class_Ozero(X18392)
        | ~ class_Rings_Olinordered__ring__strict(X18392) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff])])]) ).

fof(i_0_9011,plain,
    ! [X23438,X23439,X23440] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23440),X23439))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23440,tc_HOL_Obool)),X23439),X23438) = hAPP(hAPP(c_Finite__Set_Ofold(X23440,tc_fun(X23440,tc_HOL_Obool),c_Set_Oinsert(X23440)),X23438),X23439) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_union__fold__insert])]) ).

fof(i_0_9012,plain,
    ! [X21436,X21437] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X21437),X21436) != c_Groups_Ozero__class_Ozero(X21437)
        | c_Int_Oiszero(X21437,hAPP(c_Int_Onumber__class_Onumber__of(X21437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21436),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | ~ class_Int_Onumber__ring(X21437) )
      & ( ~ c_Int_Oiszero(X21437,hAPP(c_Int_Onumber__class_Onumber__of(X21437),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21436),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | hAPP(c_Int_Onumber__class_Onumber__of(X21437),X21436) = c_Groups_Ozero__class_Ozero(X21437)
        | ~ class_Int_Onumber__ring(X21437) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I3_J])])]) ).

fof(i_0_9013,plain,
    ! [X21472,X21473] :
      ( ( c_Groups_Ozero__class_Ozero(X21473) != hAPP(c_Int_Onumber__class_Onumber__of(X21473),X21472)
        | c_Int_Oiszero(X21473,hAPP(c_Int_Onumber__class_Onumber__of(X21473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21472))))
        | ~ class_Int_Onumber__ring(X21473) )
      & ( ~ c_Int_Oiszero(X21473,hAPP(c_Int_Onumber__class_Onumber__of(X21473),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21472))))
        | c_Groups_Ozero__class_Ozero(X21473) = hAPP(c_Int_Onumber__class_Onumber__of(X21473),X21472)
        | ~ class_Int_Onumber__ring(X21473) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__special_I1_J])])]) ).

fof(i_0_9014,plain,
    ! [X32826,X32827,X32828,X32829] :
      ( ~ c_Relation_Otrans(X32829,X32828)
      | ~ c_Relation_Otrans(X32827,X32826)
      | c_Relation_Otrans(tc_prod(X32829,X32827),c_Wellfounded_Olex__prod(X32829,X32827,X32828,X32826)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__lex__prod])]) ).

fof(i_0_9015,plain,
    ! [X28064,X28065,X28066,X28067] :
      ( ~ c_Wellfounded_Owf(X28067,X28066)
      | ~ c_Wellfounded_Owf(X28065,X28064)
      | c_Wellfounded_Owf(tc_prod(X28067,X28065),c_Wellfounded_Olex__prod(X28067,X28065,X28066,X28064)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex__prod])]) ).

cnf(i_0_9016,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_5817]) ).

fof(i_0_9017,plain,
    ! [X33833,X33834] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33834,X33833) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33834),X33833)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33834),X33833))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33834,X33833) = 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_5818])]) ).

fof(i_0_9018,plain,
    ! [X33835,X33836] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33836,X33835)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33836),X33835)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33836),X33835))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33836,X33835) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5819])]) ).

fof(i_0_9019,plain,
    ! [X29779,X29780,X29781,X29782] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29782),X29781))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X29782,X29780)),hAPP(hAPP(c_List_Ozip(X29782,X29780),X29781),X29779))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI1])]) ).

fof(i_0_9020,plain,
    ! [X29783,X29784,X29785,X29786] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29786),X29785))
      | hBOOL(hAPP(c_List_Odistinct(tc_prod(X29784,X29786)),hAPP(hAPP(c_List_Ozip(X29784,X29786),X29783),X29785))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__zipI2])]) ).

fof(i_0_9021,plain,
    ! [X25683,X25684,X25685] :
      ( ~ class_Lattices_Olattice(X25685)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25685),X25684))
      | hBOOL(hAPP(hAPP(c_member(X25685),X25683),X25684))
      | c_Big__Operators_Olattice__class_OInf__fin(X25685,hAPP(hAPP(c_Set_Oinsert(X25685),X25683),X25684)) = hAPP(hAPP(c_Finite__Set_Ofold(X25685,X25685,c_Lattices_Osemilattice__inf__class_Oinf(X25685)),X25683),X25684) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5820])]) ).

fof(i_0_9022,plain,
    ! [X23540,X23541,X23542] :
      ( ~ class_Lattices_Olattice(X23542)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23542),X23541))
      | hBOOL(hAPP(hAPP(c_member(X23542),X23540),X23541))
      | c_Big__Operators_Olattice__class_OSup__fin(X23542,hAPP(hAPP(c_Set_Oinsert(X23542),X23540),X23541)) = hAPP(hAPP(c_Finite__Set_Ofold(X23542,X23542,c_Lattices_Osemilattice__sup__class_Osup(X23542)),X23540),X23541) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5821])]) ).

fof(i_0_9023,plain,
    ! [X23056,X23057,X23058] :
      ( ~ class_Orderings_Olinorder(X23058)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23058),X23057))
      | hBOOL(hAPP(hAPP(c_member(X23058),X23056),X23057))
      | c_Big__Operators_Olinorder__class_OMax(X23058,hAPP(hAPP(c_Set_Oinsert(X23058),X23056),X23057)) = hAPP(hAPP(c_Finite__Set_Ofold(X23058,X23058,c_Orderings_Oord__class_Omax(X23058)),X23056),X23057) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5822])]) ).

fof(i_0_9024,plain,
    ! [X21823,X21824,X21825] :
      ( ~ class_Orderings_Olinorder(X21825)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21825),X21824))
      | hBOOL(hAPP(hAPP(c_member(X21825),X21823),X21824))
      | c_Big__Operators_Olinorder__class_OMin(X21825,hAPP(hAPP(c_Set_Oinsert(X21825),X21823),X21824)) = hAPP(hAPP(c_Finite__Set_Ofold(X21825,X21825,c_Orderings_Oord__class_Omin(X21825)),X21823),X21824) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5823])]) ).

fof(i_0_9025,plain,
    ! [X26983,X26984,X26985,X26986] : hAPP(c_Set_Ovimage(X26986,X26985,X26984),c_Complete__Lattice_OSup__class_OSup(tc_fun(X26985,tc_HOL_Obool),X26983)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X26985,tc_HOL_Obool),tc_fun(X26986,tc_HOL_Obool)),X26983),c_Set_Ovimage(X26986,X26985,X26984)),
    inference(variable_rename,[status(thm)],[fact_vimage__Union]) ).

fof(i_0_9026,plain,
    ! [X26987,X26988,X26989,X26990] : hAPP(c_Set_Oimage(X26990,X26989,X26988),c_Complete__Lattice_OSup__class_OSup(tc_fun(X26990,tc_HOL_Obool),X26987)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X26990,tc_HOL_Obool),tc_fun(X26989,tc_HOL_Obool)),X26987),c_Set_Oimage(X26990,X26989,X26988)),
    inference(variable_rename,[status(thm)],[fact_image__Union]) ).

fof(i_0_9027,plain,
    ! [X23941,X23942] : hBOOL(hAPP(hAPP(c_member(tc_fun(X23942,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23942,tc_HOL_Obool))),hAPP(c_Set_OPow(X23942),X23941))),
    inference(variable_rename,[status(thm)],[fact_Pow__bottom]) ).

fof(i_0_9028,plain,
    ! [X30762,X30763,X30764] :
      ( ~ class_Groups_Omonoid__add(X30764)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30764),hAPP(hAPP(c_List_Omap(X30763,X30764),hAPP(c_COMBK(X30764,X30763),c_Groups_Ozero__class_Ozero(X30764))),X30762)) = c_Groups_Ozero__class_Ozero(X30764) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__0])]) ).

fof(i_0_9029,plain,
    ! [X25127,X25128,X25129] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25129,tc_HOL_Obool)),X25128),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25129,tc_HOL_Obool)),X25128),X25127)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25129,tc_HOL_Obool)),X25128),X25127),
    inference(variable_rename,[status(thm)],[fact_Int__left__absorb]) ).

fof(i_0_9030,plain,
    ! [X23274,X23275,X23276] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23276,tc_HOL_Obool)),X23275),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23276,tc_HOL_Obool)),X23275),X23274)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23276,tc_HOL_Obool)),X23275),X23274),
    inference(variable_rename,[status(thm)],[fact_Un__left__absorb]) ).

fof(i_0_9031,plain,
    ! [X23159,X23160,X23161] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23161,tc_HOL_Obool)),X23160),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X23161,tc_HOL_Obool)),X23159),X23160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23161,tc_HOL_Obool)),X23160),X23159),
    inference(variable_rename,[status(thm)],[fact_Un__Diff__cancel]) ).

fof(i_0_9032,plain,
    ! [X30341,X30342] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30342)),X30341)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | hAPP(c_List_Orotate1(X30342),X30341) = X30341 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__length01])]) ).

fof(i_0_9033,plain,
    ! [X19322,X19323,X19324,X19325,X19326] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X19326,X19325,X19324),X19323),X19322),c_Orderings_Obot__class_Obot(tc_fun(X19325,tc_HOL_Obool))) = X19322,
    inference(variable_rename,[status(thm)],[fact_fold__image__empty]) ).

fof(i_0_9034,plain,
    ! [X33783,X33784,X33785] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33785),X33784))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33785),X33783))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33785),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X33784),X33783))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat])]) ).

cnf(i_0_9035,plain,
    c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_5824]) ).

fof(i_0_9036,plain,
    ! [X18649,X18650] :
      ( ( X18650 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18650),X18649) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18650 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18650),X18649) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18649),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18650),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X18649)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__if])]) ).

fof(i_0_9037,plain,
    ! [X31038,X31039,X31040] : c_List_Olistsp(X31040,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X31040,tc_HOL_Obool)),X31039),X31038)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(X31040),tc_HOL_Obool)),c_List_Olistsp(X31040,X31039)),c_List_Olistsp(X31040,X31038)),
    inference(variable_rename,[status(thm)],[fact_listsp__inf__eq]) ).

fof(i_0_9038,plain,
    ! [X28038,X28039,X28040,X28041,X28043,X28044,X28045,X28046,X28047] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ORangeP(X28041,X28040,X28039),X28038))
        | hBOOL(hAPP(hAPP(X28039,esk288_2(X28038,X28039)),X28038)) )
      & ( ~ hBOOL(hAPP(hAPP(X28044,X28045),X28043))
        | hBOOL(hAPP(c_Predicate_ORangeP(X28047,X28046,X28044),X28043)) ) ),
    inference(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_9039,plain,
    ! [X19918,X19919] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | X19919 = X19918
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( X19919 != X19918
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( X19919 != X19918
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( X19919 != X19918
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19918)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919) != 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),X19918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) )
      & ( X19919 != X19918
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19919) != 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),X19918)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19919) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19918) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5825])])]) ).

fof(i_0_9040,plain,
    ! [X21405,X21406] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21406),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21406),X21405)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21406))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21405))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib__neg])]) ).

fof(i_0_9041,plain,
    ! [X19690,X19691,X19692,X19693] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X19693,X19692)),c_Nitpick_Opair__box_OPairBox(X19693,X19692,X19691,X19690)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_pair__box_Osize_I2_J]) ).

fof(i_0_9042,plain,
    ! [X29673,X29674,X29675,X29676] :
      ( ( X29676 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29675)),X29674)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Obutlast(X29675,hAPP(hAPP(c_List_Olist__update(X29675,X29674),X29676),X29673)) = c_List_Obutlast(X29675,X29674) )
      & ( X29676 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29675)),X29674)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Obutlast(X29675,hAPP(hAPP(c_List_Olist__update(X29675,X29674),X29676),X29673)) = hAPP(hAPP(c_List_Olist__update(X29675,c_List_Obutlast(X29675,X29674)),X29676),X29673) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__list__update])]) ).

fof(i_0_9043,plain,
    ! [X17051,X17052,X17053,X17054,X17055] : hAPP(c_Set_Oimage(X17055,X17054,X17053),hAPP(hAPP(c_Set_Oinsert(X17055),X17052),X17051)) = hAPP(hAPP(c_Set_Oinsert(X17054),hAPP(X17053,X17052)),hAPP(c_Set_Oimage(X17055,X17054,X17053),X17051)),
    inference(variable_rename,[status(thm)],[fact_image__insert]) ).

cnf(i_0_9044,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_5596]) ).

fof(i_0_9045,plain,
    ! [X17034,X17035,X17036] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17036,tc_HOL_Obool)),X17035),X17034))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17036),X17034))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17036),X17035)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__subset])]) ).

fof(i_0_9046,plain,
    ! [X17037,X17038,X17039] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17039),X17038))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17039,tc_HOL_Obool)),X17037),X17038))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X17039),X17037)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__finite__subset])]) ).

fof(i_0_9047,plain,
    ! [X21245,X21246] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21246),hAPP(c_Groups_Ouminus__class_Ouminus(X21246),X21245)),c_Groups_Ozero__class_Ozero(X21246)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21246),c_Groups_Ozero__class_Ozero(X21246)),X21245))
        | ~ class_Groups_Oordered__ab__group__add(X21246) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21246),c_Groups_Ozero__class_Ozero(X21246)),X21245))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21246),hAPP(c_Groups_Ouminus__class_Ouminus(X21246),X21245)),c_Groups_Ozero__class_Ozero(X21246)))
        | ~ class_Groups_Oordered__ab__group__add(X21246) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less])])]) ).

fof(i_0_9048,plain,
    ! [X21237,X21238] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21238),hAPP(c_Groups_Ouminus__class_Ouminus(X21238),X21237)),c_Groups_Ozero__class_Ozero(X21238)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21238),c_Groups_Ozero__class_Ozero(X21238)),X21237))
        | ~ class_Groups_Oordered__ab__group__add(X21238) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21238),c_Groups_Ozero__class_Ozero(X21238)),X21237))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21238),hAPP(c_Groups_Ouminus__class_Ouminus(X21238),X21237)),c_Groups_Ozero__class_Ozero(X21238)))
        | ~ class_Groups_Oordered__ab__group__add(X21238) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le])])]) ).

fof(i_0_9049,plain,
    ! [X31323,X31324,X31325,X31326] :
      ( ~ class_Orderings_Olinorder(X31326)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31325)),c_List_Olinorder__class_Osort__key(X31325,X31326,X31324,X31323)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31325)),X31323) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__sort])]) ).

fof(i_0_9050,plain,
    ! [X31807,X31808,X31809,X31810] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31810)),X31809) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31808)),X31807)
      | hAPP(hAPP(c_List_Ozip(X31810,X31808),hAPP(c_List_Orev(X31810),X31809)),hAPP(c_List_Orev(X31808),X31807)) = hAPP(c_List_Orev(tc_prod(X31810,X31808)),hAPP(hAPP(c_List_Ozip(X31810,X31808),X31809),X31807)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zip__rev])]) ).

fof(i_0_9051,plain,
    ! [X20248,X20249] :
      ( ( ~ 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),X20249),X20248)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20249))
        | X20248 = 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)),X20249))
        | 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),X20249),X20248))) )
      & ( X20248 != 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),X20249),X20248))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff])])]) ).

fof(i_0_9052,plain,
    ! [X25750,X25751,X25752,X25753] :
      ( ~ class_Orderings_Olinorder(X25753)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25753,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25753,X25752,X25751)),hAPP(c_SetInterval_Oord__class_OatLeast(X25753),X25750)) = c_SetInterval_Oord__class_OatLeastAtMost(X25753,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25753),X25752),X25750),X25751) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL2])]) ).

fof(i_0_9053,plain,
    ! [X25152,X25153,X25154,X25155] :
      ( ~ class_Orderings_Olinorder(X25155)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25155,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25155,X25154,X25153)),hAPP(c_SetInterval_Oord__class_OatMost(X25155),X25152)) = c_SetInterval_Oord__class_OatLeastAtMost(X25155,X25154,hAPP(hAPP(c_Orderings_Oord__class_Omin(X25155),X25153),X25152)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostL1])]) ).

fof(i_0_9054,plain,
    ! [X29705,X29706,X29707,X29708] : hAPP(hAPP(c_List_Olist__update(X29708,hAPP(hAPP(c_List_Olist_OCons(X29708),X29707),X29706)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29705) = hAPP(hAPP(c_List_Olist_OCons(X29708),X29705),X29706),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I2_J]) ).

fof(i_0_9055,plain,
    ! [X34018,X34019,X34020,X34021,X34022,X34023] : hAPP(hAPP(hAPP(c_COMBC(X34023,X34022,X34021),X34020),X34019),X34018) = hAPP(hAPP(X34020,X34018),X34019),
    inference(variable_rename,[status(thm)],[help_c__COMBC__1]) ).

fof(i_0_9056,plain,
    ! [X34012,X34013,X34014,X34015,X34016,X34017] : hAPP(hAPP(hAPP(c_COMBB(X34017,X34016,X34015),X34014),X34013),X34012) = hAPP(X34014,hAPP(X34013,X34012)),
    inference(variable_rename,[status(thm)],[help_c__COMBB__1]) ).

fof(i_0_9057,plain,
    ! [X25974,X25975] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25975),hAPP(c_Int_Onumber__class_Onumber__of(X25975),X25974)),c_Groups_Ozero__class_Ozero(X25975)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25975),hAPP(c_Int_Onumber__class_Onumber__of(X25975),X25974)) = hAPP(c_Groups_Ouminus__class_Ouminus(X25975),hAPP(c_Int_Onumber__class_Onumber__of(X25975),X25974))
        | ~ class_Int_Onumber__ring(X25975)
        | ~ class_Rings_Olinordered__idom(X25975) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25975),hAPP(c_Int_Onumber__class_Onumber__of(X25975),X25974)),c_Groups_Ozero__class_Ozero(X25975)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25975),hAPP(c_Int_Onumber__class_Onumber__of(X25975),X25974)) = hAPP(c_Int_Onumber__class_Onumber__of(X25975),X25974)
        | ~ class_Int_Onumber__ring(X25975)
        | ~ class_Rings_Olinordered__idom(X25975) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5826])])]) ).

fof(i_0_9058,plain,
    ! [X26826,X26827,X26828,X26829] : hAPP(c_Set_Ovimage(X26829,X26828,X26827),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26828,tc_HOL_Obool)),X26826)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26829,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X26829,X26828,X26827),X26826)),
    inference(variable_rename,[status(thm)],[fact_vimage__Compl]) ).

fof(i_0_9059,plain,
    ! [X21297,X21298,X21299] : 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),X21299),X21298)),X21297),X21298) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21297,X21298),
    inference(variable_rename,[status(thm)],[fact_mod__mult__self3]) ).

fof(i_0_9060,plain,
    ! [X20759,X20760] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20760))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20759))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X20760)),hAPP(c_Int_Onat,X20759)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20760),X20759)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I1_J])]) ).

fof(i_0_9061,plain,
    ! [X20962,X20963] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20963))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20962))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X20963)),hAPP(c_Int_Onat,X20962)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20963),X20962)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J])]) ).

fof(i_0_9062,plain,
    ! [X20956,X20957] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20957))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20956))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X20957)),hAPP(c_Int_Onat,X20956)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20957),X20956)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J])]) ).

fof(i_0_9063,plain,
    ! [X20958,X20959] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20959))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20958))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20959),X20958)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X20959)),hAPP(c_Int_Onat,X20958)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__distrib])]) ).

fof(i_0_9064,plain,
    ! [X29583,X29584,X29585,X29586] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X29586,X29585))),hAPP(hAPP(c_List_Ozip(X29586,X29585),X29584),X29583)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29586)),X29584)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29585)),X29583)),
    inference(variable_rename,[status(thm)],[fact_length__zip]) ).

fof(i_0_9065,plain,
    ! [X27060,X27061,X27062,X27063] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X27063,tc_HOL_Obool),hAPP(c_Set_Oimage(X27062,tc_fun(X27063,tc_HOL_Obool),X27061),X27060)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27062,tc_fun(X27063,tc_HOL_Obool)),X27060),X27061),
    inference(variable_rename,[status(thm)],[fact_Union__image__eq]) ).

fof(i_0_9066,plain,
    ! [X26905,X26906,X26907,X26908] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X26908,tc_HOL_Obool),hAPP(c_Set_Oimage(X26907,tc_fun(X26908,tc_HOL_Obool),X26906),X26905)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26907,tc_fun(X26908,tc_HOL_Obool)),X26905),X26906),
    inference(variable_rename,[status(thm)],[fact_Inter__image__eq]) ).

fof(i_0_9067,plain,
    ! [X26909,X26910,X26911,X26912] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26912,tc_fun(X26911,tc_HOL_Obool)),X26910),X26909) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X26911,tc_HOL_Obool),hAPP(c_Set_Oimage(X26912,tc_fun(X26911,tc_HOL_Obool),X26909),X26910)),
    inference(variable_rename,[status(thm)],[fact_INTER__eq__Inter__image]) ).

fof(i_0_9068,plain,
    ! [X27056,X27057,X27058,X27059] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X27059,tc_fun(X27058,tc_HOL_Obool)),X27057),X27056) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X27058,tc_HOL_Obool),hAPP(c_Set_Oimage(X27059,tc_fun(X27058,tc_HOL_Obool),X27056),X27057)),
    inference(variable_rename,[status(thm)],[fact_UNION__eq__Union__image]) ).

fof(i_0_9069,plain,
    ! [X20198,X20199,X20200,X20201] :
      ( ~ class_Rings_Osemiring__1(X20201)
      | c_Nat_Osemiring__1__class_Oof__nat__aux(X20201,X20200,hAPP(c_Nat_OSuc,X20199),X20198) = c_Nat_Osemiring__1__class_Oof__nat__aux(X20201,X20200,X20199,hAPP(X20200,X20198)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I2_J])]) ).

fof(i_0_9070,plain,
    ! [X21388,X21389] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21389))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21388))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X21389),hAPP(c_Int_Onat,X21388)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21389,X21388)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__nat__int__functions_I2_J])]) ).

fof(i_0_9071,plain,
    ! [X21390,X21391] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21391))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21390))
      | hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21391,X21390)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X21391),hAPP(c_Int_Onat,X21390)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mod__distrib])]) ).

fof(i_0_9072,plain,
    ! [X20921,X20922] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X20922,X20921) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20922),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20922),X20921)),X20921)),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__equality_H]) ).

fof(i_0_9073,plain,
    ! [X21312,X21313] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21313,X21312) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21313),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21313),X21312)),X21312)),
    inference(variable_rename,[status(thm)],[fact_Divides_Omod__div__equality_H]) ).

fof(i_0_9074,plain,
    ! [X20278,X20279,X20280] :
      ( ~ class_Rings_Olinordered__semidom(X20280)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20280),c_Groups_Ozero__class_Ozero(X20280)),X20279))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20280),c_Groups_Ozero__class_Ozero(X20280)),hAPP(hAPP(c_Power_Opower__class_Opower(X20280),X20279),X20278))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__power])]) ).

fof(i_0_9075,plain,
    ! [X20275,X20276,X20277] :
      ( ~ class_Rings_Olinordered__semidom(X20277)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20277),c_Groups_Ozero__class_Ozero(X20277)),X20276))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20277),c_Groups_Ozero__class_Ozero(X20277)),hAPP(hAPP(c_Power_Opower__class_Opower(X20277),X20276),X20275))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__power])]) ).

fof(i_0_9076,plain,
    ! [X20284,X20285,X20286] :
      ( ~ class_Rings_Olinordered__semidom(X20286)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20286),c_Groups_Oone__class_Oone(X20286)),X20285))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20286),c_Groups_Oone__class_Oone(X20286)),hAPP(hAPP(c_Power_Opower__class_Opower(X20286),X20285),X20284))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__le__power])]) ).

fof(i_0_9077,plain,
    ! [X17117,X17118,X17119,X17120,X17121] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X17121),X17120),X17119))
      | hAPP(c_Set_Oimage(X17121,X17118,hAPP(c_COMBK(X17118,X17121),X17117)),X17119) = hAPP(hAPP(c_Set_Oinsert(X17118),X17117),c_Orderings_Obot__class_Obot(tc_fun(X17118,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant])]) ).

fof(i_0_9078,plain,
    ! [X20877,X20878] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20878)),hAPP(c_Int_Onat,X20877))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20878),X20877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20878)),hAPP(c_Int_Onat,X20877))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20877))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20878),X20877))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X20878)),hAPP(c_Int_Onat,X20877))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__conj])])]) ).

fof(i_0_9079,plain,
    ! [X27236,X27237] : hAPP(hAPP(c_Product__Type_OSigma(X27237,X27236),c_Orderings_Otop__class_Otop(tc_fun(X27237,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X27236,tc_HOL_Obool),X27237),c_Orderings_Otop__class_Otop(tc_fun(X27236,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X27237,X27236),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Times__UNIV]) ).

fof(i_0_9080,plain,
    ! [X19489,X19490] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19490),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19489),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19490),X19489))
        | X19490 = X19489 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19490),X19489))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19490),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19489),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
      & ( X19490 != X19489
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19490),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19489),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__add1__eq])])]) ).

cnf(i_0_9081,plain,
    hAPP(c_Relation_Oconverse(X1,X1),c_Relation_OId(X1)) = c_Relation_OId(X1),
    inference(split_conjunct,[status(thm)],[i_0_5827]) ).

fof(i_0_9082,plain,
    ! [X21247,X21248] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21248),hAPP(c_Groups_Ouminus__class_Ouminus(X21248),X21247)),X21247))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21248),c_Groups_Ozero__class_Ozero(X21248)),X21247))
        | ~ class_Groups_Olinordered__ab__group__add(X21248) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21248),c_Groups_Ozero__class_Ozero(X21248)),X21247))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21248),hAPP(c_Groups_Ouminus__class_Ouminus(X21248),X21247)),X21247))
        | ~ class_Groups_Olinordered__ab__group__add(X21248) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg])])]) ).

fof(i_0_9083,plain,
    ! [X21239,X21240] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21240),hAPP(c_Groups_Ouminus__class_Ouminus(X21240),X21239)),X21239))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21240),c_Groups_Ozero__class_Ozero(X21240)),X21239))
        | ~ class_Groups_Olinordered__ab__group__add(X21240) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21240),c_Groups_Ozero__class_Ozero(X21240)),X21239))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21240),hAPP(c_Groups_Ouminus__class_Ouminus(X21240),X21239)),X21239))
        | ~ class_Groups_Olinordered__ab__group__add(X21240) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff])])]) ).

fof(i_0_9084,plain,
    ! [X31045,X31046,X31047,X31048] :
      ( ( hBOOL(hAPP(c_List_Olistsp(X31048,X31047),X31046))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31048,X31047),hAPP(hAPP(c_List_Oappend(X31048),X31046),X31045))) )
      & ( hBOOL(hAPP(c_List_Olistsp(X31048,X31047),X31045))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31048,X31047),hAPP(hAPP(c_List_Oappend(X31048),X31046),X31045))) )
      & ( ~ hBOOL(hAPP(c_List_Olistsp(X31048,X31047),X31046))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31048,X31047),X31045))
        | hBOOL(hAPP(c_List_Olistsp(X31048,X31047),hAPP(hAPP(c_List_Oappend(X31048),X31046),X31045))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__in__listsp__conv])])]) ).

fof(i_0_9085,plain,
    ! [X28945,X28946,X28947,X28948] : hAPP(hAPP(c_Nat_Ocompow(X28948,X28948),X28947),hAPP(hAPP(c_Nat_Ocompow(X28948,X28948),X28946),X28945)) = hAPP(hAPP(c_Nat_Ocompow(X28948,X28948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X28946),X28947)),X28945),
    inference(variable_rename,[status(thm)],[fact_funpow__mult]) ).

fof(i_0_9086,plain,
    ! [X19427,X19428] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19428)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19427)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19428),X19427)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19428),X19427))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19428)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19427))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__number__of__int__code])]) ).

fof(i_0_9087,plain,
    ! [X20012,X20013] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20013)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20012)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20013),X20012)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20013),X20012))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20013)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20012))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__int])]) ).

fof(i_0_9088,plain,
    ! [X20010,X20011] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20011)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20010)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20011),X20010)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20011),X20010))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20011)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20010))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I2_J])]) ).

fof(i_0_9089,plain,
    ! [X19431,X19432] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19432)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19431)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19432),X19431)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19432),X19431))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19432)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19431))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__number__of__int__code])]) ).

fof(i_0_9090,plain,
    ! [X20017,X20018] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20018)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20017)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20018),X20017)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20018),X20017))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20018)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20017))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__int])]) ).

fof(i_0_9091,plain,
    ! [X20015,X20016] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20016)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20015)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20016),X20015)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20016),X20015))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20016)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20015))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I3_J])]) ).

fof(i_0_9092,plain,
    ! [X18786,X18787] :
      ( ( ~ 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),X18787),X18786)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18786),X18787)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18786),X18787))
        | 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),X18787),X18786))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__diff])]) ).

fof(i_0_9093,plain,
    ! [X19502,X19503] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19502),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19503),X19502)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19503),X19502))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19503),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19502),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq])]) ).

fof(i_0_9094,plain,
    ! [X19504,X19505] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19504),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19505),X19504)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19505),X19504))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19505),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19504),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le])]) ).

fof(i_0_9095,plain,
    ! [X21126,X21127,X21128] :
      ( ~ class_Int_Onumber__ring(X21128)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21128),hAPP(c_Groups_Ouminus__class_Ouminus(X21128),hAPP(c_Int_Onumber__class_Onumber__of(X21128),X21127))),X21126) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21128),hAPP(c_Int_Onumber__class_Onumber__of(X21128),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21127))),X21126) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__number__of__mult])]) ).

fof(i_0_9096,plain,
    ! [X18969,X18970,X18971] :
      ( ~ class_Rings_Ocomm__semiring__1(X18971)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18971),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18971),X18970),X18969)),X18969) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18971),X18970),c_Groups_Oone__class_Oone(X18971))),X18969) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J])]) ).

fof(i_0_9097,plain,
    ! [X29735,X29736,X29737,X29738] :
      ( ( hAPP(hAPP(c_List_Olist__update(X29737,X29736),X29738),X29735) != X29736
        | hAPP(hAPP(c_List_Onth(X29737),X29736),X29738) = X29735
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29738),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29737)),X29736))) )
      & ( hAPP(hAPP(c_List_Onth(X29737),X29736),X29738) != X29735
        | hAPP(hAPP(c_List_Olist__update(X29737,X29736),X29738),X29735) = X29736
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29738),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29737)),X29736))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__same__conv])])]) ).

fof(i_0_9098,plain,
    ! [X21420,X21421] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21421)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21421),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21420)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21420)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21421),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21420)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21421)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21421))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21420)))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21421),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21420)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21421),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21420)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21421))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5828])])]) ).

fof(i_0_9099,plain,
    ! [X23041,X23042,X23043] :
      ( ~ class_Orderings_Olinorder(X23043)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23043),X23042))
      | hBOOL(hAPP(hAPP(c_member(X23043),X23041),X23042))
      | X23042 = c_Orderings_Obot__class_Obot(tc_fun(X23043,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X23043,c_Orderings_Oord__class_Omax(X23043),hAPP(hAPP(c_Set_Oinsert(X23043),X23041),X23042)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X23043),X23041),c_Big__Operators_Olattice_OSup__fin(X23043,c_Orderings_Oord__class_Omax(X23043),X23042)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5829])]) ).

fof(i_0_9100,plain,
    ! [X21808,X21809,X21810] :
      ( ~ class_Orderings_Olinorder(X21810)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21810),X21809))
      | hBOOL(hAPP(hAPP(c_member(X21810),X21808),X21809))
      | X21809 = c_Orderings_Obot__class_Obot(tc_fun(X21810,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X21810,c_Orderings_Oord__class_Omin(X21810),hAPP(hAPP(c_Set_Oinsert(X21810),X21808),X21809)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21810),X21808),c_Big__Operators_Olattice_OInf__fin(X21810,c_Orderings_Oord__class_Omin(X21810),X21809)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5830])]) ).

fof(i_0_9101,plain,
    ! [X21093,X21094] : 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),X21094))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21093))),
    inference(variable_rename,[status(thm)],[fact_negative__zle]) ).

fof(i_0_9102,plain,
    ! [X25972,X25973] : 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),X25973)),X25972))),
    inference(variable_rename,[status(thm)],[fact_zero__le__zpower__abs]) ).

fof(i_0_9103,plain,
    ! [X21602,X21603,X21604] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21604),X21603)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21602),X21603)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X21604),X21602)),X21603),
    inference(variable_rename,[status(thm)],[fact_min__diff]) ).

cnf(i_0_9104,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(X1)),X2) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_5831]) ).

fof(i_0_9105,plain,
    ! [X19453,X19454,X19455] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19455),X19454)),X19453) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19455),X19453)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19454),X19453)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib]) ).

fof(i_0_9106,plain,
    ! [X19461,X19462,X19463] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19463),X19462)),X19461) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19463),X19461)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19462),X19461)),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib]) ).

fof(i_0_9107,plain,
    ! [X18537,X18538,X18539] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18539),X18538)),X18537) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18539),X18537)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18538),X18537)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib]) ).

fof(i_0_9108,plain,
    ! [X18565,X18566,X18567] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18567),X18566)),X18565) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18567),X18565)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18566),X18565)),
    inference(variable_rename,[status(thm)],[fact_diff__mult__distrib]) ).

fof(i_0_9109,plain,
    ! [X29430,X29431,X29432,X29433] : hAPP(hAPP(c_List_Onth(X29433),hAPP(hAPP(c_List_Olist_OCons(X29433),X29432),X29431)),X29430) = c_Nat_Onat_Onat__case(X29433,X29432,hAPP(c_List_Onth(X29433),X29431),X29430),
    inference(variable_rename,[status(thm)],[fact_nth_Osimps]) ).

fof(i_0_9110,plain,
    ! [X32511,X32512,X32513] : c_List_Oreplicate(X32513,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32513)),hAPP(c_List_Ofilter(X32513,hAPP(c_fequal,X32512)),X32511)),X32512) = hAPP(c_List_Ofilter(X32513,hAPP(c_fequal,X32512)),X32511),
    inference(variable_rename,[status(thm)],[fact_replicate__length__filter]) ).

fof(i_0_9111,plain,
    ! [X18985,X18986,X18987,X18988] :
      ( ( X18986 = c_Orderings_Obot__class_Obot(tc_fun(X18988,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X18988,X18987,X18986,X18985) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X18988,X18987),tc_HOL_Obool)) )
      & ( X18985 = c_Orderings_Obot__class_Obot(tc_fun(X18987,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X18988,X18987,X18986,X18985) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X18988,X18987),tc_HOL_Obool)) )
      & ( X18986 != c_Orderings_Obot__class_Obot(tc_fun(X18988,tc_HOL_Obool))
        | X18985 != c_Orderings_Obot__class_Obot(tc_fun(X18987,tc_HOL_Obool))
        | c_Sum__Type_OPlus(X18988,X18987,X18986,X18985) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X18988,X18987),tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Plus__eq__empty__conv])])]) ).

fof(i_0_9112,plain,
    ! [X33716,X33717,X33718] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33718),X33716))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33717),X33716))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33716),X33717))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33718),X33717)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33716),X33718))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33717),X33716))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33716),X33717))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33718),X33717)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5832])])]) ).

fof(i_0_9113,plain,
    ! [X33734,X33735,X33736] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33736),X33734))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33735),X33734))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33736),X33735))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33735),X33736)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33734),X33736))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33735),X33734))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33736),X33735))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33735),X33736)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5833])])]) ).

fof(i_0_9114,plain,
    ! [X31327,X31328,X31329,X31330] :
      ( ~ class_Orderings_Olinorder(X31330)
      | hAPP(c_List_Oset(X31329),c_List_Olinorder__class_Osort__key(X31329,X31330,X31328,X31327)) = hAPP(c_List_Oset(X31329),X31327) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__sort])]) ).

fof(i_0_9115,plain,
    ! [X32611,X32612,X32613] : hAPP(hAPP(c_List_Oappend(X32613),c_List_Oreplicate(X32613,X32612,X32611)),hAPP(hAPP(c_List_Olist_OCons(X32613),X32611),c_List_Olist_ONil(X32613))) = hAPP(hAPP(c_List_Olist_OCons(X32613),X32611),c_List_Oreplicate(X32613,X32612,X32611)),
    inference(variable_rename,[status(thm)],[fact_replicate__append__same]) ).

fof(i_0_9116,plain,
    ! [X33840,X33841,X33842] :
      ( ( X33842 = X33841
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33842,X33841) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X33840),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
      & ( X33841 = X33840
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33842,X33841) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X33840),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) )
      & ( X33842 != X33841
        | X33841 != X33840
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33842,X33841) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X33840),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton__iff])])]) ).

fof(i_0_9117,plain,
    ! [X27045,X27046,X27047] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X27047,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X27047,tc_HOL_Obool)),X27046),X27045)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X27047,tc_HOL_Obool)),X27046),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27047,tc_HOL_Obool),X27045)),
    inference(variable_rename,[status(thm)],[fact_Union__insert]) ).

fof(i_0_9118,plain,
    ! [X26874,X26875,X26876] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X26876,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(X26876,tc_HOL_Obool)),X26875),X26874)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26876,tc_HOL_Obool)),X26875),c_Complete__Lattice_OInf__class_OInf(tc_fun(X26876,tc_HOL_Obool),X26874)),
    inference(variable_rename,[status(thm)],[fact_Inter__insert]) ).

fof(i_0_9119,plain,
    ! [X28124,X28125] :
      ( hAPP(hAPP(c_Relation_Orel__comp(X28125,X28125,X28125),X28124),X28124) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28125,X28125),tc_HOL_Obool))
      | c_Wellfounded_Owf(X28125,X28124) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__no__loop])]) ).

fof(i_0_9120,plain,
    ! [X18194,X18195] :
      ( ( X18195 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18195),X18194) = X18194 )
      & ( X18195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18195),X18194) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18195),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X18194)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__eq__if])]) ).

fof(i_0_9121,plain,
    ! [X24553,X24554,X24555,X24556] :
      ( ~ class_Rings_Osemiring__1(X24556)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24555,X24556),hAPP(c_COMBK(X24556,X24555),X24554)),X24553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X24556),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X24556),hAPP(c_Finite__Set_Ocard(X24555),X24553))),X24554) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__constant])]) ).

fof(i_0_9122,plain,
    ! [X21669,X21670] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21670),hAPP(c_Int_Oring__1__class_Oof__int(X21670),X21669)),c_Groups_Ozero__class_Ozero(X21670)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21669),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ class_Rings_Olinordered__idom(X21670) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21669),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21670),hAPP(c_Int_Oring__1__class_Oof__int(X21670),X21669)),c_Groups_Ozero__class_Ozero(X21670)))
        | ~ class_Rings_Olinordered__idom(X21670) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__less__0__iff])])]) ).

fof(i_0_9123,plain,
    ! [X21667,X21668] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21668),hAPP(c_Int_Oring__1__class_Oof__int(X21668),X21667)),c_Groups_Ozero__class_Ozero(X21668)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21667),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ class_Rings_Olinordered__idom(X21668) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21667),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21668),hAPP(c_Int_Oring__1__class_Oof__int(X21668),X21667)),c_Groups_Ozero__class_Ozero(X21668)))
        | ~ class_Rings_Olinordered__idom(X21668) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__le__0__iff])])]) ).

fof(i_0_9124,plain,
    ! [X20665,X20666,X20667,X20668] :
      ( ~ class_Divides_Osemiring__div(X20668)
      | c_Divides_Odiv__class_Omod(X20668,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20668),X20667),c_Divides_Odiv__class_Omod(X20668,X20666,X20665)),X20665) = c_Divides_Odiv__class_Omod(X20668,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20668),X20667),X20666),X20665) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__simps_I2_J])]) ).

fof(i_0_9125,plain,
    ! [X20679,X20680,X20681,X20682] :
      ( ~ class_Divides_Osemiring__div(X20682)
      | c_Divides_Odiv__class_Omod(X20682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20682),X20681),X20680),X20679) = c_Divides_Odiv__class_Omod(X20682,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20682),X20681),c_Divides_Odiv__class_Omod(X20682,X20680,X20679)),X20679) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__right__eq])]) ).

fof(i_0_9126,plain,
    ! [X20653,X20654,X20655,X20656] :
      ( ~ class_Divides_Osemiring__div(X20656)
      | c_Divides_Odiv__class_Omod(X20656,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20656),X20655),X20654),X20653) = c_Divides_Odiv__class_Omod(X20656,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20656),X20655),c_Divides_Odiv__class_Omod(X20656,X20654,X20653)),X20653) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__right__eq])]) ).

fof(i_0_9127,plain,
    ! [X20723,X20724,X20725,X20726] :
      ( ~ class_Divides_Oring__div(X20726)
      | c_Divides_Odiv__class_Omod(X20726,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20726),X20725),X20724),X20723) = c_Divides_Odiv__class_Omod(X20726,hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20726),X20725),c_Divides_Odiv__class_Omod(X20726,X20724,X20723)),X20723) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__diff__right__eq])]) ).

fof(i_0_9128,plain,
    ! [X17206,X17207,X17208,X17209] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17209,tc_HOL_Obool)),X17208),X17207))
      | ~ hBOOL(hAPP(X17208,X17206))
      | hBOOL(hAPP(X17207,X17206)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_predicate1D])]) ).

fof(i_0_9129,plain,
    ! [X17202,X17203,X17204,X17205] :
      ( ~ hBOOL(hAPP(X17205,X17204))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17203,tc_HOL_Obool)),X17205),X17202))
      | hBOOL(hAPP(X17202,X17204)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__predicate1D])]) ).

fof(i_0_9130,plain,
    ! [X20968,X20969] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20969))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20969),X20968))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20968),X20969)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X20968)),hAPP(c_Int_Onat,X20969)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__diff__distrib])]) ).

fof(i_0_9131,plain,
    ! [X31041,X31042,X31043,X31044] :
      ( ( hBOOL(hAPP(X31043,X31042))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31044,X31043),hAPP(hAPP(c_List_Olist_OCons(X31044),X31042),X31041))) )
      & ( hBOOL(hAPP(c_List_Olistsp(X31044,X31043),X31041))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31044,X31043),hAPP(hAPP(c_List_Olist_OCons(X31044),X31042),X31041))) )
      & ( ~ hBOOL(hAPP(X31043,X31042))
        | ~ hBOOL(hAPP(c_List_Olistsp(X31044,X31043),X31041))
        | hBOOL(hAPP(c_List_Olistsp(X31044,X31043),hAPP(hAPP(c_List_Olist_OCons(X31044),X31042),X31041))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsp_Oequations_I2_J])])]) ).

fof(i_0_9132,plain,
    ! [X25744,X25745,X25746] :
      ( ~ class_Orderings_Olinorder(X25746)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25746),X25745),X25744))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25746,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25746,X25745),X25744)),hAPP(c_SetInterval_Oord__class_OatLeast(X25746),X25744)) = hAPP(c_SetInterval_Oord__class_OatLeast(X25746),X25745) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I14_J])]) ).

fof(i_0_9133,plain,
    ! [X20115,X20116] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20116),hAPP(c_Int_Onumber__class_Onumber__of(X20116),X20115)),c_Groups_Ozero__class_Ozero(X20116)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20115),c_Int_OPls))
        | ~ class_Int_Onumber__ring(X20116)
        | ~ class_Rings_Olinordered__idom(X20116) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20115),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20116),hAPP(c_Int_Onumber__class_Onumber__of(X20116),X20115)),c_Groups_Ozero__class_Ozero(X20116)))
        | ~ class_Int_Onumber__ring(X20116)
        | ~ class_Rings_Olinordered__idom(X20116) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I3_J])])]) ).

fof(i_0_9134,plain,
    ! [X20109,X20110] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20110),hAPP(c_Int_Onumber__class_Onumber__of(X20110),X20109)),c_Groups_Ozero__class_Ozero(X20110)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20109),c_Int_OPls))
        | ~ class_Int_Onumber__ring(X20110)
        | ~ class_Rings_Olinordered__idom(X20110) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20109),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20110),hAPP(c_Int_Onumber__class_Onumber__of(X20110),X20109)),c_Groups_Ozero__class_Ozero(X20110)))
        | ~ class_Int_Onumber__ring(X20110)
        | ~ class_Rings_Olinordered__idom(X20110) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I3_J])])]) ).

fof(i_0_9135,plain,
    ! [X30927,X30928,X30929,X30930] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30930)),X30929) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30928)),X30927)
      | hAPP(hAPP(c_List_Omap(tc_prod(X30930,X30928),X30930),c_Product__Type_Ofst(X30930,X30928)),hAPP(hAPP(c_List_Ozip(X30930,X30928),X30929),X30927)) = X30929 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__fst__zip])]) ).

fof(i_0_9136,plain,
    ! [X30931,X30932,X30933,X30934] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30934)),X30933) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30932)),X30931)
      | hAPP(hAPP(c_List_Omap(tc_prod(X30934,X30932),X30932),c_Product__Type_Osnd(X30934,X30932)),hAPP(hAPP(c_List_Ozip(X30934,X30932),X30933),X30931)) = X30931 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__snd__zip])]) ).

fof(i_0_9137,plain,
    ! [X20527,X20528,X20529] :
      ( ~ class_Divides_Osemiring__div(X20529)
      | X20528 = c_Groups_Ozero__class_Ozero(X20529)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20529),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20529),X20528),X20527)),X20528) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20529),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20529),X20527),X20528)),c_Groups_Oone__class_Oone(X20529)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self1])]) ).

fof(i_0_9138,plain,
    ! [X20524,X20525,X20526] :
      ( ~ class_Divides_Osemiring__div(X20526)
      | X20525 = c_Groups_Ozero__class_Ozero(X20526)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20526),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20526),X20524),X20525)),X20525) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20526),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20526),X20524),X20525)),c_Groups_Oone__class_Oone(X20526)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__add__self2])]) ).

fof(i_0_9139,plain,
    ! [X20695,X20696,X20697,X20698] :
      ( ~ class_Divides_Osemiring__div(X20698)
      | c_Divides_Odiv__class_Omod(X20698,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20698),X20697),X20696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20698),X20695),X20696)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20698),c_Divides_Odiv__class_Omod(X20698,X20697,X20695)),X20696) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult2])]) ).

fof(i_0_9140,plain,
    ! [X25970,X25971] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25971),X25970))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25971))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25970))),
    inference(variable_rename,[status(thm)],[fact_nat__abs__mult__distrib]) ).

fof(i_0_9141,plain,
    ! [X20866,X20867,X20868] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20868))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20868),X20867)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20868),X20866)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20867),X20866) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel1])]) ).

fof(i_0_9142,plain,
    ! [X20492,X20493,X20494] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20494))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20493),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20492),X20494)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20493),X20492)),X20494) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__zmult2__eq])]) ).

fof(i_0_9143,plain,
    ! [X31941,X31942,X31943,X31944,X31945] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X31945),X31944),hAPP(c_List_Oset(X31945),X31943)))
      | hBOOL(hAPP(X31942,X31944))
      | c_List_OtakeWhile(X31945,X31942,hAPP(hAPP(c_List_Oappend(X31945),X31943),X31941)) = c_List_OtakeWhile(X31945,X31942,X31943) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5834])]) ).

fof(i_0_9144,plain,
    ! [X20841,X20842] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20842)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20842)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20841)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20842)))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20842)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20841)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20842)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20841))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5835])]) ).

fof(i_0_9145,plain,
    ! [X21059,X21060] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21060)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21060)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21059)) = 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),X21059)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21060)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21060)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21059)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21060)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21059))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5836])]) ).

fof(i_0_9146,plain,
    ! [X22332,X22333,X22334,X22335,X22336] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22336,X22335,X22334),X22333),X22332) = hAPP(hAPP(X22333,hAPP(c_Product__Type_Ofst(X22336,X22335),X22332)),hAPP(c_Product__Type_Osnd(X22336,X22335),X22332)),
    inference(variable_rename,[status(thm)],[fact_split__def]) ).

fof(i_0_9147,plain,
    ! [X22321,X22322,X22323,X22324,X22325] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22325,X22324,X22323),X22322),X22321) = hAPP(hAPP(X22322,hAPP(c_Product__Type_Ofst(X22325,X22324),X22321)),hAPP(c_Product__Type_Osnd(X22325,X22324),X22321)),
    inference(variable_rename,[status(thm)],[fact_prod__case__beta]) ).

fof(i_0_9148,plain,
    ! [X22316,X22317,X22318,X22319,X22320] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22320,X22319,X22318),X22317),X22316) = hAPP(hAPP(X22317,hAPP(c_Product__Type_Ofst(X22320,X22319),X22316)),hAPP(c_Product__Type_Osnd(X22320,X22319),X22316)),
    inference(variable_rename,[status(thm)],[fact_split__beta]) ).

fof(i_0_9149,plain,
    ! [X31661,X31662] :
      ( ~ class_Orderings_Olinorder(X31662)
      | c_List_Olinorder__class_Osorted(X31662,c_List_Olinorder__class_Osort__key(X31662,X31662,c_COMBI(X31662),X31661)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__sort])]) ).

fof(i_0_9150,plain,
    ! [X30030,X30031,X30032,X30033,X30034] :
      ( ( X30033 = X30031
        | hAPP(hAPP(c_List_Oappend(X30034),X30033),hAPP(hAPP(c_List_Olist_OCons(X30034),X30032),c_List_Olist_ONil(X30034))) != hAPP(hAPP(c_List_Oappend(X30034),X30031),hAPP(hAPP(c_List_Olist_OCons(X30034),X30030),c_List_Olist_ONil(X30034))) )
      & ( X30032 = X30030
        | hAPP(hAPP(c_List_Oappend(X30034),X30033),hAPP(hAPP(c_List_Olist_OCons(X30034),X30032),c_List_Olist_ONil(X30034))) != hAPP(hAPP(c_List_Oappend(X30034),X30031),hAPP(hAPP(c_List_Olist_OCons(X30034),X30030),c_List_Olist_ONil(X30034))) )
      & ( X30033 != X30031
        | X30032 != X30030
        | hAPP(hAPP(c_List_Oappend(X30034),X30033),hAPP(hAPP(c_List_Olist_OCons(X30034),X30032),c_List_Olist_ONil(X30034))) = hAPP(hAPP(c_List_Oappend(X30034),X30031),hAPP(hAPP(c_List_Olist_OCons(X30034),X30030),c_List_Olist_ONil(X30034))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append1__eq__conv])])]) ).

fof(i_0_9151,plain,
    ! [X33807,X33808] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33808),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33807),X33808)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33808),X33807)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33808),X33807))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33808),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X33807),X33808))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__reduce])]) ).

fof(i_0_9152,plain,
    ! [X30359,X30360,X30361] :
      ( X30361 = c_List_Olist_ONil(X30360)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30360)),X30361)))
      | hAPP(c_List_Ohd(X30360),hAPP(hAPP(c_List_Odrop(X30360),X30359),X30361)) = hAPP(hAPP(c_List_Onth(X30360),X30361),X30359) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__drop__conv__nth])]) ).

fof(i_0_9153,plain,
    ! [X25847,X25848,X25849] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25849)
      | hAPP(c_Groups_Oabs__class_Oabs(X25849),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25849),hAPP(c_Groups_Oabs__class_Oabs(X25849),X25848)),hAPP(c_Groups_Oabs__class_Oabs(X25849),X25847))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X25849),hAPP(c_Groups_Oabs__class_Oabs(X25849),X25848)),hAPP(c_Groups_Oabs__class_Oabs(X25849),X25847)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__add__abs])]) ).

fof(i_0_9154,plain,
    ! [X19628,X19629,X19630,X19631,X19632] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X19632,X19631,X19630)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19632),X19629))
      | hAPP(X19630,hAPP(hAPP(c_Set_Oinsert(X19632),X19628),X19629)) = hAPP(hAPP(c_Finite__Set_Ofold(X19632,X19632,X19631),X19628),X19629) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oeq__fold__idem_H])]) ).

fof(i_0_9155,plain,
    ! [X24972,X24973,X24974] :
      ( ~ class_Lattices_Osemilattice__inf(X24974)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24974),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24974),X24973),X24972)),X24973)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le1])]) ).

fof(i_0_9156,plain,
    ! [X24969,X24970,X24971] :
      ( ~ class_Lattices_Olattice(X24971)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24971),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24971),X24970),X24969)),X24970)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I1_J])]) ).

fof(i_0_9157,plain,
    ! [X24978,X24979,X24980] :
      ( ~ class_Lattices_Osemilattice__inf(X24980)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24980),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24980),X24979),X24978)),X24978)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__le2])]) ).

fof(i_0_9158,plain,
    ! [X24975,X24976,X24977] :
      ( ~ class_Lattices_Olattice(X24977)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24977),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24977),X24976),X24975)),X24975)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I2_J])]) ).

fof(i_0_9159,plain,
    ! [X21526,X21527,X21528] :
      ( ~ class_Orderings_Olinorder(X21528)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21528),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21528),X21527),X21526)),X21527)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le1])]) ).

fof(i_0_9160,plain,
    ! [X21529,X21530,X21531] :
      ( ~ class_Orderings_Olinorder(X21531)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21531),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21531),X21530),X21529)),X21529)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__le2])]) ).

fof(i_0_9161,plain,
    ! [X19286] :
      ( ~ 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),X19286)))
      | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19286) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19286)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_expand__Suc])]) ).

fof(i_0_9162,plain,
    ! [X25468,X25469,X25470] :
      ( ~ class_Orderings_Olinorder(X25470)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25470),X25469),X25468))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25470,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25470),X25469)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25470,X25469,X25468)) = hAPP(c_SetInterval_Oord__class_OatMost(X25470),X25468) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I9_J])]) ).

fof(i_0_9163,plain,
    ! [X25560,X25561,X25562] :
      ( ~ class_Orderings_Olinorder(X25562)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25562),X25561),X25560))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25562,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25562),X25561)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25562,X25561,X25560)) = hAPP(c_SetInterval_Oord__class_OlessThan(X25562),X25560) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I7_J])]) ).

fof(i_0_9164,plain,
    ! [X25557,X25558,X25559] :
      ( ~ class_Orderings_Olinorder(X25559)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25559),X25558),X25557))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25559,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X25559),X25558)),c_SetInterval_Oord__class_OatLeastAtMost(X25559,X25558,X25557)) = hAPP(c_SetInterval_Oord__class_OatMost(X25559),X25557) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I10_J])]) ).

fof(i_0_9165,plain,
    ! [X33793,X33794,X33795] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33795),hAPP(c_Groups_Ouminus__class_Ouminus(X33795),X33794)),X33793))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33795),X33794),X33793))
        | ~ class_Rings_Ocomm__ring__1(X33795) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33795),X33794),X33793))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33795),hAPP(c_Groups_Ouminus__class_Ouminus(X33795),X33794)),X33793))
        | ~ class_Rings_Ocomm__ring__1(X33795) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff])])]) ).

fof(i_0_9166,plain,
    ! [X33676,X33677,X33678] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33678),hAPP(c_Groups_Oabs__class_Oabs(X33678),X33677)),X33676))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33678),X33677),X33676))
        | ~ class_Rings_Olinordered__idom(X33678) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33678),X33677),X33676))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33678),hAPP(c_Groups_Oabs__class_Oabs(X33678),X33677)),X33676))
        | ~ class_Rings_Olinordered__idom(X33678) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff])])]) ).

fof(i_0_9167,plain,
    ! [X25872,X25873,X25874] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25874)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25874),hAPP(c_Groups_Oabs__class_Oabs(X25874),X25873)),X25872))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25874),X25873),X25872)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__D1])]) ).

fof(i_0_9168,plain,
    ! [X24915,X24916,X24917,X24918] :
      ( ~ class_Lattices_Odistrib__lattice(X24918)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24918),X24917),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24918),X24916),X24915)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24918),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24918),X24917),X24916)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24918),X24917),X24915)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__distrib1])]) ).

fof(i_0_9169,plain,
    ! [X24911,X24912,X24913,X24914] :
      ( ~ class_Lattices_Odistrib__lattice(X24914)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24914),X24913),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24914),X24912),X24911)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24914),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24914),X24913),X24912)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24914),X24913),X24911)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__distrib1])]) ).

fof(i_0_9170,plain,
    ! [X22461,X22462,X22463,X22464] :
      ( ~ class_Orderings_Olinorder(X22464)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22464),X22463),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22464),X22462),X22461)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22464),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22464),X22463),X22462)),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22464),X22463),X22461)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__distrib1])]) ).

fof(i_0_9171,plain,
    ! [X22465,X22466,X22467,X22468] :
      ( ~ class_Orderings_Olinorder(X22468)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22468),X22467),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22468),X22466),X22465)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22468),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22468),X22467),X22466)),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22468),X22467),X22465)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__distrib1])]) ).

fof(i_0_9172,plain,
    ! [X19100,X19101,X19102,X19103] :
      ( ~ class_Rings_Ocomm__semiring__1(X19103)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19103),X19102),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19103),X19101),X19100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19103),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19103),X19102),X19101)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19103),X19102),X19100)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J])]) ).

fof(i_0_9173,plain,
    ! [X19050,X19051,X19052,X19053] :
      ( ~ class_Rings_Ocomm__semiring__1(X19053)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19053),X19052),X19051)),X19050) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19053),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19053),X19052),X19050)),X19051) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J])]) ).

fof(i_0_9174,plain,
    ! [X19016,X19017,X19018,X19019] :
      ( ~ class_Rings_Ocomm__semiring__1(X19019)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19019),X19018),X19017)),X19016) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19019),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19019),X19018),X19016)),X19017) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J])]) ).

fof(i_0_9175,plain,
    ! [X27823,X27824,X27825] : hAPP(c_Fun_Ocomp(X27825,X27825,X27824,c_Fun_Oid(X27825)),X27823) = X27823,
    inference(variable_rename,[status(thm)],[fact_id__o]) ).

fof(i_0_9176,plain,
    ! [X29540,X29541,X29542] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X29542),X29541),hAPP(c_List_Oset(X29542),X29540)))
      | 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(X29542)),X29540))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__pos__if__in__set])]) ).

cnf(i_0_9177,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_5730]) ).

fof(i_0_9178,plain,
    ! [X19277,X19278,X19279] :
      ( ~ class_Groups_Oab__semigroup__mult(X19279)
      | X19278 = c_Orderings_Obot__class_Obot(tc_fun(X19279,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19279),X19278))
      | hBOOL(hAPP(hAPP(c_member(X19279),X19277),X19278))
      | hAPP(c_Finite__Set_Ofold1(X19279,c_Groups_Otimes__class_Otimes(X19279)),hAPP(hAPP(c_Set_Oinsert(X19279),X19277),X19278)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19279),X19277),hAPP(c_Finite__Set_Ofold1(X19279,c_Groups_Otimes__class_Otimes(X19279)),X19278)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5837])]) ).

fof(i_0_9179,plain,
    ! [X28933,X28934,X28935] :
      ( ~ c_Relation_Osingle__valued(X28935,X28935,X28934)
      | c_Relation_Osingle__valued(X28935,X28935,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28935,X28935),tc_HOL_Obool),X28933),X28934)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_single__valued__rel__pow])]) ).

fof(i_0_9180,plain,
    ! [X32800,X32801,X32802,X32803] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(X32803),X32802),X32801),X32800) = 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(X32803)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(X32803),X32802)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Osingle__def]) ).

fof(i_0_9181,plain,
    ! [X28217,X28218,X28219,X28220,X28222,X28223,X28224,X28225,X28226] :
      ( ( ~ hBOOL(hAPP(c_Predicate_ODomainP(X28220,X28219,X28218),X28217))
        | hBOOL(hAPP(hAPP(X28218,X28217),esk295_2(X28217,X28218))) )
      & ( ~ hBOOL(hAPP(hAPP(X28223,X28222),X28224))
        | hBOOL(hAPP(c_Predicate_ODomainP(X28226,X28225,X28223),X28222)) ) ),
    inference(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_9182,plain,
    ! [X26144,X26145,X26146,X26147,X26148] :
      ( ( hAPP(X26146,X26145) != hAPP(X26146,X26144)
        | X26145 = X26144
        | ~ c_Fun_Oinj__on(X26148,X26147,X26146,c_Orderings_Otop__class_Otop(tc_fun(X26148,tc_HOL_Obool))) )
      & ( X26145 != X26144
        | hAPP(X26146,X26145) = hAPP(X26146,X26144)
        | ~ c_Fun_Oinj__on(X26148,X26147,X26146,c_Orderings_Otop__class_Otop(tc_fun(X26148,tc_HOL_Obool))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__eq])])]) ).

fof(i_0_9183,plain,
    ! [X26139,X26140,X26141,X26142,X26143] :
      ( ~ c_Fun_Oinj__on(X26143,X26142,X26141,c_Orderings_Otop__class_Otop(tc_fun(X26143,tc_HOL_Obool)))
      | hAPP(X26141,X26140) != hAPP(X26141,X26139)
      | X26140 = X26139 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_injD])]) ).

fof(i_0_9184,plain,
    ! [X32580,X32581,X32582,X32583] : c_List_Oreplicate(X32583,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X32582),X32581),X32580) = hAPP(hAPP(c_List_Oappend(X32583),c_List_Oreplicate(X32583,X32582,X32580)),c_List_Oreplicate(X32583,X32581,X32580)),
    inference(variable_rename,[status(thm)],[fact_replicate__add]) ).

fof(i_0_9185,plain,
    ! [X33831,X33832] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33832),X33831))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33831),X33832))
      | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33831,X33832) = 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_5838])]) ).

fof(i_0_9186,plain,
    ! [X23029,X23030,X23031] :
      ( ~ class_Orderings_Olinorder(X23031)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23031),X23030))
      | c_Big__Operators_Olattice_OSup__fin(X23031,c_Orderings_Oord__class_Omax(X23031),hAPP(hAPP(c_Set_Oinsert(X23031),X23029),X23030)) = hAPP(hAPP(c_Finite__Set_Ofold(X23031,X23031,c_Orderings_Oord__class_Omax(X23031)),X23029),X23030) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9187,plain,
    ! [X21796,X21797,X21798] :
      ( ~ class_Orderings_Olinorder(X21798)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21798),X21797))
      | c_Big__Operators_Olattice_OInf__fin(X21798,c_Orderings_Oord__class_Omin(X21798),hAPP(hAPP(c_Set_Oinsert(X21798),X21796),X21797)) = hAPP(hAPP(c_Finite__Set_Ofold(X21798,X21798,c_Orderings_Oord__class_Omin(X21798)),X21796),X21797) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oeq__fold__idem_H])]) ).

cnf(i_0_9188,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_5839]) ).

fof(i_0_9189,plain,
    ! [X19248,X19249,X19251] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk37_2(X19248,X19249)),X19248))
        | ~ hBOOL(hAPP(X19249,X19248))
        | hBOOL(hAPP(X19249,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X19251),esk37_2(X19248,X19249)))
        | ~ hBOOL(hAPP(X19249,X19251))
        | ~ hBOOL(hAPP(X19249,X19248))
        | hBOOL(hAPP(X19249,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
      & ( hBOOL(hAPP(X19249,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk37_2(X19248,X19249)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(X19249,X19248))
        | hBOOL(hAPP(X19249,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_5840])])])])]) ).

fof(i_0_9190,plain,
    ! [X30460,X30461,X30462,X30463] : hAPP(c_List_Ofoldl(X30463,X30462,X30461,X30460),c_List_Olist_ONil(X30462)) = X30460,
    inference(variable_rename,[status(thm)],[fact_foldl__Nil]) ).

fof(i_0_9191,plain,
    ! [X29976,X29977,X29978,X29979] : hAPP(c_List_Olist_Olist__case(X29979,X29978,X29977,X29976),c_List_Olist_ONil(X29978)) = X29977,
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I4_J]) ).

fof(i_0_9192,plain,
    ! [X27820,X27821,X27822] : hAPP(c_Fun_Ocomp(X27822,X27821,X27822,X27820),c_Fun_Oid(X27822)) = X27820,
    inference(variable_rename,[status(thm)],[fact_o__id]) ).

fof(i_0_9193,plain,
    ! [X18738,X18739,X18740] :
      ( ( X18739 = c_Groups_Ozero__class_Ozero(X18740)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18740),X18739),X18738) != c_Groups_Ozero__class_Ozero(X18740)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18740),c_Groups_Ozero__class_Ozero(X18740)),X18738))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18740),c_Groups_Ozero__class_Ozero(X18740)),X18739))
        | ~ class_Groups_Oordered__comm__monoid__add(X18740) )
      & ( X18738 = c_Groups_Ozero__class_Ozero(X18740)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18740),X18739),X18738) != c_Groups_Ozero__class_Ozero(X18740)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18740),c_Groups_Ozero__class_Ozero(X18740)),X18738))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18740),c_Groups_Ozero__class_Ozero(X18740)),X18739))
        | ~ class_Groups_Oordered__comm__monoid__add(X18740) )
      & ( X18739 != c_Groups_Ozero__class_Ozero(X18740)
        | X18738 != c_Groups_Ozero__class_Ozero(X18740)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18740),X18739),X18738) = c_Groups_Ozero__class_Ozero(X18740)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18740),c_Groups_Ozero__class_Ozero(X18740)),X18738))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18740),c_Groups_Ozero__class_Ozero(X18740)),X18739))
        | ~ class_Groups_Oordered__comm__monoid__add(X18740) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff])])]) ).

cnf(i_0_9194,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_5841]) ).

fof(i_0_9195,plain,
    ! [X18107,X18108,X18109] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18109),X18108))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18107),X18108)),X18109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18107),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18108),X18109)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__assoc])]) ).

fof(i_0_9196,plain,
    ! [X18118,X18119,X18120] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18120),X18119))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18118),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18119),X18120)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18118),X18119)),X18120) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__assoc])]) ).

fof(i_0_9197,plain,
    ! [X18129,X18130,X18131] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18131),X18130))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18129),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18130),X18131)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18129),X18131)),X18130) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__right])]) ).

fof(i_0_9198,plain,
    ! [X21132,X21133,X21134] :
      ( ~ class_Lattices_Oboolean__algebra(X21134)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21134),X21133),X21132))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21134),hAPP(c_Groups_Ouminus__class_Ouminus(X21134),X21132)),hAPP(c_Groups_Ouminus__class_Ouminus(X21134),X21133))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__mono])]) ).

fof(i_0_9199,plain,
    ! [X21144,X21145,X21146] :
      ( ~ class_Groups_Oordered__ab__group__add(X21146)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21146),X21145),X21144))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21146),hAPP(c_Groups_Ouminus__class_Ouminus(X21146),X21144)),hAPP(c_Groups_Ouminus__class_Ouminus(X21146),X21145))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le])]) ).

cnf(i_0_9200,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_5842]) ).

cnf(i_0_9201,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_5843]) ).

cnf(i_0_9202,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_5844]) ).

cnf(i_0_9203,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_5845]) ).

fof(i_0_9204,plain,
    ! [X21001] :
      ( ( ~ 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,X21001)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X21001)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X21001))
        | 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,X21001))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__less__nat__eq])]) ).

fof(i_0_9205,plain,
    ! [X21209,X21210] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21210,X21209)),X21210)),
    inference(variable_rename,[status(thm)],[fact_mod__less__eq__dividend]) ).

fof(i_0_9206,plain,
    ! [X25801] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25801)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X25801)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25801)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_greaterThan__Suc]) ).

fof(i_0_9207,plain,
    ! [X20183,X20184,X20185,X20186] :
      ( ~ class_Rings_Ocomm__semiring__1(X20186)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20186),hAPP(hAPP(c_Power_Opower__class_Opower(X20186),X20185),X20184)),hAPP(hAPP(c_Power_Opower__class_Opower(X20186),X20185),X20183)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20186),X20185),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20184),X20183)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J])]) ).

fof(i_0_9208,plain,
    ! [X20303,X20304,X20305,X20306] :
      ( ~ class_Groups_Omonoid__mult(X20306)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20306),X20305),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20304),X20303)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20306),hAPP(hAPP(c_Power_Opower__class_Opower(X20306),X20305),X20304)),hAPP(hAPP(c_Power_Opower__class_Opower(X20306),X20305),X20303)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__add])]) ).

fof(i_0_9209,plain,
    ! [X19640,X19641,X19642] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19642)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19642),X19641))
      | hAPP(c_Finite__Set_Ofold1(X19642,c_Groups_Otimes__class_Otimes(X19642)),hAPP(hAPP(c_Set_Oinsert(X19642),X19640),X19641)) = hAPP(hAPP(c_Finite__Set_Ofold(X19642,X19642,c_Groups_Otimes__class_Otimes(X19642)),X19640),X19641) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__eq__fold__idem])]) ).

fof(i_0_9210,plain,
    ! [X18977,X18978,X18979,X18980,X18981,X18982] :
      ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X18982)
      | X18981 = c_Groups_Ozero__class_Ozero(X18982)
      | X18980 != X18979
      | X18978 = X18977
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18982),X18980),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18982),X18981),X18978)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18982),X18979),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18982),X18981),X18977)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq])]) ).

fof(i_0_9211,plain,
    ! [X28374,X28375] : c_Hilbert__Choice_OEps(X28375,hAPP(hAPP(c_COMBC(X28375,X28375,tc_HOL_Obool),c_fequal),X28374)) = X28374,
    inference(variable_rename,[status(thm)],[fact_some__eq__trivial]) ).

fof(i_0_9212,plain,
    ! [X17782,X17783] : c_HOL_OThe(X17783,hAPP(hAPP(c_COMBC(X17783,X17783,tc_HOL_Obool),c_fequal),X17782)) = X17782,
    inference(variable_rename,[status(thm)],[fact_the__eq__trivial]) ).

fof(i_0_9213,plain,
    ! [X17761,X17762] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17762),X17761)),hAPP(c_Nat_OSuc,X17762))),
    inference(variable_rename,[status(thm)],[fact_diff__less__Suc]) ).

fof(i_0_9214,plain,
    ! [X18086,X18087] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18087),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18087),X18086)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc1]) ).

fof(i_0_9215,plain,
    ! [X18088,X18089] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18089),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18088),X18089)))),
    inference(variable_rename,[status(thm)],[fact_less__add__Suc2]) ).

fof(i_0_9216,plain,
    ! [X25357,X25358,X25359,X25360] :
      ( ~ class_Orderings_Oorder(X25360)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25360,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25360,X25359,X25358)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25360,X25358,X25357)) = c_Orderings_Obot__class_Obot(tc_fun(X25360,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I16_J])]) ).

fof(i_0_9217,plain,
    ! [X25361,X25362,X25363,X25364] :
      ( ~ class_Orderings_Oorder(X25364)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25364,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25364,X25363,X25362)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25364,X25362,X25361)) = c_Orderings_Obot__class_Obot(tc_fun(X25364,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I12_J])]) ).

fof(i_0_9218,plain,
    ! [X25298,X25299,X25300,X25301] :
      ( ~ class_Orderings_Oorder(X25301)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25301,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25301,X25300,X25299)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25301,X25299,X25298)) = c_Orderings_Obot__class_Obot(tc_fun(X25301,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I14_J])]) ).

fof(i_0_9219,plain,
    ! [X25383,X25384,X25385,X25386] :
      ( ~ class_Orderings_Oorder(X25386)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25386,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25386,X25385,X25384)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25386,X25384,X25383)) = c_Orderings_Obot__class_Obot(tc_fun(X25386,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I10_J])]) ).

fof(i_0_9220,plain,
    ! [X25365,X25366,X25367,X25368] :
      ( ~ class_Orderings_Oorder(X25368)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25368,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25368,X25367,X25366)),c_SetInterval_Oord__class_OatLeastAtMost(X25368,X25366,X25365)) = c_Orderings_Obot__class_Obot(tc_fun(X25368,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I13_J])]) ).

fof(i_0_9221,plain,
    ! [X16846,X16847] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16847,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X16847,tc_HOL_Obool))),X16846)),
    inference(variable_rename,[status(thm)],[fact_empty__subsetI]) ).

fof(i_0_9222,plain,
    ! [X28831,X28832,X28833] :
      ( ~ c_Equiv__Relations_Oequiv(X28833,X28832,X28831)
      | hAPP(hAPP(c_Relation_Orel__comp(X28833,X28833,X28833),hAPP(c_Relation_Oconverse(X28833,X28833),X28831)),X28831) = X28831 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__comp__eq])]) ).

fof(i_0_9223,plain,
    ! [X25233,X25234,X25235,X25236] :
      ( hBOOL(hAPP(hAPP(c_member(X25236),X25235),X25234))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25236,tc_HOL_Obool)),X25234),hAPP(hAPP(c_Set_Oinsert(X25236),X25235),X25233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25236,tc_HOL_Obool)),X25234),X25233) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5846])]) ).

fof(i_0_9224,plain,
    ! [X19923,X19924] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19924))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19923))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Nat__Transfer_Otsub(X19924,X19923))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J])]) ).

fof(i_0_9225,plain,
    ! [X17048,X17049,X17050] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X17050,tc_HOL_Obool)),X17049),hAPP(hAPP(c_Set_Oinsert(X17050),X17048),X17049))),
    inference(variable_rename,[status(thm)],[fact_subset__insertI]) ).

fof(i_0_9226,plain,
    ! [X20738,X20739,X20740] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20740),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20739,X20738)),X20738) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20740),X20739),X20738),
    inference(variable_rename,[status(thm)],[fact_zmod__simps_I3_J]) ).

fof(i_0_9227,plain,
    ! [X20751,X20752,X20753] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20753),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20752,X20751)),X20751) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20753),X20752),X20751),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmod__right]) ).

fof(i_0_9228,plain,
    ! [X20741,X20742,X20743] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20743),X20742),X20741) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20743),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20742,X20741)),X20741),
    inference(variable_rename,[status(thm)],[fact_zmod__zmult1__eq]) ).

fof(i_0_9229,plain,
    ! [X24383,X24384,X24385] :
      ( ~ class_Orderings_Olinorder(X24385)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24385),X24384),X24383))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X24385,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X24385),X24384)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24385,X24384),X24383)) = hAPP(c_SetInterval_Oord__class_OlessThan(X24385),X24383) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I8_J])]) ).

cnf(i_0_9230,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_5847]) ).

fof(i_0_9231,plain,
    ! [X24152,X24153] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24153),hAPP(c_Nat_OSuc,X24152)))
      | c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24153,hAPP(c_Nat_OSuc,X24152)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24152)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24153,X24152)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMostSuc__conv])]) ).

cnf(i_0_9232,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_5848]) ).

fof(i_0_9233,plain,
    ! [X26127] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X26127)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X26127),tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X26127),c_Orderings_Otop__class_Otop(tc_fun(X26127,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26127),c_Orderings_Otop__class_Otop(tc_fun(X26127,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(X26127)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(X26127),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__option__UNIV])]) ).

fof(i_0_9234,plain,
    ! [X20055,X20056,X20057] :
      ( ~ class_Rings_Olinordered__semidom(X20057)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20056),X20055))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20057),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20057),X20056)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20057),X20055))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__of__nat__less])]) ).

fof(i_0_9235,plain,
    ! [X25754,X25755,X25756,X25757] :
      ( ~ class_Orderings_Olinorder(X25757)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25757,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X25757),X25756)),c_SetInterval_Oord__class_OatLeastAtMost(X25757,X25755,X25754)) = c_SetInterval_Oord__class_OatLeastAtMost(X25757,hAPP(hAPP(c_Orderings_Oord__class_Omax(X25757),X25756),X25755),X25754) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR2])]) ).

fof(i_0_9236,plain,
    ! [X25156,X25157,X25158,X25159] :
      ( ~ class_Orderings_Olinorder(X25159)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25159,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25159),X25158)),c_SetInterval_Oord__class_OatLeastAtMost(X25159,X25157,X25156)) = c_SetInterval_Oord__class_OatLeastAtMost(X25159,X25157,hAPP(hAPP(c_Orderings_Oord__class_Omin(X25159),X25158),X25156)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Int__atLeastAtMostR1])]) ).

fof(i_0_9237,plain,
    ! [X20887,X20888] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20888),hAPP(c_Int_Onat,X20887)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20888)),X20887)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20888)),X20887))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20888),hAPP(c_Int_Onat,X20887))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__nat__eq__int__zless])]) ).

fof(i_0_9238,plain,
    ! [X24193,X24194] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24194),X24193))
        | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24193,X24194) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X24194),X24193))
        | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24193,X24194) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),X24193),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24193),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24194)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5849])]) ).

fof(i_0_9239,plain,
    ! [X20975,X20976] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20975))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,X20976)),hAPP(c_Int_Onat,X20975)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(X20976,X20975)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J])]) ).

fof(i_0_9240,plain,
    ! [X30258,X30259,X30260,X30261] : hAPP(hAPP(c_List_Odrop(X30261),X30260),hAPP(hAPP(c_List_Otake(X30261),X30259),X30258)) = hAPP(hAPP(c_List_Otake(X30261),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30259),X30260)),hAPP(hAPP(c_List_Odrop(X30261),X30260),X30258)),
    inference(variable_rename,[status(thm)],[fact_drop__take]) ).

fof(i_0_9241,plain,
    ! [X27889,X27890,X27891,X27892] : hAPP(hAPP(c_Relation_Orel__comp(X27892,X27891,X27890),X27889),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27891,X27890),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27892,X27890),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_rel__comp__empty2]) ).

fof(i_0_9242,plain,
    ! [X33417,X33418,X33419,X33420] : c_Product__Type_Ocurry(X33420,X33419,X33418,hAPP(c_Product__Type_Oprod_Oprod__case(X33420,X33419,X33418),X33417)) = X33417,
    inference(variable_rename,[status(thm)],[fact_curry__split]) ).

fof(i_0_9243,plain,
    ! [X22391] :
      ( ~ 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),X22391)))
      | 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),X22391)) = 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),X22391))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__1__number__of])]) ).

fof(i_0_9244,plain,
    ! [X21214,X21215,X21216] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21216,X21215)),X21214) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21216),X21214),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21215),X21214)),
    inference(variable_rename,[status(thm)],[fact_mod__mult__distrib]) ).

fof(i_0_9245,plain,
    ! [X33928,X33929,X33930] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33929))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33930),X33928),hAPP(hAPP(c_Power_Opower__class_Opower(X33930),X33928),X33929)))
        | ~ class_Rings_Ocomm__semiring__1(X33930) )
      & ( X33928 != c_Groups_Oone__class_Oone(X33930)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33930),X33928),hAPP(hAPP(c_Power_Opower__class_Opower(X33930),X33928),X33929)))
        | ~ class_Rings_Ocomm__semiring__1(X33930) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__power])])]) ).

fof(i_0_9246,plain,
    ! [X33906,X33907,X33908,X33909] :
      ( ~ class_Rings_Ocomm__semiring__1(X33909)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33909),X33908),X33907))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33909),X33908),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33909),X33907),X33906))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult2])]) ).

fof(i_0_9247,plain,
    ! [X33902,X33903,X33904,X33905] :
      ( ~ class_Rings_Ocomm__semiring__1(X33905)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33905),X33904),X33903))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33905),X33904),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33905),X33902),X33903))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult])]) ).

fof(i_0_9248,plain,
    ! [X23286,X23287,X23288,X23289] :
      ( ~ class_Lattices_Osemilattice__sup(X23289)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23289),X23288),X23287))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23289),X23288),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23289),X23287),X23286))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI1])]) ).

fof(i_0_9249,plain,
    ! [X23282,X23283,X23284,X23285] :
      ( ~ class_Lattices_Osemilattice__sup(X23285)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23285),X23284),X23283))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23285),X23284),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23285),X23282),X23283))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__supI2])]) ).

fof(i_0_9250,plain,
    ! [X22533,X22534,X22535,X22536] :
      ( ~ class_Orderings_Olinorder(X22536)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22536),X22535),X22534))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22536),X22535),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22536),X22534),X22533))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI1])]) ).

fof(i_0_9251,plain,
    ! [X22529,X22530,X22531,X22532] :
      ( ~ class_Orderings_Olinorder(X22532)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22532),X22531),X22530))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X22532),X22531),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22532),X22529),X22530))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oless__supI2])]) ).

fof(i_0_9252,plain,
    ! [X23319,X23320,X23321,X23322] :
      ( ~ class_Lattices_Osemilattice__sup(X23322)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23322),X23321),X23320))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23322),X23321),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23322),X23320),X23319))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI1])]) ).

fof(i_0_9253,plain,
    ! [X23315,X23316,X23317,X23318] :
      ( ~ class_Lattices_Osemilattice__sup(X23318)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23318),X23317),X23316))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23318),X23317),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23318),X23315),X23316))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__supI2])]) ).

fof(i_0_9254,plain,
    ! [X22593,X22594,X22595,X22596] :
      ( ~ class_Orderings_Olinorder(X22596)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22596),X22595),X22594))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22596),X22595),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22596),X22594),X22593))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI1])]) ).

fof(i_0_9255,plain,
    ! [X22589,X22590,X22591,X22592] :
      ( ~ class_Orderings_Olinorder(X22592)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22592),X22591),X22590))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22592),X22591),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22592),X22589),X22590))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__supI2])]) ).

cnf(i_0_9256,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_5850]) ).

fof(i_0_9257,plain,
    ! [X21358] : 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),X21358))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negative__zle__0]) ).

fof(i_0_9258,plain,
    ! [X31505,X31506,X31507,X31508,X31509] :
      ( ( c_List_Otranspose(X31506,X31505) != c_List_Olist_ONil(tc_List_Olist(X31506))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31506)),X31507),hAPP(c_List_Oset(tc_List_Olist(X31506)),X31505)))
        | X31507 = c_List_Olist_ONil(X31506) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X31509)),esk426_2(X31508,X31509)),hAPP(c_List_Oset(tc_List_Olist(X31509)),X31508)))
        | c_List_Otranspose(X31509,X31508) = c_List_Olist_ONil(tc_List_Olist(X31509)) )
      & ( esk426_2(X31508,X31509) != c_List_Olist_ONil(X31509)
        | c_List_Otranspose(X31509,X31508) = c_List_Olist_ONil(tc_List_Olist(X31509)) ) ),
    inference(distribute,[status(thm)],[inference(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_9259,plain,
    ! [X24596,X24597,X24598] :
      ( ~ class_Groups_Ocomm__monoid__add(X24598)
      | hAPP(X24597,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(X24598)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24598),X24597),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X24596)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X24598),X24597),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24596)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0__upt])]) ).

fof(i_0_9260,plain,
    ! [X23780,X23781,X23782] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23782,tc_fun(X23781,tc_HOL_Obool)),X23780),hAPP(c_COMBK(tc_fun(X23781,tc_HOL_Obool),X23782),c_Orderings_Obot__class_Obot(tc_fun(X23781,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(X23781,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UN__empty2]) ).

fof(i_0_9261,plain,
    ! [X17722,X17723,X17724] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17724),X17723))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17723),X17722))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17724)),X17722)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__trans__Suc])]) ).

fof(i_0_9262,plain,
    ! [X22390] :
      ( ~ 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),X22390)))
      | 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),X22390)) = 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),X22390))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos__1__number__of])]) ).

fof(i_0_9263,plain,
    ! [X20899,X20900] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20900))
      | 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,X20899,X20900))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__mod__sign])]) ).

fof(i_0_9264,plain,
    ! [X29628,X29629] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X29629,X29628) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29629),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29628),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_greaterThanLessThan__upto]) ).

fof(i_0_9265,plain,
    ! [X30810,X30811,X30812,X30813,X30814] : hAPP(hAPP(c_List_Omap(X30814,X30813),X30812),hAPP(hAPP(c_List_Olist_OCons(X30814),X30811),X30810)) = hAPP(hAPP(c_List_Olist_OCons(X30813),hAPP(X30812,X30811)),hAPP(hAPP(c_List_Omap(X30814,X30813),X30812),X30810)),
    inference(variable_rename,[status(thm)],[fact_map_Osimps_I2_J]) ).

fof(i_0_9266,plain,
    ! [X22655,X22656,X22657] :
      ( ~ class_Fields_Ofield__inverse__zero(X22657)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22657),c_Groups_Oone__class_Oone(X22657)),hAPP(hAPP(c_Power_Opower__class_Opower(X22657),X22656),X22655)) = hAPP(hAPP(c_Power_Opower__class_Opower(X22657),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22657),c_Groups_Oone__class_Oone(X22657)),X22656)),X22655) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__over])]) ).

fof(i_0_9267,plain,
    ! [X19436] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19436))
      | 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)),X19436))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__0__less])]) ).

fof(i_0_9268,plain,
    ! [X16953,X16954,X16955,X16956] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X16956),X16955),X16954))
      | hBOOL(hAPP(hAPP(c_member(X16956),X16955),hAPP(hAPP(c_Set_Oinsert(X16956),X16953),X16954))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insertI2])]) ).

fof(i_0_9269,plain,
    ! [X16866,X16867,X16868,X16869] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X16869),X16868),X16867))
        | hBOOL(hAPP(hAPP(c_member(X16869),X16868),hAPP(hAPP(c_Set_Oinsert(X16869),X16866),X16867))) )
      & ( X16868 != X16866
        | hBOOL(hAPP(hAPP(c_member(X16869),X16868),hAPP(hAPP(c_Set_Oinsert(X16869),X16866),X16867))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5851])])]) ).

fof(i_0_9270,plain,
    ! [X21156,X21157,X21158] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21158),X21157),hAPP(c_Groups_Ouminus__class_Ouminus(X21158),X21156)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21158),X21156),hAPP(c_Groups_Ouminus__class_Ouminus(X21158),X21157)))
        | ~ class_Groups_Oordered__ab__group__add(X21158) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21158),X21156),hAPP(c_Groups_Ouminus__class_Ouminus(X21158),X21157)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21158),X21157),hAPP(c_Groups_Ouminus__class_Ouminus(X21158),X21156)))
        | ~ class_Groups_Oordered__ab__group__add(X21158) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__iff])])]) ).

fof(i_0_9271,plain,
    ! [X21135,X21136,X21137] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21137),X21136),hAPP(c_Groups_Ouminus__class_Ouminus(X21137),X21135)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21137),X21135),hAPP(c_Groups_Ouminus__class_Ouminus(X21137),X21136)))
        | ~ class_Groups_Oordered__ab__group__add(X21137) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21137),X21135),hAPP(c_Groups_Ouminus__class_Ouminus(X21137),X21136)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21137),X21136),hAPP(c_Groups_Ouminus__class_Ouminus(X21137),X21135)))
        | ~ class_Groups_Oordered__ab__group__add(X21137) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__iff])])]) ).

fof(i_0_9272,plain,
    ! [X30611,X30612,X30613,X30614] :
      ( ( X30612 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30613)),X30614)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Olast(X30613,hAPP(hAPP(c_List_Olist__update(X30613,X30614),X30612),X30611)) = X30611
        | X30614 = c_List_Olist_ONil(X30613) )
      & ( X30612 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30613)),X30614)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | c_List_Olast(X30613,hAPP(hAPP(c_List_Olist__update(X30613,X30614),X30612),X30611)) = c_List_Olast(X30613,X30614)
        | X30614 = c_List_Olist_ONil(X30613) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__list__update])])]) ).

fof(i_0_9273,plain,
    ! [X25818,X25819] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25819),c_Groups_Osgn__class_Osgn(X25819,X25818)),c_Groups_Ozero__class_Ozero(X25819)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25819),X25818),c_Groups_Ozero__class_Ozero(X25819)))
        | ~ class_Rings_Olinordered__idom(X25819) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25819),X25818),c_Groups_Ozero__class_Ozero(X25819)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25819),c_Groups_Osgn__class_Osgn(X25819,X25818)),c_Groups_Ozero__class_Ozero(X25819)))
        | ~ class_Rings_Olinordered__idom(X25819) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__less])])]) ).

fof(i_0_9274,plain,
    ! [X29744,X29745,X29746] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29746),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29745)),X29744)))
      | hAPP(hAPP(c_List_Otake(X29745),X29746),c_List_Obutlast(X29745,X29744)) = hAPP(hAPP(c_List_Otake(X29745),X29746),X29744) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__butlast])]) ).

fof(i_0_9275,plain,
    ! [X30640,X30641,X30642] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30642),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30641)),X30640)))
      | c_List_Olast(X30641,hAPP(hAPP(c_List_Odrop(X30641),X30642),X30640)) = c_List_Olast(X30641,X30640) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__drop])]) ).

cnf(i_0_9276,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_5852]) ).

cnf(i_0_9277,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_5853]) ).

cnf(i_0_9278,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_5854]) ).

fof(i_0_9279,plain,
    ! [X22143,X22144,X22145,X22146,X22147,X22148] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22148,X22147,X22146),X22145),hAPP(hAPP(c_Product__Type_OPair(X22148,X22147),X22144),X22143)) = hAPP(hAPP(X22145,X22144),X22143),
    inference(variable_rename,[status(thm)],[fact_prod_Osimps_I2_J]) ).

fof(i_0_9280,plain,
    ! [X22137,X22138,X22139,X22140,X22141,X22142] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22142,X22141,X22140),X22139),hAPP(hAPP(c_Product__Type_OPair(X22142,X22141),X22138),X22137)) = hAPP(hAPP(X22139,X22138),X22137),
    inference(variable_rename,[status(thm)],[fact_split__conv]) ).

cnf(i_0_9281,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_5855]) ).

fof(i_0_9282,plain,
    ! [X22996,X22997,X22998] :
      ( ~ class_Orderings_Olinorder(X22998)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22998),X22997))
      | ~ hBOOL(hAPP(hAPP(c_member(X22998),X22996),X22997))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22998),X22996),c_Big__Operators_Olattice_OSup__fin(X22998,c_Orderings_Oord__class_Omax(X22998),X22997)) = c_Big__Operators_Olattice_OSup__fin(X22998,c_Orderings_Oord__class_Omax(X22998),X22997) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oin__idem])]) ).

fof(i_0_9283,plain,
    ! [X21768,X21769,X21770] :
      ( ~ class_Orderings_Olinorder(X21770)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21770),X21769))
      | ~ hBOOL(hAPP(hAPP(c_member(X21770),X21768),X21769))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21770),X21768),c_Big__Operators_Olattice_OInf__fin(X21770,c_Orderings_Oord__class_Omin(X21770),X21769)) = c_Big__Operators_Olattice_OInf__fin(X21770,c_Orderings_Oord__class_Omin(X21770),X21769) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oin__idem])]) ).

fof(i_0_9284,plain,
    ! [X21438,X21439,X21440] :
      ( hBOOL(hAPP(hAPP(c_member(X21440),X21439),X21438))
      | hBOOL(hAPP(hAPP(c_member(X21440),X21439),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21440,tc_HOL_Obool)),X21438))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5856])]) ).

fof(i_0_9285,plain,
    ! [X26930,X26931,X26932,X26933] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X26933),X26932),X26931))
        | hAPP(c_Set_Ovimage(X26930,X26933,hAPP(c_COMBK(X26933,X26930),X26932)),X26931) = c_Orderings_Otop__class_Otop(tc_fun(X26930,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(hAPP(c_member(X26933),X26932),X26931))
        | hAPP(c_Set_Ovimage(X26930,X26933,hAPP(c_COMBK(X26933,X26930),X26932)),X26931) = c_Orderings_Obot__class_Obot(tc_fun(X26930,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5857])]) ).

fof(i_0_9286,plain,
    ! [X24020,X24021,X24022,X24023,X24024] :
      ( ( X24023 = X24021
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24024,X24023),X24022) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24024,X24021),X24020)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24024),X24021),X24020))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24024),X24023),X24022))
        | ~ class_Orderings_Olinorder(X24024) )
      & ( X24022 = X24020
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24024,X24023),X24022) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24024,X24021),X24020)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24024),X24021),X24020))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24024),X24023),X24022))
        | ~ class_Orderings_Olinorder(X24024) )
      & ( X24023 != X24021
        | X24022 != X24020
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24024,X24023),X24022) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24024,X24021),X24020)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24024),X24021),X24020))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24024),X24023),X24022))
        | ~ class_Orderings_Olinorder(X24024) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__eq__iff])])]) ).

fof(i_0_9287,plain,
    ! [X24025,X24026,X24027,X24028,X24029] :
      ( ~ class_Orderings_Olinorder(X24029)
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24029,X24028),X24027) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24029,X24026),X24025)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24029),X24028),X24027))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24029),X24026),X24025))
      | X24028 = X24026 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I1_J])]) ).

fof(i_0_9288,plain,
    ! [X24030,X24031,X24032,X24033,X24034] :
      ( ~ class_Orderings_Olinorder(X24034)
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24034,X24033),X24032) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24034,X24031),X24030)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24034),X24033),X24032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24034),X24031),X24030))
      | X24032 = X24030 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__inj_I2_J])]) ).

fof(i_0_9289,plain,
    ! [X17275,X17276,X17277,X17278,X17279] :
      ( ~ c_Finite__Set_Ofolding__one(X17279,X17278,X17277)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17279),X17276))
      | hBOOL(hAPP(hAPP(c_member(X17279),X17275),X17276))
      | X17276 = c_Orderings_Obot__class_Obot(tc_fun(X17279,tc_HOL_Obool))
      | hAPP(X17277,hAPP(hAPP(c_Set_Oinsert(X17279),X17275),X17276)) = hAPP(hAPP(X17278,X17275),hAPP(X17277,X17276)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5858])]) ).

cnf(i_0_9290,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_5770]) ).

fof(i_0_9291,plain,
    ! [X22191,X22192] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22192))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22191))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22192,X22191),c_Divides_OposDivAlg(X22192,X22191))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_posDivAlg__correct])]) ).

fof(i_0_9292,plain,
    ! [X29665,X29666,X29667,X29668,X29669] :
      ( X29669 = X29668
      | hAPP(hAPP(c_List_Onth(X29667),hAPP(hAPP(c_List_Olist__update(X29667,X29666),X29669),X29665)),X29668) = hAPP(hAPP(c_List_Onth(X29667),X29666),X29668) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__list__update__neq])]) ).

fof(i_0_9293,plain,
    ! [X25374,X25375,X25376,X25377] :
      ( ~ class_Orderings_Oorder(X25377)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25377,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25377,X25376,X25375)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25377,X25375),X25374)) = c_Orderings_Obot__class_Obot(tc_fun(X25377,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I9_J])]) ).

fof(i_0_9294,plain,
    ! [X28778,X28779,X28780,X28781] : hAPP(c_Relation_Oconverse(X28781,X28781),hAPP(hAPP(c_Relation_Oinv__image(X28780,X28781),X28779),X28778)) = hAPP(hAPP(c_Relation_Oinv__image(X28780,X28781),hAPP(c_Relation_Oconverse(X28780,X28780),X28779)),X28778),
    inference(variable_rename,[status(thm)],[fact_converse__inv__image]) ).

fof(i_0_9295,plain,
    ! [X25668,X25669,X25670] :
      ( ~ class_Lattices_Olattice(X25670)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25670),X25669))
      | c_Big__Operators_Olattice__class_OInf__fin(X25670,hAPP(hAPP(c_Set_Oinsert(X25670),X25668),X25669)) = hAPP(hAPP(c_Finite__Set_Ofold(X25670,X25670,c_Lattices_Osemilattice__inf__class_Oinf(X25670)),X25668),X25669) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9296,plain,
    ! [X23526,X23527,X23528] :
      ( ~ class_Lattices_Olattice(X23528)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23528),X23527))
      | c_Big__Operators_Olattice__class_OSup__fin(X23528,hAPP(hAPP(c_Set_Oinsert(X23528),X23526),X23527)) = hAPP(hAPP(c_Finite__Set_Ofold(X23528,X23528,c_Lattices_Osemilattice__sup__class_Osup(X23528)),X23526),X23527) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oeq__fold__idem_H])]) ).

fof(i_0_9297,plain,
    ! [X23038,X23039,X23040] :
      ( ~ class_Orderings_Olinorder(X23040)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23040),X23039))
      | c_Big__Operators_Olinorder__class_OMax(X23040,hAPP(hAPP(c_Set_Oinsert(X23040),X23038),X23039)) = hAPP(hAPP(c_Finite__Set_Ofold(X23040,X23040,c_Orderings_Oord__class_Omax(X23040)),X23038),X23039) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oeq__fold__idem_H])]) ).

fof(i_0_9298,plain,
    ! [X21805,X21806,X21807] :
      ( ~ class_Orderings_Olinorder(X21807)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21807),X21806))
      | c_Big__Operators_Olinorder__class_OMin(X21807,hAPP(hAPP(c_Set_Oinsert(X21807),X21805),X21806)) = hAPP(hAPP(c_Finite__Set_Ofold(X21807,X21807,c_Orderings_Oord__class_Omin(X21807)),X21805),X21806) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oeq__fold__idem_H])]) ).

fof(i_0_9299,plain,
    ! [X28755,X28756] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X28756),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | c_Random_Olog(X28756,X28755) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28755),X28756))
        | c_Random_Olog(X28756,X28755) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X28756),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28755),X28756))
        | c_Random_Olog(X28756,X28755) = 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(X28756,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X28755),X28756))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_log_Osimps])])]) ).

fof(i_0_9300,plain,
    ! [X21335,X21336] :
      ( ~ class_Rings_Oring__1(X21336)
      | ~ hBOOL(hAPP(hAPP(c_member(X21336),X21335),c_Int_Oring__1__class_OInts(X21336)))
      | hBOOL(hAPP(hAPP(c_member(X21336),hAPP(c_Groups_Ouminus__class_Ouminus(X21336),X21335)),c_Int_Oring__1__class_OInts(X21336))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__minus])]) ).

fof(i_0_9301,plain,
    ! [X33801,X33802] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33802))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X33802),X33801))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33801),X33802)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5859])]) ).

fof(i_0_9302,plain,
    ! [X17137,X17138] :
      ( ( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17138,tc_HOL_Obool)),X17137))
        | hBOOL(hAPP(hAPP(c_member(X17138),X17137),c_Orderings_Obot__class_Obot(tc_fun(X17138,tc_HOL_Obool)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X17138),X17137),c_Orderings_Obot__class_Obot(tc_fun(X17138,tc_HOL_Obool))))
        | hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17138,tc_HOL_Obool)),X17137)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__empty__eq])]) ).

cnf(i_0_9303,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_5860]) ).

fof(i_0_9304,plain,
    ! [X25964,X25965,X25966] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X25966)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25966),c_Groups_Ozero__class_Ozero(X25966)),X25965))
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25966),hAPP(c_Groups_Oabs__class_Oabs(X25966),X25964)),X25965) = hAPP(c_Groups_Oabs__class_Oabs(X25966),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25966),X25964),X25965)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__div__pos])]) ).

fof(i_0_9305,plain,
    ! [X25939,X25940,X25941] :
      ( ~ class_Rings_Olinordered__idom(X25941)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25941),c_Groups_Ozero__class_Ozero(X25941)),X25940))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25941),hAPP(c_Groups_Oabs__class_Oabs(X25941),X25939)),X25940) = hAPP(c_Groups_Oabs__class_Oabs(X25941),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25941),X25939),X25940)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__pos])]) ).

fof(i_0_9306,plain,
    ! [X23940] : hAPP(c_Set_OPow(X23940),c_Orderings_Obot__class_Obot(tc_fun(X23940,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(X23940,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23940,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X23940,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Pow__empty]) ).

fof(i_0_9307,plain,
    ! [X24541,X24542] :
      ( hAPP(X24542,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),X24542),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24541)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),X24542),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X24541)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__shift__lb__Suc0__0])]) ).

fof(i_0_9308,plain,
    ! [X25060,X25061,X25062,X25063,X25064] :
      ( ~ class_Lattices_Olattice(X25064)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25063,X25064)),X25062),X25061),X25060) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25064),hAPP(X25062,X25060)),hAPP(X25061,X25060)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__apply])]) ).

fof(i_0_9309,plain,
    ! [X25055,X25056,X25057,X25058,X25059] :
      ( ~ class_Lattices_Olattice(X25059)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25058,X25059)),X25057),X25056),X25055) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25059),hAPP(X25057,X25055)),hAPP(X25056,X25055)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__fun__def])]) ).

fof(i_0_9310,plain,
    ! [X23179,X23180,X23181,X23182,X23183] :
      ( ~ class_Lattices_Olattice(X23183)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23182,X23183)),X23181),X23180),X23179) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23183),hAPP(X23181,X23179)),hAPP(X23180,X23179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__apply])]) ).

fof(i_0_9311,plain,
    ! [X23169,X23170,X23171,X23172,X23173] :
      ( ~ class_Lattices_Olattice(X23173)
      | hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23172,X23173)),X23171),X23170),X23169) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23173),hAPP(X23171,X23169)),hAPP(X23170,X23169)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__fun__def])]) ).

fof(i_0_9312,plain,
    ! [X17516,X17517,X17518,X17519,X17520] :
      ( ~ class_Groups_Ominus(X17520)
      | hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17519,X17520)),X17518),X17517),X17516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17520),hAPP(X17518,X17516)),hAPP(X17517,X17516)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__apply])]) ).

fof(i_0_9313,plain,
    ! [X17502,X17503,X17504,X17505,X17506] :
      ( ~ class_Groups_Ominus(X17506)
      | hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17505,X17506)),X17504),X17503),X17502) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17506),hAPP(X17504,X17502)),hAPP(X17503,X17502)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__diff__def])]) ).

fof(i_0_9314,plain,
    ! [X22127,X22128] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22128),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)),X22127))
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X22128,X22127),c_Divides_OnegDivAlg(X22128,X22127))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negDivAlg__correct])]) ).

fof(i_0_9315,plain,
    ! [X20806,X20807] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20807),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20807),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20806,X20807))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__mod__bound])]) ).

fof(i_0_9316,plain,
    ! [X27829,X27830,X27831,X27832] :
      ( ~ c_Finite__Set_Ofolding(X27832,X27831,X27830,X27829)
      | hAPP(X27829,c_Orderings_Obot__class_Obot(tc_fun(X27832,tc_HOL_Obool))) = c_Fun_Oid(X27831) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding_Oempty])]) ).

fof(i_0_9317,plain,
    ! [X22199,X22200] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22199))
        | c_Divides_Odivmod__int(X22200,X22199) = c_Divides_OposDivAlg(X22200,X22199)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22200)) )
      & ( X22200 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X22200,X22199) = 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)),X22199))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22200)) )
      & ( X22200 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odivmod__int(X22200,X22199) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22200),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22199)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22199))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22200)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22199))
        | c_Divides_Odivmod__int(X22200,X22199) = c_Divides_OnegDivAlg(X22200,X22199)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22200)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22199))
        | c_Divides_Odivmod__int(X22200,X22199) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22200),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22199)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22200)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5861])])]) ).

fof(i_0_9318,plain,
    ! [X30980,X30981] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30981),X30980))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30981)),hAPP(c_Code__Numeral_Onat__of,X30980))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30981)),hAPP(c_Code__Numeral_Onat__of,X30980)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X30981),X30980)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__def])]) ).

fof(i_0_9319,plain,
    ! [X30923,X30924] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30924)),hAPP(c_Code__Numeral_Oof__nat,X30923)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30924),X30923)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X30924),X30923))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30924)),hAPP(c_Code__Numeral_Oof__nat,X30923))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__code__numeral__code])]) ).

fof(i_0_9320,plain,
    ! [X17729,X17730] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17730)),hAPP(c_Nat_OSuc,X17729)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17730),X17729)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__SucD])]) ).

fof(i_0_9321,plain,
    ! [X17712,X17713] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17713)),hAPP(c_Nat_OSuc,X17712)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17713),X17712)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17713),X17712))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17713)),hAPP(c_Nat_OSuc,X17712))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__less__eq])]) ).

fof(i_0_9322,plain,
    ! [X30984,X30985] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X30985),X30984))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30985)),hAPP(c_Code__Numeral_Onat__of,X30984))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30985)),hAPP(c_Code__Numeral_Onat__of,X30984)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X30985),X30984)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__def])]) ).

fof(i_0_9323,plain,
    ! [X30940,X30941] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30941)),hAPP(c_Code__Numeral_Oof__nat,X30940)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30941),X30940)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X30941),X30940))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30941)),hAPP(c_Code__Numeral_Oof__nat,X30940))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__code__numeral__code])]) ).

fof(i_0_9324,plain,
    ! [X17252,X17253] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17253)),hAPP(c_Nat_OSuc,X17252)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17253),X17252)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17253),X17252))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17253)),hAPP(c_Nat_OSuc,X17252))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__mono])]) ).

fof(i_0_9325,plain,
    ! [X29473,X29474,X29475,X29476] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X29476),X29475))
      | hAPP(hAPP(c_List_Onth(X29474),hAPP(hAPP(c_List_Otake(X29474),X29475),X29473)),X29476) = hAPP(hAPP(c_List_Onth(X29474),X29473),X29476) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__take])]) ).

fof(i_0_9326,plain,
    ! [X25250,X25251,X25252] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25252,tc_HOL_Obool)),X25251),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25252,tc_HOL_Obool)),X25250),X25251)) = c_Orderings_Obot__class_Obot(tc_fun(X25252,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__disjoint]) ).

fof(i_0_9327,plain,
    ! [X31845,X31846,X31847,X31848] :
      ( ( hAPP(c_List_Orev(X31848),X31847) != hAPP(hAPP(c_List_Olist_OCons(X31848),X31846),X31845)
        | X31847 = hAPP(hAPP(c_List_Oappend(X31848),hAPP(c_List_Orev(X31848),X31845)),hAPP(hAPP(c_List_Olist_OCons(X31848),X31846),c_List_Olist_ONil(X31848))) )
      & ( X31847 != hAPP(hAPP(c_List_Oappend(X31848),hAPP(c_List_Orev(X31848),X31845)),hAPP(hAPP(c_List_Olist_OCons(X31848),X31846),c_List_Olist_ONil(X31848)))
        | hAPP(c_List_Orev(X31848),X31847) = hAPP(hAPP(c_List_Olist_OCons(X31848),X31846),X31845) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__eq__Cons__iff])]) ).

fof(i_0_9328,plain,
    ! [X20187,X20188] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20188))
      | 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),X20188),X20187))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J])]) ).

fof(i_0_9329,plain,
    ! [X20730,X20731] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20731),X20730)),X20731)),
    inference(variable_rename,[status(thm)],[fact_div__le__dividend]) ).

fof(i_0_9330,plain,
    ! [X17265,X17266] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17266),X17265)),X17266)),
    inference(variable_rename,[status(thm)],[fact_diff__le__self]) ).

fof(i_0_9331,plain,
    ! [X25550,X25551] :
      ( ~ class_Orderings_Olinorder(X25551)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X25551,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X25551),X25550)),hAPP(hAPP(c_Set_Oinsert(X25551),X25550),c_Orderings_Obot__class_Obot(tc_fun(X25551,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(X25551),X25550) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__un_I2_J])]) ).

fof(i_0_9332,plain,
    ! [X21771,X21772,X21773] :
      ( ~ class_Orderings_Olinorder(X21773)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21773),X21772))
      | ~ hBOOL(hAPP(hAPP(c_member(X21773),X21771),X21772))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21773),c_Big__Operators_Olinorder__class_OMin(X21773,X21772)),X21771)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__le])]) ).

fof(i_0_9333,plain,
    ! [X20189,X20190,X20191] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20190),X20189)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20191),X20190)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20191),X20189)),
    inference(variable_rename,[status(thm)],[fact_zpower__zadd__distrib]) ).

fof(i_0_9334,plain,
    ! [X19450,X19451,X19452] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19452),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19451),X19450)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19452),X19451)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19452),X19450)),
    inference(variable_rename,[status(thm)],[fact_zadd__zmult__distrib2]) ).

fof(i_0_9335,plain,
    ! [X19464,X19465,X19466] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19466),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19465),X19464)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19466),X19465)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19466),X19464)),
    inference(variable_rename,[status(thm)],[fact_zdiff__zmult__distrib2]) ).

fof(i_0_9336,plain,
    ! [X18534,X18535,X18536] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18536),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18535),X18534)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18536),X18535)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18536),X18534)),
    inference(variable_rename,[status(thm)],[fact_add__mult__distrib2]) ).

fof(i_0_9337,plain,
    ! [X18562,X18563,X18564] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18564),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18563),X18562)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18564),X18563)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18564),X18562)),
    inference(variable_rename,[status(thm)],[fact_diff__mult__distrib2]) ).

fof(i_0_9338,plain,
    ! [X17220,X17221,X17222] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17222),X17221)),X17220) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17222),X17220)),X17221),
    inference(variable_rename,[status(thm)],[fact_diff__commute]) ).

fof(i_0_9339,plain,
    ! [X21243,X21244] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21244),c_Groups_Ozero__class_Ozero(X21244)),hAPP(c_Groups_Ouminus__class_Ouminus(X21244),X21243)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21244),X21243),c_Groups_Ozero__class_Ozero(X21244)))
        | ~ class_Groups_Oordered__ab__group__add(X21244) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21244),X21243),c_Groups_Ozero__class_Ozero(X21244)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21244),c_Groups_Ozero__class_Ozero(X21244)),hAPP(c_Groups_Ouminus__class_Ouminus(X21244),X21243)))
        | ~ class_Groups_Oordered__ab__group__add(X21244) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less])])]) ).

fof(i_0_9340,plain,
    ! [X21233,X21234] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21234),c_Groups_Ozero__class_Ozero(X21234)),hAPP(c_Groups_Ouminus__class_Ouminus(X21234),X21233)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21234),X21233),c_Groups_Ozero__class_Ozero(X21234)))
        | ~ class_Groups_Oordered__ab__group__add(X21234) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21234),X21233),c_Groups_Ozero__class_Ozero(X21234)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21234),c_Groups_Ozero__class_Ozero(X21234)),hAPP(c_Groups_Ouminus__class_Ouminus(X21234),X21233)))
        | ~ class_Groups_Oordered__ab__group__add(X21234) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le])])]) ).

fof(i_0_9341,plain,
    ! [X33746,X33747,X33748,X33749] :
      ( ~ class_Rings_Ocomm__semiring__1(X33749)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33749),X33748),X33747))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33749),X33747),X33746))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33749),X33748),X33746)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__trans])]) ).

fof(i_0_9342,plain,
    ! [X17619,X17620,X17621,X17622] :
      ( ~ class_Orderings_Opreorder(X17622)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17622),X17621),X17620))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17622),X17620),X17619))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17622),X17621),X17619)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__trans])]) ).

fof(i_0_9343,plain,
    ! [X17695,X17696,X17697,X17698] :
      ( ~ class_Orderings_Opreorder(X17698)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17698),X17697),X17696))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17698),X17696),X17695))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17698),X17697),X17695)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less__trans])]) ).

fof(i_0_9344,plain,
    ! [X17687,X17688,X17689,X17690] :
      ( ~ class_Orderings_Opreorder(X17690)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17690),X17689),X17688))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17690),X17688),X17687))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17690),X17689),X17687)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le__trans])]) ).

fof(i_0_9345,plain,
    ! [X17623,X17624,X17625,X17626] :
      ( ~ class_Orderings_Oorder(X17626)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17626),X17625),X17624))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17626),X17623),X17625))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17626),X17623),X17624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I10_J])]) ).

fof(i_0_9346,plain,
    ! [X17699,X17700,X17701,X17702] :
      ( ~ class_Orderings_Oorder(X17702)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17702),X17701),X17700))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17702),X17699),X17701))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17702),X17699),X17700)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I8_J])]) ).

fof(i_0_9347,plain,
    ! [X17691,X17692,X17693,X17694] :
      ( ~ class_Orderings_Oorder(X17694)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17694),X17693),X17692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17694),X17691),X17693))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17694),X17691),X17692)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I7_J])]) ).

fof(i_0_9348,plain,
    ! [X17179,X17180,X17181,X17182] :
      ( ~ class_Orderings_Opreorder(X17182)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17182),X17181),X17180))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17182),X17180),X17179))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17182),X17181),X17179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__trans])]) ).

fof(i_0_9349,plain,
    ! [X17186,X17187,X17188,X17189] :
      ( ~ class_Orderings_Oorder(X17189)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17189),X17188),X17187))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17189),X17186),X17188))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17189),X17186),X17187)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I6_J])]) ).

fof(i_0_9350,plain,
    ! [X21938] :
      ( X21938 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X21938),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_9351,plain,
    ! [X22388,X22389] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22389))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22388))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22389,X22388) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X22389,X22388)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos])]) ).

fof(i_0_9352,plain,
    ! [X31923,X31924,X31925,X31926,X31927] :
      ( hBOOL(hAPP(X31927,X31926))
      | c_List_OtakeWhile(X31925,X31927,hAPP(hAPP(c_List_Oappend(X31925),X31924),hAPP(hAPP(c_List_Olist_OCons(X31925),X31926),X31923))) = c_List_OtakeWhile(X31925,X31927,X31924) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5862])]) ).

fof(i_0_9353,plain,
    ! [X17703,X17704,X17705,X17706,X17707] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17707),X17706),X17705))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17707),X17704),X17703))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17707),X17706),X17705) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17707),X17704),X17703)
        | ~ class_Groups_Oordered__ab__group__add(X17707) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17707),X17704),X17703))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17707),X17706),X17705))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17707),X17706),X17705) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17707),X17704),X17703)
        | ~ class_Groups_Oordered__ab__group__add(X17707) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less])])]) ).

fof(i_0_9354,plain,
    ! [X17280,X17281,X17282,X17283,X17284] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17284),X17283),X17282))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17284),X17281),X17280))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17284),X17283),X17282) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17284),X17281),X17280)
        | ~ class_Groups_Oordered__ab__group__add(X17284) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17284),X17281),X17280))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17284),X17283),X17282))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17284),X17283),X17282) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17284),X17281),X17280)
        | ~ class_Groups_Oordered__ab__group__add(X17284) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less__eq])])]) ).

fof(i_0_9355,plain,
    ! [X17145,X17146,X17147] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17146),X17147) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17145),X17147)
        | X17146 = X17145
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17147),X17145))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17147),X17146)) )
      & ( X17146 != X17145
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17146),X17147) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17145),X17147)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17147),X17145))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17147),X17146)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__diff__iff])])]) ).

fof(i_0_9356,plain,
    ! [X27174,X27175,X27176] : hAPP(hAPP(c_Product__Type_OSigma(X27176,X27175),X27174),hAPP(c_COMBK(tc_fun(X27175,tc_HOL_Obool),X27176),c_Orderings_Obot__class_Obot(tc_fun(X27175,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27176,X27175),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Sigma__empty2]) ).

cnf(i_0_9357,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_5863]) ).

cnf(i_0_9358,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_9359,plain,
    ! [X31285,X31286,X31287,X31288] : c_List_Oremdups(X31288,hAPP(hAPP(c_List_Omap(X31287,X31288),X31286),c_List_Oremdups(X31287,X31285))) = c_List_Oremdups(X31288,hAPP(hAPP(c_List_Omap(X31287,X31288),X31286),X31285)),
    inference(variable_rename,[status(thm)],[fact_remdups__map__remdups]) ).

fof(i_0_9360,plain,
    ! [X18972,X18973,X18974] :
      ( ~ class_Rings_Ocomm__semiring__1(X18974)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18974),X18973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18974),X18972),X18973)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18974),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18974),X18972),c_Groups_Oone__class_Oone(X18974))),X18973) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J])]) ).

cnf(i_0_9361,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_5864]) ).

cnf(i_0_9362,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_5865]) ).

fof(i_0_9363,plain,
    ! [X22386,X22387] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22387))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X22386))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22387),X22386) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(X22387,X22386)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__pos__pos])]) ).

fof(i_0_9364,plain,
    ! [X17248,X17249] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17249),X17248))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17248)),X17249)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17248)),X17249))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17249),X17248)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5866])]) ).

fof(i_0_9365,plain,
    ! [X25333,X25334,X25335,X25336] :
      ( ~ class_Orderings_Oorder(X25336)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25336,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25336,X25335),X25334)),c_SetInterval_Oord__class_OatLeastAtMost(X25336,X25334,X25333)) = c_Orderings_Obot__class_Obot(tc_fun(X25336,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I15_J])]) ).

fof(i_0_9366,plain,
    ! [X21671,X21672] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21672),c_Groups_Ozero__class_Ozero(X21672)),hAPP(c_Int_Oring__1__class_Oof__int(X21672),X21671)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21671))
        | ~ class_Rings_Olinordered__idom(X21672) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21671))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21672),c_Groups_Ozero__class_Ozero(X21672)),hAPP(c_Int_Oring__1__class_Oof__int(X21672),X21671)))
        | ~ class_Rings_Olinordered__idom(X21672) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__less__iff])])]) ).

fof(i_0_9367,plain,
    ! [X20117,X20118] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20118),c_Groups_Ozero__class_Ozero(X20118)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20118),X20117)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20117))
        | ~ class_Rings_Olinordered__semidom(X20118) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20117))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20118),c_Groups_Ozero__class_Ozero(X20118)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20118),X20117)))
        | ~ class_Rings_Olinordered__semidom(X20118) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__less__iff])])]) ).

fof(i_0_9368,plain,
    ! [X21665,X21666] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21666),c_Groups_Ozero__class_Ozero(X21666)),hAPP(c_Int_Oring__1__class_Oof__int(X21666),X21665)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21665))
        | ~ class_Rings_Olinordered__idom(X21666) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21665))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21666),c_Groups_Ozero__class_Ozero(X21666)),hAPP(c_Int_Oring__1__class_Oof__int(X21666),X21665)))
        | ~ class_Rings_Olinordered__idom(X21666) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__le__iff])])]) ).

fof(i_0_9369,plain,
    ! [X25886,X25887] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25887),hAPP(c_Groups_Oabs__class_Oabs(X25887),X25886)),c_Groups_Ozero__class_Ozero(X25887)))
        | X25886 = c_Groups_Ozero__class_Ozero(X25887)
        | ~ class_Groups_Oordered__ab__group__add__abs(X25887) )
      & ( X25886 != c_Groups_Ozero__class_Ozero(X25887)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25887),hAPP(c_Groups_Oabs__class_Oabs(X25887),X25886)),c_Groups_Ozero__class_Ozero(X25887)))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25887) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__le__zero__iff])])]) ).

fof(i_0_9370,plain,
    ! [X22384,X22385] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22385),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)),X22384))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X22385,X22384) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X22385,X22384)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__pos])]) ).

fof(i_0_9371,plain,
    ! [X23013,X23014,X23015] :
      ( ~ class_Orderings_Olinorder(X23015)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23015),X23014))
      | X23014 = c_Orderings_Obot__class_Obot(tc_fun(X23015,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OSup__fin(X23015,c_Orderings_Oord__class_Omax(X23015),hAPP(hAPP(c_Set_Oinsert(X23015),X23013),X23014)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X23015),X23013),c_Big__Operators_Olattice_OSup__fin(X23015,c_Orderings_Oord__class_Omax(X23015),X23014)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Oinsert__idem])]) ).

fof(i_0_9372,plain,
    ! [X21787,X21788,X21789] :
      ( ~ class_Orderings_Olinorder(X21789)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21789),X21788))
      | X21788 = c_Orderings_Obot__class_Obot(tc_fun(X21789,tc_HOL_Obool))
      | c_Big__Operators_Olattice_OInf__fin(X21789,c_Orderings_Oord__class_Omin(X21789),hAPP(hAPP(c_Set_Oinsert(X21789),X21787),X21788)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21789),X21787),c_Big__Operators_Olattice_OInf__fin(X21789,c_Orderings_Oord__class_Omin(X21789),X21788)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Oinsert__idem])]) ).

fof(i_0_9373,plain,
    ! [X25894,X25895] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25895)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25895),hAPP(c_Groups_Oabs__class_Oabs(X25895),X25894)),c_Groups_Ozero__class_Ozero(X25895))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5867])]) ).

fof(i_0_9374,plain,
    ! [X20036,X20037] :
      ( ~ class_Rings_Olinordered__semidom(X20037)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20037),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20037),X20036)),c_Groups_Ozero__class_Ozero(X20037))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5868])]) ).

fof(i_0_9375,plain,
    ! [X33867,X33868,X33869] :
      ( ~ class_Divides_Osemiring__div(X33869)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33869),X33868),X33867))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33869),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33869),X33867),X33868)),X33868) = X33867 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__mult__self])]) ).

fof(i_0_9376,plain,
    ! [X20100,X20101,X20102] :
      ( ~ class_Rings_Oring__1(X20102)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20101),X20100))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20100),X20101)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20102),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20102),X20100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20102),X20101)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__diff])]) ).

cnf(i_0_9377,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_5869]) ).

fof(i_0_9378,plain,
    ! [X20121,X20122] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20122),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20121)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20121) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20121),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20121)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20122)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20122),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20121),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20122)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20121)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20122),X20121))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20122),c_Int_OPls)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5870])])]) ).

fof(i_0_9379,plain,
    ! [X21057,X21058] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21058)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21058)),X21057) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21057) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21058)))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X21058)),X21057) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21058)),X21057)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5871])]) ).

fof(i_0_9380,plain,
    ! [X22382,X22383] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X22383),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)),X22382))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22383),X22382) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(X22383,X22382)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__neg__pos])]) ).

fof(i_0_9381,plain,
    ! [X16831,X16832] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X16832),X16831))
      | v_P(X16831,X16832) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_assms_I1_J])]) ).

fof(i_0_9382,plain,
    ! [X17018,X17019,X17020] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17020),hAPP(hAPP(c_Set_Oinsert(X17020),X17019),X17018)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17020),X17018)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17020),X17018))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X17020),hAPP(hAPP(c_Set_Oinsert(X17020),X17019),X17018))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__insert])]) ).

cnf(i_0_9383,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_5872]) ).

fof(i_0_9384,plain,
    ! [X26963,X26964,X26965] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26965)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26965),X26964))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26965),X26963),c_Complete__Lattice_OInf__class_OInf(X26965,X26964)) = hAPP(hAPP(c_Finite__Set_Ofold(X26965,X26965,c_Lattices_Osemilattice__inf__class_Oinf(X26965)),X26963),X26964) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Inf__fold__inf])]) ).

fof(i_0_9385,plain,
    ! [X27088,X27089,X27090] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X27090)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27090),X27089))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27090),X27088),c_Complete__Lattice_OSup__class_OSup(X27090,X27089)) = hAPP(hAPP(c_Finite__Set_Ofold(X27090,X27090,c_Lattices_Osemilattice__sup__class_Osup(X27090)),X27088),X27089) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Sup__fold__sup])]) ).

cnf(i_0_9386,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_9387,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_9388,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_9389,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_9390,plain,
    ! [X25277,X25278] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25278,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25278,tc_HOL_Obool)),X25277)),X25277) = c_Orderings_Obot__class_Obot(tc_fun(X25278,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__disjoint2]) ).

fof(i_0_9391,plain,
    ! [X26188,X26189] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26189,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26189,tc_HOL_Obool)),X26188)),X26188) = c_Orderings_Otop__class_Otop(tc_fun(X26189,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__partition2]) ).

fof(i_0_9392,plain,
    ! [X26122,X26123] : c_Sum__Type_OPlus(X26123,X26122,c_Orderings_Otop__class_Otop(tc_fun(X26123,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26122,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(X26123,X26122),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__Plus__UNIV]) ).

fof(i_0_9393,plain,
    ! [X25788,X25789,X25790] :
      ( ~ class_Orderings_Oorder(X25790)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25790,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X25790,X25789,X25788)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25790),X25788)) = c_Orderings_Obot__class_Obot(tc_fun(X25790,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I7_J])]) ).

fof(i_0_9394,plain,
    ! [X25798,X25799,X25800] :
      ( ~ class_Orderings_Oorder(X25800)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25800,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X25800,X25799,X25798)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25800),X25798)) = c_Orderings_Obot__class_Obot(tc_fun(X25800,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I5_J])]) ).

fof(i_0_9395,plain,
    ! [X25758,X25759,X25760] :
      ( ~ class_Orderings_Oorder(X25760)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25760,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X25760,X25759,X25758)),hAPP(c_SetInterval_Oord__class_OatLeast(X25760),X25758)) = c_Orderings_Obot__class_Obot(tc_fun(X25760,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I6_J])]) ).

fof(i_0_9396,plain,
    ! [X28757,X28758,X28759] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28759),X28758))
        | c_Random_Ominus__shift(X28757,X28759,X28758) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X28757),X28759)),X28758) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X28759),X28758))
        | c_Random_Ominus__shift(X28757,X28759,X28758) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X28759),X28758) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5873])]) ).

fof(i_0_9397,plain,
    ! [X20113,X20114] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20114),c_Groups_Ozero__class_Ozero(X20114)),hAPP(c_Int_Onumber__class_Onumber__of(X20114),X20113)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20113))
        | ~ class_Int_Onumber__ring(X20114)
        | ~ class_Rings_Olinordered__idom(X20114) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20113))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20114),c_Groups_Ozero__class_Ozero(X20114)),hAPP(c_Int_Onumber__class_Onumber__of(X20114),X20113)))
        | ~ class_Int_Onumber__ring(X20114)
        | ~ class_Rings_Olinordered__idom(X20114) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__special_I1_J])])]) ).

fof(i_0_9398,plain,
    ! [X20111,X20112] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20112),c_Groups_Ozero__class_Ozero(X20112)),hAPP(c_Int_Onumber__class_Onumber__of(X20112),X20111)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20111))
        | ~ class_Int_Onumber__ring(X20112)
        | ~ class_Rings_Olinordered__idom(X20112) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20111))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20112),c_Groups_Ozero__class_Ozero(X20112)),hAPP(c_Int_Onumber__class_Onumber__of(X20112),X20111)))
        | ~ class_Int_Onumber__ring(X20112)
        | ~ class_Rings_Olinordered__idom(X20112) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__special_I1_J])])]) ).

fof(i_0_9399,plain,
    ! [X21025,X21026,X21027] :
      ( ( ~ hBOOL(hAPP(X21027,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21026,X21025)))
        | epred2_3(X21027,X21025,X21026) )
      & ( ~ epred2_3(X21027,X21025,X21026)
        | hBOOL(hAPP(X21027,c_Divides_Odiv__class_Omod(tc_Int_Oint,X21026,X21025))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5874])]) ).

fof(i_0_9400,plain,
    ! [X28142,X28143,X28144] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28144,X28143)),X28142))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X28144),hAPP(c_Relation_ODomain(X28144,X28143),X28142))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Domain])]) ).

fof(i_0_9401,plain,
    ! [X27958,X27959,X27960] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X27960,X27959)),X27958))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X27959),hAPP(c_Relation_ORange(X27960,X27959),X27958))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Range])]) ).

fof(i_0_9402,plain,
    ! [X18712,X18713,X18714,X18715] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X18715,X18714,X18713),X18712))
      | X18713 != c_Orderings_Obot__class_Obot(tc_fun(X18715,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1Set__nonempty])]) ).

fof(i_0_9403,plain,
    ! [X25989,X25990] : hAPP(hAPP(c_Nitpick_Oint__gcd,X25990),X25989) = 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),X25990)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25989)))),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Oint__gcd__def]) ).

fof(i_0_9404,plain,
    ! [X30824,X30825,X30826,X30827,X30828] : hAPP(hAPP(c_List_Odrop(X30828),X30827),hAPP(hAPP(c_List_Omap(X30826,X30828),X30825),X30824)) = hAPP(hAPP(c_List_Omap(X30826,X30828),X30825),hAPP(hAPP(c_List_Odrop(X30826),X30827),X30824)),
    inference(variable_rename,[status(thm)],[fact_drop__map]) ).

fof(i_0_9405,plain,
    ! [X30797,X30798,X30799,X30800,X30801] : hAPP(hAPP(c_List_Otake(X30801),X30800),hAPP(hAPP(c_List_Omap(X30799,X30801),X30798),X30797)) = hAPP(hAPP(c_List_Omap(X30799,X30801),X30798),hAPP(hAPP(c_List_Otake(X30799),X30800),X30797)),
    inference(variable_rename,[status(thm)],[fact_take__map]) ).

fof(i_0_9406,plain,
    ! [X31457,X31458,X31459,X31460] : hAPP(c_List_Ofilter(X31460,X31459),hAPP(hAPP(c_List_Oappend(X31460),X31458),X31457)) = hAPP(hAPP(c_List_Oappend(X31460),hAPP(c_List_Ofilter(X31460,X31459),X31458)),hAPP(c_List_Ofilter(X31460,X31459),X31457)),
    inference(variable_rename,[status(thm)],[fact_filter__append]) ).

fof(i_0_9407,plain,
    ! [X29940,X29941] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29941),X29940))
        | c_List_Oupto(X29941,X29940) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X29941),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29941),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29940)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X29941),X29940))
        | c_List_Oupto(X29941,X29940) = c_List_Olist_ONil(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5875])]) ).

fof(i_0_9408,plain,
    ! [X28118,X28119,X28120,X28121,X28122] :
      ( ( ~ c_Wellfounded_Owf(X28119,X28118)
        | hBOOL(hAPP(hAPP(c_member(X28119),X28120),c_Wellfounded_Oacc(X28119,X28118))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(X28122),esk290_2(X28121,X28122)),c_Wellfounded_Oacc(X28122,X28121)))
        | c_Wellfounded_Owf(X28122,X28121) ) ),
    inference(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_9409,plain,
    ! [X23059,X23060] :
      ( ~ class_Groups_Olinordered__ab__group__add(X23060)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23060),X23059))
      | X23059 = c_Orderings_Obot__class_Obot(tc_fun(X23060,tc_HOL_Obool))
      | hAPP(c_Groups_Ouminus__class_Ouminus(X23060),c_Big__Operators_Olinorder__class_OMax(X23060,X23059)) = c_Big__Operators_Olinorder__class_OMin(X23060,hAPP(c_Set_Oimage(X23060,X23060,c_Groups_Ouminus__class_Ouminus(X23060)),X23059)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Max__eq__Min])]) ).

fof(i_0_9410,plain,
    ! [X23061,X23062] :
      ( ~ class_Groups_Olinordered__ab__group__add(X23062)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23062),X23061))
      | X23061 = c_Orderings_Obot__class_Obot(tc_fun(X23062,tc_HOL_Obool))
      | hAPP(c_Groups_Ouminus__class_Ouminus(X23062),c_Big__Operators_Olinorder__class_OMin(X23062,X23061)) = c_Big__Operators_Olinorder__class_OMax(X23062,hAPP(c_Set_Oimage(X23062,X23062,c_Groups_Ouminus__class_Ouminus(X23062)),X23061)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__Min__eq__Max])]) ).

fof(i_0_9411,plain,
    ! [X27048,X27049] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27049),c_Complete__Lattice_OSup__class_OSup(tc_fun(X27049,tc_HOL_Obool),X27048)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X27049,tc_HOL_Obool)),X27048)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UnionD])]) ).

fof(i_0_9412,plain,
    ! [X21386,X21387] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X21387))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21387),X21386)),X21387) = 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_9413,plain,
    ! [X25816,X25817] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25817),c_Groups_Ozero__class_Ozero(X25817)),c_Groups_Osgn__class_Osgn(X25817,X25816)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25817),c_Groups_Ozero__class_Ozero(X25817)),X25816))
        | ~ class_Rings_Olinordered__idom(X25817) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25817),c_Groups_Ozero__class_Ozero(X25817)),X25816))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25817),c_Groups_Ozero__class_Ozero(X25817)),c_Groups_Osgn__class_Osgn(X25817,X25816)))
        | ~ class_Rings_Olinordered__idom(X25817) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__greater])])]) ).

fof(i_0_9414,plain,
    ! [X33777,X33778,X33779] :
      ( ~ class_Divides_Oring__div(X33779)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33779),X33778),X33777))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33779),hAPP(c_Groups_Ouminus__class_Ouminus(X33779),X33777)),X33778) = hAPP(c_Groups_Ouminus__class_Ouminus(X33779),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33779),X33777),X33778)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__neg__div])]) ).

cnf(i_0_9415,plain,
    c_Int_OBit0(X1) != c_Int_OBit1(X2),
    inference(split_conjunct,[status(thm)],[i_0_5876]) ).

cnf(i_0_9416,plain,
    c_Int_OBit1(X1) != c_Int_OBit0(X2),
    inference(split_conjunct,[status(thm)],[i_0_5877]) ).

fof(i_0_9417,plain,
    ! [X20691,X20692,X20693,X20694] :
      ( ~ class_Divides_Osemiring__div(X20694)
      | c_Divides_Odiv__class_Omod(X20694,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20694),X20693),X20692),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20694),X20693),X20691)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20694),X20693),c_Divides_Odiv__class_Omod(X20694,X20692,X20691)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__mult1])]) ).

fof(i_0_9418,plain,
    ! [X26369,X26370,X26371,X26372] :
      ( ( X26372 != c_Orderings_Obot__class_Obot(tc_fun(X26371,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26371,tc_fun(X26370,tc_HOL_Obool)),X26372),hAPP(c_COMBK(tc_fun(X26370,tc_HOL_Obool),X26371),X26369)) = c_Orderings_Otop__class_Otop(tc_fun(X26370,tc_HOL_Obool)) )
      & ( X26372 = c_Orderings_Obot__class_Obot(tc_fun(X26371,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26371,tc_fun(X26370,tc_HOL_Obool)),X26372),hAPP(c_COMBK(tc_fun(X26370,tc_HOL_Obool),X26371),X26369)) = X26369 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INT__constant])]) ).

fof(i_0_9419,plain,
    ! [X23776,X23777,X23778,X23779] :
      ( ( X23779 != c_Orderings_Obot__class_Obot(tc_fun(X23778,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23778,tc_fun(X23777,tc_HOL_Obool)),X23779),hAPP(c_COMBK(tc_fun(X23777,tc_HOL_Obool),X23778),X23776)) = c_Orderings_Obot__class_Obot(tc_fun(X23777,tc_HOL_Obool)) )
      & ( X23779 = c_Orderings_Obot__class_Obot(tc_fun(X23778,tc_HOL_Obool))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23778,tc_fun(X23777,tc_HOL_Obool)),X23779),hAPP(c_COMBK(tc_fun(X23777,tc_HOL_Obool),X23778),X23776)) = X23776 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_UN__constant])]) ).

fof(i_0_9420,plain,
    ! [X32797,X32798,X32799] : c_Random__Sequence_Oempty(X32799,X32798,X32797) = 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(X32799)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(X32799)),
    inference(variable_rename,[status(thm)],[fact_Random__Sequence_Oempty__def]) ).

fof(i_0_9421,plain,
    ! [X20445,X20446,X20447,X20448] :
      ( ( X20447 != c_Groups_Ozero__class_Ozero(X20448)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20448),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20448),X20447),X20446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20448),X20447),X20445)) = c_Groups_Ozero__class_Ozero(X20448)
        | ~ class_Divides_Osemiring__div(X20448) )
      & ( X20447 = c_Groups_Ozero__class_Ozero(X20448)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20448),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20448),X20447),X20446)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20448),X20447),X20445)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20448),X20446),X20445)
        | ~ class_Divides_Osemiring__div(X20448) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1__if])])]) ).

fof(i_0_9422,plain,
    ! [X22832,X22833,X22834,X22835] :
      ( ~ class_Fields_Ofield__inverse__zero(X22835)
      | X22834 = c_Groups_Ozero__class_Ozero(X22835)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22835),X22834),X22833)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22835),X22834),X22832)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22835),X22833),X22832) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__left])]) ).

fof(i_0_9423,plain,
    ! [X22836,X22837,X22838,X22839] :
      ( ~ class_Fields_Ofield__inverse__zero(X22839)
      | X22838 = c_Groups_Ozero__class_Ozero(X22839)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22839),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22839),X22837),X22838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22839),X22836),X22838)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22839),X22837),X22836) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__divide__mult__cancel__right])]) ).

fof(i_0_9424,plain,
    ! [X20431,X20432,X20433,X20434] :
      ( ~ class_Divides_Osemiring__div(X20434)
      | X20433 = c_Groups_Ozero__class_Ozero(X20434)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20434),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20434),X20433),X20432)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20434),X20433),X20431)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20434),X20432),X20431) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult1])]) ).

fof(i_0_9425,plain,
    ! [X20435,X20436,X20437,X20438] :
      ( ~ class_Divides_Osemiring__div(X20438)
      | X20437 = c_Groups_Ozero__class_Ozero(X20438)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20438),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20438),X20436),X20437)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20438),X20435),X20437)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20438),X20436),X20435) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__mult2])]) ).

cnf(i_0_9426,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_5878]) ).

fof(i_0_9427,plain,
    ! [X21306,X21307,X21308,X21309] : hAPP(c_Nat_Onat_Onat__rec(X21309,X21308,X21307),hAPP(c_Nat_OSuc,X21306)) = hAPP(hAPP(X21307,X21306),hAPP(c_Nat_Onat_Onat__rec(X21309,X21308,X21307),X21306)),
    inference(variable_rename,[status(thm)],[fact_nat__rec__Suc]) ).

fof(i_0_9428,plain,
    ! [X17981,X17982,X17983] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17983),X17982))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17983),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17982),X17981))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add1])]) ).

fof(i_0_9429,plain,
    ! [X17859,X17860,X17861] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17861),X17860))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17861),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17860),X17859))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J])]) ).

fof(i_0_9430,plain,
    ! [X17978,X17979,X17980] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17980),X17979))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17980),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17978),X17979))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__less__add2])]) ).

fof(i_0_9431,plain,
    ! [X17862,X17863,X17864] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17864),X17863))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17864),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17862),X17863))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J])]) ).

fof(i_0_9432,plain,
    ! [X18027,X18028,X18029] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18029),X18028))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18029),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18028),X18027))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add1])]) ).

fof(i_0_9433,plain,
    ! [X17868,X17869,X17870] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17870),X17869))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17870),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17869),X17868))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J])]) ).

fof(i_0_9434,plain,
    ! [X18024,X18025,X18026] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18026),X18025))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18026),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18024),X18025))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__le__add2])]) ).

fof(i_0_9435,plain,
    ! [X17865,X17866,X17867] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17867),X17866))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17867),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17865),X17866))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J])]) ).

fof(i_0_9436,plain,
    ! [X20771,X20772,X20773,X20774] :
      ( ~ class_Divides_Osemiring__div(X20774)
      | c_Divides_Odiv__class_Omod(X20774,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20774),X20773),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20774),X20772),X20771)),X20772) = c_Divides_Odiv__class_Omod(X20774,X20773,X20772) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2])]) ).

fof(i_0_9437,plain,
    ! [X20767,X20768,X20769,X20770] :
      ( ~ class_Divides_Osemiring__div(X20770)
      | c_Divides_Odiv__class_Omod(X20770,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20770),X20769),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20770),X20768),X20767)),X20767) = c_Divides_Odiv__class_Omod(X20770,X20769,X20767) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1])]) ).

fof(i_0_9438,plain,
    ! [X18764,X18765,X18767,X18768,X18769] :
      ( ( X18765 = hAPP(c_Nat_OSuc,esk24_2(X18764,X18765))
        | X18765 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18765),hAPP(c_Nat_OSuc,X18764))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk24_2(X18764,X18765)),X18764))
        | X18765 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18765),hAPP(c_Nat_OSuc,X18764))) )
      & ( X18768 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18768),hAPP(c_Nat_OSuc,X18767))) )
      & ( X18768 != hAPP(c_Nat_OSuc,X18769)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18769),X18767))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18768),hAPP(c_Nat_OSuc,X18767))) ) ),
    inference(distribute,[status(thm)],[inference(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_9439,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_5879]) ).

fof(i_0_9440,plain,
    ! [X32859,X32860,X32861,X32863,X32864,X32865] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32860),X32861),c_Orderings_Otop__class_Otop(tc_fun(X32860,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X32859,X32861))
        | hBOOL(hAPP(X32859,esk503_1(X32859))) )
      & ( hBOOL(hAPP(hAPP(c_member(X32865),esk504_2(X32863,X32865)),c_Orderings_Otop__class_Otop(tc_fun(X32865,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(X32863,X32864)) )
      & ( hBOOL(hAPP(X32863,esk504_2(X32863,X32865)))
        | ~ hBOOL(hAPP(X32863,X32864)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__UNIV])])])])])]) ).

fof(i_0_9441,plain,
    ! [X30375,X30376] :
      ( X30376 = c_List_Olist_ONil(X30375)
      | hAPP(c_List_Orotate1(X30375),X30376) = hAPP(hAPP(c_List_Oappend(X30375),hAPP(c_List_Otl(X30375),X30376)),hAPP(hAPP(c_List_Olist_OCons(X30375),hAPP(c_List_Ohd(X30375),X30376)),c_List_Olist_ONil(X30375))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl])]) ).

cnf(i_0_9442,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_5880]) ).

fof(i_0_9443,plain,
    ! [X30954,X30955,X30956,X30957] :
      ( ~ class_Groups_Ocomm__monoid__add(X30957)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X30957),X30956),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30955,X30954))) = hAPP(c_List_Omonoid__add__class_Olistsum(X30957),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X30957),X30956),c_List_Oupto(X30955,X30954))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__set__upto__conv__listsum__int])]) ).

fof(i_0_9444,plain,
    ! [X30958,X30959,X30960,X30961] :
      ( ~ class_Groups_Ocomm__monoid__add(X30961)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30961),hAPP(hAPP(c_List_Omap(tc_Int_Oint,X30961),X30960),c_List_Oupto(X30959,X30958))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,X30961),X30960),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X30959,X30958))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_interv__listsum__conv__setsum__set__int])]) ).

fof(i_0_9445,plain,
    ! [X25073,X25074,X25075,X25076] :
      ( ~ class_Lattices_Osemilattice__inf(X25076)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25076),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25076),X25075),X25074)),X25073) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25076),X25075),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25076),X25074),X25073)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oassoc])]) ).

fof(i_0_9446,plain,
    ! [X25065,X25066,X25067,X25068] :
      ( ~ class_Lattices_Osemilattice__inf(X25068)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25068),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25068),X25067),X25066)),X25065) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25068),X25067),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25068),X25066),X25065)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__assoc])]) ).

fof(i_0_9447,plain,
    ! [X25069,X25070,X25071,X25072] :
      ( ~ class_Lattices_Olattice(X25072)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25072),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25072),X25071),X25070)),X25069) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25072),X25071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25072),X25070),X25069)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I2_J])]) ).

fof(i_0_9448,plain,
    ! [X23188,X23189,X23190,X23191] :
      ( ~ class_Lattices_Olattice(X23191)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23191),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23191),X23190),X23189)),X23188) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23191),X23190),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23191),X23189),X23188)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I6_J])]) ).

fof(i_0_9449,plain,
    ! [X23192,X23193,X23194,X23195] :
      ( ~ class_Lattices_Osemilattice__sup(X23195)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23195),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23195),X23194),X23193)),X23192) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23195),X23194),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23195),X23193),X23192)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oassoc])]) ).

fof(i_0_9450,plain,
    ! [X23184,X23185,X23186,X23187] :
      ( ~ class_Lattices_Osemilattice__sup(X23187)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23187),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23187),X23186),X23185)),X23184) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23187),X23186),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23187),X23185),X23184)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__assoc])]) ).

fof(i_0_9451,plain,
    ! [X22495,X22496,X22497,X22498] :
      ( ~ class_Orderings_Olinorder(X22498)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22498),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22498),X22497),X22496)),X22495) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22498),X22497),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22498),X22496),X22495)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oassoc])]) ).

fof(i_0_9452,plain,
    ! [X22491,X22492,X22493,X22494] :
      ( ~ class_Orderings_Olinorder(X22494)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22494),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22494),X22493),X22492)),X22491) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22494),X22493),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22494),X22492),X22491)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__assoc])]) ).

fof(i_0_9453,plain,
    ! [X21519,X21520,X21521,X21522] :
      ( ~ class_Orderings_Olinorder(X21522)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21522),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21522),X21521),X21520)),X21519) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21522),X21521),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21522),X21520),X21519)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__assoc])]) ).

fof(i_0_9454,plain,
    ! [X21515,X21516,X21517,X21518] :
      ( ~ class_Orderings_Olinorder(X21518)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21518),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21518),X21517),X21516)),X21515) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21518),X21517),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21518),X21516),X21515)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oassoc])]) ).

fof(i_0_9455,plain,
    ! [X20253,X20254,X20255] :
      ( ~ class_Groups_Omonoid__mult(X20255)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20255),hAPP(hAPP(c_Power_Opower__class_Opower(X20255),X20254),X20253)),X20254) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20255),X20254),hAPP(hAPP(c_Power_Opower__class_Opower(X20255),X20254),X20253)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__commutes])]) ).

fof(i_0_9456,plain,
    ! [X19054,X19055,X19056,X19057] :
      ( ~ class_Rings_Ocomm__semiring__1(X19057)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19057),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19057),X19056),X19055)),X19054) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19057),X19056),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19057),X19055),X19054)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J])]) ).

fof(i_0_9457,plain,
    ! [X18324,X18325,X18326,X18327] :
      ( ~ class_Groups_Oab__semigroup__mult(X18327)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18327),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18327),X18326),X18325)),X18324) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18327),X18326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18327),X18325),X18324)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__mult__class_Omult__ac_I1_J])]) ).

fof(i_0_9458,plain,
    ! [X19020,X19021,X19022,X19023] :
      ( ~ class_Rings_Ocomm__semiring__1(X19023)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19023),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19023),X19022),X19021)),X19020) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19023),X19022),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19023),X19021),X19020)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J])]) ).

fof(i_0_9459,plain,
    ! [X17855,X17856,X17857,X17858] :
      ( ~ class_Groups_Oab__semigroup__add(X17858)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17858),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17858),X17857),X17856)),X17855) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17858),X17857),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17858),X17856),X17855)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__semigroup__add__class_Oadd__ac_I1_J])]) ).

fof(i_0_9460,plain,
    ! [X22521,X22522,X22523,X22524] :
      ( ~ class_Rings_Odivision__ring(X22524)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22524),X22523),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22524),X22522),X22521)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22524),X22523),X22522)),X22521) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times__divide__eq__right])]) ).

fof(i_0_9461,plain,
    ! [X19058,X19059,X19060,X19061] :
      ( ~ class_Rings_Ocomm__semiring__1(X19061)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19061),X19060),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19061),X19059),X19058)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19061),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19061),X19060),X19059)),X19058) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J])]) ).

fof(i_0_9462,plain,
    ! [X19024,X19025,X19026,X19027] :
      ( ~ class_Rings_Ocomm__semiring__1(X19027)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19027),X19026),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19027),X19025),X19024)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19027),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19027),X19026),X19025)),X19024) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J])]) ).

fof(i_0_9463,plain,
    ! [X31298,X31299,X31300] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X31300),X31299),hAPP(c_List_Oset(X31300),X31298)))
        | c_List_Oremdups(X31300,hAPP(hAPP(c_List_Olist_OCons(X31300),X31299),X31298)) = c_List_Oremdups(X31300,X31298) )
      & ( hBOOL(hAPP(hAPP(c_member(X31300),X31299),hAPP(c_List_Oset(X31300),X31298)))
        | c_List_Oremdups(X31300,hAPP(hAPP(c_List_Olist_OCons(X31300),X31299),X31298)) = hAPP(hAPP(c_List_Olist_OCons(X31300),X31299),c_List_Oremdups(X31300,X31298)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5881])]) ).

fof(i_0_9464,plain,
    ! [X30615,X30616] :
      ( X30616 = c_List_Olist_ONil(X30615)
      | c_List_Olast(X30615,X30616) = hAPP(hAPP(c_List_Onth(X30615),X30616),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30615)),X30616)),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_9465,plain,
    ! [X21484,X21485] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21484),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X21485),X21484) = hAPP(c_Groups_Ouminus__class_Ouminus(X21485),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21485),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21484))))
        | ~ class_Rings_Oring__1(X21485) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X21484),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Oring__1__class_Oof__int(X21485),X21484) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21485),hAPP(c_Int_Onat,X21484))
        | ~ class_Rings_Oring__1(X21485) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5882])])]) ).

fof(i_0_9466,plain,
    ! [X20135,X20136] :
      ( ~ class_Int_Onumber__ring(X20136)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X20135))
      | hBOOL(hAPP(hAPP(c_member(X20136),hAPP(c_Int_Onumber__class_Onumber__of(X20136),X20135)),c_Nat_Osemiring__1__class_ONats(X20136))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__number__of])]) ).

fof(i_0_9467,plain,
    ! [X23935,X23936] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23936),X23935))
      | hAPP(c_Finite__Set_Ocard(tc_fun(X23936,tc_HOL_Obool)),hAPP(c_Set_OPow(X23936),X23935)) = 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(X23936),X23935)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__Pow])]) ).

fof(i_0_9468,plain,
    ! [X25765] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25765)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),X25765)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X25765),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_atLeast__Suc]) ).

fof(i_0_9469,plain,
    ! [X25292,X25293,X25294] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25294,tc_HOL_Obool)),X25293),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25294,tc_HOL_Obool)),X25292)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25294,tc_HOL_Obool)),X25293),X25292),
    inference(variable_rename,[status(thm)],[fact_Diff__Compl]) ).

fof(i_0_9470,plain,
    ! [X25295,X25296,X25297] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25297,tc_HOL_Obool)),X25296),X25295) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25297,tc_HOL_Obool)),X25296),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25297,tc_HOL_Obool)),X25295)),
    inference(variable_rename,[status(thm)],[fact_Diff__eq]) ).

fof(i_0_9471,plain,
    ! [X18719] :
      ( ~ class_Rings_Olinordered__semidom(X18719)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18719),c_Groups_Ozero__class_Ozero(X18719)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18719),c_Groups_Oone__class_Oone(X18719)),c_Groups_Oone__class_Oone(X18719)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__two])]) ).

fof(i_0_9472,plain,
    ! [X21482,X21483] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X21483,X21482)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21483),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan__int]) ).

fof(i_0_9473,plain,
    ! [X32576,X32577,X32578,X32579] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X32579),X32578))
      | hAPP(hAPP(c_List_Onth(X32577),c_List_Oreplicate(X32577,X32578,X32576)),X32579) = X32576 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__replicate])]) ).

fof(i_0_9474,plain,
    ! [X22731,X22732,X22733] :
      ( ~ class_Orderings_Olinorder(X22733)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X22733),X22732))
      | ~ hBOOL(hAPP(hAPP(c_member(X22733),X22731),X22732))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22733),X22731),c_Big__Operators_Olattice_OInf__fin(X22733,c_Orderings_Oord__class_Omin(X22733),X22732)) = X22731 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__Inf__absorb])]) ).

fof(i_0_9475,plain,
    ! [X23019,X23020,X23021] :
      ( ~ class_Orderings_Olinorder(X23021)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23021),X23020))
      | ~ hBOOL(hAPP(hAPP(c_member(X23021),X23019),X23020))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X23021),X23019),c_Big__Operators_Olattice_OSup__fin(X23021,c_Orderings_Oord__class_Omax(X23021),X23020)) = X23019 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__Sup__absorb])]) ).

fof(i_0_9476,plain,
    ! [X21241,X21242] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21242),X21241),hAPP(c_Groups_Ouminus__class_Ouminus(X21242),X21241)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21242),X21241),c_Groups_Ozero__class_Ozero(X21242)))
        | ~ class_Rings_Olinordered__idom(X21242) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21242),X21241),c_Groups_Ozero__class_Ozero(X21242)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X21242),X21241),hAPP(c_Groups_Ouminus__class_Ouminus(X21242),X21241)))
        | ~ class_Rings_Olinordered__idom(X21242) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff])])]) ).

fof(i_0_9477,plain,
    ! [X21235,X21236] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21236),X21235),hAPP(c_Groups_Ouminus__class_Ouminus(X21236),X21235)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21236),X21235),c_Groups_Ozero__class_Ozero(X21236)))
        | ~ class_Groups_Olinordered__ab__group__add(X21236) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21236),X21235),c_Groups_Ozero__class_Ozero(X21236)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21236),X21235),hAPP(c_Groups_Ouminus__class_Ouminus(X21236),X21235)))
        | ~ class_Groups_Olinordered__ab__group__add(X21236) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff])])]) ).

fof(i_0_9478,plain,
    ! [X25253,X25254,X25255] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25255,tc_HOL_Obool)),X25254),X25253) != c_Orderings_Obot__class_Obot(tc_fun(X25255,tc_HOL_Obool))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X25255,tc_HOL_Obool)),X25254),X25253) = X25254 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Diff__triv])]) ).

fof(i_0_9479,plain,
    ! [X30577,X30578,X30579,X30580,X30581] :
      ( ~ class_Orderings_Olinorder(X30581)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30580,X30581,X30579),X30578),X30577) != c_List_Olist_ONil(X30580) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__not__Nil])]) ).

fof(i_0_9480,plain,
    ! [X21968,X21969,X21970,X21971] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21971)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21970),X21969))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21970,X21971),hAPP(c_COMBK(X21971,X21970),X21968)),X21969) = hAPP(hAPP(c_Power_Opower__class_Opower(X21971),X21968),hAPP(c_Finite__Set_Ocard(X21970),X21969)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__constant])]) ).

fof(i_0_9481,plain,
    ! [X32647,X32648] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32648),X32647))
        | c_Lazy__Sequence_Osmall__lazy_H(X32648,X32647) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X32648),X32647))
        | c_Lazy__Sequence_Osmall__lazy_H(X32648,X32647) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X32647),c_Lazy__Sequence_Osmall__lazy_H(X32648,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X32647),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5883])]) ).

fof(i_0_9482,plain,
    ! [X19384,X19385,X19386] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X19386)
      | X19385 = c_Orderings_Obot__class_Obot(tc_fun(X19386,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19386),X19385))
      | hAPP(c_Finite__Set_Ofold1(X19386,c_Groups_Otimes__class_Otimes(X19386)),hAPP(hAPP(c_Set_Oinsert(X19386),X19384),X19385)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19386),X19384),hAPP(c_Finite__Set_Ofold1(X19386,c_Groups_Otimes__class_Otimes(X19386)),X19385)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__insert__idem])]) ).

fof(i_0_9483,plain,
    ! [X25271,X25272,X25273,X25274] :
      ( ~ class_Orderings_Oorder(X25274)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25274,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25274,X25273),X25272)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25274,X25272),X25271)) = c_Orderings_Obot__class_Obot(tc_fun(X25274,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I11_J])]) ).

fof(i_0_9484,plain,
    ! [X18794,X18795] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18795),hAPP(c_Nat_OSuc,X18794)) = 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),X18795),X18794)),
    inference(variable_rename,[status(thm)],[fact_diff__Suc]) ).

fof(i_0_9485,plain,
    ! [X30077,X30078,X30079,X30080] : hAPP(hAPP(c_List_Oappend(X30080),hAPP(hAPP(c_List_Oappend(X30080),X30079),X30078)),X30077) = hAPP(hAPP(c_List_Oappend(X30080),X30079),hAPP(hAPP(c_List_Oappend(X30080),X30078),X30077)),
    inference(variable_rename,[status(thm)],[fact_append__assoc]) ).

fof(i_0_9486,plain,
    ! [X30035,X30036,X30037,X30038] : hAPP(hAPP(c_List_Oappend(X30038),hAPP(hAPP(c_List_Olist_OCons(X30038),X30037),X30036)),X30035) = hAPP(hAPP(c_List_Olist_OCons(X30038),X30037),hAPP(hAPP(c_List_Oappend(X30038),X30036),X30035)),
    inference(variable_rename,[status(thm)],[fact_append__Cons]) ).

fof(i_0_9487,plain,
    ! [X33944,X33945] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X33945),X33944))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33944))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X33945),X33944)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le])]) ).

fof(i_0_9488,plain,
    ! [X33610,X33611] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33611),X33610))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X33610))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X33611),X33610)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__le])]) ).

fof(i_0_9489,plain,
    ! [X30446,X30447,X30448] :
      ( X30448 = c_List_Olist_ONil(X30447)
      | hAPP(hAPP(c_List_Otake(X30447),hAPP(c_Nat_OSuc,X30446)),X30448) = hAPP(hAPP(c_List_Olist_OCons(X30447),hAPP(c_List_Ohd(X30447),X30448)),hAPP(hAPP(c_List_Otake(X30447),X30446),hAPP(c_List_Otl(X30447),X30448))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__Suc])]) ).

fof(i_0_9490,plain,
    ! [X24351] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24351))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24351) = 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,X24351))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__atLeastZeroLessThan__int])]) ).

fof(i_0_9491,plain,
    ! [X29434,X29435,X29436,X29437] :
      ( ( X29437 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X29436),hAPP(hAPP(c_List_Olist_OCons(X29436),X29435),X29434)),X29437) = X29435 )
      & ( X29437 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Onth(X29436),hAPP(hAPP(c_List_Olist_OCons(X29436),X29435),X29434)),X29437) = hAPP(hAPP(c_List_Onth(X29436),X29434),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X29437),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_9492,plain,
    ! [X17100,X17101,X17102,X17103] :
      ( ( X17103 != c_Orderings_Obot__class_Obot(tc_fun(X17102,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17102,X17101,hAPP(c_COMBK(X17101,X17102),X17100)),X17103) = c_Orderings_Obot__class_Obot(tc_fun(X17101,tc_HOL_Obool)) )
      & ( X17103 = c_Orderings_Obot__class_Obot(tc_fun(X17102,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17102,X17101,hAPP(c_COMBK(X17101,X17102),X17100)),X17103) = hAPP(hAPP(c_Set_Oinsert(X17101),X17100),c_Orderings_Obot__class_Obot(tc_fun(X17101,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__constant__conv])]) ).

cnf(i_0_9493,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_5842]) ).

cnf(i_0_9494,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_5844]) ).

cnf(i_0_9495,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_5843]) ).

cnf(i_0_9496,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_5845]) ).

fof(i_0_9497,plain,
    ! [X30899,X30900,X30901,X30902] :
      ( ~ class_Groups_Ocomm__monoid__add(X30902)
      | ~ hBOOL(hAPP(c_List_Odistinct(X30901),X30900))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30902),hAPP(hAPP(c_List_Omap(X30901,X30902),X30899),X30900)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X30901,X30902),X30899),hAPP(c_List_Oset(X30901),X30900)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__distinct__conv__setsum__set])]) ).

fof(i_0_9498,plain,
    ! [X20265,X20266,X20267,X20268] :
      ( ~ class_Groups_Omonoid__mult(X20268)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20268),X20267),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20266),X20265)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20268),hAPP(hAPP(c_Power_Opower__class_Opower(X20268),X20267),X20266)),X20265) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__mult])]) ).

fof(i_0_9499,plain,
    ! [X20163,X20164,X20165,X20166] :
      ( ~ class_Rings_Ocomm__semiring__1(X20166)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20166),hAPP(hAPP(c_Power_Opower__class_Opower(X20166),X20165),X20164)),X20163) = hAPP(hAPP(c_Power_Opower__class_Opower(X20166),X20165),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20164),X20163)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J])]) ).

fof(i_0_9500,plain,
    ! [X21202,X21203,X21204] :
      ( ~ class_Divides_Oring__div(X21204)
      | c_Divides_Odiv__class_Omod(X21204,hAPP(c_Groups_Ouminus__class_Ouminus(X21204),X21203),X21202) = c_Divides_Odiv__class_Omod(X21204,hAPP(c_Groups_Ouminus__class_Ouminus(X21204),c_Divides_Odiv__class_Omod(X21204,X21203,X21202)),X21202) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__eq])]) ).

fof(i_0_9501,plain,
    ! [X30443,X30444,X30445] : hAPP(c_List_Otl(X30445),hAPP(hAPP(c_List_Otake(X30445),X30444),X30443)) = hAPP(hAPP(c_List_Otake(X30445),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30444),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(X30445),X30443)),
    inference(variable_rename,[status(thm)],[fact_tl__take]) ).

fof(i_0_9502,plain,
    ! [X25930,X25931,X25932] :
      ( ~ class_Rings_Olinordered__idom(X25932)
      | hAPP(c_Groups_Oabs__class_Oabs(X25932),hAPP(hAPP(c_Power_Opower__class_Opower(X25932),hAPP(c_Groups_Ouminus__class_Ouminus(X25932),X25931)),X25930)) = hAPP(c_Groups_Oabs__class_Oabs(X25932),hAPP(hAPP(c_Power_Opower__class_Opower(X25932),X25931),X25930)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus])]) ).

cnf(i_0_9503,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_5884]) ).

cnf(i_0_9504,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_5885]) ).

fof(i_0_9505,plain,
    ! [X25671,X25672,X25673] :
      ( ~ class_Lattices_Olattice(X25673)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25673),X25672))
      | hBOOL(hAPP(hAPP(c_member(X25673),X25671),X25672))
      | X25672 = c_Orderings_Obot__class_Obot(tc_fun(X25673,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X25673,hAPP(hAPP(c_Set_Oinsert(X25673),X25671),X25672)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25673),X25671),c_Big__Operators_Olattice__class_OInf__fin(X25673,X25672)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5886])]) ).

fof(i_0_9506,plain,
    ! [X23534,X23535,X23536] :
      ( ~ class_Lattices_Olattice(X23536)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23536),X23535))
      | hBOOL(hAPP(hAPP(c_member(X23536),X23534),X23535))
      | X23535 = c_Orderings_Obot__class_Obot(tc_fun(X23536,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X23536,hAPP(hAPP(c_Set_Oinsert(X23536),X23534),X23535)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23536),X23534),c_Big__Operators_Olattice__class_OSup__fin(X23536,X23535)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5887])]) ).

fof(i_0_9507,plain,
    ! [X23050,X23051,X23052] :
      ( ~ class_Orderings_Olinorder(X23052)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23052),X23051))
      | hBOOL(hAPP(hAPP(c_member(X23052),X23050),X23051))
      | X23051 = c_Orderings_Obot__class_Obot(tc_fun(X23052,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X23052,hAPP(hAPP(c_Set_Oinsert(X23052),X23050),X23051)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X23052),X23050),c_Big__Operators_Olinorder__class_OMax(X23052,X23051)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5888])]) ).

fof(i_0_9508,plain,
    ! [X21817,X21818,X21819] :
      ( ~ class_Orderings_Olinorder(X21819)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21819),X21818))
      | hBOOL(hAPP(hAPP(c_member(X21819),X21817),X21818))
      | X21818 = c_Orderings_Obot__class_Obot(tc_fun(X21819,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X21819,hAPP(hAPP(c_Set_Oinsert(X21819),X21817),X21818)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21819),X21817),c_Big__Operators_Olinorder__class_OMin(X21819,X21818)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5889])]) ).

fof(i_0_9509,plain,
    ! [X26172,X26173] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26173),c_Orderings_Otop__class_Otop(tc_fun(X26173,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(X26173),X26172) != hAPP(c_Finite__Set_Ocard(X26173),c_Orderings_Otop__class_Otop(tc_fun(X26173,tc_HOL_Obool)))
      | X26172 = c_Orderings_Otop__class_Otop(tc_fun(X26173,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__eq__UNIV__imp__eq__UNIV])]) ).

fof(i_0_9510,plain,
    ! [X30313,X30314,X30315,X30316] :
      ( ( X30316 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X30315),X30316),hAPP(hAPP(c_List_Olist_OCons(X30315),X30314),X30313)) = hAPP(hAPP(c_List_Olist_OCons(X30315),X30314),X30313) )
      & ( X30316 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Odrop(X30315),X30316),hAPP(hAPP(c_List_Olist_OCons(X30315),X30314),X30313)) = hAPP(hAPP(c_List_Odrop(X30315),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30316),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X30313) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_drop__Cons_H])]) ).

fof(i_0_9511,plain,
    ! [X21366] : 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,X21366))))),
    inference(variable_rename,[status(thm)],[fact_neg__zminus__int]) ).

fof(i_0_9512,plain,
    ! [X16898,X16899,X16900,X16901] :
      ( ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X16901),X16900),X16899),X16898))
        | X16900 = X16898
        | hBOOL(hAPP(X16899,X16898)) )
      & ( X16900 != X16898
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X16901),X16900),X16899),X16898)) )
      & ( ~ hBOOL(hAPP(X16899,X16898))
        | hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X16901),X16900),X16899),X16898)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).

fof(i_0_9513,plain,
    ! [X33790,X33791,X33792] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33792),X33791),hAPP(c_Groups_Ouminus__class_Ouminus(X33792),X33790)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33792),X33791),X33790))
        | ~ class_Rings_Ocomm__ring__1(X33792) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33792),X33791),X33790))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33792),X33791),hAPP(c_Groups_Ouminus__class_Ouminus(X33792),X33790)))
        | ~ class_Rings_Ocomm__ring__1(X33792) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff])])]) ).

fof(i_0_9514,plain,
    ! [X33673,X33674,X33675] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33675),X33674),hAPP(c_Groups_Oabs__class_Oabs(X33675),X33673)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33675),X33674),X33673))
        | ~ class_Rings_Olinordered__idom(X33675) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33675),X33674),X33673))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33675),X33674),hAPP(c_Groups_Oabs__class_Oabs(X33675),X33673)))
        | ~ class_Rings_Olinordered__idom(X33675) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__abs__iff])])]) ).

fof(i_0_9515,plain,
    ! [X24363,X24364,X24365] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X24365),X24364),hAPP(c_SetInterval_Oord__class_OlessThan(X24365),X24363)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24365),X24364),X24363))
        | ~ class_Orderings_Oord(X24365) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24365),X24364),X24363))
        | hBOOL(hAPP(hAPP(c_member(X24365),X24364),hAPP(c_SetInterval_Oord__class_OlessThan(X24365),X24363)))
        | ~ class_Orderings_Oord(X24365) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__iff])])]) ).

fof(i_0_9516,plain,
    ! [X25778,X25779,X25780] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X25780),X25779),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25780),X25778)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25780),X25778),X25779))
        | ~ class_Orderings_Oord(X25780) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25780),X25778),X25779))
        | hBOOL(hAPP(hAPP(c_member(X25780),X25779),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25780),X25778)))
        | ~ class_Orderings_Oord(X25780) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__iff])])]) ).

fof(i_0_9517,plain,
    ! [X25311,X25312,X25313] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X25313),X25312),hAPP(c_SetInterval_Oord__class_OatMost(X25313),X25311)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25313),X25312),X25311))
        | ~ class_Orderings_Oord(X25313) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25313),X25312),X25311))
        | hBOOL(hAPP(hAPP(c_member(X25313),X25312),hAPP(c_SetInterval_Oord__class_OatMost(X25313),X25311)))
        | ~ class_Orderings_Oord(X25313) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__iff])])]) ).

fof(i_0_9518,plain,
    ! [X25734,X25735,X25736] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X25736),X25735),hAPP(c_SetInterval_Oord__class_OatLeast(X25736),X25734)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25736),X25734),X25735))
        | ~ class_Orderings_Oord(X25736) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25736),X25734),X25735))
        | hBOOL(hAPP(hAPP(c_member(X25736),X25735),hAPP(c_SetInterval_Oord__class_OatLeast(X25736),X25734)))
        | ~ class_Orderings_Oord(X25736) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__iff])])]) ).

fof(i_0_9519,plain,
    ! [X24178,X24179,X24180] :
      ( ~ class_Groups_Oordered__ab__group__add(X24180)
      | hAPP(c_Set_Oimage(X24180,X24180,c_Groups_Ouminus__class_Ouminus(X24180)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24180,X24179,X24178)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24180,hAPP(c_Groups_Ouminus__class_Ouminus(X24180),X24178)),hAPP(c_Groups_Ouminus__class_Ouminus(X24180),X24179)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanAtMost])]) ).

fof(i_0_9520,plain,
    ! [X17483,X17484,X17485,X17486,X17487] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17487,X17486,X17485)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17487),X17484))
      | ~ hBOOL(hAPP(hAPP(c_member(X17487),X17483),X17484))
      | hAPP(hAPP(X17486,X17483),hAPP(X17485,X17484)) = hAPP(X17485,X17484) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oin__idem])]) ).

fof(i_0_9521,plain,
    ! [X22999,X23000,X23001] :
      ( ~ class_Orderings_Olinorder(X23001)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23001),X23000))
      | ~ hBOOL(hAPP(hAPP(c_member(X23001),X22999),X23000))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23001),X22999),c_Big__Operators_Olinorder__class_OMax(X23001,X23000))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__ge])]) ).

cnf(i_0_9522,plain,
    ( c_List_Oall__interval__nat(X1,X2,X3)
    | ~ c_List_Olist__all(tc_Nat_Onat,X1,c_List_Oupt(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_5890]) ).

fof(i_0_9523,plain,
    ! [X29630,X29631] :
      ( ~ class_Groups_Ocomm__monoid__add(X29631)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29631),X29630) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,X29631),hAPP(c_List_Onth(X29631),X29630)),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(X29631)),X29630))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__setsum__nth])]) ).

fof(i_0_9524,plain,
    ! [X20092,X20093] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X20093),X20092))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20092)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20093)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20092),X20093)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiff__int])]) ).

fof(i_0_9525,plain,
    ! [X19447] : 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)),X19447)),X19447) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_odd__nonzero]) ).

fof(i_0_9526,plain,
    ! [X28192,X28193] : hAPP(c_Relation_OField(X28193),X28192) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X28193,tc_HOL_Obool)),hAPP(c_Relation_ODomain(X28193,X28193),X28192)),hAPP(c_Relation_ORange(X28193,X28193),X28192)),
    inference(variable_rename,[status(thm)],[fact_Field__def]) ).

cnf(i_0_9527,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_5891]) ).

fof(i_0_9528,plain,
    ! [X24044,X24045] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24045,X24044) = 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),X24045),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24044))),
    inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I2_J]) ).

fof(i_0_9529,plain,
    ! [X29942,X29943,X29944] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29944))
        | c_List_Osublist(X29943,hAPP(hAPP(c_List_Olist_OCons(X29943),X29942),c_List_Olist_ONil(X29943)),X29944) = hAPP(hAPP(c_List_Olist_OCons(X29943),X29942),c_List_Olist_ONil(X29943)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29944))
        | c_List_Osublist(X29943,hAPP(hAPP(c_List_Olist_OCons(X29943),X29942),c_List_Olist_ONil(X29943)),X29944) = c_List_Olist_ONil(X29943) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5892])]) ).

fof(i_0_9530,plain,
    ! [X20871,X20872] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20872))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20872),X20871)),X20872) = X20871 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__m])]) ).

fof(i_0_9531,plain,
    ! [X20869,X20870] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20870))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20869),X20870)),X20870) = X20869 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self__is__m])]) ).

cnf(i_0_9532,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_5893]) ).

cnf(i_0_9533,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_5894]) ).

fof(i_0_9534,plain,
    ! [X21362,X21363] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21363,X21362) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21363,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21362)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21363,X21362) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21363,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21362)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21363,X21362)),X21362) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus2__eq__if])]) ).

fof(i_0_9535,plain,
    ! [X26132,X26133] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X26133,tc_HOL_Obool)),X26132),c_Orderings_Otop__class_Otop(tc_fun(X26133,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_subset__UNIV]) ).

fof(i_0_9536,plain,
    ! [X21090] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21090)))
        | 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),X21090)) = 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),X21090)))
        | 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),X21090)) = 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),X21090))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5895])]) ).

cnf(i_0_9537,plain,
    c_Relation_Osingle__valued(X1,X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5896]) ).

fof(i_0_9538,plain,
    ! [X33710,X33711,X33712] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33712),X33711))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33711),X33710))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33712),X33710)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans])]) ).

fof(i_0_9539,plain,
    ! [X19470,X19471,X19472] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19472),X19471))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19471),X19470))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19472),X19470)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__trans])]) ).

fof(i_0_9540,plain,
    ! [X17215,X17216,X17217] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17217),X17216))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17216),X17215))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17217),X17215)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__trans])]) ).

fof(i_0_9541,plain,
    ! [X33768,X33769,X33770,X33771] :
      ( ~ class_Divides_Osemiring__div(X33771)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33771),X33770),X33769))
      | c_Divides_Odiv__class_Omod(X33771,c_Divides_Odiv__class_Omod(X33771,X33768,X33769),X33770) = c_Divides_Odiv__class_Omod(X33771,X33768,X33770) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__cancel])]) ).

fof(i_0_9542,plain,
    ! [X18975,X18976] :
      ( ~ class_Rings_Ocomm__semiring__1(X18976)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18976),X18975),X18975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18976),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18976),c_Groups_Oone__class_Oone(X18976)),c_Groups_Oone__class_Oone(X18976))),X18975) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J])]) ).

fof(i_0_9543,plain,
    ! [X17648,X17649,X17650] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17650),X17649),X17648))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17650),X17649),X17648))
        | ~ class_Orderings_Opreorder(X17650) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17650),X17648),X17649))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17650),X17649),X17648))
        | ~ class_Orderings_Opreorder(X17650) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17650),X17649),X17648))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17650),X17648),X17649))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17650),X17649),X17648))
        | ~ class_Orderings_Opreorder(X17650) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5897])])]) ).

fof(i_0_9544,plain,
    ! [X17967,X17968,X17969,X17970] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17970),X17969))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17968),X17969) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17970),X17967)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17968),X17967)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__eq__less])]) ).

fof(i_0_9545,plain,
    ! [X33780,X33781,X33782] :
      ( ~ class_Divides_Oring__div(X33782)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33782),X33781),X33780))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33782),X33780),hAPP(c_Groups_Ouminus__class_Ouminus(X33782),X33781)) = hAPP(c_Groups_Ouminus__class_Ouminus(X33782),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33782),X33780),X33781)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__neg])]) ).

fof(i_0_9546,plain,
    ! [X17727,X17728] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17728)),X17727))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17728),X17727)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessD])]) ).

fof(i_0_9547,plain,
    ! [X17759,X17760] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17760)),X17759))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17760),X17759)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__lessD])]) ).

fof(i_0_9548,plain,
    ! [X17751,X17752] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17752)),X17751))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17752),X17751)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17752),X17751))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17752)),X17751)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__le__eq])]) ).

fof(i_0_9549,plain,
    ! [X17747,X17748] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17748),X17747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17748)),X17747)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17748)),X17747))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17748),X17747)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le])]) ).

fof(i_0_9550,plain,
    ! [X17258,X17259] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17259)),X17258))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17259),X17258)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leD])]) ).

fof(i_0_9551,plain,
    ! [X17786,X17787,X17788] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17788),X17787))
      | hBOOL(hAPP(hAPP(c_member(X17788),X17786),X17787))
      | hAPP(c_Finite__Set_Ocard(X17788),hAPP(hAPP(c_Set_Oinsert(X17788),X17786),X17787)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X17788),X17787)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5898])]) ).

fof(i_0_9552,plain,
    ! [X30262,X30263,X30264,X30265] : hAPP(hAPP(c_List_Odrop(X30265),X30264),hAPP(hAPP(c_List_Odrop(X30265),X30263),X30262)) = hAPP(hAPP(c_List_Odrop(X30265),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30264),X30263)),X30262),
    inference(variable_rename,[status(thm)],[fact_drop__drop]) ).

fof(i_0_9553,plain,
    ! [X29500,X29501,X29502,X29503] : hAPP(hAPP(c_List_Otake(X29503),X29502),hAPP(hAPP(c_List_Otake(X29503),X29501),X29500)) = hAPP(hAPP(c_List_Otake(X29503),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X29502),X29501)),X29500),
    inference(variable_rename,[status(thm)],[fact_take__take]) ).

fof(i_0_9554,plain,
    ! [X20552,X20553,X20554] :
      ( ( ~ hBOOL(hAPP(X20554,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20553),X20552)))
        | epred1_3(X20554,X20552,X20553) )
      & ( ~ epred1_3(X20554,X20552,X20553)
        | hBOOL(hAPP(X20554,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20553),X20552))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5899])]) ).

fof(i_0_9555,plain,
    ! [X26878,X26879,X26880] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26880)
      | ~ hBOOL(hAPP(hAPP(c_member(X26880),X26879),X26878))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26880),c_Complete__Lattice_OInf__class_OInf(X26880,X26878)),X26879)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__lower])]) ).

fof(i_0_9556,plain,
    ! [X20002,X20004,X20005,X20007] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk54_1(X20002)))
        | hBOOL(hAPP(X20002,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20004))) )
      & ( ~ hBOOL(hAPP(X20002,esk54_1(X20002)))
        | hBOOL(hAPP(X20002,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20004))) )
      & ( ~ hBOOL(hAPP(X20005,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk55_1(X20005))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20007))
        | hBOOL(hAPP(X20005,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_transfer__int__nat__quantifiers_I1_J])])])])])]) ).

fof(i_0_9557,plain,
    ! [X20757,X20758] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20758))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20758),X20757)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,X20758)),hAPP(c_Int_Onat,X20757)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__div__distrib])]) ).

fof(i_0_9558,plain,
    ! [X20964,X20965] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20965))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20965),X20964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,X20965)),hAPP(c_Int_Onat,X20964)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__distrib])]) ).

fof(i_0_9559,plain,
    ! [X24052,X24053] :
      ( ~ c_Nat__Transfer_Ois__nat(X24053)
      | ~ c_Nat__Transfer_Ois__nat(X24052)
      | c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24053,X24052) = 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,X24053),hAPP(c_Int_Onat,X24052))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__functions])]) ).

fof(i_0_9560,plain,
    ! [X31530] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(X31530)),c_List_Otranspose__rel(X31530)),c_List_Olist_ONil(tc_List_Olist(X31530))))
      | c_List_Otranspose(X31530,c_List_Olist_ONil(tc_List_Olist(X31530))) = c_List_Olist_ONil(tc_List_Olist(X31530)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpose_Opsimps_I1_J])]) ).

fof(i_0_9561,plain,
    ! [X21211,X21212,X21213] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21213),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21212,X21211)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21213),X21212),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21213),X21211)),
    inference(variable_rename,[status(thm)],[fact_mod__mult__distrib2]) ).

fof(i_0_9562,plain,
    ! [X20152,X20153] :
      ( ( X20153 != X20152
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20153) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20152) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20153) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X20152)
        | X20153 = X20152 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__relations_I3_J])]) ).

fof(i_0_9563,plain,
    ! [X30093,X30094,X30095] : hAPP(c_List_Oset(X30095),hAPP(hAPP(c_List_Oappend(X30095),X30094),X30093)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30095,tc_HOL_Obool)),hAPP(c_List_Oset(X30095),X30094)),hAPP(c_List_Oset(X30095),X30093)),
    inference(variable_rename,[status(thm)],[fact_set__append]) ).

fof(i_0_9564,plain,
    ! [X17551,X17552] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17552),X17551))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17552)),hAPP(c_Nat_OSuc,X17551))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mono])]) ).

fof(i_0_9565,plain,
    ! [X16957,X16958,X16959,X16960] :
      ( ( hAPP(hAPP(c_Set_Oinsert(X16960),X16959),X16958) != hAPP(hAPP(c_Set_Oinsert(X16960),X16959),X16957)
        | X16958 = X16957
        | hBOOL(hAPP(hAPP(c_member(X16960),X16959),X16957))
        | hBOOL(hAPP(hAPP(c_member(X16960),X16959),X16958)) )
      & ( X16958 != X16957
        | hAPP(hAPP(c_Set_Oinsert(X16960),X16959),X16958) = hAPP(hAPP(c_Set_Oinsert(X16960),X16959),X16957)
        | hBOOL(hAPP(hAPP(c_member(X16960),X16959),X16957))
        | hBOOL(hAPP(hAPP(c_member(X16960),X16959),X16958)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5900])])]) ).

fof(i_0_9566,plain,
    ! [X20289,X20290,X20291,X20292] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(X20292),X20291),X20290) != hAPP(hAPP(c_Power_Opower__class_Opower(X20292),X20291),X20289)
        | X20290 = X20289
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20292),c_Groups_Oone__class_Oone(X20292)),X20291))
        | ~ class_Rings_Olinordered__semidom(X20292) )
      & ( X20290 != X20289
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20292),X20291),X20290) = hAPP(hAPP(c_Power_Opower__class_Opower(X20292),X20291),X20289)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20292),c_Groups_Oone__class_Oone(X20292)),X20291))
        | ~ class_Rings_Olinordered__semidom(X20292) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__inject__exp])])]) ).

fof(i_0_9567,plain,
    ! [X29980,X29981,X29982] : c_List_Olistset(X29982,hAPP(hAPP(c_List_Olist_OCons(tc_fun(X29982,tc_HOL_Obool)),X29981),X29980)) = c_List_Oset__Cons(X29982,X29981,c_List_Olistset(X29982,X29980)),
    inference(variable_rename,[status(thm)],[fact_listset_Osimps_I2_J]) ).

fof(i_0_9568,plain,
    ! [X32875,X32876,X32877] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32876),X32877),c_Orderings_Obot__class_Obot(tc_fun(X32876,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(X32875,X32877)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bex__empty])]) ).

fof(i_0_9569,plain,
    ! [X26968,X26969] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26969)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26969),X26968))
      | c_Complete__Lattice_OSup__class_OSup(X26969,X26968) = hAPP(hAPP(c_Finite__Set_Ofold(X26969,X26969,c_Lattices_Osemilattice__sup__class_Osup(X26969)),c_Orderings_Obot__class_Obot(X26969)),X26968) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fold__sup])]) ).

fof(i_0_9570,plain,
    ! [X26745,X26746] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26746)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26746),X26745))
      | c_Complete__Lattice_OInf__class_OInf(X26746,X26745) = hAPP(hAPP(c_Finite__Set_Ofold(X26746,X26746,c_Lattices_Osemilattice__inf__class_Oinf(X26746)),c_Orderings_Otop__class_Otop(X26746)),X26745) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fold__inf])]) ).

fof(i_0_9571,plain,
    ! [X20214,X20215] :
      ( ( X20215 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20214),X20215) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X20215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20214),X20215) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20214),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20214),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20215),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_9572,plain,
    ! [X24118,X24119,X24120] :
      ( ~ class_Groups_Oordered__ab__group__add(X24120)
      | hAPP(c_Set_Oimage(X24120,X24120,c_Groups_Ouminus__class_Ouminus(X24120)),c_SetInterval_Oord__class_OatLeastAtMost(X24120,X24119,X24118)) = c_SetInterval_Oord__class_OatLeastAtMost(X24120,hAPP(c_Groups_Ouminus__class_Ouminus(X24120),X24118),hAPP(c_Groups_Ouminus__class_Ouminus(X24120),X24119)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastAtMost])]) ).

fof(i_0_9573,plain,
    ! [X21652,X21653,X21654] :
      ( ~ class_Groups_Oordered__ab__group__add(X21654)
      | hAPP(c_Set_Oimage(X21654,X21654,c_Groups_Ouminus__class_Ouminus(X21654)),c_SetInterval_Oord__class_OgreaterThanLessThan(X21654,X21653,X21652)) = c_SetInterval_Oord__class_OgreaterThanLessThan(X21654,hAPP(c_Groups_Ouminus__class_Ouminus(X21654),X21652),hAPP(c_Groups_Ouminus__class_Ouminus(X21654),X21653)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThanLessThan])]) ).

fof(i_0_9574,plain,
    ! [X16840,X16841,X16842] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X16842),X16840),X16841))
        | hAPP(c_Finite__Set_Ocard(X16842),hAPP(hAPP(c_Set_Oinsert(X16842),X16840),X16841)) = hAPP(c_Finite__Set_Ocard(X16842),X16841)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16842),X16841)) )
      & ( hBOOL(hAPP(hAPP(c_member(X16842),X16840),X16841))
        | hAPP(c_Finite__Set_Ocard(X16842),hAPP(hAPP(c_Set_Oinsert(X16842),X16840),X16841)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X16842),X16841))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16842),X16841)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5901])])]) ).

fof(i_0_9575,plain,
    ! [X24386] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24386)) = 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),X24386))),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc__eq__insert__0]) ).

fof(i_0_9576,plain,
    ! [X22179,X22180] : c_Code__Numeral_Odiv__mod__code__numeral(X22180,X22179) = 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),X22180),X22179)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X22180,X22179)),
    inference(variable_rename,[status(thm)],[fact_div__mod__code__numeral__def]) ).

fof(i_0_9577,plain,
    ! [X22006,X22007] : c_Divides_Odivmod__int(X22007,X22006) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22007),X22006)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X22007,X22006)),
    inference(variable_rename,[status(thm)],[fact_divmod__int__mod__div]) ).

fof(i_0_9578,plain,
    ! [X21227,X21228] : 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,X21228,X21227)),X21227) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21228),X21227),
    inference(variable_rename,[status(thm)],[fact_zminus__zmod]) ).

fof(i_0_9579,plain,
    ! [X20800,X20801] :
      ( ( hAPP(c_Int_Onat,X20801) != hAPP(c_Int_Onat,X20800)
        | X20801 = X20800
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20800))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20801)) )
      & ( X20801 != X20800
        | hAPP(c_Int_Onat,X20801) = hAPP(c_Int_Onat,X20800)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20800))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20801)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__nat__nat__iff])])]) ).

fof(i_0_9580,plain,
    ! [X20798,X20799] :
      ( ( hAPP(c_Int_Onat,X20799) != hAPP(c_Int_Onat,X20798)
        | X20799 = X20798
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20798))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20799)) )
      & ( X20799 != X20798
        | hAPP(c_Int_Onat,X20799) = hAPP(c_Int_Onat,X20798)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20798))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20799)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__relations_I1_J])])]) ).

fof(i_0_9581,plain,
    ! [X20085,X20086,X20088,X20089,X20090] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20086),X20085))
        | X20085 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20086),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk57_2(X20085,X20086)))) )
      & ( X20088 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20089),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X20090)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20089),X20088)) ) ),
    inference(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_9582,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_5902]) ).

fof(i_0_9583,plain,
    ! [X21316,X21317] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21317),X21316)),X21316) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21317),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21317,X21316)),
    inference(variable_rename,[status(thm)],[fact_div__mod__equality_H]) ).

fof(i_0_9584,plain,
    ! [X18113,X18114] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18114),X18113))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18113),X18114)),X18114) = X18113 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse2])]) ).

fof(i_0_9585,plain,
    ! [X20105] :
      ( ( ~ 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),X20105)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20105)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20105))
        | 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),X20105))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__int__conv])]) ).

fof(i_0_9586,plain,
    ! [X20960,X20961] :
      ( ( X20961 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20960))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20961) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20960) )
      & ( 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),X20960)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20961) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20960) )
      & ( X20961 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20960))
        | ~ 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),X20960)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20961) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20960) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff__number__of])])]) ).

fof(i_0_9587,plain,
    ! [X23952,X23953] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X23953,tc_HOL_Obool)),hAPP(c_Set_OPow(X23953),X23952)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(X23953),X23952)) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23953),X23952))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X23953,tc_HOL_Obool)),hAPP(c_Set_OPow(X23953),X23952))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Pow__iff])]) ).

fof(i_0_9588,plain,
    ! [X28212,X28213,X28214,X28215,X28216] :
      ( ~ hBOOL(hAPP(hAPP(X28216,X28215),X28214))
      | hBOOL(hAPP(c_Predicate_ODomainP(X28213,X28212,X28216),X28215)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_DomainP_Ointros])]) ).

fof(i_0_9589,plain,
    ! [X28017,X28018,X28019,X28020,X28021] :
      ( ~ hBOOL(hAPP(hAPP(X28021,X28020),X28019))
      | hBOOL(hAPP(c_Predicate_ORangeP(X28018,X28017,X28021),X28019)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_RangeP_Ointros])]) ).

fof(i_0_9590,plain,
    ! [X32439,X32440,X32441] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32441)),c_List_Osplice(X32441,X32440,X32439)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32441)),X32440)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32441)),X32439)),
    inference(variable_rename,[status(thm)],[fact_length__splice]) ).

fof(i_0_9591,plain,
    ! [X29914,X29915] :
      ( ( ~ 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(X29915)),X29914)))
        | X29914 != c_List_Olist_ONil(X29915) )
      & ( X29914 = c_List_Olist_ONil(X29915)
        | 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(X29915)),X29914))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__greater__0__conv])]) ).

fof(i_0_9592,plain,
    ! [X25747,X25748,X25749] :
      ( ~ class_Orderings_Oorder(X25749)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25749,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25749,X25748),X25747)),hAPP(c_SetInterval_Oord__class_OatLeast(X25749),X25747)) = c_Orderings_Obot__class_Obot(tc_fun(X25749,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I8_J])]) ).

fof(i_0_9593,plain,
    ! [X17757,X17758] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17757),hAPP(c_Nat_OSuc,X17758)))
        | X17757 = X17758
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17758),X17757)) )
      & ( X17757 != X17758
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17757),hAPP(c_Nat_OSuc,X17758)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17758),X17757)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq])])]) ).

cnf(i_0_9594,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_5903]) ).

fof(i_0_9595,plain,
    ! [X20895,X20896] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20896))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20896),X20895))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X20896,X20895) = X20896 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__pos__pos__trivial])]) ).

fof(i_0_9596,plain,
    ! [X25719,X25720] :
      ( ~ class_Orderings_Oorder(X25720)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25720,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25720),X25719)),hAPP(c_SetInterval_Oord__class_OatLeast(X25720),X25719)) = hAPP(hAPP(c_Set_Oinsert(X25720),X25719),c_Orderings_Obot__class_Obot(tc_fun(X25720,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__Int__atLeast])]) ).

fof(i_0_9597,plain,
    ! [X17708,X17709] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17709),X17708))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17708),hAPP(c_Nat_OSuc,X17709))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17708),hAPP(c_Nat_OSuc,X17709)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17709),X17708)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5904])]) ).

cnf(i_0_9598,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5905]) ).

fof(i_0_9599,plain,
    ! [X30084,X30085,X30086] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30086)),hAPP(hAPP(c_List_Oappend(X30086),X30085),X30084)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30086)),X30085)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30086)),X30084)),
    inference(variable_rename,[status(thm)],[fact_length__append]) ).

fof(i_0_9600,plain,
    ! [X21656,X21657] :
      ( ( X21657 != X21656
        | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21657) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21656)
        | ~ c_Nat__Transfer_Onat__set(X21656)
        | ~ c_Nat__Transfer_Onat__set(X21657) )
      & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21657) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21656)
        | X21657 = X21656
        | ~ c_Nat__Transfer_Onat__set(X21656)
        | ~ c_Nat__Transfer_Onat__set(X21657) ) ),
    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_9601,plain,
    ! [X21891,X21892,X21893,X21894,X21895] :
      ( ~ class_Rings_Ocomm__semiring__1(X21894)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21893),X21892))
      | ~ hBOOL(hAPP(hAPP(c_member(X21893),X21895),X21892))
      | hAPP(X21891,X21895) != c_Groups_Ozero__class_Ozero(X21894)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21893,X21894),X21891),X21892) = c_Groups_Ozero__class_Ozero(X21894) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__zero])])]) ).

fof(i_0_9602,plain,
    ! [X20783,X20784,X20785] :
      ( ( X20785 != 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),X20785),X20784)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20785),X20783)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X20785 = 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),X20785),X20784)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20785),X20783)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20784),X20783) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__div__cancel__disj])]) ).

fof(i_0_9603,plain,
    ! [X23943,X23944] : hBOOL(hAPP(hAPP(c_member(tc_fun(X23944,tc_HOL_Obool)),X23943),hAPP(c_Set_OPow(X23944),X23943))),
    inference(variable_rename,[status(thm)],[fact_Pow__top]) ).

fof(i_0_9604,plain,
    ! [X31849,X31850,X31851] : hAPP(c_List_Orev(X31851),hAPP(hAPP(c_List_Olist_OCons(X31851),X31850),X31849)) = hAPP(hAPP(c_List_Oappend(X31851),hAPP(c_List_Orev(X31851),X31849)),hAPP(hAPP(c_List_Olist_OCons(X31851),X31850),c_List_Olist_ONil(X31851))),
    inference(variable_rename,[status(thm)],[fact_rev_Osimps_I2_J]) ).

cnf(i_0_9605,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_5906]) ).

fof(i_0_9606,plain,
    ! [X20473,X20474] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20474),X20473))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20474),X20473) = 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_9607,plain,
    ! [X20460,X20461] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20461),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)),X20461))
        | X20460 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20461),X20460) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20460),X20461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20461))
        | X20460 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20461),X20460) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20461),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20461),X20460))
        | X20460 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20461),X20460) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20460),X20461))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20461),X20460))
        | X20460 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20461),X20460) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X20460 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20461),X20460) = 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)),X20461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20461),X20460))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20461),X20460) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20461),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20460),X20461))
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20461),X20460) = 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_9608,plain,
    ! [X25666,X25667] :
      ( ~ class_Lattices_Olattice(X25667)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25667),X25666))
      | X25666 = c_Orderings_Obot__class_Obot(tc_fun(X25667,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25667),c_Big__Operators_Olattice__class_OInf__fin(X25667,X25666)),c_Big__Operators_Olattice__class_OSup__fin(X25667,X25666))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__le__Sup])]) ).

fof(i_0_9609,plain,
    ! [X32517,X32518,X32519,X32520] : hAPP(hAPP(c_List_Omap(X32520,X32519),hAPP(c_COMBK(X32519,X32520),X32518)),X32517) = c_List_Oreplicate(X32519,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32520)),X32517),X32518),
    inference(variable_rename,[status(thm)],[fact_map__replicate__const]) ).

fof(i_0_9610,plain,
    ! [X33079,X33080,X33081,X33082,X33083] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33083,X33082)
      | ~ hBOOL(hAPP(hAPP(X33082,X33081),X33080))
      | ~ hBOOL(hAPP(hAPP(X33082,X33080),X33079))
      | hBOOL(hAPP(hAPP(X33082,X33081),X33079)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__transp])]) ).

fof(i_0_9611,plain,
    ! [X32940,X32941,X32942,X32943,X32944] :
      ( ~ c_Predicate_Otransp(X32944,X32943)
      | ~ hBOOL(hAPP(hAPP(X32943,X32942),X32941))
      | ~ hBOOL(hAPP(hAPP(X32943,X32941),X32940))
      | hBOOL(hAPP(hAPP(X32943,X32942),X32940)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transpE])]) ).

fof(i_0_9612,plain,
    ! [X26676,X26677,X26678,X26679,X26680] :
      ( ~ c_Equiv__Relations_Oequivp(X26680,X26679)
      | ~ hBOOL(hAPP(hAPP(X26679,X26678),X26677))
      | ~ hBOOL(hAPP(hAPP(X26679,X26677),X26676))
      | hBOOL(hAPP(hAPP(X26679,X26678),X26676)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__transp])]) ).

fof(i_0_9613,plain,
    ! [X17296,X17297,X17298,X17299,X17300] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17300,X17299,X17298)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X17300),X17297))
      | X17297 = c_Orderings_Obot__class_Obot(tc_fun(X17300,tc_HOL_Obool))
      | hAPP(X17298,hAPP(hAPP(c_Set_Oinsert(X17300),X17296),X17297)) = hAPP(hAPP(X17299,X17296),hAPP(X17298,X17297)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oinsert__idem])]) ).

fof(i_0_9614,plain,
    ! [X21205,X21206,X21207,X21208] :
      ( ~ class_Divides_Oring__div(X21208)
      | c_Divides_Odiv__class_Omod(X21208,X21207,X21206) != c_Divides_Odiv__class_Omod(X21208,X21205,X21206)
      | c_Divides_Odiv__class_Omod(X21208,hAPP(c_Groups_Ouminus__class_Ouminus(X21208),X21207),X21206) = c_Divides_Odiv__class_Omod(X21208,hAPP(c_Groups_Ouminus__class_Ouminus(X21208),X21205),X21206) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__minus__cong])]) ).

fof(i_0_9615,plain,
    ! [X31203,X31204] : hAPP(c_Set_Oimage(tc_List_Olist(X31204),tc_fun(X31204,tc_HOL_Obool),c_List_Oset(X31204)),hAPP(c_List_Oset(tc_List_Olist(X31204)),c_Enum_Osublists(X31204,X31203))) = hAPP(c_Set_OPow(X31204),hAPP(c_List_Oset(X31204),X31203)),
    inference(variable_rename,[status(thm)],[fact_sublists__powset]) ).

fof(i_0_9616,plain,
    ! [X27099,X27100] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X27100,tc_HOL_Obool),X27099) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X27100,tc_HOL_Obool),tc_fun(X27100,tc_HOL_Obool)),X27099),c_COMBI(tc_fun(X27100,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Union__def]) ).

fof(i_0_9617,plain,
    ! [X26981,X26982] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X26982,tc_HOL_Obool),X26981) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X26982,tc_HOL_Obool),tc_fun(X26982,tc_HOL_Obool)),X26981),c_COMBI(tc_fun(X26982,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_Inter__def]) ).

fof(i_0_9618,plain,
    ! [X31928,X31929,X31930,X31931] :
      ( ( ~ hBOOL(hAPP(X31931,X31930))
        | c_List_OtakeWhile(X31929,X31931,hAPP(hAPP(c_List_Olist_OCons(X31929),X31930),X31928)) = hAPP(hAPP(c_List_Olist_OCons(X31929),X31930),c_List_OtakeWhile(X31929,X31931,X31928)) )
      & ( hBOOL(hAPP(X31931,X31930))
        | c_List_OtakeWhile(X31929,X31931,hAPP(hAPP(c_List_Olist_OCons(X31929),X31930),X31928)) = c_List_Olist_ONil(X31929) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5907])]) ).

fof(i_0_9619,plain,
    ! [X25968] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25968)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | X25968 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( X25968 != 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),X25968)),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_9620,plain,
    ! [X20084] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20084)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X20084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X20084 != 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),X20084)),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_9621,plain,
    ! [X20971,X20972] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20972))
      | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X20972)),X20971) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20972),X20971)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J])]) ).

fof(i_0_9622,plain,
    ! [X20973,X20974] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20974))
      | hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20974),X20973)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,X20974)),X20973) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__power__eq])]) ).

fof(i_0_9623,plain,
    ! [X18046,X18047,X18048] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18048),X18047)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18048),X18046)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18047),X18046),
    inference(variable_rename,[status(thm)],[fact_diff__cancel]) ).

fof(i_0_9624,plain,
    ! [X18043,X18044,X18045] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18045),X18044)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18043),X18044)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18045),X18043),
    inference(variable_rename,[status(thm)],[fact_diff__cancel2]) ).

fof(i_0_9625,plain,
    ! [X20167,X20168,X20169] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20169),X20168)),X20167) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X20169),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20168),X20167)),
    inference(variable_rename,[status(thm)],[fact_zpower__zpower]) ).

fof(i_0_9626,plain,
    ! [X19456,X19457,X19458] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19458),X19457)),X19456) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19458),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19457),X19456)),
    inference(variable_rename,[status(thm)],[fact_zmult__assoc]) ).

fof(i_0_9627,plain,
    ! [X18938,X18939,X18940] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18940),X18939)),X18938) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18939),X18938)),
    inference(variable_rename,[status(thm)],[fact_nat__mult__assoc]) ).

fof(i_0_9628,plain,
    ! [X19478,X19479,X19480] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19480),X19479)),X19478) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19479),X19478)),
    inference(variable_rename,[status(thm)],[fact_zadd__assoc]) ).

fof(i_0_9629,plain,
    ! [X17827,X17828,X17829] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17829),X17828)),X17827) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17829),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17828),X17827)),
    inference(variable_rename,[status(thm)],[fact_nat__add__assoc]) ).

fof(i_0_9630,plain,
    ! [X18049,X18050,X18051] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18051),X18050)),X18049) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18051),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18050),X18049)),
    inference(variable_rename,[status(thm)],[fact_diff__diff__left]) ).

fof(i_0_9631,plain,
    ! [X20732,X20733,X20734] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20734),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20733),X20732)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20734),X20733)),X20732),
    inference(variable_rename,[status(thm)],[fact_div__mult2__eq]) ).

fof(i_0_9632,plain,
    ! [X28280,X28281,X28282] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X28281),X28282),c_Orderings_Obot__class_Obot(tc_fun(X28281,tc_HOL_Obool))))
      | hBOOL(hAPP(X28280,X28282)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ball__empty])]) ).

fof(i_0_9633,plain,
    ! [X24945,X24946,X24947] :
      ( ~ class_Orderings_Oorder(X24947)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24947,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24947),X24946)),c_SetInterval_Oord__class_OgreaterThanAtMost(X24947,X24946,X24945)) = c_Orderings_Obot__class_Obot(tc_fun(X24947,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I3_J])]) ).

fof(i_0_9634,plain,
    ! [X24966,X24967,X24968] :
      ( ~ class_Orderings_Oorder(X24968)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24968,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X24968),X24967)),c_SetInterval_Oord__class_OgreaterThanLessThan(X24968,X24967,X24966)) = c_Orderings_Obot__class_Obot(tc_fun(X24968,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I1_J])]) ).

fof(i_0_9635,plain,
    ! [X25351,X25352,X25353] :
      ( ~ class_Orderings_Oorder(X25353)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25353,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X25353),X25352)),c_SetInterval_Oord__class_OatLeastAtMost(X25353,X25352,X25351)) = c_Orderings_Obot__class_Obot(tc_fun(X25353,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I4_J])]) ).

fof(i_0_9636,plain,
    ! [X20889,X20890] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20890),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20889),X20890))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X20890,X20889) = X20890 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__neg__neg__trivial])]) ).

fof(i_0_9637,plain,
    ! [X30806,X30807,X30808,X30809] : hAPP(c_List_Oset(X30809),hAPP(hAPP(c_List_Omap(X30808,X30809),X30807),X30806)) = hAPP(c_Set_Oimage(X30808,X30809,X30807),hAPP(c_List_Oset(X30808),X30806)),
    inference(variable_rename,[status(thm)],[fact_set__map]) ).

fof(i_0_9638,plain,
    ! [X30228,X30229,X30230] : hAPP(hAPP(c_List_Oappend(X30230),hAPP(hAPP(c_List_Otake(X30230),X30229),X30228)),hAPP(hAPP(c_List_Odrop(X30230),X30229),X30228)) = X30228,
    inference(variable_rename,[status(thm)],[fact_append__take__drop__id]) ).

fof(i_0_9639,plain,
    ! [X20009] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20009)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[i_0_5908]) ).

fof(i_0_9640,plain,
    ! [X21195,X21196] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21196),X21195) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21196,X21195)),X21195),
    inference(variable_rename,[status(thm)],[fact_mod__Suc__eq__Suc__mod]) ).

fof(i_0_9641,plain,
    ! [X20120] :
      ( ( ~ 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),X20120)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20120)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X20120))
        | 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),X20120))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__0__number__of])]) ).

fof(i_0_9642,plain,
    ! [X32251,X32252,X32253,X32254] :
      ( ( ~ c_List_Olist__ex(X32254,X32253,hAPP(hAPP(c_List_Oappend(X32254),X32252),X32251))
        | c_List_Olist__ex(X32254,X32253,X32252)
        | c_List_Olist__ex(X32254,X32253,X32251) )
      & ( ~ c_List_Olist__ex(X32254,X32253,X32252)
        | c_List_Olist__ex(X32254,X32253,hAPP(hAPP(c_List_Oappend(X32254),X32252),X32251)) )
      & ( ~ c_List_Olist__ex(X32254,X32253,X32251)
        | c_List_Olist__ex(X32254,X32253,hAPP(hAPP(c_List_Oappend(X32254),X32252),X32251)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__append])])]) ).

fof(i_0_9643,plain,
    ! [X20482,X20483] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20483),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20482),X20483))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20483),X20482) = 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_9644,plain,
    ( c_Int_OMin = X1
    | c_Int_OMin != c_Int_OBit1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5909]) ).

cnf(i_0_9645,plain,
    ( X1 = c_Int_OMin
    | c_Int_OBit1(X1) != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[i_0_5910]) ).

fof(i_0_9646,plain,
    ! [X29493,X29494,X29495,X29496] : hAPP(hAPP(c_List_Otake(X29496),hAPP(c_Nat_OSuc,X29495)),hAPP(hAPP(c_List_Olist_OCons(X29496),X29494),X29493)) = hAPP(hAPP(c_List_Olist_OCons(X29496),X29494),hAPP(hAPP(c_List_Otake(X29496),X29495),X29493)),
    inference(variable_rename,[status(thm)],[fact_take__Suc__Cons]) ).

fof(i_0_9647,plain,
    ! [X32630,X32631,X32632] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X32632)
      | ~ class_Lazy__Sequence_Osmall__lazy(X32631)
      | c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(X32632,X32631),X32630) = c_Lazy__Sequence_Oproduct(X32632,X32631,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X32632,X32630),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(X32631,X32630)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_small__lazy__prod__def])]) ).

fof(i_0_9648,plain,
    ! [X30755,X30756,X30757,X30758,X30759,X30760,X30761] :
      ( hAPP(hAPP(c_List_Omap(X30761,X30760),X30759),X30758) != hAPP(hAPP(c_List_Omap(X30757,X30760),X30756),X30755)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30761)),X30758) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30757)),X30755) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__eq__imp__length__eq])]) ).

cnf(i_0_9649,plain,
    c_Int_OBit1(X1) != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[i_0_5911]) ).

cnf(i_0_9650,plain,
    c_Int_OPls != c_Int_OBit1(X1),
    inference(split_conjunct,[status(thm)],[i_0_5912]) ).

fof(i_0_9651,plain,
    ! [X31205,X31206] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31206))),c_Enum_Osublists(X31206,X31205)) = 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(X31206)),X31205)),
    inference(variable_rename,[status(thm)],[fact_length__sublists]) ).

fof(i_0_9652,plain,
    ! [X20836] : 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)),X20836)) = X20836,
    inference(variable_rename,[status(thm)],[fact_transfer__int__nat__set__return__embed]) ).

fof(i_0_9653,plain,
    ! [X22351,X22352,X22353,X22354,X22355] :
      ( hAPP(c_Product__Type_Ofst(X22355,X22354),hAPP(hAPP(c_Product__Type_OPair(X22355,X22354),X22353),X22352)) != X22351
      | X22353 = X22351 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fst__eqD])]) ).

fof(i_0_9654,plain,
    ! [X22360,X22361,X22362,X22363,X22364] :
      ( hAPP(c_Product__Type_Osnd(X22364,X22363),hAPP(hAPP(c_Product__Type_OPair(X22364,X22363),X22362),X22361)) != X22360
      | X22361 = X22360 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snd__eqD])]) ).

cnf(i_0_9655,plain,
    c_Relation_Osym(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5913]) ).

cnf(i_0_9656,plain,
    c_Relation_Oantisym(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5914]) ).

cnf(i_0_9657,plain,
    c_Relation_Otrans(X1,c_Relation_OId(X1)),
    inference(split_conjunct,[status(thm)],[i_0_5915]) ).

cnf(i_0_9658,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_5893]) ).

cnf(i_0_9659,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_5894]) ).

fof(i_0_9660,plain,
    ! [X21675] :
      ( ~ c_Nat__Transfer_Onat__set(X21675)
      | 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),X21675)) = X21675 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__set__return__embed])]) ).

fof(i_0_9661,plain,
    ! [X23598,X23599] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X23599,X23599)),X23598))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X23599),hAPP(c_Relation_OField(X23599),X23598))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__Field])]) ).

fof(i_0_9662,plain,
    ! [X24181,X24182,X24183] :
      ( ~ class_Groups_Oordered__ab__group__add(X24183)
      | hAPP(c_Set_Oimage(X24183,X24183,c_Groups_Ouminus__class_Ouminus(X24183)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24183,X24182),X24181)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X24183,hAPP(c_Groups_Ouminus__class_Ouminus(X24183),X24181),hAPP(c_Groups_Ouminus__class_Ouminus(X24183),X24182)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeastLessThan])]) ).

fof(i_0_9663,plain,
    ! [X17720,X17721] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17721),X17720))
      | hAPP(c_Nat_OSuc,X17721) = X17720
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17721)),X17720)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__lessI])]) ).

fof(i_0_9664,plain,
    ! [X18944,X18946,X18947,X18948] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X18944))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X18946),X18944))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18946),esk31_1(X18944))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk32_2(X18947,X18948)),X18947))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X18947)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_2(X18947,X18948)),X18948))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X18947)) ) ),
    inference(distribute,[status(thm)],[inference(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_9665,plain,
    ! [X18954,X18956,X18957,X18958] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X18954))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X18956),X18954))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18956),esk33_1(X18954))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk34_2(X18957,X18958)),X18957))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X18957)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk34_2(X18957,X18958)),X18958))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X18957)) ) ),
    inference(distribute,[status(thm)],[inference(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_9666,plain,
    ! [X19929,X19930] :
      ( ( ~ 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),X19929)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19930),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19929)) = hAPP(c_Int_Onumber__class_Onumber__of(X19930),X19929)
        | ~ class_Int_Onumber__ring(X19930) )
      & ( 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),X19929)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19930),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19929)) = c_Groups_Ozero__class_Ozero(X19930)
        | ~ class_Int_Onumber__ring(X19930) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5916])])]) ).

fof(i_0_9667,plain,
    ! [X21353,X21354,X21355] :
      ( ~ class_Int_Onumber__ring(X21355)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21355),hAPP(c_Int_Onumber__class_Onumber__of(X21355),X21354)),hAPP(c_Int_Onumber__class_Onumber__of(X21355),X21353)) = hAPP(c_Int_Onumber__class_Onumber__of(X21355),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21354),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21353))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__number__of__eq])]) ).

fof(i_0_9668,plain,
    ! [X31218,X31219,X31220] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31220),X31219))
      | hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X31220)),c_Enum_On__lists(X31220,X31218,X31219))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__n__lists])]) ).

fof(i_0_9669,plain,
    ! [X16843,X16844,X16845] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16845),X16844))
      | hBOOL(hAPP(hAPP(c_member(X16845),X16843),X16844))
      | hAPP(c_Finite__Set_Ocard(X16845),hAPP(hAPP(c_Set_Oinsert(X16845),X16843),X16844)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X16845),X16844)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5917])]) ).

fof(i_0_9670,plain,
    ! [X20939] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X20939)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20939)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20939))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X20939))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__nat__eq])]) ).

fof(i_0_9671,plain,
    ! [X17675,X17676,X17677] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17677),X17676),X17675))
        | X17676 = X17675
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17677),X17676),X17675))
        | ~ class_Orderings_Olinorder(X17677) )
      & ( X17676 != X17675
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17677),X17676),X17675))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17677),X17676),X17675))
        | ~ class_Orderings_Olinorder(X17677) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5918])])]) ).

fof(i_0_9672,plain,
    ! [X30637,X30638,X30639] : c_List_Olast(X30639,hAPP(hAPP(c_List_Oappend(X30639),X30638),hAPP(hAPP(c_List_Olist_OCons(X30639),X30637),c_List_Olist_ONil(X30639)))) = X30637,
    inference(variable_rename,[status(thm)],[fact_last__snoc]) ).

fof(i_0_9673,plain,
    ! [X30154,X30155,X30156] : c_List_Obutlast(X30156,hAPP(hAPP(c_List_Oappend(X30156),X30155),hAPP(hAPP(c_List_Olist_OCons(X30156),X30154),c_List_Olist_ONil(X30156)))) = X30155,
    inference(variable_rename,[status(thm)],[fact_butlast__snoc]) ).

fof(i_0_9674,plain,
    ! [X28624,X28625] : hAPP(hAPP(c_Relation_Orel__comp(X28625,X28625,X28625),c_Transitive__Closure_Ortrancl(X28625,X28624)),c_Transitive__Closure_Ortrancl(X28625,X28624)) = c_Transitive__Closure_Ortrancl(X28625,X28624),
    inference(variable_rename,[status(thm)],[fact_rtrancl__idemp__self__comp]) ).

fof(i_0_9675,plain,
    ! [X22372,X22373,X22374] : hAPP(c_Product__Type_Ofst(X22374,X22373),X22372) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X22374,X22373,X22374),c_COMBK(X22374,X22373)),X22372),
    inference(variable_rename,[status(thm)],[fact_fst__def]) ).

fof(i_0_9676,plain,
    ! [X29414] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X29414)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X29414),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5919]) ).

fof(i_0_9677,plain,
    ! [X28870,X28871] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28871,X28871)),X28870))
      | ~ c_Wellfounded_Oacyclic(X28871,X28870)
      | c_Wellfounded_Owf(X28871,hAPP(c_Relation_Oconverse(X28871,X28871),X28870)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf__converse])]) ).

fof(i_0_9678,plain,
    ! [X17183,X17184,X17185] :
      ( ~ class_Orderings_Oorder(X17185)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17185),X17184),X17183))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17185),X17183),X17184))
      | X17183 = X17184 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I5_J])]) ).

fof(i_0_9679,plain,
    ! [X17176,X17177,X17178] :
      ( ~ class_Orderings_Oorder(X17178)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17178),X17177),X17176))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17178),X17176),X17177))
      | X17177 = X17176 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym])]) ).

fof(i_0_9680,plain,
    ! [X17157,X17158,X17159] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17159),X17157),X17158))
        | X17157 = X17158
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17159),X17158),X17157))
        | ~ class_Orderings_Oorder(X17159) )
      & ( X17157 != X17158
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17159),X17157),X17158))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17159),X17158),X17157))
        | ~ class_Orderings_Oorder(X17159) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__antisym__conv])])]) ).

fof(i_0_9681,plain,
    ! [X17151,X17152,X17153] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17153),X17152),X17151))
        | X17152 != X17151
        | ~ class_Orderings_Oorder(X17153) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17153),X17151),X17152))
        | X17152 != X17151
        | ~ class_Orderings_Oorder(X17153) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17153),X17152),X17151))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17153),X17151),X17152))
        | X17152 = X17151
        | ~ class_Orderings_Oorder(X17153) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__iff])])]) ).

fof(i_0_9682,plain,
    ! [X21310,X21311] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X21311),X21310))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21310,X21311) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21310),X21311),X21311) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__mod__geq])]) ).

fof(i_0_9683,plain,
    ! [X33837,X33838] :
      ( X33838 != X33837
      | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33838,X33837) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X33838),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_OatLeastAtMost__singleton_H])]) ).

fof(i_0_9684,plain,
    ! [X32065,X32066,X32067] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X32067),X32066),hAPP(c_List_Oset(X32067),X32065)))
      | c_List_Oinsert(X32067,X32066,X32065) = X32065 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__set__insert])]) ).

fof(i_0_9685,plain,
    ! [X32053,X32054,X32055] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X32055),X32054),hAPP(c_List_Oset(X32055),X32053)))
        | c_List_Oinsert(X32055,X32054,X32053) = X32053 )
      & ( hBOOL(hAPP(hAPP(c_member(X32055),X32054),hAPP(c_List_Oset(X32055),X32053)))
        | c_List_Oinsert(X32055,X32054,X32053) = hAPP(hAPP(c_List_Olist_OCons(X32055),X32054),X32053) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5920])]) ).

fof(i_0_9686,plain,
    ! [X17124,X17125] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17125),X17124))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17124)),X17125) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17124),X17125)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__le])]) ).

fof(i_0_9687,plain,
    ! [X17600,X17601,X17602] :
      ( ~ class_Orderings_Oorder(X17602)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17602),X17601),X17600))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17602),X17600),X17601)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5921])]) ).

fof(i_0_9688,plain,
    ! [X17563,X17564,X17565] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17565),X17564),X17563))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17565),X17563),X17564))
        | X17564 = X17563
        | ~ class_Orderings_Olinorder(X17565) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17565),X17563),X17564))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17565),X17564),X17563))
        | ~ class_Orderings_Olinorder(X17565) )
      & ( X17564 != X17563
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17565),X17564),X17563))
        | ~ class_Orderings_Olinorder(X17565) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5922])])]) ).

fof(i_0_9689,plain,
    ! [X17669,X17670,X17671] :
      ( ~ class_Orderings_Olinorder(X17671)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17671),X17670),X17669))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17671),X17669),X17670)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5923])]) ).

fof(i_0_9690,plain,
    ! [X17636,X17637,X17638] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17638),X17637),X17636))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17638),X17636),X17637))
        | ~ class_Orderings_Olinorder(X17638) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17638),X17636),X17637))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17638),X17637),X17636))
        | ~ class_Orderings_Olinorder(X17638) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5924])])]) ).

fof(i_0_9691,plain,
    ! [X17639,X17640,X17641] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17641),X17640),X17639))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17641),X17639),X17640))
        | ~ class_Orderings_Olinorder(X17641) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17641),X17639),X17640))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17641),X17640),X17639))
        | ~ class_Orderings_Olinorder(X17641) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5925])])]) ).

fof(i_0_9692,plain,
    ! [X17627,X17628,X17629] :
      ( ~ class_Orderings_Opreorder(X17629)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17629),X17628),X17627))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17629),X17627),X17628)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5926])]) ).

fof(i_0_9693,plain,
    ! [X17597,X17598,X17599] :
      ( ~ class_Orderings_Opreorder(X17599)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17599),X17598),X17597))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17599),X17597),X17598)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5927])]) ).

fof(i_0_9694,plain,
    ! [X17588,X17589,X17590] :
      ( ~ class_Orderings_Opreorder(X17590)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17590),X17589),X17588))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17590),X17588),X17589)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5928])]) ).

fof(i_0_9695,plain,
    ! [X17585,X17586,X17587] :
      ( ~ class_Orderings_Opreorder(X17587)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17587),X17586),X17585))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17587),X17585),X17586)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5929])]) ).

fof(i_0_9696,plain,
    ! [X25913,X25914] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25914)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25914),hAPP(c_Groups_Ouminus__class_Ouminus(X25914),X25913)),hAPP(c_Groups_Oabs__class_Oabs(X25914),X25913))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self])]) ).

fof(i_0_9697,plain,
    ! [X18263,X18264] :
      ( ~ class_Rings_Olinordered__ring(X18264)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18264),c_Groups_Ozero__class_Ozero(X18264)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18264),X18263),X18263))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__square])]) ).

fof(i_0_9698,plain,
    ! [X18153,X18154] :
      ( ~ class_Rings_Olinordered__semidom(X18154)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18154),X18153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18154),X18153),c_Groups_Oone__class_Oone(X18154)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__add__one])]) ).

fof(i_0_9699,plain,
    ! [X25892,X25893] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25893),c_Groups_Ozero__class_Ozero(X25893)),hAPP(c_Groups_Oabs__class_Oabs(X25893),X25892)))
        | X25892 != c_Groups_Ozero__class_Ozero(X25893)
        | ~ class_Groups_Oordered__ab__group__add__abs(X25893) )
      & ( X25892 = c_Groups_Ozero__class_Ozero(X25893)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25893),c_Groups_Ozero__class_Ozero(X25893)),hAPP(c_Groups_Oabs__class_Oabs(X25893),X25892)))
        | ~ class_Groups_Oordered__ab__group__add__abs(X25893) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__abs__iff])])]) ).

fof(i_0_9700,plain,
    ! [X22211,X22212,X22213,X22214] :
      ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X22214,X22213),X22212))
      | ~ hBOOL(hAPP(hAPP(X22213,X22211),X22212))
      | hBOOL(hAPP(c_Wellfounded_Oaccp(X22214,X22213),X22211)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__downward])]) ).

fof(i_0_9701,plain,
    ! [X20123,X20124] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20124),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20124)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20123)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20124),c_Int_OPls))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20124)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20123)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20124),X20123)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5930])]) ).

fof(i_0_9702,plain,
    ! [X30371,X30372] :
      ( X30372 = c_List_Olist_ONil(X30371)
      | hBOOL(hAPP(hAPP(c_member(X30371),hAPP(c_List_Ohd(X30371),X30372)),hAPP(c_List_Oset(X30371),X30372))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__in__set])]) ).

fof(i_0_9703,plain,
    ! [X33839] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33839,X33839) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X33839),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_dvd_OatLeastAtMost__singleton]) ).

fof(i_0_9704,plain,
    ! [X32652,X32653,X32654] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X32654)),c_Lazy__Sequence_Olazy__sequence_OInsert(X32654,X32653,X32652)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X32654)),X32652)),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_9705,plain,
    ! [X20172,X20173,X20174] :
      ( ~ class_Rings_Ocomm__semiring__1(X20174)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20174),hAPP(hAPP(c_Power_Opower__class_Opower(X20174),X20173),X20172)),X20173) = hAPP(hAPP(c_Power_Opower__class_Opower(X20174),X20173),hAPP(c_Nat_OSuc,X20172)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J])]) ).

fof(i_0_9706,plain,
    ! [X20296,X20297,X20298] :
      ( ~ class_Groups_Omonoid__mult(X20298)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20298),X20297),hAPP(c_Nat_OSuc,X20296)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20298),hAPP(hAPP(c_Power_Opower__class_Opower(X20298),X20297),X20296)),X20297) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc2])]) ).

fof(i_0_9707,plain,
    ! [X31313,X31314] :
      ( ~ class_Orderings_Olinorder(X31314)
      | c_List_Olinorder__class_Osorted__list__of__set(X31314,hAPP(c_List_Oset(X31314),X31313)) = c_List_Olinorder__class_Osort__key(X31314,X31314,c_COMBI(X31314),c_List_Oremdups(X31314,X31313)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__sort__remdups])]) ).

fof(i_0_9708,plain,
    ! [X29218,X29219,X29220] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29220)),hAPP(hAPP(c_List_Olist_OCons(X29220),X29219),X29218)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29220)),X29218)),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_9709,plain,
    ! [X31225,X31226,X31227] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X31227))),c_Enum_On__lists(X31227,X31226,X31225)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31227)),X31225)),X31226),
    inference(variable_rename,[status(thm)],[fact_length__n__lists]) ).

fof(i_0_9710,plain,
    ! [X19996,X19997,X19999,X20000] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19997))
        | ~ hBOOL(hAPP(X19996,X19997))
        | hBOOL(hAPP(X19996,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk52_1(X19996)))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk53_1(X19999)))
        | ~ hBOOL(hAPP(X19999,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20000))) )
      & ( hBOOL(hAPP(X19999,esk53_1(X19999)))
        | ~ hBOOL(hAPP(X19999,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20000))) ) ),
    inference(distribute,[status(thm)],[inference(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_9711,plain,
    ! [X17755,X17756] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17756),X17755))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17756)),X17755)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__leI])]) ).

fof(i_0_9712,plain,
    ! [X25652,X25653,X25654] :
      ( ~ class_Lattices_Olattice(X25654)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25654),X25653))
      | ~ hBOOL(hAPP(hAPP(c_member(X25654),X25652),X25653))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25654),X25652),c_Big__Operators_Olattice__class_OInf__fin(X25654,X25653)) = c_Big__Operators_Olattice__class_OInf__fin(X25654,X25653) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oin__idem])]) ).

fof(i_0_9713,plain,
    ! [X23510,X23511,X23512] :
      ( ~ class_Lattices_Olattice(X23512)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23512),X23511))
      | ~ hBOOL(hAPP(hAPP(c_member(X23512),X23510),X23511))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23512),X23510),c_Big__Operators_Olattice__class_OSup__fin(X23512,X23511)) = c_Big__Operators_Olattice__class_OSup__fin(X23512,X23511) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oin__idem])]) ).

fof(i_0_9714,plain,
    ! [X23006,X23007,X23008] :
      ( ~ class_Orderings_Olinorder(X23008)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23008),X23007))
      | ~ hBOOL(hAPP(hAPP(c_member(X23008),X23006),X23007))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X23008),X23006),c_Big__Operators_Olinorder__class_OMax(X23008,X23007)) = c_Big__Operators_Olinorder__class_OMax(X23008,X23007) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oin__idem])]) ).

fof(i_0_9715,plain,
    ! [X21780,X21781,X21782] :
      ( ~ class_Orderings_Olinorder(X21782)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21782),X21781))
      | ~ hBOOL(hAPP(hAPP(c_member(X21782),X21780),X21781))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21782),X21780),c_Big__Operators_Olinorder__class_OMin(X21782,X21781)) = c_Big__Operators_Olinorder__class_OMin(X21782,X21781) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oin__idem])]) ).

fof(i_0_9716,plain,
    ! [X27064,X27065,X27066] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X27066)
      | ~ hBOOL(hAPP(hAPP(c_member(X27066),X27065),X27064))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X27066),X27065),c_Complete__Lattice_OSup__class_OSup(X27066,X27064))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__upper])]) ).

cnf(i_0_9717,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_5931]) ).

fof(i_0_9718,plain,
    ! [X32266,X32267,X32268,X32269] :
      ( ( ~ c_List_Olist__ex(X32269,X32268,hAPP(hAPP(c_List_Olist_OCons(X32269),X32267),X32266))
        | hBOOL(hAPP(X32268,X32267))
        | c_List_Olist__ex(X32269,X32268,X32266) )
      & ( ~ hBOOL(hAPP(X32268,X32267))
        | c_List_Olist__ex(X32269,X32268,hAPP(hAPP(c_List_Olist_OCons(X32269),X32267),X32266)) )
      & ( ~ c_List_Olist__ex(X32269,X32268,X32266)
        | c_List_Olist__ex(X32269,X32268,hAPP(hAPP(c_List_Olist_OCons(X32269),X32267),X32266)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__simps_I1_J])])]) ).

fof(i_0_9719,plain,
    ! [X25354,X25355,X25356] :
      ( ~ class_Orderings_Oorder(X25356)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25356,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X25356),X25355)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X25356,X25355),X25354)) = c_Orderings_Obot__class_Obot(tc_fun(X25356,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ivl__disj__int_I2_J])]) ).

fof(i_0_9720,plain,
    ! [X18880,X18881] :
      ( ( X18880 != c_Orderings_Obot__class_Obot(tc_fun(X18881,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(X18881),X18880))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X18881),X18880))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X18881),X18880))) )
      & ( X18880 = c_Orderings_Obot__class_Obot(tc_fun(X18881,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18881),X18880))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X18881),X18880))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__gt__0__iff])])]) ).

fof(i_0_9721,plain,
    ! [X29426,X29427,X29428,X29429] : hAPP(hAPP(c_List_Onth(X29429),hAPP(hAPP(c_List_Olist_OCons(X29429),X29428),X29427)),hAPP(c_Nat_OSuc,X29426)) = hAPP(hAPP(c_List_Onth(X29429),X29427),X29426),
    inference(variable_rename,[status(thm)],[fact_nth__Cons__Suc]) ).

fof(i_0_9722,plain,
    ! [X30680,X30681,X30682,X30683] : hAPP(hAPP(c_List_Omap(X30683,X30682),X30681),hAPP(c_List_Otl(X30683),X30680)) = hAPP(c_List_Otl(X30682),hAPP(hAPP(c_List_Omap(X30683,X30682),X30681),X30680)),
    inference(variable_rename,[status(thm)],[fact_map__tl]) ).

fof(i_0_9723,plain,
    ! [X31800,X31801,X31802,X31803] : hAPP(c_List_Orev(X31803),hAPP(hAPP(c_List_Omap(X31802,X31803),X31801),X31800)) = hAPP(hAPP(c_List_Omap(X31802,X31803),X31801),hAPP(c_List_Orev(X31802),X31800)),
    inference(variable_rename,[status(thm)],[fact_rev__map]) ).

fof(i_0_9724,plain,
    ! [X33472,X33473,X33474] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X33474),X33473),c_Quotient_ORespects(X33474,X33472)))
        | hBOOL(hAPP(hAPP(X33472,X33473),X33473)) )
      & ( ~ hBOOL(hAPP(hAPP(X33472,X33473),X33473))
        | hBOOL(hAPP(hAPP(c_member(X33474),X33473),c_Quotient_ORespects(X33474,X33472))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__respects])]) ).

fof(i_0_9725,plain,
    ! [X16936,X16937] : ~ hBOOL(hAPP(hAPP(c_member(X16937),X16936),c_Orderings_Obot__class_Obot(tc_fun(X16937,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5932]) ).

fof(i_0_9726,plain,
    ! [X16870,X16871] : ~ hBOOL(hAPP(hAPP(c_member(X16871),X16870),c_Orderings_Obot__class_Obot(tc_fun(X16871,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[i_0_5933]) ).

fof(i_0_9727,plain,
    ! [X33874,X33875,X33876] :
      ( ~ class_Divides_Osemiring__div(X33876)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33876),X33875),X33874))
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33876),X33875),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33876),X33874),X33875)) = X33874 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__mult__div__cancel])]) ).

fof(i_0_9728,plain,
    ! [X20786,X20787,X20789,X20790] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk58_1(X20786)))
        | ~ hBOOL(hAPP(X20786,X20787)) )
      & ( hBOOL(hAPP(X20786,hAPP(c_Int_Onat,esk58_1(X20786))))
        | ~ hBOOL(hAPP(X20786,X20787)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20790))
        | ~ hBOOL(hAPP(X20789,hAPP(c_Int_Onat,X20790)))
        | hBOOL(hAPP(X20789,esk59_1(X20789))) ) ),
    inference(distribute,[status(thm)],[inference(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_9729,plain,
    ! [X18849,X18850] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X18850),X18849)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X18850),X18849)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__ge__0__finite])]) ).

cnf(i_0_9730,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_5869]) ).

fof(i_0_9731,plain,
    ! [X32300,X32301,X32302,X32303] :
      ( ( c_List_Olist__all(X32303,X32302,X32301)
        | ~ c_List_Olist__all(X32303,X32302,hAPP(hAPP(c_List_Oappend(X32303),X32301),X32300)) )
      & ( c_List_Olist__all(X32303,X32302,X32300)
        | ~ c_List_Olist__all(X32303,X32302,hAPP(hAPP(c_List_Oappend(X32303),X32301),X32300)) )
      & ( ~ c_List_Olist__all(X32303,X32302,X32301)
        | ~ c_List_Olist__all(X32303,X32302,X32300)
        | c_List_Olist__all(X32303,X32302,hAPP(hAPP(c_List_Oappend(X32303),X32301),X32300)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__append])])]) ).

fof(i_0_9732,plain,
    ! [X18851] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18851))
      | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18851),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = X18851 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__pred])]) ).

fof(i_0_9733,plain,
    ! [X17004,X17005,X17006] :
      ( hAPP(hAPP(c_Set_Oinsert(X17006),X17005),c_Orderings_Obot__class_Obot(tc_fun(X17006,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(X17006),X17004),c_Orderings_Obot__class_Obot(tc_fun(X17006,tc_HOL_Obool)))
      | X17005 = X17004 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__inject])]) ).

fof(i_0_9734,plain,
    ! [X30992] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X30992),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,X30992)) = X30992 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__inverse])]) ).

fof(i_0_9735,plain,
    ! [X22679,X22680,X22681,X22682] :
      ( ( X22680 = c_Groups_Ozero__class_Ozero(X22682)
        | X22681 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22682),hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)),X22680)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22682),X22681),X22680) != hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)
        | ~ class_Fields_Ofield__inverse__zero(X22682)
        | ~ class_Int_Onumber(X22682) )
      & ( X22680 != c_Groups_Ozero__class_Ozero(X22682)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679) = c_Groups_Ozero__class_Ozero(X22682)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22682),X22681),X22680) != hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)
        | ~ class_Fields_Ofield__inverse__zero(X22682)
        | ~ class_Int_Onumber(X22682) )
      & ( X22680 = c_Groups_Ozero__class_Ozero(X22682)
        | X22680 != c_Groups_Ozero__class_Ozero(X22682)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22682),X22681),X22680) = hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)
        | ~ class_Fields_Ofield__inverse__zero(X22682)
        | ~ class_Int_Onumber(X22682) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679) != c_Groups_Ozero__class_Ozero(X22682)
        | X22680 != c_Groups_Ozero__class_Ozero(X22682)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22682),X22681),X22680) = hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)
        | ~ class_Fields_Ofield__inverse__zero(X22682)
        | ~ class_Int_Onumber(X22682) )
      & ( X22680 = c_Groups_Ozero__class_Ozero(X22682)
        | X22681 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22682),hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)),X22680)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22682),X22681),X22680) = hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)
        | ~ class_Fields_Ofield__inverse__zero(X22682)
        | ~ class_Int_Onumber(X22682) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679) != c_Groups_Ozero__class_Ozero(X22682)
        | X22681 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22682),hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)),X22680)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22682),X22681),X22680) = hAPP(c_Int_Onumber__class_Onumber__of(X22682),X22679)
        | ~ class_Fields_Ofield__inverse__zero(X22682)
        | ~ class_Int_Onumber(X22682) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of])])]) ).

fof(i_0_9736,plain,
    ! [X22675,X22676,X22677,X22678] :
      ( ( X22675 = c_Groups_Ozero__class_Ozero(X22678)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22678),hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677)),X22675) = X22676
        | hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22678),X22676),X22675)
        | ~ class_Fields_Ofield__inverse__zero(X22678)
        | ~ class_Int_Onumber(X22678) )
      & ( X22675 != c_Groups_Ozero__class_Ozero(X22678)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) = c_Groups_Ozero__class_Ozero(X22678)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22678),X22676),X22675)
        | ~ class_Fields_Ofield__inverse__zero(X22678)
        | ~ class_Int_Onumber(X22678) )
      & ( X22675 = c_Groups_Ozero__class_Ozero(X22678)
        | X22675 != c_Groups_Ozero__class_Ozero(X22678)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22678),X22676),X22675)
        | ~ class_Fields_Ofield__inverse__zero(X22678)
        | ~ class_Int_Onumber(X22678) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) != c_Groups_Ozero__class_Ozero(X22678)
        | X22675 != c_Groups_Ozero__class_Ozero(X22678)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22678),X22676),X22675)
        | ~ class_Fields_Ofield__inverse__zero(X22678)
        | ~ class_Int_Onumber(X22678) )
      & ( X22675 = c_Groups_Ozero__class_Ozero(X22678)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22678),hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677)),X22675) != X22676
        | hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22678),X22676),X22675)
        | ~ class_Fields_Ofield__inverse__zero(X22678)
        | ~ class_Int_Onumber(X22678) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) != c_Groups_Ozero__class_Ozero(X22678)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22678),hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677)),X22675) != X22676
        | hAPP(c_Int_Onumber__class_Onumber__of(X22678),X22677) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22678),X22676),X22675)
        | ~ class_Fields_Ofield__inverse__zero(X22678)
        | ~ class_Int_Onumber(X22678) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of])])]) ).

fof(i_0_9737,plain,
    ! [X17256,X17257] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17257),hAPP(c_Nat_OSuc,X17256)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17257),X17256))
      | X17257 = hAPP(c_Nat_OSuc,X17256) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5934])]) ).

fof(i_0_9738,plain,
    ! [X17250,X17251] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17251),hAPP(c_Nat_OSuc,X17250)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17251),X17250))
        | X17251 = hAPP(c_Nat_OSuc,X17250) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17251),X17250))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17251),hAPP(c_Nat_OSuc,X17250))) )
      & ( X17251 != hAPP(c_Nat_OSuc,X17250)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17251),hAPP(c_Nat_OSuc,X17250))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__Suc__eq])])]) ).

fof(i_0_9739,plain,
    ! [X30643,X30644] :
      ( X30644 = c_List_Olist_ONil(X30643)
      | hAPP(hAPP(c_List_Oappend(X30643),c_List_Obutlast(X30643,X30644)),hAPP(hAPP(c_List_Olist_OCons(X30643),c_List_Olast(X30643,X30644)),c_List_Olist_ONil(X30643))) = X30644 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__butlast__last__id])]) ).

cnf(i_0_9740,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_5935]) ).

fof(i_0_9741,plain,
    ! [X22348,X22349,X22350] : hAPP(hAPP(c_Product__Type_OPair(X22350,X22349),hAPP(c_Product__Type_Ofst(X22350,X22349),X22348)),hAPP(c_Product__Type_Osnd(X22350,X22349),X22348)) = X22348,
    inference(variable_rename,[status(thm)],[fact_pair__collapse]) ).

fof(i_0_9742,plain,
    ! [X22345,X22346,X22347] : X22347 = hAPP(hAPP(c_Product__Type_OPair(X22346,X22345),hAPP(c_Product__Type_Ofst(X22346,X22345),X22347)),hAPP(c_Product__Type_Osnd(X22346,X22345),X22347)),
    inference(variable_rename,[status(thm)],[fact_surjective__pairing]) ).

fof(i_0_9743,plain,
    ! [X24191,X24192] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24192),X24191))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24192),hAPP(c_Nat_OSuc,X24191)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24191),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24192),X24191)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24192),X24191))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24192),hAPP(c_Nat_OSuc,X24191)) = 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_5936])]) ).

fof(i_0_9744,plain,
    ! [X30549,X30550,X30551,X30552] :
      ( ~ class_Orderings_Olinorder(X30552)
      | hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X30551,X30552,X30550),X30549),c_List_Olist_ONil(X30551)) = hAPP(hAPP(c_List_Olist_OCons(X30551),X30549),c_List_Olist_ONil(X30551)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insort__key_Osimps_I1_J])]) ).

fof(i_0_9745,plain,
    ! [X32062,X32063,X32064] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X32064),X32063))
      | hBOOL(hAPP(c_List_Odistinct(X32064),c_List_Oinsert(X32064,X32062,X32063))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__insert])]) ).

fof(i_0_9746,plain,
    ! [X31937,X31938,X31939] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31939),X31938))
      | hBOOL(hAPP(c_List_Odistinct(X31939),c_List_OtakeWhile(X31939,X31937,X31938))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile])]) ).

fof(i_0_9747,plain,
    ! [X29832,X29833,X29834] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29834),X29833))
      | hBOOL(hAPP(c_List_Odistinct(X29834),c_List_Oremove1(X29834,X29832,X29833))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remove1])]) ).

fof(i_0_9748,plain,
    ! [X29776,X29777,X29778] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29778),X29777))
      | hBOOL(hAPP(c_List_Odistinct(X29778),c_List_Osublist(X29778,X29777,X29776))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__sublistI])]) ).

fof(i_0_9749,plain,
    ! [X32655,X32656,X32657,X32658] : c_Lazy__Sequence_Oappend(X32658,c_Lazy__Sequence_Olazy__sequence_OInsert(X32658,X32657,X32656),X32655) = c_Lazy__Sequence_Olazy__sequence_OInsert(X32658,X32657,c_Lazy__Sequence_Oappend(X32658,X32656,X32655)),
    inference(variable_rename,[status(thm)],[fact__01]) ).

fof(i_0_9750,plain,
    ! [X29861,X29862,X29863,X29864] : c_List_Oremove1(X29864,X29863,c_List_Oremove1(X29864,X29862,X29861)) = c_List_Oremove1(X29864,X29862,c_List_Oremove1(X29864,X29863,X29861)),
    inference(variable_rename,[status(thm)],[fact_remove1__commute]) ).

fof(i_0_9751,plain,
    ! [X19718,X19719,X19720,X19721,X19722,X19723] :
      ( ~ c_Finite__Set_Ofun__left__comm(X19723,X19722,X19721)
      | hAPP(hAPP(X19721,X19720),hAPP(hAPP(X19721,X19719),X19718)) = hAPP(hAPP(X19721,X19719),hAPP(hAPP(X19721,X19720),X19718)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofun__left__comm])]) ).

fof(i_0_9752,plain,
    ! [X25318,X25319,X25320] :
      ( ~ class_Lattices_Olattice(X25320)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25320),X25319))
      | ~ hBOOL(hAPP(hAPP(c_member(X25320),X25318),X25319))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25320),X25318),c_Big__Operators_Olattice__class_OSup__fin(X25320,X25319)) = X25318 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__Sup__absorb])]) ).

fof(i_0_9753,plain,
    ! [X25649,X25650,X25651] :
      ( ~ class_Lattices_Olattice(X25651)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25651),X25650))
      | ~ hBOOL(hAPP(hAPP(c_member(X25651),X25649),X25650))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25651),X25649),c_Big__Operators_Olattice__class_OInf__fin(X25651,X25650)) = X25649 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__Inf__absorb])]) ).

fof(i_0_9754,plain,
    ! [X28248] : c_Wellfounded_OwfP(X28248,hAPP(c_COMBK(tc_fun(X28248,tc_HOL_Obool),X28248),hAPP(c_COMBK(tc_HOL_Obool,X28248),c_fFalse))),
    inference(variable_rename,[status(thm)],[fact_wfP__empty]) ).

fof(i_0_9755,plain,
    ! [X33223,X33224] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk528_2(X33223,X33224)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | hBOOL(hAPP(X33224,X33223)) )
      & ( ~ hBOOL(hAPP(X33224,hAPP(c_Code__Numeral_Oof__nat,esk528_2(X33223,X33224))))
        | hBOOL(hAPP(X33224,X33223)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__induct])])])]) ).

fof(i_0_9756,plain,
    ! [X31453,X31454,X31455,X31456] :
      ( ( ~ hBOOL(hAPP(X31456,X31455))
        | hAPP(c_List_Ofilter(X31454,X31456),hAPP(hAPP(c_List_Olist_OCons(X31454),X31455),X31453)) = hAPP(hAPP(c_List_Olist_OCons(X31454),X31455),hAPP(c_List_Ofilter(X31454,X31456),X31453)) )
      & ( hBOOL(hAPP(X31456,X31455))
        | hAPP(c_List_Ofilter(X31454,X31456),hAPP(hAPP(c_List_Olist_OCons(X31454),X31455),X31453)) = hAPP(c_List_Ofilter(X31454,X31456),X31453) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5937])]) ).

fof(i_0_9757,plain,
    ! [X33913,X33914,X33915] :
      ( ~ class_Rings_Ocomm__semiring__1(X33915)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33915),X33914),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33915),X33914),X33913))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__left])]) ).

fof(i_0_9758,plain,
    ! [X33910,X33911,X33912] :
      ( ~ class_Rings_Ocomm__semiring__1(X33912)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33912),X33911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33912),X33910),X33911))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__triv__right])]) ).

fof(i_0_9759,plain,
    ! [X23339,X23340,X23341] :
      ( ~ class_Lattices_Olattice(X23341)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23341),X23340),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23341),X23340),X23339))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I3_J])]) ).

fof(i_0_9760,plain,
    ! [X23336,X23337,X23338] :
      ( ~ class_Lattices_Osemilattice__sup(X23338)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23338),X23337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23338),X23337),X23336))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge1])]) ).

fof(i_0_9761,plain,
    ! [X23333,X23334,X23335] :
      ( ~ class_Lattices_Olattice(X23335)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23335),X23334),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23335),X23333),X23334))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__ord_I4_J])]) ).

fof(i_0_9762,plain,
    ! [X23330,X23331,X23332] :
      ( ~ class_Lattices_Osemilattice__sup(X23332)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23332),X23331),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23332),X23330),X23331))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__ge2])]) ).

fof(i_0_9763,plain,
    ! [X22607,X22608,X22609] :
      ( ~ class_Orderings_Olinorder(X22609)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22609),X22608),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22609),X22608),X22607))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI1])]) ).

fof(i_0_9764,plain,
    ! [X22604,X22605,X22606] :
      ( ~ class_Orderings_Olinorder(X22606)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22606),X22605),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22606),X22604),X22605))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__maxI2])]) ).

fof(i_0_9765,plain,
    ! [X27577,X27578,X27579] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X27579),X27578),hAPP(c_Set_OCollect(X27579),X27577)))
        | hBOOL(hAPP(X27577,X27578)) )
      & ( ~ hBOOL(hAPP(X27577,X27578))
        | hBOOL(hAPP(hAPP(c_member(X27579),X27578),hAPP(c_Set_OCollect(X27579),X27577))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq])]) ).

fof(i_0_9766,plain,
    ! [X27574,X27575,X27576] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27576),X27575),hAPP(c_Set_OCollect(X27576),X27574)))
      | hBOOL(hAPP(X27574,X27575)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectD])]) ).

fof(i_0_9767,plain,
    ! [X27571,X27572,X27573] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X27573),X27572),hAPP(c_Set_OCollect(X27573),X27571)))
      | hBOOL(hAPP(X27571,X27572)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectE])]) ).

fof(i_0_9768,plain,
    ! [X21004] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21004))
      | hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X21004)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X21004)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__nat__eq__nat__zadd1])]) ).

cnf(i_0_9769,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_5848]) ).

fof(i_0_9770,plain,
    ! [X29846,X29847,X29848,X29849] :
      ( ( X29849 != X29848
        | c_List_Oremove1(X29847,X29849,hAPP(hAPP(c_List_Olist_OCons(X29847),X29848),X29846)) = X29846 )
      & ( X29849 = X29848
        | c_List_Oremove1(X29847,X29849,hAPP(hAPP(c_List_Olist_OCons(X29847),X29848),X29846)) = hAPP(hAPP(c_List_Olist_OCons(X29847),X29848),c_List_Oremove1(X29847,X29849,X29846)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1_Osimps_I2_J])]) ).

fof(i_0_9771,plain,
    ! [X33626,X33627,X33628,X33629] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33629),X33627),X33628) != X33626
        | X33627 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33629),X33626),X33628)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33629),X33628),X33627))
        | X33628 = c_Groups_Ozero__class_Ozero(X33629)
        | ~ class_Divides_Osemiring__div(X33629) )
      & ( X33627 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33629),X33626),X33628)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X33629),X33627),X33628) = X33626
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33629),X33628),X33627))
        | X33628 = c_Groups_Ozero__class_Ozero(X33629)
        | ~ class_Divides_Osemiring__div(X33629) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__div__eq__mult])])]) ).

fof(i_0_9772,plain,
    ! [X17725,X17726] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17726),hAPP(c_Nat_OSuc,X17725)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17726),X17725))
      | X17726 = X17725 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5938])]) ).

fof(i_0_9773,plain,
    ! [X17716,X17717] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17717),X17716))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17717),hAPP(c_Nat_OSuc,X17716)))
      | X17716 = X17717 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5939])]) ).

fof(i_0_9774,plain,
    ! [X17714,X17715] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17715),hAPP(c_Nat_OSuc,X17714)))
        | X17715 = X17714
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17715),X17714)) )
      & ( X17715 != X17714
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17715),hAPP(c_Nat_OSuc,X17714)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17715),X17714)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5940])])]) ).

fof(i_0_9775,plain,
    ! [X17710,X17711] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17711),hAPP(c_Nat_OSuc,X17710)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17711),X17710))
        | X17711 = X17710 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17711),X17710))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17711),hAPP(c_Nat_OSuc,X17710))) )
      & ( X17711 != X17710
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17711),hAPP(c_Nat_OSuc,X17710))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq])])]) ).

cnf(i_0_9776,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X2),c_Divides_Odivmod__nat(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_5941]) ).

cnf(i_0_9777,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_5942]) ).

cnf(i_0_9778,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_5943]) ).

fof(i_0_9779,plain,
    ! [X25302,X25303,X25304] : hAPP(c_Relation_OImage(X25304,X25304,c_Relation_OId__on(X25304,X25303)),X25302) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25304,tc_HOL_Obool)),X25303),X25302),
    inference(variable_rename,[status(thm)],[fact_Image__Id__on]) ).

fof(i_0_9780,plain,
    ! [X25085,X25086,X25087,X25088] :
      ( ~ class_Lattices_Osemilattice__inf(X25088)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25088),X25087),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25088),X25086),X25085)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25088),X25086),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25088),X25087),X25085)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__commute])]) ).

fof(i_0_9781,plain,
    ! [X25077,X25078,X25079,X25080] :
      ( ~ class_Lattices_Osemilattice__inf(X25080)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25080),X25079),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25080),X25078),X25077)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25080),X25078),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25080),X25079),X25077)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__commute])]) ).

fof(i_0_9782,plain,
    ! [X25081,X25082,X25083,X25084] :
      ( ~ class_Lattices_Olattice(X25084)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25084),X25083),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25084),X25082),X25081)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25084),X25082),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25084),X25083),X25081)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I3_J])]) ).

fof(i_0_9783,plain,
    ! [X23200,X23201,X23202,X23203] :
      ( ~ class_Lattices_Olattice(X23203)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23203),X23202),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23203),X23201),X23200)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23203),X23201),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23203),X23202),X23200)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I7_J])]) ).

fof(i_0_9784,plain,
    ! [X23204,X23205,X23206,X23207] :
      ( ~ class_Lattices_Osemilattice__sup(X23207)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23207),X23206),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23207),X23205),X23204)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23207),X23205),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23207),X23206),X23204)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__commute])]) ).

fof(i_0_9785,plain,
    ! [X23196,X23197,X23198,X23199] :
      ( ~ class_Lattices_Osemilattice__sup(X23199)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23199),X23198),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23199),X23197),X23196)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23199),X23197),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23199),X23198),X23196)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__commute])]) ).

fof(i_0_9786,plain,
    ! [X22503,X22504,X22505,X22506] :
      ( ~ class_Orderings_Olinorder(X22506)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22506),X22505),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22506),X22504),X22503)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22506),X22504),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22506),X22505),X22503)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute])]) ).

fof(i_0_9787,plain,
    ! [X22499,X22500,X22501,X22502] :
      ( ~ class_Orderings_Olinorder(X22502)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22502),X22501),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22502),X22500),X22499)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22502),X22500),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22502),X22501),X22499)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute])]) ).

fof(i_0_9788,plain,
    ! [X21511,X21512,X21513,X21514] :
      ( ~ class_Orderings_Olinorder(X21514)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21514),X21513),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21514),X21512),X21511)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21514),X21512),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21514),X21513),X21511)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__commute])]) ).

fof(i_0_9789,plain,
    ! [X21507,X21508,X21509,X21510] :
      ( ~ class_Orderings_Olinorder(X21510)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21510),X21509),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21510),X21508),X21507)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21510),X21508),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21510),X21509),X21507)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__commute])]) ).

fof(i_0_9790,plain,
    ! [X19062,X19063,X19064,X19065] :
      ( ~ class_Rings_Ocomm__semiring__1(X19065)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19065),X19064),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19065),X19063),X19062)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19065),X19063),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19065),X19064),X19062)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J])]) ).

fof(i_0_9791,plain,
    ! [X19028,X19029,X19030,X19031] :
      ( ~ class_Rings_Ocomm__semiring__1(X19031)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19031),X19030),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19031),X19029),X19028)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19031),X19029),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19031),X19030),X19028)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J])]) ).

fof(i_0_9792,plain,
    ! [X21171,X21172,X21173] :
      ( ~ class_Groups_Ogroup__add(X21173)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21173),X21172),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21173),hAPP(c_Groups_Ouminus__class_Ouminus(X21173),X21172)),X21171)) = X21171 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__minus__cancel])]) ).

fof(i_0_9793,plain,
    ! [X18960,X18961,X18962] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18962),X18961) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18962),X18960)
        | X18961 = X18960
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18962)) )
      & ( X18961 != X18960
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18962),X18961) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18962),X18960)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18962)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1])])]) ).

fof(i_0_9794,plain,
    ! [X17749,X17750] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17750),hAPP(c_Nat_OSuc,X17749)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17750),X17749)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17750),X17749))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17750),hAPP(c_Nat_OSuc,X17749))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le])]) ).

fof(i_0_9795,plain,
    ! [X20845] : 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),X20845)) = 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),X20845))),
    inference(variable_rename,[status(thm)],[fact_one__div__nat__number__of]) ).

fof(i_0_9796,plain,
    ! [X20950,X20951,X20952,X20953,X20954] :
      ( ( X20950 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20952)
        | hBOOL(hAPP(X20951,X20952))
        | ~ hBOOL(hAPP(X20951,hAPP(c_Int_Onat,X20950))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20950),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(X20951,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X20951,hAPP(c_Int_Onat,X20950))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20953),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | X20953 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk65_2(X20953,X20954))
        | hBOOL(hAPP(X20954,hAPP(c_Int_Onat,X20953))) )
      & ( ~ hBOOL(hAPP(X20954,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X20953 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk65_2(X20953,X20954))
        | hBOOL(hAPP(X20954,hAPP(c_Int_Onat,X20953))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X20953),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(X20954,esk65_2(X20953,X20954)))
        | hBOOL(hAPP(X20954,hAPP(c_Int_Onat,X20953))) )
      & ( ~ hBOOL(hAPP(X20954,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(X20954,esk65_2(X20953,X20954)))
        | hBOOL(hAPP(X20954,hAPP(c_Int_Onat,X20953))) ) ),
    inference(distribute,[status(thm)],[inference(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_9797,plain,
    ! [X30243,X30244,X30245] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30245),X30244))
      | hBOOL(hAPP(c_List_Odistinct(X30245),hAPP(hAPP(c_List_Odrop(X30245),X30243),X30244))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__drop])]) ).

fof(i_0_9798,plain,
    ! [X29773,X29774,X29775] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29775),X29774))
      | hBOOL(hAPP(c_List_Odistinct(X29775),hAPP(hAPP(c_List_Otake(X29775),X29773),X29774))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__take])]) ).

fof(i_0_9799,plain,
    ! [X16848,X16849,X16850] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X16850),X16849))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X16850),hAPP(hAPP(c_Set_Oinsert(X16850),X16848),X16849))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite_OinsertI])]) ).

fof(i_0_9800,plain,
    ! [X24012,X24013] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24013,X24012)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24013),hAPP(c_Nat_OSuc,X24012)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastAtMost]) ).

fof(i_0_9801,plain,
    ! [X26366,X26367,X26368] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26368,tc_fun(X26367,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26368,tc_HOL_Obool))),X26366) = c_Orderings_Otop__class_Otop(tc_fun(X26367,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_INT__empty]) ).

fof(i_0_9802,plain,
    ! [X21360,X21361] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21361)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21360)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21361),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21360))),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I6_J]) ).

fof(i_0_9803,plain,
    ! [X26192,X26193] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26193,tc_HOL_Obool)),X26192) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26193,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26193,tc_HOL_Obool))),X26192),
    inference(variable_rename,[status(thm)],[fact_Compl__eq__Diff__UNIV]) ).

fof(i_0_9804,plain,
    ! [X30802,X30803,X30804,X30805] : hAPP(hAPP(c_List_Omap(X30805,X30804),X30803),c_List_Obutlast(X30805,X30802)) = c_List_Obutlast(X30804,hAPP(hAPP(c_List_Omap(X30805,X30804),X30803),X30802)),
    inference(variable_rename,[status(thm)],[fact_map__butlast]) ).

fof(i_0_9805,plain,
    ! [X23004,X23005] :
      ( ~ class_Orderings_Olinorder(X23005)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23005),X23004))
      | X23004 = c_Orderings_Obot__class_Obot(tc_fun(X23005,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(X23005),c_Big__Operators_Olinorder__class_OMax(X23005,X23004)),X23004)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__in])]) ).

fof(i_0_9806,plain,
    ! [X21778,X21779] :
      ( ~ class_Orderings_Olinorder(X21779)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21779),X21778))
      | X21778 = c_Orderings_Obot__class_Obot(tc_fun(X21779,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(X21779),c_Big__Operators_Olinorder__class_OMin(X21779,X21778)),X21778)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__in])]) ).

fof(i_0_9807,plain,
    ! [X33221] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X33221),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | X33221 = hAPP(c_Code__Numeral_Onat__of,esk527_1(X33221)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__of__cases])])]) ).

fof(i_0_9808,plain,
    ! [X20792,X20794,X20795,X20797] :
      ( ( ~ hBOOL(hAPP(X20792,esk60_1(X20792)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20794))
        | hBOOL(hAPP(X20792,hAPP(c_Int_Onat,X20794))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk61_1(X20795)))
        | hBOOL(hAPP(X20795,X20797)) )
      & ( ~ hBOOL(hAPP(X20795,hAPP(c_Int_Onat,esk61_1(X20795))))
        | hBOOL(hAPP(X20795,X20797)) ) ),
    inference(distribute,[status(thm)],[inference(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_9809,plain,
    ! [X16965,X16966,X16967] : hBOOL(hAPP(hAPP(c_member(X16967),X16966),hAPP(hAPP(c_Set_Oinsert(X16967),X16966),X16965))),
    inference(variable_rename,[status(thm)],[fact_insertI1]) ).

fof(i_0_9810,plain,
    ! [X21279,X21280] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21280,X21279)) != X21279
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21280),X21279) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21280,X21279)) = X21279
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,X21280),X21279) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21280,X21279)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__Suc])]) ).

fof(i_0_9811,plain,
    ! [X33178] : c_Hilbert__Choice_Oinv__into(X33178,X33178,c_Orderings_Otop__class_Otop(tc_fun(X33178,tc_HOL_Obool)),c_Fun_Oid(X33178)) = c_Fun_Oid(X33178),
    inference(variable_rename,[status(thm)],[fact_inv__id]) ).

cnf(i_0_9812,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_5944]) ).

cnf(i_0_9813,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_5945]) ).

fof(i_0_9814,plain,
    ! [X16902,X16903,X16904,X16905] : hAPP(hAPP(c_Set_Oinsert(X16905),X16904),hAPP(hAPP(c_Set_Oinsert(X16905),X16903),X16902)) = hAPP(hAPP(c_Set_Oinsert(X16905),X16903),hAPP(hAPP(c_Set_Oinsert(X16905),X16904),X16902)),
    inference(variable_rename,[status(thm)],[fact_insert__commute]) ).

fof(i_0_9815,plain,
    ! [X17465,X17466,X17467,X17468] :
      ( ~ c_Finite__Set_Ofolding__one(X17468,X17467,X17466)
      | hAPP(X17466,hAPP(hAPP(c_Set_Oinsert(X17468),X17465),c_Orderings_Obot__class_Obot(tc_fun(X17468,tc_HOL_Obool)))) = X17465 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Osingleton])]) ).

fof(i_0_9816,plain,
    ! [X17763,X17764] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17764),hAPP(c_Nat_OSuc,X17763)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17764),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X17763),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__eq__diff__pred]) ).

fof(i_0_9817,plain,
    ! [X19574,X19575,X19576,X19577] : hAPP(hAPP(c_Finite__Set_Ofold(X19577,X19576,X19575),X19574),c_Orderings_Obot__class_Obot(tc_fun(X19577,tc_HOL_Obool))) = X19574,
    inference(variable_rename,[status(thm)],[fact_fold__empty]) ).

cnf(i_0_9818,plain,
    ( c_List_Olist__all(tc_Nat_Onat,X1,c_List_Oupt(X2,X3))
    | ~ c_List_Oall__interval__nat(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_5890]) ).

fof(i_0_9819,plain,
    ! [X30275,X30276,X30277] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30277)),hAPP(hAPP(c_List_Odrop(X30277),X30276),X30275)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30277)),X30275)),X30276),
    inference(variable_rename,[status(thm)],[fact_length__drop]) ).

fof(i_0_9820,plain,
    ! [X29497,X29498,X29499] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29499)),hAPP(hAPP(c_List_Otake(X29499),X29498),X29497)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29499)),X29497)),X29498),
    inference(variable_rename,[status(thm)],[fact_length__take]) ).

cnf(i_0_9821,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_5946]) ).

fof(i_0_9822,plain,
    ! [X26209] :
      ( ~ class_Nat_Osemiring__char__0(X26209)
      | c_Fun_Oinj__on(tc_Nat_Onat,X26209,c_Nat_Osemiring__1__class_Oof__nat(X26209),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_9823,plain,
    ! [X30420,X30421,X30422] : hAPP(hAPP(c_List_Otake(X30422),X30421),hAPP(c_List_Otl(X30422),X30420)) = hAPP(c_List_Otl(X30422),hAPP(hAPP(c_List_Otake(X30422),hAPP(c_Nat_OSuc,X30421)),X30420)),
    inference(variable_rename,[status(thm)],[fact_take__tl]) ).

fof(i_0_9824,plain,
    ! [X18090,X18091,X18093,X18094,X18095] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18091),X18090))
        | X18090 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18091),esk19_2(X18090,X18091))) )
      & ( X18093 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18094),X18095))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18094),X18093)) ) ),
    inference(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_9825,plain,
    ! [X32531,X32532,X32533,X32534] : hAPP(hAPP(c_List_Odrop(X32534),X32533),c_List_Oreplicate(X32534,X32532,X32531)) = c_List_Oreplicate(X32534,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32532),X32533),X32531),
    inference(variable_rename,[status(thm)],[fact_drop__replicate]) ).

fof(i_0_9826,plain,
    ! [X32541,X32542,X32543,X32544] : hAPP(hAPP(c_List_Otake(X32544),X32543),c_List_Oreplicate(X32544,X32542,X32541)) = c_List_Oreplicate(X32544,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X32543),X32542),X32541),
    inference(variable_rename,[status(thm)],[fact_take__replicate]) ).

cnf(i_0_9827,plain,
    ( c_Transitive__Closure_Otrancl(X1,X2) = X2
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5947]) ).

fof(i_0_9828,plain,
    ! [X24077,X24078,X24079] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X24079,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(X24079,X24078,X24077)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24079),X24078),X24077))
        | ~ class_Orderings_Oorder(X24079) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24079),X24078),X24077))
        | c_Orderings_Obot__class_Obot(tc_fun(X24079,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(X24079,X24078,X24077)
        | ~ class_Orderings_Oorder(X24079) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5948])])]) ).

fof(i_0_9829,plain,
    ! [X23495,X23496,X23497] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X23497,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(X23497,X23496,X23495)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23497),X23496),X23495))
        | ~ class_Orderings_Oorder(X23497) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23497),X23496),X23495))
        | c_Orderings_Obot__class_Obot(tc_fun(X23497,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(X23497,X23496,X23495)
        | ~ class_Orderings_Oorder(X23497) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5949])])]) ).

fof(i_0_9830,plain,
    ! [X24080,X24081,X24082] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(X24082,X24081,X24080) != c_Orderings_Obot__class_Obot(tc_fun(X24082,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24082),X24081),X24080))
        | ~ class_Orderings_Oorder(X24082) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24082),X24081),X24080))
        | c_SetInterval_Oord__class_OatLeastAtMost(X24082,X24081,X24080) = c_Orderings_Obot__class_Obot(tc_fun(X24082,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X24082) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5950])])]) ).

fof(i_0_9831,plain,
    ! [X23492,X23493,X23494] :
      ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(X23494,X23493,X23492) != c_Orderings_Obot__class_Obot(tc_fun(X23494,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23494),X23493),X23492))
        | ~ class_Orderings_Oorder(X23494) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23494),X23493),X23492))
        | c_SetInterval_Oord__class_OgreaterThanAtMost(X23494,X23493,X23492) = c_Orderings_Obot__class_Obot(tc_fun(X23494,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X23494) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5951])])]) ).

fof(i_0_9832,plain,
    ! [X24851] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24851) = 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),X24851))),
    inference(variable_rename,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__functions_I1_J]) ).

fof(i_0_9833,plain,
    ! [X32328,X32329,X32330,X32331] :
      ( ( hBOOL(hAPP(X32330,X32329))
        | ~ c_List_Olist__all(X32331,X32330,hAPP(hAPP(c_List_Olist_OCons(X32331),X32329),X32328)) )
      & ( c_List_Olist__all(X32331,X32330,X32328)
        | ~ c_List_Olist__all(X32331,X32330,hAPP(hAPP(c_List_Olist_OCons(X32331),X32329),X32328)) )
      & ( ~ hBOOL(hAPP(X32330,X32329))
        | ~ c_List_Olist__all(X32331,X32330,X32328)
        | c_List_Olist__all(X32331,X32330,hAPP(hAPP(c_List_Olist_OCons(X32331),X32329),X32328)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__simps_I1_J])])]) ).

fof(i_0_9834,plain,
    ! [X25927,X25928,X25929] :
      ( ~ class_Fields_Olinordered__field(X25929)
      | X25928 = c_Groups_Ozero__class_Ozero(X25929)
      | hAPP(c_Groups_Oabs__class_Oabs(X25929),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25929),X25927),X25928)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25929),hAPP(c_Groups_Oabs__class_Oabs(X25929),X25927)),hAPP(c_Groups_Oabs__class_Oabs(X25929),X25928)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__abs__divide])]) ).

fof(i_0_9835,plain,
    ! [X19283,X19284] :
      ( ( hBOOL(hAPP(hAPP(c_member(X19284),esk43_2(X19283,X19284)),X19283))
        | hAPP(c_Finite__Set_Ocard(X19284),X19283) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19284),X19283)) )
      & ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Finite__Set_Ocard(X19284),X19283) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19284),X19283)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card_Oneutral])])])]) ).

fof(i_0_9836,plain,
    ! [X25279,X25280] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25280,tc_HOL_Obool)),X25279),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25280,tc_HOL_Obool)),X25279)) = c_Orderings_Obot__class_Obot(tc_fun(X25280,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__disjoint]) ).

fof(i_0_9837,plain,
    ! [X26190,X26191] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26191,tc_HOL_Obool)),X26190),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26191,tc_HOL_Obool)),X26190)) = c_Orderings_Otop__class_Otop(tc_fun(X26191,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__partition]) ).

fof(i_0_9838,plain,
    ! [X18200,X18201,X18202] : c_Fun_Oinj__on(X18202,X18201,X18200,c_Orderings_Obot__class_Obot(tc_fun(X18202,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_inj__on__empty]) ).

fof(i_0_9839,plain,
    ! [X33708,X33709] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33709),X33708))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33708),X33709))
      | X33709 = X33708 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym])]) ).

fof(i_0_9840,plain,
    ! [X33706,X33707] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33707),X33706))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33706),X33707))
      | X33707 = X33706 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__antisym])]) ).

fof(i_0_9841,plain,
    ! [X33698,X33699] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33699),X33698))
        | X33699 = X33698
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33699),X33698)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33698),X33699))
        | X33699 = X33698
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33699),X33698)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5952])])]) ).

fof(i_0_9842,plain,
    ! [X33696,X33697] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33697),X33696))
        | X33697 = X33696
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33697),X33696)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33696),X33697))
        | X33697 = X33696
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33697),X33696)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5953])])]) ).

fof(i_0_9843,plain,
    ! [X33694,X33695] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33694),X33695))
        | X33694 = X33695
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33695),X33694)) )
      & ( X33694 != X33695
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33694),X33695))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33695),X33694)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv])])]) ).

fof(i_0_9844,plain,
    ! [X33690,X33691] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33691),X33690))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33691),X33690))
        | X33691 = X33690 )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33690),X33691))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33691),X33690))
        | X33691 = X33690 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5954])])]) ).

fof(i_0_9845,plain,
    ! [X33688,X33689] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33689),X33688))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33689),X33688))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33688),X33689)) )
      & ( X33689 != X33688
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33689),X33688))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33688),X33689)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33689),X33688))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33689),X33688))
        | X33689 = X33688 )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33688),X33689))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33689),X33688))
        | X33689 = X33688 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5955])])]) ).

fof(i_0_9846,plain,
    ! [X33686,X33687] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33687),X33686))
        | X33687 = X33686
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33687),X33686)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33686),X33687))
        | X33687 = X33686
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33687),X33686)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33687),X33686))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33686),X33687))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33687),X33686)) )
      & ( X33687 != X33686
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33687),X33686)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5956])])]) ).

fof(i_0_9847,plain,
    ! [X33684,X33685] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33685),X33684))
        | X33685 != X33684 )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33684),X33685))
        | X33685 != X33684 )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33685),X33684))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33684),X33685))
        | X33685 = X33684 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff])])]) ).

fof(i_0_9848,plain,
    ! [X19473,X19474] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19474),X19473))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19473),X19474))
      | X19474 = X19473 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zle__antisym])]) ).

fof(i_0_9849,plain,
    ! [X17218,X17219] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17219),X17218))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17218),X17219))
      | X17219 = X17218 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__antisym])]) ).

cnf(i_0_9850,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_5709]) ).

fof(i_0_9851,plain,
    ! [X20843] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20843))
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X20843) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20843),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__minus1])]) ).

fof(i_0_9852,plain,
    ! [X33482,X33483,X33484,X33485] :
      ( ~ c_Equiv__Relations_Oequivp(X33485,X33484)
      | c_Quotient_OBabs(X33485,X33483,c_Quotient_ORespects(X33485,X33484),X33482) = X33482 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_babs__reg__eqv])]) ).

fof(i_0_9853,plain,
    ! [X25657,X25658,X25659] :
      ( ~ class_Lattices_Olattice(X25659)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25659),X25658))
      | X25658 = c_Orderings_Obot__class_Obot(tc_fun(X25659,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X25659,hAPP(hAPP(c_Set_Oinsert(X25659),X25657),X25658)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25659),X25657),c_Big__Operators_Olattice__class_OInf__fin(X25659,X25658)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oinsert__idem])]) ).

fof(i_0_9854,plain,
    ! [X23515,X23516,X23517] :
      ( ~ class_Lattices_Olattice(X23517)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23517),X23516))
      | X23516 = c_Orderings_Obot__class_Obot(tc_fun(X23517,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X23517,hAPP(hAPP(c_Set_Oinsert(X23517),X23515),X23516)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23517),X23515),c_Big__Operators_Olattice__class_OSup__fin(X23517,X23516)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oinsert__idem])]) ).

fof(i_0_9855,plain,
    ! [X23032,X23033,X23034] :
      ( ~ class_Orderings_Olinorder(X23034)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23034),X23033))
      | X23033 = c_Orderings_Obot__class_Obot(tc_fun(X23034,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMax(X23034,hAPP(hAPP(c_Set_Oinsert(X23034),X23032),X23033)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X23034),X23032),c_Big__Operators_Olinorder__class_OMax(X23034,X23033)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max__insert])]) ).

fof(i_0_9856,plain,
    ! [X21799,X21800,X21801] :
      ( ~ class_Orderings_Olinorder(X21801)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21801),X21800))
      | X21800 = c_Orderings_Obot__class_Obot(tc_fun(X21801,tc_HOL_Obool))
      | c_Big__Operators_Olinorder__class_OMin(X21801,hAPP(hAPP(c_Set_Oinsert(X21801),X21799),X21800)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21801),X21799),c_Big__Operators_Olinorder__class_OMin(X21801,X21800)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min__insert])]) ).

fof(i_0_9857,plain,
    ! [X23379,X23380,X23381] :
      ( ( X23380 = c_Orderings_Obot__class_Obot(tc_fun(X23381,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23381,tc_HOL_Obool)),X23380),X23379) != c_Orderings_Obot__class_Obot(tc_fun(X23381,tc_HOL_Obool)) )
      & ( X23379 = c_Orderings_Obot__class_Obot(tc_fun(X23381,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23381,tc_HOL_Obool)),X23380),X23379) != c_Orderings_Obot__class_Obot(tc_fun(X23381,tc_HOL_Obool)) )
      & ( X23380 != c_Orderings_Obot__class_Obot(tc_fun(X23381,tc_HOL_Obool))
        | X23379 != c_Orderings_Obot__class_Obot(tc_fun(X23381,tc_HOL_Obool))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23381,tc_HOL_Obool)),X23380),X23379) = c_Orderings_Obot__class_Obot(tc_fun(X23381,tc_HOL_Obool)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Un__empty])])]) ).

fof(i_0_9858,plain,
    ! [X30081,X30082,X30083] :
      ( ~ class_Groups_Omonoid__add(X30083)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X30083),hAPP(hAPP(c_List_Oappend(X30083),X30082),X30081)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X30083),hAPP(c_List_Omonoid__add__class_Olistsum(X30083),X30082)),hAPP(c_List_Omonoid__add__class_Olistsum(X30083),X30081)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__append])]) ).

fof(i_0_9859,plain,
    ! [X25869,X25870,X25871] :
      ( ~ class_Fields_Olinordered__field__inverse__zero(X25871)
      | hAPP(c_Groups_Oabs__class_Oabs(X25871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25871),X25870),X25869)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X25871),hAPP(c_Groups_Oabs__class_Oabs(X25871),X25870)),hAPP(c_Groups_Oabs__class_Oabs(X25871),X25869)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__divide])]) ).

fof(i_0_9860,plain,
    ! [X25850,X25851,X25852] :
      ( ~ class_Rings_Olinordered__idom(X25852)
      | hAPP(c_Groups_Oabs__class_Oabs(X25852),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25852),X25851),X25850)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25852),hAPP(c_Groups_Oabs__class_Oabs(X25852),X25851)),hAPP(c_Groups_Oabs__class_Oabs(X25852),X25850)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult])]) ).

fof(i_0_9861,plain,
    ! [X25215,X25216,X25217] :
      ( ~ class_Lattices_Oboolean__algebra(X25217)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X25217),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25217),X25216),X25215)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25217),hAPP(c_Groups_Ouminus__class_Ouminus(X25217),X25216)),hAPP(c_Groups_Ouminus__class_Ouminus(X25217),X25215)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf])]) ).

fof(i_0_9862,plain,
    ! [X25218,X25219,X25220] :
      ( ~ class_Lattices_Oboolean__algebra(X25220)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X25220),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X25220),X25219),X25218)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25220),hAPP(c_Groups_Ouminus__class_Ouminus(X25220),X25219)),hAPP(c_Groups_Ouminus__class_Ouminus(X25220),X25218)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup])]) ).

fof(i_0_9863,plain,
    ! [X22661,X22662,X22663] :
      ( ~ class_Groups_Olinordered__ab__group__add(X22663)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22663),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22663),X22662),X22661)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X22663),hAPP(c_Groups_Ouminus__class_Ouminus(X22663),X22662)),hAPP(c_Groups_Ouminus__class_Ouminus(X22663),X22661)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__max__eq__min])]) ).

fof(i_0_9864,plain,
    ! [X22658,X22659,X22660] :
      ( ~ class_Groups_Olinordered__ab__group__add(X22660)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22660),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22660),X22659),X22658)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22660),hAPP(c_Groups_Ouminus__class_Ouminus(X22660),X22659)),hAPP(c_Groups_Ouminus__class_Ouminus(X22660),X22658)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__min__eq__max])]) ).

fof(i_0_9865,plain,
    ! [X21165,X21166,X21167] :
      ( ~ class_Groups_Oab__group__add(X21167)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21167),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21167),X21166),X21165)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21167),hAPP(c_Groups_Ouminus__class_Ouminus(X21167),X21166)),hAPP(c_Groups_Ouminus__class_Ouminus(X21167),X21165)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__distrib])]) ).

fof(i_0_9866,plain,
    ! [X21168,X21169,X21170] :
      ( ~ class_Groups_Ogroup__add(X21170)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21170),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21170),X21169),X21168)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21170),hAPP(c_Groups_Ouminus__class_Ouminus(X21170),X21168)),hAPP(c_Groups_Ouminus__class_Ouminus(X21170),X21169)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add])]) ).

cnf(i_0_9867,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_5524]) ).

cnf(i_0_9868,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_5957]) ).

fof(i_0_9869,plain,
    ! [X23947,X23948,X23949] : hAPP(c_Set_Oimage(X23948,tc_fun(X23948,tc_HOL_Obool),X23949),X23947) != hAPP(c_Set_OPow(X23948),X23947),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cantors__paradox])]) ).

fof(i_0_9870,plain,
    ! [X16909,X16910,X16911] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16909,tc_HOL_Obool)),X16911),X16910))
        | X16911 != X16910 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16909,tc_HOL_Obool)),X16910),X16911))
        | X16911 != X16910 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5958])])]) ).

fof(i_0_9871,plain,
    ! [X16919,X16920,X16921] :
      ( X16921 != X16920
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16919,tc_HOL_Obool)),X16921),X16920)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD1])]) ).

fof(i_0_9872,plain,
    ! [X16916,X16917,X16918] :
      ( X16918 != X16917
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16916,tc_HOL_Obool)),X16917),X16918)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equalityD2])]) ).

fof(i_0_9873,plain,
    ! [X17247] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17247)),X17247)),
    inference(variable_rename,[status(thm)],[i_0_5959]) ).

fof(i_0_9874,plain,
    ! [X21432,X21433] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21433))
        | c_SMT_Oz3div(X21432,X21433) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21432),X21433) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21433))
        | c_SMT_Oz3div(X21432,X21433) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21432),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21433))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5960])]) ).

fof(i_0_9875,plain,
    ! [X30635,X30636] :
      ( X30636 = c_List_Olist_ONil(X30635)
      | hBOOL(hAPP(hAPP(c_member(X30635),c_List_Olast(X30635,X30636)),hAPP(c_List_Oset(X30635),X30636))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__in__set])]) ).

fof(i_0_9876,plain,
    ! [X18531,X18532,X18533] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18533)),X18532) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18533)),X18531)
        | X18532 = X18531 )
      & ( X18532 != X18531
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18533)),X18532) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18533)),X18531) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1])]) ).

fof(i_0_9877,plain,
    ! [X22115,X22116,X22117,X22118,X22119,X22120] :
      ( ( X22118 = X22116
        | hAPP(hAPP(c_Product__Type_OPair(X22120,X22119),X22118),X22117) != hAPP(hAPP(c_Product__Type_OPair(X22120,X22119),X22116),X22115) )
      & ( X22117 = X22115
        | hAPP(hAPP(c_Product__Type_OPair(X22120,X22119),X22118),X22117) != hAPP(hAPP(c_Product__Type_OPair(X22120,X22119),X22116),X22115) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__inject])])]) ).

fof(i_0_9878,plain,
    ! [X22109,X22110,X22111,X22112,X22113,X22114] :
      ( ( X22112 = X22110
        | hAPP(hAPP(c_Product__Type_OPair(X22114,X22113),X22112),X22111) != hAPP(hAPP(c_Product__Type_OPair(X22114,X22113),X22110),X22109) )
      & ( X22111 = X22109
        | hAPP(hAPP(c_Product__Type_OPair(X22114,X22113),X22112),X22111) != hAPP(hAPP(c_Product__Type_OPair(X22114,X22113),X22110),X22109) )
      & ( X22112 != X22110
        | X22111 != X22109
        | hAPP(hAPP(c_Product__Type_OPair(X22114,X22113),X22112),X22111) = hAPP(hAPP(c_Product__Type_OPair(X22114,X22113),X22110),X22109) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__eq])])]) ).

fof(i_0_9879,plain,
    ! [X21364,X21365] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21365,X21364) != 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),X21365),X21364) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21365,X21364) = 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),X21365),X21364) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21364),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21365,X21364)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zmod__zminus1__eq__if])]) ).

fof(i_0_9880,plain,
    ! [X21292,X21293] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21293),X21292))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21293,X21292) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21293),X21292),X21292) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5961])]) ).

fof(i_0_9881,plain,
    ! [X21290,X21291] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21291),X21290))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21291,X21290) = X21291 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21291),X21290))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21291,X21290) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21291),X21290),X21290) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5962])]) ).

fof(i_0_9882,plain,
    ! [X32056,X32057,X32058] :
      ( hBOOL(hAPP(hAPP(c_member(X32058),X32057),hAPP(c_List_Oset(X32058),X32056)))
      | c_List_Oinsert(X32058,X32057,X32056) = hAPP(hAPP(c_List_Olist_OCons(X32058),X32057),X32056) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5963])]) ).

fof(i_0_9883,plain,
    ! [X16925,X16926] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X16926,tc_HOL_Obool)),X16925),X16925)),
    inference(variable_rename,[status(thm)],[fact_subset__refl]) ).

fof(i_0_9884,plain,
    ! [X24014,X24015] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24015),X24014)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24015)),hAPP(c_Nat_OSuc,X24014)),
    inference(variable_rename,[status(thm)],[fact_image__Suc__atLeastLessThan]) ).

fof(i_0_9885,plain,
    ! [X31795,X31796,X31797] : hAPP(c_List_Orev(X31797),hAPP(hAPP(c_List_Oappend(X31797),X31796),X31795)) = hAPP(hAPP(c_List_Oappend(X31797),hAPP(c_List_Orev(X31797),X31795)),hAPP(c_List_Orev(X31797),X31796)),
    inference(variable_rename,[status(thm)],[fact_rev__append]) ).

fof(i_0_9886,plain,
    ! [X30329,X30330,X30331,X30332] :
      ( hAPP(c_List_Orotate1(X30332),c_List_Olist_ONil(X30332)) = c_List_Olist_ONil(X30332)
      & hAPP(c_List_Orotate1(X30331),hAPP(hAPP(c_List_Olist_OCons(X30331),X30330),X30329)) = hAPP(hAPP(c_List_Oappend(X30331),X30329),hAPP(hAPP(c_List_Olist_OCons(X30331),X30330),c_List_Olist_ONil(X30331))) ),
    inference(variable_rename,[status(thm)],[fact_rotate__simps]) ).

fof(i_0_9887,plain,
    ! [X17718,X17719] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17719),X17718))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17719),hAPP(c_Nat_OSuc,X17718))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__SucI])]) ).

fof(i_0_9888,plain,
    ! [X17753,X17754] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17754),X17753))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17754),hAPP(c_Nat_OSuc,X17753))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__less__Suc])]) ).

fof(i_0_9889,plain,
    ! [X17254,X17255] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17255),X17254))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17255),hAPP(c_Nat_OSuc,X17254))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__SucI])]) ).

fof(i_0_9890,plain,
    ! [X29647,X29648] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X29648,X29647) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X29648),c_Groups_Oone__class_Oone(tc_Int_Oint)),X29647)),
    inference(variable_rename,[status(thm)],[fact_greaterThanAtMost__upto]) ).

fof(i_0_9891,plain,
    ! [X19234,X19235] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19235),X19234),X19234) != c_Groups_Ozero__class_Ozero(X19235)
        | X19234 = c_Groups_Ozero__class_Ozero(X19235)
        | ~ hBOOL(hAPP(hAPP(c_member(X19235),X19234),c_Int_Oring__1__class_OInts(X19235)))
        | ~ class_Int_Oring__char__0(X19235) )
      & ( X19234 != c_Groups_Ozero__class_Ozero(X19235)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19235),X19234),X19234) = c_Groups_Ozero__class_Ozero(X19235)
        | ~ hBOOL(hAPP(hAPP(c_member(X19235),X19234),c_Int_Oring__1__class_OInts(X19235)))
        | ~ class_Int_Oring__char__0(X19235) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__double__eq__0__iff])])]) ).

fof(i_0_9892,plain,
    ! [X20970] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20970))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),X20970) = 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_9893,plain,
    ! [X25130,X25131,X25132] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25132,tc_HOL_Obool)),X25131),X25130) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25132,tc_HOL_Obool)),X25130),X25131),
    inference(variable_rename,[status(thm)],[fact_Int__commute]) ).

fof(i_0_9894,plain,
    ! [X23277,X23278,X23279] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23279,tc_HOL_Obool)),X23278),X23277) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23279,tc_HOL_Obool)),X23277),X23278),
    inference(variable_rename,[status(thm)],[fact_Un__commute]) ).

fof(i_0_9895,plain,
    ! [X23933] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk140_1(X23933)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23933)) )
      & ( X23933 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk140_1(X23933))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X23933)) ) ),
    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_9896,plain,
    ! [X22827,X22828,X22829,X22830,X22831] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22831),X22828),X22830) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22831),X22827),X22829)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22831),X22828),X22829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22831),X22827),X22830)
        | X22829 = c_Groups_Ozero__class_Ozero(X22831)
        | X22830 = c_Groups_Ozero__class_Ozero(X22831)
        | ~ class_Fields_Ofield(X22831) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22831),X22828),X22829) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22831),X22827),X22830)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22831),X22828),X22830) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22831),X22827),X22829)
        | X22829 = c_Groups_Ozero__class_Ozero(X22831)
        | X22830 = c_Groups_Ozero__class_Ozero(X22831)
        | ~ class_Fields_Ofield(X22831) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_frac__eq__eq])])]) ).

fof(i_0_9897,plain,
    ! [X20923,X20924] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20924),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20923),X20924)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X20923),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20923,X20924)),
    inference(variable_rename,[status(thm)],[fact_zmult__div__cancel]) ).

fof(i_0_9898,plain,
    ! [X21314,X21315] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21315),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X21314),X21315)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21314),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21314,X21315)),
    inference(variable_rename,[status(thm)],[fact_mult__div__cancel]) ).

fof(i_0_9899,plain,
    ! [X30995,X30996] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X30996),X30995) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30996)),hAPP(c_Code__Numeral_Onat__of,X30995))),
    inference(variable_rename,[status(thm)],[fact_div__code__numeral__def]) ).

fof(i_0_9900,plain,
    ! [X30978,X30979] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),X30979),X30978) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30979)),hAPP(c_Code__Numeral_Onat__of,X30978))),
    inference(variable_rename,[status(thm)],[fact_times__code__numeral__def]) ).

fof(i_0_9901,plain,
    ! [X30993,X30994] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X30994),X30993) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30994)),hAPP(c_Code__Numeral_Onat__of,X30993))),
    inference(variable_rename,[status(thm)],[fact_plus__code__numeral__def]) ).

fof(i_0_9902,plain,
    ! [X30990,X30991] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30991),X30990) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30991)),hAPP(c_Code__Numeral_Onat__of,X30990))),
    inference(variable_rename,[status(thm)],[fact_minus__code__numeral__def]) ).

fof(i_0_9903,plain,
    ! [X18121,X18122] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18122),X18121))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18122),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18121),X18122)) = X18121 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__add__diff__inverse])]) ).

fof(i_0_9904,plain,
    ! [X17273,X17274] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17274),X17273))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17273),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17273),X17274)) = X17274 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__diff__cancel])]) ).

fof(i_0_9905,plain,
    ! [X17450,X17451,X17452,X17453] : c_Nat_Onat_Onat__case(X17453,X17452,X17451,hAPP(c_Nat_OSuc,X17450)) = hAPP(X17451,X17450),
    inference(variable_rename,[status(thm)],[fact_nat__case__Suc]) ).

fof(i_0_9906,plain,
    ! [X29632,X29633,X29634] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29632) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X29633),hAPP(c_List_Oset(tc_Nat_Onat),X29632)))
        | X29633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk390_1(X29634)),hAPP(c_List_Oset(tc_Nat_Onat),X29634)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29634) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( esk390_1(X29634) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X29634) = 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_9907,plain,
    ! [X17684,X17685,X17686] :
      ( ~ class_Orderings_Oorder(X17686)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17686),X17685),X17684))
      | X17684 = X17685
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17686),X17685),X17684)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I11_J])]) ).

fof(i_0_9908,plain,
    ! [X17681,X17682,X17683] :
      ( ~ class_Orderings_Oorder(X17683)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17683),X17682),X17681))
      | X17682 = X17681
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17683),X17682),X17681)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__neq__trans])]) ).

fof(i_0_9909,plain,
    ! [X17678,X17679,X17680] :
      ( ~ class_Orderings_Oorder(X17680)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17680),X17679),X17678))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17680),X17679),X17678))
      | X17679 = X17678 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__imp__less__or__eq])]) ).

fof(i_0_9910,plain,
    ! [X17663,X17664,X17665] :
      ( ~ class_Orderings_Oorder(X17665)
      | X17664 = X17663
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17665),X17664),X17663))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17665),X17664),X17663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__neq__le__trans])]) ).

fof(i_0_9911,plain,
    ! [X17651,X17652,X17653] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17653),X17652),X17651))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17653),X17652),X17651))
        | X17652 = X17651
        | ~ class_Orderings_Oorder(X17653) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17653),X17652),X17651))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17653),X17652),X17651))
        | ~ class_Orderings_Oorder(X17653) )
      & ( X17652 != X17651
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17653),X17652),X17651))
        | ~ class_Orderings_Oorder(X17653) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__le__less])])]) ).

fof(i_0_9912,plain,
    ! [X17645,X17646,X17647] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17647),X17646),X17645))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17647),X17646),X17645))
        | ~ class_Orderings_Oorder(X17647) )
      & ( X17646 != X17645
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17647),X17646),X17645))
        | ~ class_Orderings_Oorder(X17647) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17647),X17646),X17645))
        | X17646 = X17645
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17647),X17646),X17645))
        | ~ class_Orderings_Oorder(X17647) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__le])])]) ).

fof(i_0_9913,plain,
    ! [X17660,X17661,X17662] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17662),X17661),X17660))
        | X17661 = X17660
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17662),X17661),X17660))
        | ~ class_Orderings_Olinorder(X17662) )
      & ( X17661 != X17660
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17662),X17661),X17660))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17662),X17661),X17660))
        | ~ class_Orderings_Olinorder(X17662) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5964])])]) ).

fof(i_0_9914,plain,
    ! [X17666,X17667,X17668] :
      ( ~ class_Orderings_Oorder(X17668)
      | X17667 = X17666
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17668),X17666),X17667))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17668),X17666),X17667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_xt1_I12_J])]) ).

fof(i_0_9915,plain,
    ! [X19312,X19313,X19314] :
      ( ~ class_Int_Onumber__ring(X19314)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19314),hAPP(c_Int_Onumber__class_Onumber__of(X19314),X19313)),hAPP(c_Int_Onumber__class_Onumber__of(X19314),X19312)) = hAPP(c_Int_Onumber__class_Onumber__of(X19314),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19313),X19312)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I32_J])]) ).

fof(i_0_9916,plain,
    ! [X19302,X19303,X19304] :
      ( ~ class_Int_Onumber__ring(X19304)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19304),hAPP(c_Int_Onumber__class_Onumber__of(X19304),X19303)),hAPP(c_Int_Onumber__class_Onumber__of(X19304),X19302)) = hAPP(c_Int_Onumber__class_Onumber__of(X19304),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19303),X19302)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__number__of__eq])]) ).

fof(i_0_9917,plain,
    ! [X21629,X21630,X21631] :
      ( ~ class_Rings_Oring__1(X21631)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21631),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21630),X21629)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21631),hAPP(c_Int_Oring__1__class_Oof__int(X21631),X21630)),hAPP(c_Int_Oring__1__class_Oof__int(X21631),X21629)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__mult])]) ).

fof(i_0_9918,plain,
    ! [X21624,X21625,X21626] :
      ( ~ class_Rings_Oring__1(X21626)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21626),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21625),X21624)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21626),hAPP(c_Int_Oring__1__class_Oof__int(X21626),X21625)),hAPP(c_Int_Oring__1__class_Oof__int(X21626),X21624)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__add])]) ).

fof(i_0_9919,plain,
    ! [X21633,X21634,X21635] :
      ( ~ class_Rings_Oring__1(X21635)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21635),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21634),X21633)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21635),hAPP(c_Int_Oring__1__class_Oof__int(X21635),X21634)),hAPP(c_Int_Oring__1__class_Oof__int(X21635),X21633)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__diff])]) ).

fof(i_0_9920,plain,
    ! [X20067,X20068,X20069] :
      ( ~ class_Rings_Osemiring__1(X20069)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20068),X20067)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20069),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20069),X20068)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20069),X20067)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__mult])]) ).

fof(i_0_9921,plain,
    ! [X20064,X20065,X20066] :
      ( ~ class_Rings_Osemiring__1(X20066)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20066),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20065),X20064)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20066),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20066),X20065)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20066),X20064)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__add])]) ).

fof(i_0_9922,plain,
    ! [X19309,X19310,X19311] :
      ( ~ class_Int_Onumber__ring(X19311)
      | hAPP(c_Int_Onumber__class_Onumber__of(X19311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19310),X19309)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19311),hAPP(c_Int_Onumber__class_Onumber__of(X19311),X19310)),hAPP(c_Int_Onumber__class_Onumber__of(X19311),X19309)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__mult])]) ).

fof(i_0_9923,plain,
    ! [X19299,X19300,X19301] :
      ( ~ class_Int_Onumber__ring(X19301)
      | hAPP(c_Int_Onumber__class_Onumber__of(X19301),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19300),X19299)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19301),hAPP(c_Int_Onumber__class_Onumber__of(X19301),X19300)),hAPP(c_Int_Onumber__class_Onumber__of(X19301),X19299)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__add])]) ).

fof(i_0_9924,plain,
    ! [X19319,X19320,X19321] :
      ( ~ class_Int_Onumber__ring(X19321)
      | hAPP(c_Int_Onumber__class_Onumber__of(X19321),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19320),X19319)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X19321),hAPP(c_Int_Onumber__class_Onumber__of(X19321),X19320)),hAPP(c_Int_Onumber__class_Onumber__of(X19321),X19319)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__diff])]) ).

fof(i_0_9925,plain,
    ! [X31152,X31153,X31154] : c_Enum_Oproduct(X31154,X31153,c_List_Olist_ONil(X31154),X31152) = c_List_Olist_ONil(tc_prod(X31154,X31153)),
    inference(variable_rename,[status(thm)],[fact_product_Osimps_I1_J]) ).

fof(i_0_9926,plain,
    ! [X22729,X22730] :
      ( ~ class_Fields_Ofield__inverse__zero(X22730)
      | ~ class_Int_Onumber__ring(X22730)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22730),hAPP(c_Int_Onumber__class_Onumber__of(X22730),c_Int_OMin)),X22729) = hAPP(c_Groups_Ouminus__class_Ouminus(X22730),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22730),c_Groups_Oone__class_Oone(X22730)),X22729)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus1__divide])]) ).

fof(i_0_9927,plain,
    ! [X24404,X24405,X24406] :
      ( ~ class_Groups_Ocomm__monoid__add(X24406)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24405,X24406),hAPP(c_COMBK(X24406,X24405),c_Groups_Ozero__class_Ozero(X24406))),X24404) = c_Groups_Ozero__class_Ozero(X24406) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__0])]) ).

fof(i_0_9928,plain,
    ! [X21879,X21880,X21881] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21881)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21880,X21881),hAPP(c_COMBK(X21881,X21880),c_Groups_Oone__class_Oone(X21881))),X21879) = c_Groups_Oone__class_Oone(X21881) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__1])]) ).

fof(i_0_9929,plain,
    ! [X24189,X24190] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24190),c_Groups_Oone__class_Oone(tc_Int_Oint))),X24189) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X24190,X24189),
    inference(variable_rename,[status(thm)],[fact_atLeastPlusOneLessThan__greaterThanLessThan__int]) ).

fof(i_0_9930,plain,
    ! [X17672,X17673,X17674] :
      ( ~ class_Orderings_Opreorder(X17674)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17674),X17673),X17672))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17674),X17673),X17672)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__le])]) ).

fof(i_0_9931,plain,
    ! [X32508,X32509,X32510] :
      ( X32510 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Otl(X32509),c_List_Oreplicate(X32509,X32510,X32508)) = c_List_Oreplicate(X32509,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X32510),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X32508) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__replicate])]) ).

fof(i_0_9932,plain,
    ! [X22237,X22238] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22238),X22237)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X22238),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X22237)),
    inference(variable_rename,[status(thm)],[fact_negateSnd__eq]) ).

fof(i_0_9933,plain,
    ! [X25976,X25977] :
      ( ~ class_Int_Onumber__ring(X25977)
      | ~ class_Rings_Olinordered__idom(X25977)
      | hAPP(c_Groups_Oabs__class_Oabs(X25977),hAPP(hAPP(c_Power_Opower__class_Opower(X25977),hAPP(c_Int_Onumber__class_Onumber__of(X25977),c_Int_OMin)),X25976)) = c_Groups_Oone__class_Oone(X25977) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__power__minus__one])]) ).

fof(i_0_9934,plain,
    ! [X24094,X24095,X24096] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24096,X24095),X24094) != c_Orderings_Obot__class_Obot(tc_fun(X24096,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24096),X24095),X24094))
        | ~ class_Orderings_Oorder(X24096) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24096),X24095),X24094))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24096,X24095),X24094) = c_Orderings_Obot__class_Obot(tc_fun(X24096,tc_HOL_Obool))
        | ~ class_Orderings_Oorder(X24096) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5965])])]) ).

fof(i_0_9935,plain,
    ! [X24097,X24098,X24099] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X24099,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24099,X24098),X24097)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24099),X24098),X24097))
        | ~ class_Orderings_Oorder(X24099) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24099),X24098),X24097))
        | c_Orderings_Obot__class_Obot(tc_fun(X24099,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24099,X24098),X24097)
        | ~ class_Orderings_Oorder(X24099) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5966])])]) ).

cnf(i_0_9936,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_5967]) ).

fof(i_0_9937,plain,
    ! [X25053,X25054] :
      ( ~ c_Nat__Transfer_Onat__set(X25054)
      | ~ c_Nat__Transfer_Onat__set(X25053)
      | c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X25054),X25053)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J])]) ).

fof(i_0_9938,plain,
    ! [X23481,X23482] :
      ( ~ c_Nat__Transfer_Onat__set(X23482)
      | ~ c_Nat__Transfer_Onat__set(X23481)
      | c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X23482),X23481)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J])]) ).

fof(i_0_9939,plain,
    ! [X20026,X20027,X20029,X20030,X20031] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20027),X20026))
        | X20026 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20027),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk56_2(X20026,X20027))) )
      & ( X20029 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X20030),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20031))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20030),X20029)) ) ),
    inference(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_9940,plain,
    ! [X32602,X32603,X32604,X32605,X32606] : hAPP(hAPP(c_List_Omap(X32606,X32605),X32604),c_List_Oreplicate(X32606,X32603,X32602)) = c_List_Oreplicate(X32605,X32603,hAPP(X32604,X32602)),
    inference(variable_rename,[status(thm)],[fact_map__replicate]) ).

fof(i_0_9941,plain,
    ! [X31431,X31432,X31433,X31434] : hAPP(c_List_Ofilter(X31434,X31433),c_List_Oremove1(X31434,X31432,X31431)) = c_List_Oremove1(X31434,X31432,hAPP(c_List_Ofilter(X31434,X31433),X31431)),
    inference(variable_rename,[status(thm)],[fact_filter__remove1]) ).

fof(i_0_9942,plain,
    ! [X30645,X30646,X30647,X30648] :
      ( ( X30645 != c_List_Olist_ONil(X30648)
        | hAPP(hAPP(c_List_Oappend(X30648),X30647),hAPP(hAPP(c_List_Olist_OCons(X30648),X30646),c_List_Olist_ONil(X30648))) != X30645 )
      & ( c_List_Obutlast(X30648,X30645) = X30647
        | hAPP(hAPP(c_List_Oappend(X30648),X30647),hAPP(hAPP(c_List_Olist_OCons(X30648),X30646),c_List_Olist_ONil(X30648))) != X30645 )
      & ( c_List_Olast(X30648,X30645) = X30646
        | hAPP(hAPP(c_List_Oappend(X30648),X30647),hAPP(hAPP(c_List_Olist_OCons(X30648),X30646),c_List_Olist_ONil(X30648))) != X30645 )
      & ( X30645 = c_List_Olist_ONil(X30648)
        | c_List_Obutlast(X30648,X30645) != X30647
        | c_List_Olast(X30648,X30645) != X30646
        | hAPP(hAPP(c_List_Oappend(X30648),X30647),hAPP(hAPP(c_List_Olist_OCons(X30648),X30646),c_List_Olist_ONil(X30648))) = X30645 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_snoc__eq__iff__butlast])])]) ).

fof(i_0_9943,plain,
    ! [X23615] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X23615),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | X23615 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,esk123_1(X23615)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negD])])]) ).

fof(i_0_9944,plain,
    ! [X21640,X21641] :
      ( ~ class_Rings_Oring__1(X21641)
      | hBOOL(hAPP(hAPP(c_member(X21641),hAPP(c_Int_Oring__1__class_Oof__int(X21641),X21640)),c_Int_Oring__1__class_OInts(X21641))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__int])]) ).

fof(i_0_9945,plain,
    ! [X20210,X20211] :
      ( ~ class_Rings_Osemiring__1(X20211)
      | hBOOL(hAPP(hAPP(c_member(X20211),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20211),X20210)),c_Nat_Osemiring__1__class_ONats(X20211))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__in__Nats])]) ).

fof(i_0_9946,plain,
    ! [X20074,X20075] :
      ( ~ class_Rings_Oring__1(X20075)
      | hBOOL(hAPP(hAPP(c_member(X20075),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20075),X20074)),c_Int_Oring__1__class_OInts(X20075))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__of__nat])]) ).

fof(i_0_9947,plain,
    ! [X19350,X19351] :
      ( ~ class_Int_Onumber__ring(X19351)
      | hBOOL(hAPP(hAPP(c_member(X19351),hAPP(c_Int_Onumber__class_Onumber__of(X19351),X19350)),c_Int_Oring__1__class_OInts(X19351))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__number__of])]) ).

fof(i_0_9948,plain,
    ! [X18196] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18196))
      | hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18196),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X18196 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__diff__1])]) ).

fof(i_0_9949,plain,
    ! [X18197] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18197))
      | X18197 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18197),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_9950,plain,
    ! [X30982] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X30982)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_nat__of]) ).

fof(i_0_9951,plain,
    ! [X20777,X20778,X20779] :
      ( ~ class_Divides_Osemiring__div(X20779)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20779),c_Divides_Odiv__class_Omod(X20779,X20778,X20777)),X20777) = c_Groups_Ozero__class_Ozero(X20779) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__div__trivial])]) ).

fof(i_0_9952,plain,
    ! [X22156] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X22156) = 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),X22156),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[fact_negDivAlg__minus1]) ).

fof(i_0_9953,plain,
    ! [X32623,X32624,X32625] : hAPP(c_List_Oset(X32625),c_List_Oreplicate(X32625,hAPP(c_Nat_OSuc,X32624),X32623)) = hAPP(hAPP(c_Set_Oinsert(X32625),X32623),c_Orderings_Obot__class_Obot(tc_fun(X32625,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_set__replicate__Suc]) ).

fof(i_0_9954,plain,
    ! [X24130,X24131] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X24131))
      | c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24131,X24130)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__nat__int__set__function__closures])]) ).

fof(i_0_9955,plain,
    ! [X23002,X23003] :
      ( ~ class_Orderings_Olinorder(X23003)
      | c_Big__Operators_Olattice_OSup__fin(X23003,c_Orderings_Oord__class_Omax(X23003),hAPP(hAPP(c_Set_Oinsert(X23003),X23002),c_Orderings_Obot__class_Obot(tc_fun(X23003,tc_HOL_Obool)))) = X23002 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_Osingleton])]) ).

fof(i_0_9956,plain,
    ! [X21774,X21775] :
      ( ~ class_Orderings_Olinorder(X21775)
      | c_Big__Operators_Olattice_OInf__fin(X21775,c_Orderings_Oord__class_Omin(X21775),hAPP(hAPP(c_Set_Oinsert(X21775),X21774),c_Orderings_Obot__class_Obot(tc_fun(X21775,tc_HOL_Obool)))) = X21774 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_Osingleton])]) ).

fof(i_0_9957,plain,
    ! [X19435] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19435)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19435))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19435)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less])]) ).

fof(i_0_9958,plain,
    ! [X24964,X24965] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24965,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X24965,tc_HOL_Obool))),X24964) = c_Orderings_Obot__class_Obot(tc_fun(X24965,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Int__empty__left]) ).

fof(i_0_9959,plain,
    ! [X26135,X26136] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26136,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26136,tc_HOL_Obool))),X26135) = c_Orderings_Otop__class_Otop(tc_fun(X26136,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Un__UNIV__left]) ).

fof(i_0_9960,plain,
    ! [X17373,X17374] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17374,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X17374,tc_HOL_Obool))),X17373) = c_Orderings_Obot__class_Obot(tc_fun(X17374,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_empty__Diff]) ).

fof(i_0_9961,plain,
    ! [X27157,X27158,X27159] : hAPP(hAPP(c_Product__Type_OSigma(X27159,X27158),c_Orderings_Obot__class_Obot(tc_fun(X27159,tc_HOL_Obool))),X27157) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27159,X27158),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Sigma__empty1]) ).

fof(i_0_9962,plain,
    ! [X18540] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18540),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18540),X18540))),
    inference(variable_rename,[status(thm)],[fact_le__square]) ).

fof(i_0_9963,plain,
    ! [X18039,X18040] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18040),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18040),X18039))),
    inference(variable_rename,[status(thm)],[fact_le__add1]) ).

fof(i_0_9964,plain,
    ! [X18041,X18042] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18042),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18041),X18042))),
    inference(variable_rename,[status(thm)],[fact_le__add2]) ).

fof(i_0_9965,plain,
    ! [X22683,X22684,X22685,X22686] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684) = c_Groups_Ozero__class_Ozero(X22686)
        | X22685 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22686),X22683),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22686),X22685),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684)) != X22683
        | ~ class_Fields_Ofield__inverse__zero(X22686)
        | ~ class_Int_Onumber(X22686) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684) != c_Groups_Ozero__class_Ozero(X22686)
        | X22683 = c_Groups_Ozero__class_Ozero(X22686)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22686),X22685),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684)) != X22683
        | ~ class_Fields_Ofield__inverse__zero(X22686)
        | ~ class_Int_Onumber(X22686) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684) = c_Groups_Ozero__class_Ozero(X22686)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684) != c_Groups_Ozero__class_Ozero(X22686)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22686),X22685),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684)) = X22683
        | ~ class_Fields_Ofield__inverse__zero(X22686)
        | ~ class_Int_Onumber(X22686) )
      & ( X22683 != c_Groups_Ozero__class_Ozero(X22686)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684) != c_Groups_Ozero__class_Ozero(X22686)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22686),X22685),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684)) = X22683
        | ~ class_Fields_Ofield__inverse__zero(X22686)
        | ~ class_Int_Onumber(X22686) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684) = c_Groups_Ozero__class_Ozero(X22686)
        | X22685 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22686),X22683),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22686),X22685),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684)) = X22683
        | ~ class_Fields_Ofield__inverse__zero(X22686)
        | ~ class_Int_Onumber(X22686) )
      & ( X22683 != c_Groups_Ozero__class_Ozero(X22686)
        | X22685 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22686),X22683),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684))
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22686),X22685),hAPP(c_Int_Onumber__class_Onumber__of(X22686),X22684)) = X22683
        | ~ class_Fields_Ofield__inverse__zero(X22686)
        | ~ class_Int_Onumber(X22686) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1])])]) ).

fof(i_0_9966,plain,
    ! [X22671,X22672,X22673,X22674] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671) = c_Groups_Ozero__class_Ozero(X22674)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22674),X22673),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671)) = X22672
        | X22673 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22674),X22672),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671))
        | ~ class_Fields_Ofield__inverse__zero(X22674)
        | ~ class_Int_Onumber(X22674) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671) != c_Groups_Ozero__class_Ozero(X22674)
        | X22673 = c_Groups_Ozero__class_Ozero(X22674)
        | X22673 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22674),X22672),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671))
        | ~ class_Fields_Ofield__inverse__zero(X22674)
        | ~ class_Int_Onumber(X22674) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671) = c_Groups_Ozero__class_Ozero(X22674)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671) != c_Groups_Ozero__class_Ozero(X22674)
        | X22673 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22674),X22672),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671))
        | ~ class_Fields_Ofield__inverse__zero(X22674)
        | ~ class_Int_Onumber(X22674) )
      & ( X22673 != c_Groups_Ozero__class_Ozero(X22674)
        | hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671) != c_Groups_Ozero__class_Ozero(X22674)
        | X22673 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22674),X22672),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671))
        | ~ class_Fields_Ofield__inverse__zero(X22674)
        | ~ class_Int_Onumber(X22674) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671) = c_Groups_Ozero__class_Ozero(X22674)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22674),X22673),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671)) != X22672
        | X22673 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22674),X22672),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671))
        | ~ class_Fields_Ofield__inverse__zero(X22674)
        | ~ class_Int_Onumber(X22674) )
      & ( X22673 != c_Groups_Ozero__class_Ozero(X22674)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22674),X22673),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671)) != X22672
        | X22673 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22674),X22672),hAPP(c_Int_Onumber__class_Onumber__of(X22674),X22671))
        | ~ class_Fields_Ofield__inverse__zero(X22674)
        | ~ class_Int_Onumber(X22674) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1])])]) ).

fof(i_0_9967,plain,
    ! [X17633,X17634,X17635] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17634),X17635))
        | hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | X17635 = X17634
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17635),X17634)) )
      & ( ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | X17635 = X17634
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17635),X17634)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17634),X17635))
        | hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17635),X17634)) )
      & ( ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17635),X17634)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17634),X17635))
        | hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | X17635 = X17634
        | ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635)) )
      & ( ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | X17635 = X17634
        | ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17634),X17635))
        | hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635)) )
      & ( ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635))
        | ~ hBOOL(hAPP(hAPP(X17633,X17634),X17635)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__cases])])]) ).

fof(i_0_9968,plain,
    ! [X20158] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),X20158) = 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)),X20158)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J]) ).

fof(i_0_9969,plain,
    ! [X30049,X30050,X30051,X30052,X30053,X30054] :
      ( hAPP(hAPP(c_List_Oappend(X30054),X30053),X30052) != X30051
      | X30050 != hAPP(hAPP(c_List_Oappend(X30054),X30052),X30049)
      | hAPP(hAPP(c_List_Oappend(X30054),X30053),X30050) = hAPP(hAPP(c_List_Oappend(X30054),X30051),X30049) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__eq__appendI])]) ).

fof(i_0_9970,plain,
    ! [X30039,X30040,X30041,X30042,X30043,X30044] :
      ( hAPP(hAPP(c_List_Olist_OCons(X30044),X30043),X30042) != X30041
      | X30040 != hAPP(hAPP(c_List_Oappend(X30044),X30042),X30039)
      | hAPP(hAPP(c_List_Olist_OCons(X30044),X30043),X30040) = hAPP(hAPP(c_List_Oappend(X30044),X30041),X30039) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Cons__eq__appendI])]) ).

fof(i_0_9971,plain,
    ! [X19481,X19482,X19483] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19483),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19482),X19481)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19482),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19483),X19481)),
    inference(variable_rename,[status(thm)],[fact_zadd__left__commute]) ).

fof(i_0_9972,plain,
    ! [X17830,X17831,X17832] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17832),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17831),X17830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17831),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17832),X17830)),
    inference(variable_rename,[status(thm)],[fact_nat__add__left__commute]) ).

fof(i_0_9973,plain,
    ! [X29645,X29646] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X29646),X29645) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29646,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X29645),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__upto]) ).

fof(i_0_9974,plain,
    ! [X22664,X22665] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X22665),X22664)),X22664) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22665),X22664),
    inference(variable_rename,[status(thm)],[fact_nat__minus__add__max]) ).

fof(i_0_9975,plain,
    ! [X22704] :
      ( ~ class_Orderings_Olinorder(X22704)
      | c_Orderings_Oord_Omin(X22704,hAPP(c_COMBC(X22704,X22704,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X22704))) = c_Orderings_Oord__class_Omax(X22704) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__min])]) ).

fof(i_0_9976,plain,
    ! [X21722] :
      ( ~ class_Orderings_Olinorder(X21722)
      | c_Orderings_Oord_Omax(X21722,hAPP(c_COMBC(X21722,X21722,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X21722))) = c_Orderings_Oord__class_Omin(X21722) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dual__max])]) ).

fof(i_0_9977,plain,
    ! [X30486] :
      ( ~ class_Groups_Omonoid__add(X30486)
      | c_List_Omonoid__add__class_Olistsum(X30486) = c_List_Ofoldl(X30486,X30486,c_Groups_Oplus__class_Oplus(X30486),c_Groups_Ozero__class_Ozero(X30486)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__foldl])]) ).

fof(i_0_9978,plain,
    ! [X20439,X20440,X20441] :
      ( ~ class_Divides_Osemiring__div(X20441)
      | X20440 = c_Groups_Ozero__class_Ozero(X20441)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20441),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20441),X20440),X20439)),X20440) = X20439 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self1__is__id])]) ).

fof(i_0_9979,plain,
    ! [X20442,X20443,X20444] :
      ( ~ class_Divides_Osemiring__div(X20444)
      | X20443 = c_Groups_Ozero__class_Ozero(X20444)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20444),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20444),X20442),X20443)),X20443) = X20442 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__mult__self2__is__id])]) ).

fof(i_0_9980,plain,
    ! [X18110,X18111,X18112] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18111),X18112) != X18110
        | X18111 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18110),X18112)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18112),X18111)) )
      & ( X18111 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18110),X18112)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18111),X18112) = X18110
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18112),X18111)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__imp__diff__is__add])])]) ).

fof(i_0_9981,plain,
    ! [X21223,X21224] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X21224,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21223)) = 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),X21224),X21223)),
    inference(variable_rename,[status(thm)],[fact_zmod__zminus2]) ).

fof(i_0_9982,plain,
    ! [X31289,X31290,X31291] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31291),X31290))
      | c_List_Oremove1(X31291,X31289,c_List_Oremdups(X31291,X31290)) = c_List_Oremdups(X31291,c_List_Oremove1(X31291,X31289,X31290)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remove1__remdups])]) ).

fof(i_0_9983,plain,
    ! [X28323,X28324] :
      ( ( c_Wellfounded_Oacyclic(X28324,X28323)
        | ~ c_Nitpick_Owf_H(X28324,X28323) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28324,X28324)),X28323))
        | c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ c_Nitpick_Owf_H(X28324,X28323) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28324,X28324)),X28323))
        | ~ c_Wellfounded_Oacyclic(X28324,X28323)
        | c_Nitpick_Owf_H(X28324,X28323) )
      & ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ c_Wellfounded_Oacyclic(X28324,X28323)
        | c_Nitpick_Owf_H(X28324,X28323) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nitpick_Owf_H__def])])]) ).

fof(i_0_9984,plain,
    ! [X28315,X28316] :
      ( ( ~ c_Wellfounded_Owf(X28316,X28315)
        | c_Wellfounded_Oacyclic(X28316,X28315)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28316,X28316)),X28315)) )
      & ( ~ c_Wellfounded_Oacyclic(X28316,X28315)
        | c_Wellfounded_Owf(X28316,X28315)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28316,X28316)),X28315)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__iff__acyclic__if__finite])])]) ).

fof(i_0_9985,plain,
    ! [X28317,X28318] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X28318,X28318)),X28317))
      | ~ c_Wellfounded_Oacyclic(X28318,X28317)
      | c_Wellfounded_Owf(X28318,X28317) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__acyclic__wf])]) ).

fof(i_0_9986,plain,
    ! [X31780,X31781] : c_Fun_Oinj__on(tc_List_Olist(X31781),tc_List_Olist(X31781),c_List_Orev(X31781),X31780),
    inference(variable_rename,[status(thm)],[fact_inj__on__rev]) ).

fof(i_0_9987,plain,
    ! [X31398,X31399,X31400] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31400),X31399))
      | hBOOL(hAPP(c_List_Odistinct(X31400),hAPP(c_List_Ofilter(X31400,X31398),X31399))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__filter])]) ).

fof(i_0_9988,plain,
    ! [X26688,X26689,X26690,X26691,X26692,X26693,X26694,X26697] :
      ( ( ~ hBOOL(hAPP(hAPP(X26688,X26690),X26691))
        | hAPP(X26688,X26690) = hAPP(X26688,X26691)
        | ~ c_Equiv__Relations_Oequivp(X26689,X26688) )
      & ( hAPP(X26688,X26692) != hAPP(X26688,X26693)
        | hBOOL(hAPP(hAPP(X26688,X26692),X26693))
        | ~ c_Equiv__Relations_Oequivp(X26689,X26688) )
      & ( ~ hBOOL(hAPP(hAPP(X26694,esk239_1(X26694)),esk240_1(X26694)))
        | hAPP(X26694,esk239_1(X26694)) != hAPP(X26694,esk240_1(X26694))
        | c_Equiv__Relations_Oequivp(X26697,X26694) )
      & ( hBOOL(hAPP(hAPP(X26694,esk239_1(X26694)),esk240_1(X26694)))
        | hAPP(X26694,esk239_1(X26694)) = hAPP(X26694,esk240_1(X26694))
        | c_Equiv__Relations_Oequivp(X26697,X26694) ) ),
    inference(distribute,[status(thm)],[inference(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_9989,plain,
    ! [X17949,X17950,X17951] :
      ( ~ class_Groups_Ogroup__add(X17951)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17951),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17951),X17950),X17949)),X17949) = X17950 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__add__cancel])]) ).

fof(i_0_9990,plain,
    ! [X17946,X17947,X17948] :
      ( ~ class_Groups_Ogroup__add(X17948)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17948),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17948),X17947),X17946)),X17946) = X17947 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__diff__cancel])]) ).

fof(i_0_9991,plain,
    ! [X31317,X31318,X31319] :
      ( ~ class_Orderings_Olinorder(X31319)
      | c_List_Olinorder__class_Osort__key(X31318,X31319,X31317,c_List_Olist_ONil(X31318)) = c_List_Olist_ONil(X31318) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sort__key__simps_I1_J])]) ).

fof(i_0_9992,plain,
    ! [X28145,X28146,X28147] : hAPP(c_Set_Oimage(tc_prod(X28147,X28146),X28147,c_Product__Type_Ofst(X28147,X28146)),X28145) = hAPP(c_Relation_ODomain(X28147,X28146),X28145),
    inference(variable_rename,[status(thm)],[fact_fst__eq__Domain]) ).

fof(i_0_9993,plain,
    ! [X27961,X27962,X27963] : hAPP(c_Set_Oimage(tc_prod(X27963,X27962),X27962,c_Product__Type_Osnd(X27963,X27962)),X27961) = hAPP(c_Relation_ORange(X27963,X27962),X27961),
    inference(variable_rename,[status(thm)],[fact_snd__eq__Range]) ).

fof(i_0_9994,plain,
    ! [X28979,X28980,X28981] :
      ( ( ~ c_Relation_Ototal__on(X28981,X28980,hAPP(c_Relation_Oconverse(X28981,X28981),X28979))
        | c_Relation_Ototal__on(X28981,X28980,X28979) )
      & ( ~ c_Relation_Ototal__on(X28981,X28980,X28979)
        | c_Relation_Ototal__on(X28981,X28980,hAPP(c_Relation_Oconverse(X28981,X28981),X28979)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__converse])]) ).

fof(i_0_9995,plain,
    ! [X28796,X28797,X28798] :
      ( ( ~ c_Relation_Orefl__on(X28798,X28797,hAPP(c_Relation_Oconverse(X28798,X28798),X28796))
        | c_Relation_Orefl__on(X28798,X28797,X28796) )
      & ( ~ c_Relation_Orefl__on(X28798,X28797,X28796)
        | c_Relation_Orefl__on(X28798,X28797,hAPP(c_Relation_Oconverse(X28798,X28798),X28796)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_refl__on__converse])]) ).

fof(i_0_9996,plain,
    ! [X21677] :
      ( ~ c_Nat__Transfer_Onat__set(X21677)
      | hAPP(c_Finite__Set_Ocard(tc_Int_Oint),X21677) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X21677)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J])]) ).

fof(i_0_9997,plain,
    ! [X21663,X21664] :
      ( ~ c_Nat__Transfer_Onat__set(X21664)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X21663),X21664))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21663)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J])]) ).

fof(i_0_9998,plain,
    ! [X21645,X21646,X21647] :
      ( ( ~ c_Nat__Transfer_Onat__set(X21645)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X21646),X21645))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21646)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk74_1(X21647)),X21647))
        | c_Nat__Transfer_Onat__set(X21647) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk74_1(X21647)))
        | c_Nat__Transfer_Onat__set(X21647) ) ),
    inference(distribute,[status(thm)],[inference(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_9999,plain,
    ! [X27500] : c_Relation_Orefl__on(X27500,c_Orderings_Obot__class_Obot(tc_fun(X27500,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27500,X27500),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_refl__on__empty]) ).

fof(i_0_10000,plain,
    ! [X24491,X24492] : hAPP(c_Finite__Set_Ocard(X24492),X24491) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24492,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,X24492),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X24491),
    inference(variable_rename,[status(thm)],[fact_card__eq__setsum]) ).

fof(i_0_10001,plain,
    ! [X22268,X22269,X22270,X22271] :
      ( ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22271,X22270),X22269))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X22271,X22270),X22268))
      | X22269 = X22268 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__nat__rel__unique])]) ).

fof(i_0_10002,plain,
    ! [X21091,X21092] :
      ( ~ class_Groups_Oordered__ab__group__add(X21092)
      | c_Fun_Oinj__on(X21092,X21092,c_Groups_Ouminus__class_Ouminus(X21092),X21091) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inj__uminus])]) ).

fof(i_0_10003,plain,
    ! [X30999,X31000] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X31000,X30999) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,X31000),hAPP(c_Code__Numeral_Onat__of,X30999))),
    inference(variable_rename,[status(thm)],[fact_mod__code__numeral__def]) ).

fof(i_0_10004,plain,
    ! [X29423,X29424,X29425] : hAPP(hAPP(c_List_Onth(X29425),hAPP(hAPP(c_List_Olist_OCons(X29425),X29424),X29423)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X29424,
    inference(variable_rename,[status(thm)],[fact_nth__Cons__0]) ).

fof(i_0_10005,plain,
    ! [X33084,X33085] :
      ( ( hBOOL(hAPP(hAPP(X33084,esk519_2(X33084,X33085)),esk519_2(X33084,X33085)))
        | ~ c_Equiv__Relations_Opart__equivp(X33085,X33084) )
      & ( c_Predicate_Osymp(X33085,X33084)
        | ~ c_Equiv__Relations_Opart__equivp(X33085,X33084) )
      & ( c_Predicate_Otransp(X33085,X33084)
        | ~ c_Equiv__Relations_Opart__equivp(X33085,X33084) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5968])])])]) ).

fof(i_0_10006,plain,
    ! [X33052,X33053,X33055,X33056,X33057] :
      ( ( hBOOL(hAPP(hAPP(X33052,esk515_2(X33052,X33053)),esk515_2(X33052,X33053)))
        | ~ c_Equiv__Relations_Opart__equivp(X33053,X33052) )
      & ( c_Predicate_Osymp(X33053,X33052)
        | ~ c_Equiv__Relations_Opart__equivp(X33053,X33052) )
      & ( c_Predicate_Otransp(X33053,X33052)
        | ~ c_Equiv__Relations_Opart__equivp(X33053,X33052) )
      & ( ~ hBOOL(hAPP(hAPP(X33055,X33057),X33057))
        | ~ c_Predicate_Osymp(X33056,X33055)
        | ~ c_Predicate_Otransp(X33056,X33055)
        | c_Equiv__Relations_Opart__equivp(X33056,X33055) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__refl__symp__transp])])])])])]) ).

fof(i_0_10007,plain,
    ! [X17023,X17024,X17025,X17026] :
      ( ( hAPP(c_Set_Oimage(X17026,X17025,X17024),X17023) != c_Orderings_Obot__class_Obot(tc_fun(X17025,tc_HOL_Obool))
        | X17023 = c_Orderings_Obot__class_Obot(tc_fun(X17026,tc_HOL_Obool)) )
      & ( X17023 != c_Orderings_Obot__class_Obot(tc_fun(X17026,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(X17026,X17025,X17024),X17023) = c_Orderings_Obot__class_Obot(tc_fun(X17025,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__is__empty])]) ).

fof(i_0_10008,plain,
    ! [X17030,X17031,X17032,X17033] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X17033,tc_HOL_Obool)) != hAPP(c_Set_Oimage(X17032,X17033,X17031),X17030)
        | X17030 = c_Orderings_Obot__class_Obot(tc_fun(X17032,tc_HOL_Obool)) )
      & ( X17030 != c_Orderings_Obot__class_Obot(tc_fun(X17032,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(X17033,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X17032,X17033,X17031),X17030) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__is__image])]) ).

fof(i_0_10009,plain,
    ! [X29869,X29870] : c_List_Olistrelp(X29870,X29869,c_List_Olist_ONil(X29870),c_List_Olist_ONil(X29870)),
    inference(variable_rename,[status(thm)],[fact_listrelp_ONil]) ).

fof(i_0_10010,plain,
    ! [X29867,X29868] : c_List_Olistrelp(X29868,X29867,c_List_Olist_ONil(X29868),c_List_Olist_ONil(X29868)),
    inference(variable_rename,[status(thm)],[fact_listrelp_Oequations_I1_J]) ).

fof(i_0_10011,plain,
    ! [X30820,X30821,X30822,X30823] :
      ( X30823 = c_List_Olist_ONil(X30822)
      | hAPP(c_List_Ohd(X30821),hAPP(hAPP(c_List_Omap(X30822,X30821),X30820),X30823)) = hAPP(X30820,hAPP(c_List_Ohd(X30822),X30823)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__map])]) ).

fof(i_0_10012,plain,
    ! [X20195,X20196,X20197] :
      ( ~ class_Rings_Osemiring__1(X20197)
      | c_Nat_Osemiring__1__class_Oof__nat__aux(X20197,X20196,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X20195) = X20195 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__aux_Osimps_I1_J])]) ).

fof(i_0_10013,plain,
    ! [X24102,X24103,X24104,X24105] :
      ( ( X24104 = X24103
        | c_SetInterval_Oord__class_OatLeastAtMost(X24105,X24104,X24103) != hAPP(hAPP(c_Set_Oinsert(X24105),X24102),c_Orderings_Obot__class_Obot(tc_fun(X24105,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X24105) )
      & ( X24103 = X24102
        | c_SetInterval_Oord__class_OatLeastAtMost(X24105,X24104,X24103) != hAPP(hAPP(c_Set_Oinsert(X24105),X24102),c_Orderings_Obot__class_Obot(tc_fun(X24105,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X24105) )
      & ( X24104 != X24103
        | X24103 != X24102
        | c_SetInterval_Oord__class_OatLeastAtMost(X24105,X24104,X24103) = hAPP(hAPP(c_Set_Oinsert(X24105),X24102),c_Orderings_Obot__class_Obot(tc_fun(X24105,tc_HOL_Obool)))
        | ~ class_Orderings_Oorder(X24105) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton__iff])])]) ).

fof(i_0_10014,plain,
    ! [X32434,X32435,X32436,X32437,X32438] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X32438),X32437),X32436),X32435),X32434) = c_New__DSequence_Opos__single(X32438,X32437),
    inference(variable_rename,[status(thm)],[fact_pos__single__def]) ).

fof(i_0_10015,plain,
    ! [X32415,X32416,X32417,X32418,X32419] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X32419),X32418),X32417),X32416),X32415) = c_New__DSequence_Oneg__single(X32419,X32418),
    inference(variable_rename,[status(thm)],[fact_neg__single__def]) ).

fof(i_0_10016,plain,
    ! [X25863,X25864,X25865] :
      ( ~ class_Rings_Olinordered__idom(X25865)
      | hAPP(c_Groups_Oabs__class_Oabs(X25865),hAPP(hAPP(c_Power_Opower__class_Opower(X25865),X25864),X25863)) = hAPP(hAPP(c_Power_Opower__class_Opower(X25865),hAPP(c_Groups_Oabs__class_Oabs(X25865),X25864)),X25863) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__abs])]) ).

fof(i_0_10017,plain,
    ! [X22559,X22560,X22561] :
      ( ~ class_Rings_Odivision__ring(X22561)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22561),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22561),X22560),X22559)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22561),hAPP(c_Groups_Ouminus__class_Ouminus(X22561),X22560)),X22559) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__left])]) ).

fof(i_0_10018,plain,
    ! [X21186,X21187,X21188] :
      ( ~ class_Rings_Oring(X21188)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21188),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21188),X21187),X21186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21188),hAPP(c_Groups_Ouminus__class_Ouminus(X21188),X21187)),X21186) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__left])]) ).

fof(i_0_10019,plain,
    ! [X20505,X20506,X20507,X20508] : hAPP(hAPP(c_Power_Opower_Opower(X20508,X20507,X20506),X20505),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X20507,
    inference(variable_rename,[status(thm)],[fact_power_Opower_Opower__0]) ).

fof(i_0_10020,plain,
    ! [X33595,X33596,X33597] : c_Lazy__Sequence_Omap(X33597,X33596,X33595,c_Lazy__Sequence_Olazy__sequence_OEmpty(X33597)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X33596),
    inference(variable_rename,[status(thm)],[fact__07]) ).

fof(i_0_10021,plain,
    ! [X32081,X32082,X32083] : c_List_Omaps(X32083,X32082,X32081,c_List_Olist_ONil(X32083)) = c_List_Olist_ONil(X32082),
    inference(variable_rename,[status(thm)],[fact_maps__simps_I2_J]) ).

cnf(i_0_10022,plain,
    ( X1 = X2
    | c_Code__Numeral_OSuc__code__numeral(X1) != c_Code__Numeral_OSuc__code__numeral(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5969]) ).

fof(i_0_10023,plain,
    ! [X24083,X24084,X24085] :
      ( ~ class_Orderings_Oorder(X24085)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X24085),X24084),X24083))
      | c_SetInterval_Oord__class_OatLeastAtMost(X24085,X24083,X24084) = c_Orderings_Obot__class_Obot(tc_fun(X24085,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastatMost__empty])]) ).

fof(i_0_10024,plain,
    ! [X23489,X23490,X23491] :
      ( ~ class_Orderings_Oorder(X23491)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23491),X23490),X23489))
      | c_SetInterval_Oord__class_OgreaterThanAtMost(X23491,X23489,X23490) = c_Orderings_Obot__class_Obot(tc_fun(X23491,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanAtMost__empty])]) ).

fof(i_0_10025,plain,
    ! [X21649,X21650,X21651] :
      ( ~ class_Orderings_Oorder(X21651)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21651),X21650),X21649))
      | c_SetInterval_Oord__class_OgreaterThanLessThan(X21651,X21649,X21650) = c_Orderings_Obot__class_Obot(tc_fun(X21651,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThanLessThan__empty])]) ).

fof(i_0_10026,plain,
    ! [X33800] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33800),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | X33800 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X33800 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33800),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1])]) ).

fof(i_0_10027,plain,
    ! [X30417,X30418,X30419] :
      ( X30419 = c_List_Olist_ONil(X30418)
      | hAPP(c_List_Otl(X30418),hAPP(hAPP(c_List_Oappend(X30418),X30419),X30417)) = hAPP(hAPP(c_List_Oappend(X30418),hAPP(c_List_Otl(X30418),X30419)),X30417) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tl__append2])]) ).

fof(i_0_10028,plain,
    ! [X20823,X20824] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X20824,X20823)),X20823) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__zdiv__trivial]) ).

fof(i_0_10029,plain,
    ! [X22341,X22342,X22343,X22344] :
      ( ( hAPP(c_Product__Type_Ofst(X22342,X22341),X22344) = hAPP(c_Product__Type_Ofst(X22342,X22341),X22343)
        | X22344 != X22343 )
      & ( hAPP(c_Product__Type_Osnd(X22342,X22341),X22344) = hAPP(c_Product__Type_Osnd(X22342,X22341),X22343)
        | X22344 != X22343 )
      & ( hAPP(c_Product__Type_Ofst(X22342,X22341),X22344) != hAPP(c_Product__Type_Ofst(X22342,X22341),X22343)
        | hAPP(c_Product__Type_Osnd(X22342,X22341),X22344) != hAPP(c_Product__Type_Osnd(X22342,X22341),X22343)
        | X22344 = X22343 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Pair__fst__snd__eq])])]) ).

fof(i_0_10030,plain,
    ! [X22337,X22338,X22339,X22340] :
      ( hAPP(c_Product__Type_Ofst(X22340,X22339),X22338) != hAPP(c_Product__Type_Ofst(X22340,X22339),X22337)
      | hAPP(c_Product__Type_Osnd(X22340,X22339),X22338) != hAPP(c_Product__Type_Osnd(X22340,X22339),X22337)
      | X22338 = X22337 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_prod__eqI])]) ).

fof(i_0_10031,plain,
    ! [X27794,X27795] : c_Fun_Oinj__on(X27795,X27795,c_Fun_Oid(X27795),X27794),
    inference(variable_rename,[status(thm)],[fact_inj__on__id]) ).

fof(i_0_10032,plain,
    ! [X18353,X18354] : c_Fun_Oinj__on(X18354,X18354,c_COMBI(X18354),X18353),
    inference(variable_rename,[status(thm)],[fact_inj__on__id2]) ).

fof(i_0_10033,plain,
    ! [X25813,X25814,X25815] :
      ( ~ class_Rings_Olinordered__idom(X25815)
      | c_Groups_Osgn__class_Osgn(X25815,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),X25814),X25813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25815),c_Groups_Osgn__class_Osgn(X25815,X25814)),c_Groups_Osgn__class_Osgn(X25815,X25813)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__times])]) ).

fof(i_0_10034,plain,
    ! [X31695,X31696,X31697] :
      ( ~ class_Orderings_Olinorder(X31697)
      | ~ c_List_Olinorder__class_Osorted(X31697,X31696)
      | ~ hBOOL(hAPP(c_List_Odistinct(X31697),X31696))
      | ~ c_List_Olinorder__class_Osorted(X31697,X31695)
      | ~ hBOOL(hAPP(c_List_Odistinct(X31697),X31695))
      | hAPP(c_List_Oset(X31697),X31696) != hAPP(c_List_Oset(X31697),X31695)
      | X31696 = X31695 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__distinct__set__unique])]) ).

fof(i_0_10035,plain,
    ! [X30234,X30235,X30236,X30237] : hAPP(hAPP(c_List_Odrop(X30237),hAPP(c_Nat_OSuc,X30236)),hAPP(hAPP(c_List_Olist_OCons(X30237),X30235),X30234)) = hAPP(hAPP(c_List_Odrop(X30237),X30236),X30234),
    inference(variable_rename,[status(thm)],[fact_drop__Suc__Cons]) ).

cnf(i_0_10036,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_10037,plain,
    ! [X25881,X25882,X25883] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25883)
      | hAPP(c_Groups_Oabs__class_Oabs(X25883),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25883),X25882),X25881)) = hAPP(c_Groups_Oabs__class_Oabs(X25883),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25883),X25881),X25882)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__commute])]) ).

cnf(i_0_10038,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_5970]) ).

fof(i_0_10039,plain,
    ! [X32794,X32795,X32796] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X32796,X32795,X32794,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X32795,
    inference(variable_rename,[status(thm)],[fact_code__numeral_Orecs_I1_J]) ).

fof(i_0_10040,plain,
    ! [X25984,X25985,X25986] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X25986,X25985,X25984,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X25985,
    inference(variable_rename,[status(thm)],[fact_code__numeral_Osimps_I4_J]) ).

fof(i_0_10041,plain,
    ! [X18646,X18647,X18648] : c_Nat_Onat_Onat__case(X18648,X18647,X18646,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18647,
    inference(variable_rename,[status(thm)],[fact_nat__case__0]) ).

fof(i_0_10042,plain,
    ! [X20810,X20811] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20811)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20810)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20811),X20810)),
    inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I1_J]) ).

fof(i_0_10043,plain,
    ! [X20045,X20046] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20046)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20045)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20046),X20045)),
    inference(variable_rename,[status(thm)],[fact_zmult__int]) ).

fof(i_0_10044,plain,
    ! [X20041,X20042] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20042)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20041)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20042),X20041)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J]) ).

fof(i_0_10045,plain,
    ! [X19433,X19434] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19434)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19433)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19434),X19433)),
    inference(variable_rename,[status(thm)],[fact_times__numeral__code_I5_J]) ).

fof(i_0_10046,plain,
    ! [X20021,X20022] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20022)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20021)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20022),X20021)),
    inference(variable_rename,[status(thm)],[fact_zadd__int]) ).

fof(i_0_10047,plain,
    ! [X20019,X20020] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20020)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20019)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X20020),X20019)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J]) ).

fof(i_0_10048,plain,
    ! [X19429,X19430] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19430)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19429)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19430),X19429)),
    inference(variable_rename,[status(thm)],[fact_plus__numeral__code_I9_J]) ).

cnf(i_0_10049,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_5971]) ).

fof(i_0_10050,plain,
    ! [X21217,X21218] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21218),X21217)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21218)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21217)),
    inference(variable_rename,[status(thm)],[fact_zminus__zadd__distrib]) ).

fof(i_0_10051,plain,
    ! [X20812,X20813] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20813),X20812)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20813)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20812)),
    inference(variable_rename,[status(thm)],[fact_zdiv__int]) ).

fof(i_0_10052,plain,
    ! [X20043,X20044] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20044),X20043)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20044)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20043)),
    inference(variable_rename,[status(thm)],[fact_int__mult]) ).

fof(i_0_10053,plain,
    ! [X32588,X32589,X32590,X32591] :
      ( ( ~ hBOOL(hAPP(X32591,X32590))
        | hAPP(c_List_Ofilter(X32589,X32591),c_List_Oreplicate(X32589,X32588,X32590)) = c_List_Oreplicate(X32589,X32588,X32590) )
      & ( hBOOL(hAPP(X32591,X32590))
        | hAPP(c_List_Ofilter(X32589,X32591),c_List_Oreplicate(X32589,X32588,X32590)) = c_List_Olist_ONil(X32589) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5972])]) ).

fof(i_0_10054,plain,
    ! [X26116,X26117] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26117,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26117,tc_HOL_Obool))),X26116) = X26116,
    inference(variable_rename,[status(thm)],[fact_Int__UNIV__left]) ).

fof(i_0_10055,plain,
    ! [X23384,X23385] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23385,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23385,tc_HOL_Obool))),X23384) = X23384,
    inference(variable_rename,[status(thm)],[fact_Un__empty__left]) ).

fof(i_0_10056,plain,
    ! [X19442,X19443] :
      ( ( X19443 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19443),X19442) != 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)),X19443)) )
      & ( X19442 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19443),X19442) != 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)),X19443)) )
      & ( X19443 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X19442 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19443),X19442) = 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)),X19443)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff])])]) ).

cnf(i_0_10057,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(split_conjunct,[status(thm)],[fact_succ__Pls]) ).

fof(i_0_10058,plain,
    ! [X19352,X19353,X19354] : hAPP(c_Finite__Set_Ofold1(X19354,X19353),hAPP(hAPP(c_Set_Oinsert(X19354),X19352),c_Orderings_Obot__class_Obot(tc_fun(X19354,tc_HOL_Obool)))) = X19352,
    inference(variable_rename,[status(thm)],[fact_fold1__singleton]) ).

fof(i_0_10059,plain,
    ! [X30751,X30752,X30753,X30754] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30754)),hAPP(hAPP(c_List_Omap(X30753,X30754),X30752),X30751)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30753)),X30751),
    inference(variable_rename,[status(thm)],[fact_length__map]) ).

fof(i_0_10060,plain,
    ! [X29677,X29678,X29679,X29680] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29680)),hAPP(hAPP(c_List_Olist__update(X29680,X29679),X29678),X29677)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29680)),X29679),
    inference(variable_rename,[status(thm)],[fact_length__list__update]) ).

fof(i_0_10061,plain,
    ! [X21642,X21643,X21644] :
      ( ~ class_Rings_Oring__1(X21644)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21644),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21643),X21642)) = hAPP(hAPP(c_Power_Opower__class_Opower(X21644),hAPP(c_Int_Oring__1__class_Oof__int(X21644),X21643)),X21642) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__power])]) ).

fof(i_0_10062,plain,
    ! [X20262,X20263,X20264] :
      ( ~ class_Rings_Osemiring__1(X20264)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20264),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20263),X20262)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20264),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20264),X20263)),X20262) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__power])]) ).

fof(i_0_10063,plain,
    ! [X19506,X19507] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19507),X19506))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19507),X19506)) )
      & ( X19507 != X19506
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19507),X19506)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19507),X19506))
        | X19507 = X19506
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19507),X19506)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zless__le])])]) ).

fof(i_0_10064,plain,
    ! [X17737,X17738] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17738),X17737))
      | X17738 = X17737
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17738),X17737)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__neq__implies__less])]) ).

fof(i_0_10065,plain,
    ! [X17733,X17734] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17734),X17733))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17734),X17733))
        | X17734 = X17733 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17734),X17733))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17734),X17733)) )
      & ( X17734 != X17733
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17734),X17733)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq])])]) ).

fof(i_0_10066,plain,
    ! [X17731,X17732] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17732),X17731))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17732),X17731)) )
      & ( X17732 != X17731
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17732),X17731)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17732),X17731))
        | X17732 = X17731
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17732),X17731)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__less__le])])]) ).

cnf(i_0_10067,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(X1)) = X1
    | ~ c_List_Onat__list(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_5973]) ).

fof(i_0_10068,plain,
    ! [X19355,X19356,X19357,X19358] :
      ( X19358 != c_Finite__Set_Ofold1(X19357,X19356)
      | hAPP(X19358,hAPP(hAPP(c_Set_Oinsert(X19357),X19355),c_Orderings_Obot__class_Obot(tc_fun(X19357,tc_HOL_Obool)))) = X19355 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fold1__singleton__def])]) ).

fof(i_0_10069,plain,
    ! [X30441,X30442] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30442)),hAPP(c_List_Otl(X30442),X30441)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30442)),X30441)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__tl]) ).

fof(i_0_10070,plain,
    ! [X17816,X17817,X17818,X17819,X17820] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(X17820,X17819,X17818)
      | hAPP(hAPP(X17818,X17817),hAPP(hAPP(X17818,X17817),X17816)) = hAPP(hAPP(X17818,X17817),X17816) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem_Ofun__left__idem])]) ).

fof(i_0_10071,plain,
    ! [X21655] : 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)),X21655)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J]) ).

fof(i_0_10072,plain,
    ! [X23999,X24000] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24000,X23999))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost__int]) ).

fof(i_0_10073,plain,
    ! [X23479,X23480] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X23480,X23479))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost__int]) ).

fof(i_0_10074,plain,
    ! [X21486,X21487] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X21487,X21486))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan__int]) ).

fof(i_0_10075,plain,
    ! [X23997,X23998] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X23998,X23997))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastAtMost]) ).

fof(i_0_10076,plain,
    ! [X23477,X23478] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X23478,X23477))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanAtMost]) ).

fof(i_0_10077,plain,
    ! [X21704,X21705] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X21705,X21704))),
    inference(variable_rename,[status(thm)],[fact_finite__greaterThanLessThan]) ).

fof(i_0_10078,plain,
    ! [X18770] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18770),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | X18770 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18770 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18770),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_10079,plain,
    ! [X18502] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X18502),
    inference(variable_rename,[status(thm)],[fact_inj__Suc]) ).

fof(i_0_10080,plain,
    ! [X17776,X17777] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17777),X17776))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17777),X17776)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J])]) ).

fof(i_0_10081,plain,
    ! [X17739,X17740] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17740),X17739))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17740),X17739)) )
      & ( X17740 != X17739
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17740),X17739)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__or__eq__imp__le])])]) ).

fof(i_0_10082,plain,
    ! [X17735,X17736] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17736),X17735))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17736),X17735)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__le__nat])]) ).

fof(i_0_10083,plain,
    ! [X24091,X24092,X24093] :
      ( ~ class_Orderings_Oorder(X24093)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24093),X24092),X24091))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X24093,X24091),X24092) = c_Orderings_Obot__class_Obot(tc_fun(X24093,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastLessThan__empty])]) ).

fof(i_0_10084,plain,
    ! [X17193,X17194,X17195] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X17195),X17194),hAPP(c_fequal,X17193)))
        | X17194 = X17193 )
      & ( X17194 != X17193
        | hBOOL(hAPP(hAPP(c_member(X17195),X17194),hAPP(c_fequal,X17193))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__mem])]) ).

fof(i_0_10085,plain,
    ! [X30664,X30665,X30666,X30667] :
      ( X30667 = c_List_Olist_ONil(X30666)
      | c_List_Olast(X30665,hAPP(hAPP(c_List_Omap(X30666,X30665),X30664),X30667)) = hAPP(X30664,c_List_Olast(X30666,X30667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__map])]) ).

cnf(i_0_10086,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_5974]) ).

fof(i_0_10087,plain,
    ! [X21174,X21175,X21176] :
      ( ~ class_Groups_Ogroup__add(X21176)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21176),hAPP(c_Groups_Ouminus__class_Ouminus(X21176),X21175)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21176),X21175),X21174)) = X21174 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__add__cancel])]) ).

fof(i_0_10088,plain,
    ! [X16938,X16939,X16940,X16941,X16942] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X16939),X16940),X16938))
        | X16938 != c_Orderings_Obot__class_Obot(tc_fun(X16939,tc_HOL_Obool)) )
      & ( X16941 = c_Orderings_Obot__class_Obot(tc_fun(X16942,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(X16942),esk3_2(X16941,X16942)),X16941)) ) ),
    inference(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_10089,plain,
    ! [X16944,X16945,X16947,X16948,X16949] :
      ( ( hBOOL(hAPP(hAPP(c_member(X16945),esk4_2(X16944,X16945)),X16944))
        | X16944 = c_Orderings_Obot__class_Obot(tc_fun(X16945,tc_HOL_Obool)) )
      & ( X16947 != c_Orderings_Obot__class_Obot(tc_fun(X16948,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(X16948),X16949),X16947)) ) ),
    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_5975])])])])]) ).

fof(i_0_10090,plain,
    ! [X29898,X29899,X29900] :
      ( hBOOL(hAPP(hAPP(c_member(X29900),X29899),hAPP(c_List_Oset(X29900),X29898)))
      | c_List_Oremove1(X29900,X29899,X29898) = X29898 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5976])]) ).

cnf(i_0_10091,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_5977]) ).

fof(i_0_10092,plain,
    ! [X21673,X21674] :
      ( ~ class_Rings_Oring__1(X21674)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21673))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21674),hAPP(c_Int_Onat,X21673)) = hAPP(c_Int_Oring__1__class_Oof__int(X21674),X21673) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__nat])]) ).

fof(i_0_10093,plain,
    ! [X21225,X21226] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21226),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21225)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X21226,X21225)),
    inference(variable_rename,[status(thm)],[fact_zmod__zminus__zminus]) ).

fof(i_0_10094,plain,
    ! [X21323,X21324] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21324),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21323)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21324,X21323)),
    inference(variable_rename,[status(thm)],[fact_Divides_Otransfer__int__nat__functions_I2_J]) ).

fof(i_0_10095,plain,
    ! [X21321,X21322] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21322,X21321)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21322),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21321)),
    inference(variable_rename,[status(thm)],[fact_zmod__int]) ).

fof(i_0_10096,plain,
    ! [X25806,X25807] :
      ( ( X25806 != c_Groups_Ozero__class_Ozero(X25807)
        | c_Groups_Osgn__class_Osgn(X25807,X25806) = c_Groups_Ozero__class_Ozero(X25807)
        | ~ class_Groups_Osgn__if(X25807) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25806))
        | c_Groups_Osgn__class_Osgn(X25807,X25806) = c_Groups_Oone__class_Oone(X25807)
        | X25806 = c_Groups_Ozero__class_Ozero(X25807)
        | ~ class_Groups_Osgn__if(X25807) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25807),c_Groups_Ozero__class_Ozero(X25807)),X25806))
        | c_Groups_Osgn__class_Osgn(X25807,X25806) = hAPP(c_Groups_Ouminus__class_Ouminus(X25807),c_Groups_Oone__class_Oone(X25807))
        | X25806 = c_Groups_Ozero__class_Ozero(X25807)
        | ~ class_Groups_Osgn__if(X25807) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5978])])]) ).

fof(i_0_10097,plain,
    ! [X29806,X29807] :
      ( ~ class_Groups_Ocomm__monoid__add(X29807)
      | ~ hBOOL(hAPP(c_List_Odistinct(X29807),X29806))
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29807),X29806) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X29807,X29807),c_COMBI(X29807)),hAPP(c_List_Oset(X29807),X29806)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__listsum__conv__Setsum])]) ).

fof(i_0_10098,plain,
    ! [X20175,X20176,X20177] :
      ( ~ class_Rings_Ocomm__semiring__1(X20177)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20177),X20176),hAPP(hAPP(c_Power_Opower__class_Opower(X20177),X20176),X20175)) = hAPP(hAPP(c_Power_Opower__class_Opower(X20177),X20176),hAPP(c_Nat_OSuc,X20175)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J])]) ).

fof(i_0_10099,plain,
    ! [X20293,X20294,X20295] :
      ( ~ class_Power_Opower(X20295)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20295),X20294),hAPP(c_Nat_OSuc,X20293)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20295),X20294),hAPP(hAPP(c_Power_Opower__class_Opower(X20295),X20294),X20293)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__Suc])]) ).

fof(i_0_10100,plain,
    ! [X20178,X20179,X20180] :
      ( ~ class_Rings_Ocomm__semiring__1(X20180)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20180),X20179),hAPP(c_Nat_OSuc,X20178)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20180),X20179),hAPP(hAPP(c_Power_Opower__class_Opower(X20180),X20179),X20178)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J])]) ).

fof(i_0_10101,plain,
    ! [X25796,X25797] :
      ( ~ class_Groups_Oordered__ab__group__add(X25797)
      | hAPP(c_Set_Oimage(X25797,X25797,c_Groups_Ouminus__class_Ouminus(X25797)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25797),X25796)) = hAPP(c_SetInterval_Oord__class_OlessThan(X25797),hAPP(c_Groups_Ouminus__class_Ouminus(X25797),X25796)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__greaterThan])]) ).

fof(i_0_10102,plain,
    ! [X25763,X25764] :
      ( ~ class_Groups_Oordered__ab__group__add(X25764)
      | hAPP(c_Set_Oimage(X25764,X25764,c_Groups_Ouminus__class_Ouminus(X25764)),hAPP(c_SetInterval_Oord__class_OatLeast(X25764),X25763)) = hAPP(c_SetInterval_Oord__class_OatMost(X25764),hAPP(c_Groups_Ouminus__class_Ouminus(X25764),X25763)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atLeast])]) ).

fof(i_0_10103,plain,
    ! [X25761,X25762] :
      ( ~ class_Groups_Oordered__ab__group__add(X25762)
      | hAPP(c_Set_Oimage(X25762,X25762,c_Groups_Ouminus__class_Ouminus(X25762)),hAPP(c_SetInterval_Oord__class_OatMost(X25762),X25761)) = hAPP(c_SetInterval_Oord__class_OatLeast(X25762),hAPP(c_Groups_Ouminus__class_Ouminus(X25762),X25761)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__atMost])]) ).

fof(i_0_10104,plain,
    ! [X25794,X25795] :
      ( ~ class_Groups_Oordered__ab__group__add(X25795)
      | hAPP(c_Set_Oimage(X25795,X25795,c_Groups_Ouminus__class_Ouminus(X25795)),hAPP(c_SetInterval_Oord__class_OlessThan(X25795),X25794)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X25795),hAPP(c_Groups_Ouminus__class_Ouminus(X25795),X25794)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_image__uminus__lessThan])]) ).

fof(i_0_10105,plain,
    ! [X32525,X32526,X32527] : c_List_Oreplicate(X32527,hAPP(c_Nat_OSuc,X32526),X32525) = hAPP(hAPP(c_List_Olist_OCons(X32527),X32525),c_List_Oreplicate(X32527,X32526,X32525)),
    inference(variable_rename,[status(thm)],[fact_replicate__Suc]) ).

cnf(i_0_10106,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_5979]) ).

cnf(i_0_10107,plain,
    ( c_List_Oupt(X2,X1) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_5980]) ).

cnf(i_0_10108,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_5979]) ).

fof(i_0_10109,plain,
    ! [X21434,X21435] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21435))
        | c_SMT_Oz3mod(X21434,X21435) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X21434,X21435) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21435))
        | c_SMT_Oz3mod(X21434,X21435) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X21434,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21435)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5981])]) ).

fof(i_0_10110,plain,
    ! [X32620,X32621,X32622] :
      ( ( X32622 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Oset(X32621),c_List_Oreplicate(X32621,X32622,X32620)) = c_Orderings_Obot__class_Obot(tc_fun(X32621,tc_HOL_Obool)) )
      & ( X32622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_List_Oset(X32621),c_List_Oreplicate(X32621,X32622,X32620)) = hAPP(hAPP(c_Set_Oinsert(X32621),X32620),c_Orderings_Obot__class_Obot(tc_fun(X32621,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate__conv__if])]) ).

fof(i_0_10111,plain,
    ! [X32617,X32618,X32619] :
      ( X32619 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Oset(X32618),c_List_Oreplicate(X32618,X32619,X32617)) = hAPP(hAPP(c_Set_Oinsert(X32618),X32617),c_Orderings_Obot__class_Obot(tc_fun(X32618,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__replicate])]) ).

fof(i_0_10112,plain,
    ! [X25890,X25891] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25891)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25891),c_Groups_Ozero__class_Ozero(X25891)),X25890))
      | hAPP(c_Groups_Oabs__class_Oabs(X25891),X25890) = X25890 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__pos])]) ).

fof(i_0_10113,plain,
    ! [X25888,X25889] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25889)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25889),c_Groups_Ozero__class_Ozero(X25889)),X25888))
      | hAPP(c_Groups_Oabs__class_Oabs(X25889),X25888) = X25888 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonneg])]) ).

fof(i_0_10114,plain,
    ! [X25957,X25958] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25958),X25957),c_Groups_Ozero__class_Ozero(X25958)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25958),X25957) = hAPP(c_Groups_Ouminus__class_Ouminus(X25958),X25957)
        | ~ class_Groups_Oabs__if(X25958) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25958),X25957),c_Groups_Ozero__class_Ozero(X25958)))
        | hAPP(c_Groups_Oabs__class_Oabs(X25958),X25957) = X25957
        | ~ class_Groups_Oabs__if(X25958) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5982])])]) ).

fof(i_0_10115,plain,
    ! [X25959,X25960] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25960)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25960),X25959),c_Groups_Ozero__class_Ozero(X25960)))
      | hAPP(c_Groups_Oabs__class_Oabs(X25960),X25959) = hAPP(c_Groups_Ouminus__class_Ouminus(X25960),X25959) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__neg])]) ).

fof(i_0_10116,plain,
    ! [X25955,X25956] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25956)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25956),X25955),c_Groups_Ozero__class_Ozero(X25956)))
      | hAPP(c_Groups_Oabs__class_Oabs(X25956),X25955) = hAPP(c_Groups_Ouminus__class_Ouminus(X25956),X25955) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos])]) ).

fof(i_0_10117,plain,
    ! [X25804,X25805] :
      ( ~ class_Rings_Olinordered__idom(X25805)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25805),X25804),c_Groups_Ozero__class_Ozero(X25805)))
      | c_Groups_Osgn__class_Osgn(X25805,X25804) = hAPP(c_Groups_Ouminus__class_Ouminus(X25805),c_Groups_Oone__class_Oone(X25805)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__neg])]) ).

fof(i_0_10118,plain,
    ! [X25802,X25803] :
      ( ( c_Groups_Osgn__class_Osgn(X25803,X25802) != hAPP(c_Groups_Ouminus__class_Ouminus(X25803),c_Groups_Oone__class_Oone(X25803))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),X25802),c_Groups_Ozero__class_Ozero(X25803)))
        | ~ class_Rings_Olinordered__idom(X25803) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25803),X25802),c_Groups_Ozero__class_Ozero(X25803)))
        | c_Groups_Osgn__class_Osgn(X25803,X25802) = hAPP(c_Groups_Ouminus__class_Ouminus(X25803),c_Groups_Oone__class_Oone(X25803))
        | ~ class_Rings_Olinordered__idom(X25803) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__neg])])]) ).

fof(i_0_10119,plain,
    ! [X33075,X33076,X33077,X33078] :
      ( ~ c_Equiv__Relations_Opart__equivp(X33078,X33077)
      | ~ hBOOL(hAPP(hAPP(X33077,X33076),X33075))
      | hBOOL(hAPP(hAPP(X33077,X33075),X33076)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivp__symp])]) ).

fof(i_0_10120,plain,
    ! [X32949,X32950,X32951,X32952] :
      ( ~ c_Predicate_Osymp(X32952,X32951)
      | ~ hBOOL(hAPP(hAPP(X32951,X32950),X32949))
      | hBOOL(hAPP(hAPP(X32951,X32949),X32950)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sympE])]) ).

fof(i_0_10121,plain,
    ! [X26681,X26682,X26683,X26684] :
      ( ~ c_Equiv__Relations_Oequivp(X26684,X26683)
      | ~ hBOOL(hAPP(hAPP(X26683,X26682),X26681))
      | hBOOL(hAPP(hAPP(X26683,X26681),X26682)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__symp])]) ).

fof(i_0_10122,plain,
    ! [X33670,X33671,X33672] :
      ( ~ class_Divides_Osemiring__div(X33672)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33672),X33671),X33670))
      | c_Divides_Odiv__class_Omod(X33672,X33670,X33671) = c_Groups_Ozero__class_Ozero(X33672) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__imp__mod__0])]) ).

fof(i_0_10123,plain,
    ! [X33667,X33668,X33669] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33669),X33668),X33667))
        | c_Divides_Odiv__class_Omod(X33669,X33667,X33668) = c_Groups_Ozero__class_Ozero(X33669)
        | ~ class_Divides_Osemiring__div(X33669) )
      & ( c_Divides_Odiv__class_Omod(X33669,X33667,X33668) != c_Groups_Ozero__class_Ozero(X33669)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33669),X33668),X33667))
        | ~ class_Divides_Osemiring__div(X33669) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__eq__mod__eq__0])])]) ).

fof(i_0_10124,plain,
    ! [X29747,X29748] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29748)),c_List_Obutlast(X29748,X29747)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29748)),X29747)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_length__butlast]) ).

fof(i_0_10125,plain,
    ! [X18638] :
      ( ~ class_Rings_Olinordered__semidom(X18638)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18638),c_Groups_Oone__class_Oone(X18638)),c_Groups_Ozero__class_Ozero(X18638))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5983])]) ).

fof(i_0_10126,plain,
    ! [X18635] :
      ( ~ class_Rings_Olinordered__semidom(X18635)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18635),c_Groups_Oone__class_Oone(X18635)),c_Groups_Ozero__class_Ozero(X18635))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5984])]) ).

fof(i_0_10127,plain,
    ! [X18099,X18100] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18100),X18099))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18099),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18100),X18099)) = X18100 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5985])]) ).

fof(i_0_10128,plain,
    ! [X29822,X29823] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X29823)),c_List_Olist_ONil(X29823)),c_List_Olists(X29823,X29822))),
    inference(variable_rename,[status(thm)],[fact_lists_ONil]) ).

fof(i_0_10129,plain,
    ! [X25822,X25823] :
      ( ~ class_Rings_Olinordered__idom(X25823)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25823),c_Groups_Ozero__class_Ozero(X25823)),X25822))
      | c_Groups_Osgn__class_Osgn(X25823,X25822) = c_Groups_Oone__class_Oone(X25823) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__pos])]) ).

fof(i_0_10130,plain,
    ! [X25820,X25821] :
      ( ( c_Groups_Osgn__class_Osgn(X25821,X25820) != c_Groups_Oone__class_Oone(X25821)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25821),c_Groups_Ozero__class_Ozero(X25821)),X25820))
        | ~ class_Rings_Olinordered__idom(X25821) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X25821),c_Groups_Ozero__class_Ozero(X25821)),X25820))
        | c_Groups_Osgn__class_Osgn(X25821,X25820) = c_Groups_Oone__class_Oone(X25821)
        | ~ class_Rings_Olinordered__idom(X25821) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__1__pos])])]) ).

fof(i_0_10131,plain,
    ! [X22640,X22641,X22642] :
      ( ~ class_Rings_Odivision__ring(X22642)
      | X22641 = c_Groups_Ozero__class_Ozero(X22642)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22642),hAPP(c_Groups_Ouminus__class_Ouminus(X22642),X22640)),hAPP(c_Groups_Ouminus__class_Ouminus(X22642),X22641)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22642),X22640),X22641) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__divide])]) ).

fof(i_0_10132,plain,
    ! [X29964] : c_List_Olistset(X29964,c_List_Olist_ONil(tc_fun(X29964,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29964)),c_List_Olist_ONil(X29964)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29964),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_listset_Osimps_I1_J]) ).

fof(i_0_10133,plain,
    ! [X29945] : c_List_Olists(X29945,c_Orderings_Obot__class_Obot(tc_fun(X29945,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(X29945)),c_List_Olist_ONil(X29945)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(X29945),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_lists__empty]) ).

fof(i_0_10134,plain,
    ! [X27563,X27564,X27565] :
      ( ~ hBOOL(hAPP(X27565,X27564))
      | hBOOL(hAPP(hAPP(c_member(X27563),X27564),hAPP(c_Set_OCollect(X27563),X27565))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_CollectI])]) ).

fof(i_0_10135,plain,
    ! [X31782,X31783] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X31783),hAPP(c_List_Orev(X31783),X31782)))
        | hBOOL(hAPP(c_List_Odistinct(X31783),X31782)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31783),X31782))
        | hBOOL(hAPP(c_List_Odistinct(X31783),hAPP(c_List_Orev(X31783),X31782))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__rev])]) ).

fof(i_0_10136,plain,
    ! [X30246,X30247] :
      ( ( ~ hBOOL(hAPP(c_List_Odistinct(X30247),hAPP(c_List_Orotate1(X30247),X30246)))
        | hBOOL(hAPP(c_List_Odistinct(X30247),X30246)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X30247),X30246))
        | hBOOL(hAPP(c_List_Odistinct(X30247),hAPP(c_List_Orotate1(X30247),X30246))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct1__rotate])]) ).

fof(i_0_10137,plain,
    ! [X24473,X24474] : hAPP(hAPP(c_Equiv__Relations_Oquotient(X24474),c_Orderings_Obot__class_Obot(tc_fun(X24474,tc_HOL_Obool))),X24473) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24474,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_quotient__empty]) ).

fof(i_0_10138,plain,
    ! [X27841,X27842] : hAPP(c_Product__Type_Oprod_Oprod__case(X27842,X27841,tc_prod(X27842,X27841)),c_Product__Type_OPair(X27842,X27841)) = c_Fun_Oid(tc_prod(X27842,X27841)),
    inference(variable_rename,[status(thm)],[fact_split__Pair]) ).

fof(i_0_10139,plain,
    ! [X24996,X24997,X24998] :
      ( ~ class_Lattices_Osemilattice__inf(X24998)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24998),X24997),X24996))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24998),X24997),X24996) = X24997 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb1])]) ).

fof(i_0_10140,plain,
    ! [X24981,X24982,X24983] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24983),X24982),X24981))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24983),X24982),X24981) = X24982
        | ~ class_Lattices_Osemilattice__inf(X24983) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24983),X24982),X24981) != X24982
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X24983),X24982),X24981))
        | ~ class_Lattices_Osemilattice__inf(X24983) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__inf])])]) ).

fof(i_0_10141,plain,
    ! [X24999,X25000,X25001] :
      ( ~ class_Lattices_Osemilattice__inf(X25001)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25001),X25000),X24999))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25001),X24999),X25000) = X25000 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__absorb2])]) ).

fof(i_0_10142,plain,
    ! [X23327,X23328,X23329] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23329),X23328),X23327))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23329),X23328),X23327) = X23327
        | ~ class_Lattices_Osemilattice__sup(X23329) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23329),X23328),X23327) != X23327
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23329),X23328),X23327))
        | ~ class_Lattices_Osemilattice__sup(X23329) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_le__iff__sup])])]) ).

fof(i_0_10143,plain,
    ! [X23312,X23313,X23314] :
      ( ~ class_Lattices_Osemilattice__sup(X23314)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23314),X23313),X23312))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23314),X23313),X23312) = X23312 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb2])]) ).

fof(i_0_10144,plain,
    ! [X23309,X23310,X23311] :
      ( ~ class_Lattices_Osemilattice__sup(X23311)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23311),X23310),X23309))
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23311),X23309),X23310) = X23309 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__absorb1])]) ).

fof(i_0_10145,plain,
    ! [X22601,X22602,X22603] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22603),X22602),X22601))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22603),X22602),X22601) = X22601
        | ~ class_Orderings_Olinorder(X22603) )
      & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X22603),X22602),X22601) != X22601
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22603),X22602),X22601))
        | ~ class_Orderings_Olinorder(X22603) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__sup])])]) ).

fof(i_0_10146,plain,
    ! [X22586,X22587,X22588] :
      ( ~ class_Orderings_Olinorder(X22588)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22588),X22587),X22586))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22588),X22587),X22586) = X22586 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb2])]) ).

fof(i_0_10147,plain,
    ! [X22583,X22584,X22585] :
      ( ~ class_Orderings_Olinorder(X22585)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X22585),X22584),X22583))
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22585),X22583),X22584) = X22583 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__absorb1])]) ).

fof(i_0_10148,plain,
    ! [X21547,X21548,X21549] :
      ( ~ class_Orderings_Olinorder(X21549)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21549),X21548),X21547))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21549),X21548),X21547) = X21548 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb1])]) ).

fof(i_0_10149,plain,
    ! [X21532,X21533,X21534] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21534),X21533),X21532))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21534),X21533),X21532) = X21533
        | ~ class_Orderings_Olinorder(X21534) )
      & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X21534),X21533),X21532) != X21533
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21534),X21533),X21532))
        | ~ class_Orderings_Olinorder(X21534) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ole__iff__inf])])]) ).

fof(i_0_10150,plain,
    ! [X21550,X21551,X21552] :
      ( ~ class_Orderings_Olinorder(X21552)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X21552),X21551),X21550))
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21552),X21550),X21551) = X21551 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__absorb2])]) ).

fof(i_0_10151,plain,
    ! [X27068,X27069] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X27069)
      | c_Complete__Lattice_OSup__class_OSup(X27069,hAPP(hAPP(c_Set_Oinsert(X27069),X27068),c_Orderings_Obot__class_Obot(tc_fun(X27069,tc_HOL_Obool)))) = X27068 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__singleton])]) ).

fof(i_0_10152,plain,
    ! [X26889,X26890] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26890)
      | c_Complete__Lattice_OInf__class_OInf(X26890,hAPP(hAPP(c_Set_Oinsert(X26890),X26889),c_Orderings_Obot__class_Obot(tc_fun(X26890,tc_HOL_Obool)))) = X26889 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__singleton])]) ).

fof(i_0_10153,plain,
    ! [X25647,X25648] :
      ( ~ class_Lattices_Olattice(X25648)
      | c_Big__Operators_Olattice__class_OInf__fin(X25648,hAPP(hAPP(c_Set_Oinsert(X25648),X25647),c_Orderings_Obot__class_Obot(tc_fun(X25648,tc_HOL_Obool)))) = X25647 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Osingleton])]) ).

fof(i_0_10154,plain,
    ! [X23485,X23486] :
      ( ~ class_Lattices_Olattice(X23486)
      | c_Big__Operators_Olattice__class_OSup__fin(X23486,hAPP(hAPP(c_Set_Oinsert(X23486),X23485),c_Orderings_Obot__class_Obot(tc_fun(X23486,tc_HOL_Obool)))) = X23485 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Osingleton])]) ).

fof(i_0_10155,plain,
    ! [X22994,X22995] :
      ( ~ class_Orderings_Olinorder(X22995)
      | c_Big__Operators_Olinorder__class_OMax(X22995,hAPP(hAPP(c_Set_Oinsert(X22995),X22994),c_Orderings_Obot__class_Obot(tc_fun(X22995,tc_HOL_Obool)))) = X22994 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Osingleton])]) ).

fof(i_0_10156,plain,
    ! [X21763,X21764] :
      ( ~ class_Orderings_Olinorder(X21764)
      | c_Big__Operators_Olinorder__class_OMin(X21764,hAPP(hAPP(c_Set_Oinsert(X21764),X21763),c_Orderings_Obot__class_Obot(tc_fun(X21764,tc_HOL_Obool)))) = X21763 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Osingleton])]) ).

fof(i_0_10157,plain,
    ! [X18720,X18721] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,X18721)),X18720) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18721),X18720)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc]) ).

cnf(i_0_10158,plain,
    ( c_Int_OBit1(X1) = c_Int_OMin
    | X1 != c_Int_OMin ),
    inference(split_conjunct,[status(thm)],[i_0_5910]) ).

cnf(i_0_10159,plain,
    ( c_Int_OMin = c_Int_OBit1(X1)
    | c_Int_OMin != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_5909]) ).

cnf(i_0_10160,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_5755]) ).

fof(i_0_10161,plain,
    ! [X18052,X18053] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18053),X18052)),X18053) = X18052,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse]) ).

fof(i_0_10162,plain,
    ! [X18054,X18055] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18055),X18054)),X18054) = X18055,
    inference(variable_rename,[status(thm)],[fact_diff__add__inverse2]) ).

fof(i_0_10163,plain,
    ! [X32633,X32634,X32635,X32636] : hAPP(c_New__DSequence_Opos__union(X32636,X32635,X32634),X32633) = c_Lazy__Sequence_Oappend(X32636,hAPP(X32635,X32633),hAPP(X32634,X32633)),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__union__def]) ).

fof(i_0_10164,plain,
    ! [X27042,X27043,X27044] :
      ( ~ c_Equiv__Relations_Oequiv(X27044,X27043,X27042)
      | c_Complete__Lattice_OSup__class_OSup(tc_fun(X27044,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(X27044),X27043),X27042)) = X27043 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Union__quotient])]) ).

fof(i_0_10165,plain,
    ! [X22784,X22785,X22786] :
      ( ~ class_Fields_Ofield__inverse__zero(X22786)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22786),hAPP(c_Groups_Ouminus__class_Ouminus(X22786),X22785)),hAPP(c_Groups_Ouminus__class_Ouminus(X22786),X22784)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22786),X22785),X22784) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__divide])]) ).

fof(i_0_10166,plain,
    ! [X25853,X25854] :
      ( ~ class_Rings_Olinordered__idom(X25854)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25854),hAPP(c_Groups_Oabs__class_Oabs(X25854),X25853)),hAPP(c_Groups_Oabs__class_Oabs(X25854),X25853)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25854),X25853),X25853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__mult__self])]) ).

fof(i_0_10167,plain,
    ! [X21180,X21181,X21182] :
      ( ~ class_Rings_Oring(X21182)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21182),hAPP(c_Groups_Ouminus__class_Ouminus(X21182),X21181)),hAPP(c_Groups_Ouminus__class_Ouminus(X21182),X21180)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21182),X21181),X21180) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__minus])]) ).

fof(i_0_10168,plain,
    ! [X21183,X21184,X21185] :
      ( ~ class_Rings_Oring(X21185)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21185),hAPP(c_Groups_Ouminus__class_Ouminus(X21185),X21184)),X21183) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21185),X21184),hAPP(c_Groups_Ouminus__class_Ouminus(X21185),X21183)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__commute])]) ).

fof(i_0_10169,plain,
    ! [X28249,X28250,X28251,X28252,X28253] :
      ( ( ~ c_Wellfounded_OwfP(X28250,X28249)
        | hBOOL(hAPP(c_Wellfounded_Oaccp(X28250,X28249),X28251)) )
      & ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X28253,X28252),esk298_2(X28252,X28253)))
        | c_Wellfounded_OwfP(X28253,X28252) ) ),
    inference(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_10170,plain,
    ! [X22637,X22638,X22639] :
      ( ~ class_Rings_Odivision__ring(X22639)
      | X22638 = c_Groups_Ozero__class_Ozero(X22639)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22639),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22639),X22637),X22638)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22639),X22637),hAPP(c_Groups_Ouminus__class_Ouminus(X22639),X22638)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__minus__divide__right])]) ).

cnf(i_0_10171,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_5986]) ).

fof(i_0_10172,plain,
    ! [X24475,X24476,X24477] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24477,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(X24477),X24476),X24475)
        | X24476 = c_Orderings_Obot__class_Obot(tc_fun(X24477,tc_HOL_Obool)) )
      & ( X24476 != c_Orderings_Obot__class_Obot(tc_fun(X24477,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24477,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(X24477),X24476),X24475) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty2])]) ).

fof(i_0_10173,plain,
    ! [X24478,X24479,X24480] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(X24480),X24479),X24478) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24480,tc_HOL_Obool),tc_HOL_Obool))
        | X24479 = c_Orderings_Obot__class_Obot(tc_fun(X24480,tc_HOL_Obool)) )
      & ( X24479 != c_Orderings_Obot__class_Obot(tc_fun(X24480,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(X24480),X24479),X24478) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X24480,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_quotient__is__empty])]) ).

fof(i_0_10174,plain,
    ! [X23521,X23522] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X23522,X23521)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X23521),X23522)),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost__int]) ).

fof(i_0_10175,plain,
    ! [X17560,X17561,X17562] :
      ( ( X17561 = X17560
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17562),X17561),X17560))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17562),X17560),X17561))
        | ~ class_Orderings_Olinorder(X17562) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17562),X17561),X17560))
        | X17561 != X17560
        | ~ class_Orderings_Olinorder(X17562) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17562),X17560),X17561))
        | X17561 != X17560
        | ~ class_Orderings_Olinorder(X17562) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff])])]) ).

fof(i_0_10176,plain,
    ! [X18839,X18840,X18841] :
      ( ~ class_Rings_Olinordered__idom(X18841)
      | X18840 = X18839
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18841),X18840),X18839))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18841),X18839),X18840)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5987])]) ).

fof(i_0_10177,plain,
    ! [X17630,X17631,X17632] :
      ( ~ class_Orderings_Olinorder(X17632)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17632),X17631),X17630))
      | X17631 = X17630
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17632),X17630),X17631)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5988])]) ).

fof(i_0_10178,plain,
    ! [X17572,X17573,X17574] :
      ( ~ class_Orderings_Olinorder(X17574)
      | X17573 = X17572
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17574),X17573),X17572))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17574),X17572),X17573)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5989])]) ).

fof(i_0_10179,plain,
    ! [X17569,X17570,X17571] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17571),X17569),X17570))
        | X17569 = X17570
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17571),X17570),X17569))
        | ~ class_Orderings_Olinorder(X17571) )
      & ( X17569 != X17570
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17571),X17569),X17570))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17571),X17570),X17569))
        | ~ class_Orderings_Olinorder(X17571) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5990])])]) ).

fof(i_0_10180,plain,
    ! [X17566,X17567,X17568] :
      ( ~ class_Orderings_Olinorder(X17568)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17568),X17567),X17566))
      | X17567 = X17566
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17568),X17566),X17567)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__less__linear])]) ).

fof(i_0_10181,plain,
    ! [X20637,X20638,X20639] :
      ( ~ class_Divides_Osemiring__div(X20639)
      | c_Divides_Odiv__class_Omod(X20639,c_Divides_Odiv__class_Omod(X20639,X20638,X20637),X20637) = c_Divides_Odiv__class_Omod(X20639,X20638,X20637) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mod__trivial])]) ).

fof(i_0_10182,plain,
    ! [X24962,X24963] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X24963,tc_HOL_Obool)),X24962),c_Orderings_Obot__class_Obot(tc_fun(X24963,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24963,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Int__empty__right]) ).

fof(i_0_10183,plain,
    ! [X26137,X26138] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26138,tc_HOL_Obool)),X26137),c_Orderings_Otop__class_Otop(tc_fun(X26138,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26138,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Un__UNIV__right]) ).

fof(i_0_10184,plain,
    ! [X26165,X26166] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X26166,tc_HOL_Obool)),X26165),c_Orderings_Otop__class_Otop(tc_fun(X26166,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X26166,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__UNIV]) ).

fof(i_0_10185,plain,
    ! [X28129,X28130] : hAPP(c_Relation_ODomain(X28130,X28129),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28130,X28129),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X28130,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__empty]) ).

fof(i_0_10186,plain,
    ! [X27941,X27942] : hAPP(c_Relation_ORange(X27942,X27941),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27942,X27941),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27941,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__empty]) ).

fof(i_0_10187,plain,
    ! [X22356,X22357,X22358,X22359] : hAPP(c_Product__Type_Ofst(X22359,X22358),hAPP(hAPP(c_Product__Type_OPair(X22359,X22358),X22357),X22356)) = X22357,
    inference(variable_rename,[status(thm)],[fact_fst__conv]) ).

fof(i_0_10188,plain,
    ! [X22365,X22366,X22367,X22368] : hAPP(c_Product__Type_Osnd(X22368,X22367),hAPP(hAPP(c_Product__Type_OPair(X22368,X22367),X22366),X22365)) = X22365,
    inference(variable_rename,[status(thm)],[fact_snd__conv]) ).

cnf(i_0_10189,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_10190,plain,
    ! [X18033,X18034,X18036,X18037,X18038] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18034),X18033))
        | X18033 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18034),esk18_2(X18033,X18034)) )
      & ( X18036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18037),X18038)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18037),X18036)) ) ),
    inference(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_10191,plain,
    ! [X16950,X16951,X16952] :
      ( ~ hBOOL(hAPP(hAPP(c_member(X16952),X16951),X16950))
      | hAPP(hAPP(c_Set_Oinsert(X16952),X16951),X16950) = X16950 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).

fof(i_0_10192,plain,
    ! [X17127,X17128] : c_Set_Othe__elem(X17128,hAPP(hAPP(c_Set_Oinsert(X17128),X17127),c_Orderings_Obot__class_Obot(tc_fun(X17128,tc_HOL_Obool)))) = X17127,
    inference(variable_rename,[status(thm)],[fact_the__elem__eq]) ).

fof(i_0_10193,plain,
    ! [X17657,X17658,X17659] :
      ( ~ class_Orderings_Olinorder(X17659)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17659),X17658),X17657))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17659),X17657),X17658)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5991])]) ).

fof(i_0_10194,plain,
    ! [X17642,X17643,X17644] :
      ( ~ class_Orderings_Olinorder(X17644)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17644),X17643),X17642))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17644),X17642),X17643)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__le__less__linear])]) ).

fof(i_0_10195,plain,
    ! [X17654,X17655,X17656] :
      ( ~ class_Orderings_Olinorder(X17656)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17656),X17655),X17654))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17656),X17654),X17655)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5992])]) ).

fof(i_0_10196,plain,
    ! [X17190,X17191,X17192] :
      ( ~ class_Orderings_Olinorder(X17192)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17192),X17191),X17190))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17192),X17190),X17191)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5993])]) ).

fof(i_0_10197,plain,
    ! [X17148,X17149,X17150] :
      ( ~ class_Orderings_Olinorder(X17150)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17150),X17149),X17148))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17150),X17148),X17149)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_linorder__linear])]) ).

cnf(i_0_10198,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_5994]) ).

cnf(i_0_10199,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_5995]) ).

fof(i_0_10200,plain,
    ! [X29642,X29643,X29644] :
      ( ~ class_Groups_Omonoid__add(X29644)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29644),hAPP(hAPP(c_List_Olist_OCons(X29644),X29643),X29642)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X29644),X29643),hAPP(c_List_Omonoid__add__class_Olistsum(X29644),X29642)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I2_J])]) ).

fof(i_0_10201,plain,
    ! [X22781,X22782,X22783] :
      ( ~ class_Fields_Ofield__inverse__zero(X22783)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X22783),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22783),X22782),X22781)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22783),X22782),hAPP(c_Groups_Ouminus__class_Ouminus(X22783),X22781)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__divide__right])]) ).

fof(i_0_10202,plain,
    ! [X21189,X21190,X21191] :
      ( ~ class_Rings_Oring(X21191)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21191),X21190),X21189)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21191),X21190),hAPP(c_Groups_Ouminus__class_Ouminus(X21191),X21189)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__mult__right])]) ).

fof(i_0_10203,plain,
    ! [X31059,X31060] : c_List_Opartition(X31060,X31059,c_List_Olist_ONil(X31060)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X31060),tc_List_Olist(X31060)),c_List_Olist_ONil(X31060)),c_List_Olist_ONil(X31060)),
    inference(variable_rename,[status(thm)],[fact_partition_Osimps_I1_J]) ).

cnf(i_0_10204,plain,
    c_Int_Osucc(c_Int_Opred(X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_5996]) ).

fof(i_0_10205,plain,
    ! [X29916,X29917,X29918] : hAPP(hAPP(c_List_Otake(X29918),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X29918),X29917),X29916)) = hAPP(hAPP(c_List_Olist_OCons(X29918),X29917),c_List_Olist_ONil(X29918)),
    inference(variable_rename,[status(thm)],[fact_take__1__Cons]) ).

fof(i_0_10206,plain,
    ! [X33014,X33015,X33016,X33017] :
      ( ~ c_Relation_Osym(X33017,X33016)
      | c_Relation_Osym(X33015,hAPP(hAPP(c_Relation_Oinv__image(X33017,X33015),X33016),X33014)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__inv__image])]) ).

fof(i_0_10207,plain,
    ! [X32849,X32850,X32851,X32852] :
      ( ~ c_Relation_Otrans(X32852,X32851)
      | c_Relation_Otrans(X32850,hAPP(hAPP(c_Relation_Oinv__image(X32852,X32850),X32851),X32849)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__inv__image])]) ).

fof(i_0_10208,plain,
    ! [X28060,X28061,X28062,X28063] :
      ( ~ c_Wellfounded_Owf(X28063,X28062)
      | c_Wellfounded_Owf(X28061,hAPP(hAPP(c_Relation_Oinv__image(X28063,X28061),X28062),X28060)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__inv__image])]) ).

fof(i_0_10209,plain,
    ! [X23108,X23109,X23110,X23111] :
      ( ~ c_FunDef_Oreduction__pair(X23111,X23110)
      | c_FunDef_Oreduction__pair(X23109,hAPP(hAPP(c_FunDef_Orp__inv__image(X23111,X23109),X23110),X23108)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp])]) ).

fof(i_0_10210,plain,
    ! [X33750,X33751] :
      ( ~ class_Rings_Ocomm__semiring__1(X33751)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33751),c_Groups_Ozero__class_Ozero(X33751)),X33750))
      | X33750 = c_Groups_Ozero__class_Ozero(X33751) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__left])]) ).

fof(i_0_10211,plain,
    ! [X20650,X20651,X20652] :
      ( ~ class_Divides_Osemiring__div(X20652)
      | c_Divides_Odiv__class_Omod(X20652,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20652),X20651),X20650),X20651) = c_Divides_Odiv__class_Omod(X20652,X20650,X20651) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self1])]) ).

fof(i_0_10212,plain,
    ! [X20647,X20648,X20649] :
      ( ~ class_Divides_Osemiring__div(X20649)
      | c_Divides_Odiv__class_Omod(X20649,hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20649),X20648),X20647),X20647) = c_Divides_Odiv__class_Omod(X20649,X20648,X20647) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__add__self2])]) ).

fof(i_0_10213,plain,
    ! [X30238,X30239,X30240,X30241,X30242] :
      ( hAPP(hAPP(c_List_Odrop(X30242),X30241),X30240) != hAPP(hAPP(c_List_Olist_OCons(X30242),X30239),X30238)
      | hAPP(hAPP(c_List_Onth(X30242),X30240),X30241) = X30239 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nth__via__drop])]) ).

fof(i_0_10214,plain,
    ! [X22555,X22556] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,X22556)),hAPP(c_Nat_OSuc,X22555)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22556),X22555)),
    inference(variable_rename,[status(thm)],[fact_max__Suc__Suc]) ).

fof(i_0_10215,plain,
    ! [X21600,X21601] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,X21601)),hAPP(c_Nat_OSuc,X21600)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X21601),X21600)),
    inference(variable_rename,[status(thm)],[fact_min__Suc__Suc]) ).

fof(i_0_10216,plain,
    ! [X30921,X30922] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30922)),hAPP(c_Code__Numeral_Oof__nat,X30921)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X30922),X30921)),
    inference(variable_rename,[status(thm)],[fact_times__code__numeral__code]) ).

fof(i_0_10217,plain,
    ! [X30938,X30939] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,X30939)),hAPP(c_Code__Numeral_Oof__nat,X30938)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X30939),X30938)),
    inference(variable_rename,[status(thm)],[fact_plus__code__numeral__code]) ).

fof(i_0_10218,plain,
    ! [X20156,X20157] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20157)),X20156) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20157),X20156)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J]) ).

fof(i_0_10219,plain,
    ! [X20142,X20143] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20143)),X20142) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20143),X20142)),
    inference(variable_rename,[status(thm)],[fact_zpower__int]) ).

fof(i_0_10220,plain,
    ! [X21221,X21222] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21222)),X21221) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21222),X21221)),
    inference(variable_rename,[status(thm)],[fact_zmult__zminus]) ).

fof(i_0_10221,plain,
    ! [X20144,X20145] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20145),X20144)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20145)),X20144),
    inference(variable_rename,[status(thm)],[fact_int__power]) ).

fof(i_0_10222,plain,
    ! [X32068,X32069,X32070] : hAPP(c_List_Oset(X32070),c_List_Oinsert(X32070,X32069,X32068)) = hAPP(hAPP(c_Set_Oinsert(X32070),X32069),hAPP(c_List_Oset(X32070),X32068)),
    inference(variable_rename,[status(thm)],[fact_List_Oset__insert]) ).

cnf(i_0_10223,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_5997]) ).

fof(i_0_10224,plain,
    ! [X32451,X32452,X32453] : c_List_Osplice(X32453,hAPP(hAPP(c_List_Olist_OCons(X32453),X32452),X32451),c_List_Olist_ONil(X32453)) = hAPP(hAPP(c_List_Olist_OCons(X32453),X32452),X32451),
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I2_J]) ).

fof(i_0_10225,plain,
    ! [X25884,X25885] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25885)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25885),c_Groups_Ozero__class_Ozero(X25885)),hAPP(c_Groups_Oabs__class_Oabs(X25885),X25884))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__zero])]) ).

fof(i_0_10226,plain,
    ! [X20034,X20035] :
      ( ~ class_Rings_Olinordered__semidom(X20035)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20035),c_Groups_Ozero__class_Ozero(X20035)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20035),X20034))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__imp__of__nat])]) ).

fof(i_0_10227,plain,
    ! [X20032,X20033] :
      ( ~ class_Rings_Olinordered__semidom(X20033)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20033),c_Groups_Ozero__class_Ozero(X20033)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20033),X20032))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0__le__iff])]) ).

fof(i_0_10228,plain,
    ! [X25095,X25096,X25097] :
      ( ~ class_Lattices_Osemilattice__inf(X25097)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25097),X25096),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25097),X25096),X25095)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25097),X25096),X25095) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oleft__idem])]) ).

fof(i_0_10229,plain,
    ! [X25089,X25090,X25091] :
      ( ~ class_Lattices_Osemilattice__inf(X25091)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25091),X25090),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25091),X25090),X25089)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25091),X25090),X25089) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__left__idem])]) ).

fof(i_0_10230,plain,
    ! [X25092,X25093,X25094] :
      ( ~ class_Lattices_Olattice(X25094)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25094),X25093),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25094),X25093),X25092)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25094),X25093),X25092) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I4_J])]) ).

fof(i_0_10231,plain,
    ! [X23211,X23212,X23213] :
      ( ~ class_Lattices_Olattice(X23213)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23213),X23212),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23213),X23212),X23211)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23213),X23212),X23211) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I8_J])]) ).

fof(i_0_10232,plain,
    ! [X23214,X23215,X23216] :
      ( ~ class_Lattices_Osemilattice__sup(X23216)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23216),X23215),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23216),X23215),X23214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23216),X23215),X23214) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oleft__idem])]) ).

fof(i_0_10233,plain,
    ! [X23208,X23209,X23210] :
      ( ~ class_Lattices_Osemilattice__sup(X23210)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23210),X23209),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23210),X23209),X23208)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23210),X23209),X23208) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__left__idem])]) ).

fof(i_0_10234,plain,
    ! [X22510,X22511,X22512] :
      ( ~ class_Orderings_Olinorder(X22512)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22512),X22511),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22512),X22511),X22510)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22512),X22511),X22510) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__idem])]) ).

fof(i_0_10235,plain,
    ! [X22507,X22508,X22509] :
      ( ~ class_Orderings_Olinorder(X22509)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22509),X22508),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22509),X22508),X22507)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22509),X22508),X22507) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__idem])]) ).

fof(i_0_10236,plain,
    ! [X21504,X21505,X21506] :
      ( ~ class_Orderings_Olinorder(X21506)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21506),X21505),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21506),X21505),X21504)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21506),X21505),X21504) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__left__idem])]) ).

fof(i_0_10237,plain,
    ! [X21501,X21502,X21503] :
      ( ~ class_Orderings_Olinorder(X21503)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21503),X21502),hAPP(hAPP(c_Orderings_Oord__class_Omin(X21503),X21502),X21501)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21503),X21502),X21501) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oleft__idem])]) ).

fof(i_0_10238,plain,
    ! [X18369,X18370,X18371] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X18371)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18371),X18370),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18371),X18370),X18369)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18371),X18370),X18369) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__left__idem])]) ).

fof(i_0_10239,plain,
    ! [X33559,X33560,X33561] : c_Lazy__Sequence_Oflat(X33561,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X33561),X33560,X33559)) = c_Lazy__Sequence_Oappend(X33561,X33560,c_Lazy__Sequence_Oflat(X33561,X33559)),
    inference(variable_rename,[status(thm)],[fact__03]) ).

fof(i_0_10240,plain,
    ! [X32160,X32161,X32163] :
      ( ( hAPP(c_List_Oset(X32161),esk453_2(X32160,X32161)) = X32160
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32161),X32160))
        | ~ class_Orderings_Olinorder(X32161) )
      & ( c_List_Olinorder__class_Osorted(X32161,esk453_2(X32160,X32161))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32161),X32160))
        | ~ class_Orderings_Olinorder(X32161) )
      & ( hBOOL(hAPP(c_List_Odistinct(X32161),esk453_2(X32160,X32161)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32161),X32160))
        | ~ class_Orderings_Olinorder(X32161) )
      & ( hAPP(c_List_Oset(X32161),X32163) != X32160
        | ~ c_List_Olinorder__class_Osorted(X32161,X32163)
        | ~ hBOOL(hAPP(c_List_Odistinct(X32161),X32163))
        | X32163 = esk453_2(X32160,X32161)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X32161),X32160))
        | ~ class_Orderings_Olinorder(X32161) ) ),
    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_10241,plain,
    ! [X30380,X30381,X30382] : hAPP(hAPP(c_List_Odrop(X30382),X30381),hAPP(c_List_Otl(X30382),X30380)) = hAPP(c_List_Otl(X30382),hAPP(hAPP(c_List_Odrop(X30382),X30381),X30380)),
    inference(variable_rename,[status(thm)],[fact_drop__tl]) ).

fof(i_0_10242,plain,
    ! [X30383,X30384,X30385] : hAPP(c_List_Otl(X30385),hAPP(hAPP(c_List_Odrop(X30385),X30384),X30383)) = hAPP(hAPP(c_List_Odrop(X30385),X30384),hAPP(c_List_Otl(X30385),X30383)),
    inference(variable_rename,[status(thm)],[fact_tl__drop]) ).

fof(i_0_10243,plain,
    ! [X29504,X29505,X29506] : hAPP(c_List_Oset(X29506),hAPP(hAPP(c_List_Olist_OCons(X29506),X29505),X29504)) = hAPP(hAPP(c_Set_Oinsert(X29506),X29505),hAPP(c_List_Oset(X29506),X29504)),
    inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I2_J]) ).

fof(i_0_10244,plain,
    ! [X24150,X24151] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24151,X24150)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24150)),X24151),
    inference(variable_rename,[status(thm)],[fact_card__atLeastAtMost]) ).

fof(i_0_10245,plain,
    ! [X16933,X16934,X16935] :
      ( X16935 != c_Orderings_Obot__class_Obot(tc_fun(X16934,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_member(X16934),X16933),X16935)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5998])]) ).

fof(i_0_10246,plain,
    ! [X27828] : hAPP(c_Set_Oimage(X27828,X27828,c_Fun_Oid(X27828)),c_Orderings_Otop__class_Otop(tc_fun(X27828,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X27828,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_surj__id]) ).

fof(i_0_10247,plain,
    ! [X33469,X33470,X33471] :
      ( ( ~ hBOOL(hAPP(c_Quotient_ORespects(X33471,X33470),X33469))
        | hBOOL(hAPP(hAPP(X33470,X33469),X33469)) )
      & ( ~ hBOOL(hAPP(hAPP(X33470,X33469),X33469))
        | hBOOL(hAPP(c_Quotient_ORespects(X33471,X33470),X33469)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Respects__def])]) ).

fof(i_0_10248,plain,
    ! [X28376,X28377,X28379,X28380,X28381] :
      ( ( ~ hBOOL(hAPP(X28377,c_Hilbert__Choice_OEps(X28376,X28377)))
        | hBOOL(hAPP(X28377,esk315_2(X28376,X28377))) )
      & ( ~ hBOOL(hAPP(X28380,X28381))
        | hBOOL(hAPP(X28380,c_Hilbert__Choice_OEps(X28379,X28380))) ) ),
    inference(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_10249,plain,
    ! [X31424,X31425,X31426] : hAPP(c_Product__Type_Ofst(tc_List_Olist(X31426),tc_List_Olist(X31426)),c_List_Opartition(X31426,X31425,X31424)) = hAPP(c_List_Ofilter(X31426,X31425),X31424),
    inference(variable_rename,[status(thm)],[fact_partition__filter1]) ).

fof(i_0_10250,plain,
    ! [X19888] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X19888))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19888)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19888))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X19888)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_5999])]) ).

fof(i_0_10251,plain,
    ! [X33226] :
      ( X33226 = hAPP(c_Code__Numeral_Oof__nat,esk529_1(X33226))
      & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk529_1(X33226)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6000])])]) ).

fof(i_0_10252,plain,
    ! [X33609] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X33609)),
    inference(variable_rename,[status(thm)],[fact_dvd__1__left]) ).

fof(i_0_10253,plain,
    ! [X26621,X26622] : hBOOL(hAPP(hAPP(c_member(X26622),X26621),c_Orderings_Otop__class_Otop(tc_fun(X26622,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_iso__tuple__UNIV__I]) ).

fof(i_0_10254,plain,
    ! [X26101,X26102] : hBOOL(hAPP(hAPP(c_member(X26102),X26101),c_Orderings_Otop__class_Otop(tc_fun(X26102,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_UNIV__I]) ).

fof(i_0_10255,plain,
    ! [X20946,X20947] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20947))
        | X20947 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20946)
        | hAPP(c_Int_Onat,X20947) != X20946 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20947))
        | X20946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Int_Onat,X20947) != X20946 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20947))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20947))
        | hAPP(c_Int_Onat,X20947) = X20946 )
      & ( X20946 != 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)),X20947))
        | hAPP(c_Int_Onat,X20947) = X20946 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20947))
        | X20947 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20946)
        | hAPP(c_Int_Onat,X20947) = X20946 )
      & ( X20946 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20947 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20946)
        | hAPP(c_Int_Onat,X20947) = X20946 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6001])])]) ).

fof(i_0_10256,plain,
    ! [X20944,X20945] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20944))
        | X20944 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20945)
        | X20945 != hAPP(c_Int_Onat,X20944) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20944))
        | X20945 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20945 != hAPP(c_Int_Onat,X20944) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20944))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20944))
        | X20945 = hAPP(c_Int_Onat,X20944) )
      & ( X20945 != 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)),X20944))
        | X20945 = hAPP(c_Int_Onat,X20944) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20944))
        | X20944 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20945)
        | X20945 = hAPP(c_Int_Onat,X20944) )
      & ( X20945 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20944 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20945)
        | X20945 = hAPP(c_Int_Onat,X20944) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6002])])]) ).

fof(i_0_10257,plain,
    ! [X21490,X21491,X21492] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21492,tc_HOL_Obool)),X21491) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21492,tc_HOL_Obool)),X21490)
        | X21491 = X21490 )
      & ( X21491 != X21490
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21492,tc_HOL_Obool)),X21491) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21492,tc_HOL_Obool)),X21490) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__eq__Compl__iff])]) ).

fof(i_0_10258,plain,
    ! [X21114,X21115,X21116,X21117] :
      ( ~ class_Groups_Ouminus(X21117)
      | hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21116,X21117)),X21115),X21114) = hAPP(c_Groups_Ouminus__class_Ouminus(X21117),hAPP(X21115,X21114)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_uminus__apply])]) ).

fof(i_0_10259,plain,
    ! [X21108,X21109,X21110,X21111] :
      ( ~ class_Groups_Ouminus(X21111)
      | hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21110,X21111)),X21109),X21108) = hAPP(c_Groups_Ouminus__class_Ouminus(X21111),hAPP(X21109,X21108)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__Compl__def])]) ).

fof(i_0_10260,plain,
    ! [X20886] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20886))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X20886)) = X20886 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20886))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X20886)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6003])]) ).

fof(i_0_10261,plain,
    ! [X20883] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20883))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X20883)) = X20883 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__0__le])]) ).

fof(i_0_10262,plain,
    ! [X19925,X19926] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19926),X19925))
      | c_Nat__Transfer_Otsub(X19925,X19926) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19925),X19926) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tsub__eq])]) ).

fof(i_0_10263,plain,
    ! [X19867,X19868] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19868),X19867))
        | c_Nat__Transfer_Otsub(X19867,X19868) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19867),X19868) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19868),X19867))
        | c_Nat__Transfer_Otsub(X19867,X19868) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6004])]) ).

fof(i_0_10264,plain,
    ! [X30969,X30970] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,X30970)),hAPP(c_Code__Numeral_Oof__nat,X30969)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X30970),X30969)),
    inference(variable_rename,[status(thm)],[fact_subtract__code__numeral__code]) ).

fof(i_0_10265,plain,
    ! [X20884,X20885] :
      ( ( X20885 = hAPP(c_Int_Onat,X20884)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20885) != X20884 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20884))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20885) != X20884 )
      & ( X20885 != hAPP(c_Int_Onat,X20884)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20884))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20885) = X20884 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__eq__iff])])]) ).

fof(i_0_10266,plain,
    ! [X21718,X21719,X21720,X21721] :
      ( ~ c_Big__Operators_Osemilattice__big(X21721,X21720,X21719)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21721),X21718))
      | hAPP(X21719,X21718) = hAPP(c_Finite__Set_Ofold1(X21721,X21720),X21718) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semilattice__big_OF__eq])]) ).

fof(i_0_10267,plain,
    ! [X19366,X19367,X19368,X19369] :
      ( ~ c_Finite__Set_Ofolding__one(X19369,X19368,X19367)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X19369),X19366))
      | hAPP(X19367,X19366) = hAPP(c_Finite__Set_Ofold1(X19369,X19368),X19366) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one_Oeq__fold])]) ).

fof(i_0_10268,plain,
    ! [X19941,X19942] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19941)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19942),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19941)) = c_Groups_Ozero__class_Ozero(X19942)
        | ~ class_Int_Onumber__ring(X19942) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19941)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19942),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19941)) = hAPP(c_Int_Onumber__class_Onumber__of(X19942),X19941)
        | ~ class_Int_Onumber__ring(X19942) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6005])])]) ).

fof(i_0_10269,plain,
    ! [X27052] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X27052,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X27052,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X27052,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Union__UNIV]) ).

fof(i_0_10270,plain,
    ! [X27038] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X27038,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X27038,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X27038,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Union__empty]) ).

fof(i_0_10271,plain,
    ! [X26877] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X26877,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26877,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X26877,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Inter__UNIV]) ).

fof(i_0_10272,plain,
    ! [X26873] : c_Complete__Lattice_OInf__class_OInf(tc_fun(X26873,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X26873,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26873,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Inter__empty]) ).

cnf(i_0_10273,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_5709]) ).

fof(i_0_10274,plain,
    ! [X16906,X16907,X16908] : hAPP(hAPP(c_Set_Oinsert(X16908),X16907),hAPP(hAPP(c_Set_Oinsert(X16908),X16907),X16906)) = hAPP(hAPP(c_Set_Oinsert(X16908),X16907),X16906),
    inference(variable_rename,[status(thm)],[fact_insert__absorb2]) ).

cnf(i_0_10275,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_Bit1__Min]) ).

fof(i_0_10276,plain,
    ! [X26524,X26525,X26526,X26527] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26527)
      | X26526 = c_Orderings_Obot__class_Obot(tc_fun(X26525,tc_HOL_Obool))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X26525,X26527),X26526),hAPP(c_COMBK(X26527,X26525),X26524)) = X26524 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_INF__const])]) ).

fof(i_0_10277,plain,
    ! [X23922,X23923,X23924,X23925] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X23925)
      | X23924 = c_Orderings_Obot__class_Obot(tc_fun(X23923,tc_HOL_Obool))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X23923,X23925),X23924),hAPP(c_COMBK(X23925,X23923),X23922)) = X23922 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SUP__const])]) ).

cnf(i_0_10278,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),c_List_Olist_ONil(X1)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6006]) ).

fof(i_0_10279,plain,
    ! [X26089,X26090,X26091] :
      ( ~ class_Lattices_Oboolean__algebra(X26091)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26091),X26090),X26089) != c_Orderings_Obot__class_Obot(X26091)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26091),X26090),X26089) != c_Orderings_Otop__class_Otop(X26091)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X26091),X26090) = X26089 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__unique])]) ).

fof(i_0_10280,plain,
    ! [X18722,X18723] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18723),hAPP(c_Nat_OSuc,X18722)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18723),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18723),X18722)),
    inference(variable_rename,[status(thm)],[fact_mult__Suc__right]) ).

cnf(i_0_10281,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_6007]) ).

fof(i_0_10282,plain,
    ! [X24129] : 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)),X24129))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastZeroLessThan__int]) ).

fof(i_0_10283,plain,
    ! [X31483,X31484] : c_List_Otranspose(X31484,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31484)),c_List_Olist_ONil(X31484)),X31483)) = c_List_Otranspose(X31484,X31483),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I2_J]) ).

fof(i_0_10284,plain,
    ! [X31435,X31436,X31437,X31438] :
      ( hBOOL(hAPP(X31438,X31437))
      | c_List_Oremove1(X31436,X31437,hAPP(c_List_Ofilter(X31436,X31438),X31435)) = hAPP(c_List_Ofilter(X31436,X31438),X31435) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6008])]) ).

fof(i_0_10285,plain,
    ! [X23591] : hAPP(c_Relation_OField(X23591),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X23591,X23591),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X23591,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Field__empty]) ).

fof(i_0_10286,plain,
    ! [X21197,X21198] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X21198),X21197))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21198,X21197) = X21198 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__less])]) ).

fof(i_0_10287,plain,
    ! [X24162,X24163] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24163),c_Groups_Oone__class_Oone(tc_Int_Oint)),X24162) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X24163,X24162),
    inference(variable_rename,[status(thm)],[fact_atLeastPlusOneAtMost__greaterThanAtMost__int]) ).

fof(i_0_10288,plain,
    ! [X27070,X27071,X27072] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X27072)
      | c_Complete__Lattice_OSup__class_OSup(X27072,hAPP(hAPP(c_Set_Oinsert(X27072),X27071),X27070)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X27072),X27071),c_Complete__Lattice_OSup__class_OSup(X27072,X27070)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__insert])]) ).

fof(i_0_10289,plain,
    ! [X26893,X26894,X26895] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26895)
      | c_Complete__Lattice_OInf__class_OInf(X26895,hAPP(hAPP(c_Set_Oinsert(X26895),X26894),X26893)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26895),X26894),c_Complete__Lattice_OInf__class_OInf(X26895,X26893)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__insert])]) ).

fof(i_0_10290,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_10291,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_10292,plain,
    ! [X32059,X32060,X32061] : c_List_Oinsert(X32061,X32060,c_List_Oremdups(X32061,X32059)) = c_List_Oremdups(X32061,c_List_Oinsert(X32061,X32060,X32059)),
    inference(variable_rename,[status(thm)],[fact_insert__remdups]) ).

fof(i_0_10293,plain,
    ! [X32325,X32326,X32327] :
      ( ( ~ c_List_Olist__all(X32327,X32326,hAPP(c_List_Orev(X32327),X32325))
        | c_List_Olist__all(X32327,X32326,X32325) )
      & ( ~ c_List_Olist__all(X32327,X32326,X32325)
        | c_List_Olist__all(X32327,X32326,hAPP(c_List_Orev(X32327),X32325)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__rev])]) ).

fof(i_0_10294,plain,
    ! [X32263,X32264,X32265] :
      ( ( ~ c_List_Olist__ex(X32265,X32264,hAPP(c_List_Orev(X32265),X32263))
        | c_List_Olist__ex(X32265,X32264,X32263) )
      & ( ~ c_List_Olist__ex(X32265,X32264,X32263)
        | c_List_Olist__ex(X32265,X32264,hAPP(c_List_Orev(X32265),X32263)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__ex__rev])]) ).

fof(i_0_10295,plain,
    ! [X30121,X30122,X30123] :
      ( ( X30123 != c_List_Olist_ONil(X30122)
        | c_List_Obutlast(X30122,hAPP(hAPP(c_List_Oappend(X30122),X30121),X30123)) = c_List_Obutlast(X30122,X30121) )
      & ( X30123 = c_List_Olist_ONil(X30122)
        | c_List_Obutlast(X30122,hAPP(hAPP(c_List_Oappend(X30122),X30121),X30123)) = hAPP(hAPP(c_List_Oappend(X30122),X30121),c_List_Obutlast(X30122,X30123)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast__append])]) ).

fof(i_0_10296,plain,
    ! [X29837,X29838,X29839] :
      ( ( X29839 != c_List_Olist_ONil(X29838)
        | c_List_Obutlast(X29838,hAPP(hAPP(c_List_Olist_OCons(X29838),X29837),X29839)) = c_List_Olist_ONil(X29838) )
      & ( X29839 = c_List_Olist_ONil(X29838)
        | c_List_Obutlast(X29838,hAPP(hAPP(c_List_Olist_OCons(X29838),X29837),X29839)) = hAPP(hAPP(c_List_Olist_OCons(X29838),X29837),c_List_Obutlast(X29838,X29839)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_butlast_Osimps_I2_J])]) ).

fof(i_0_10297,plain,
    ! [X26841,X26842,X26843] : hAPP(c_Set_Ovimage(X26843,X26842,X26841),c_Orderings_Otop__class_Otop(tc_fun(X26842,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26843,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_vimage__UNIV]) ).

fof(i_0_10298,plain,
    ! [X26805,X26806,X26807] : hAPP(c_Set_Ovimage(X26807,X26806,X26805),c_Orderings_Obot__class_Obot(tc_fun(X26806,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X26807,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_vimage__empty]) ).

fof(i_0_10299,plain,
    ! [X24035,X24036,X24037] : hAPP(c_Relation_OImage(X24037,X24036,X24035),c_Orderings_Obot__class_Obot(tc_fun(X24037,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X24036,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Image__empty]) ).

fof(i_0_10300,plain,
    ! [X17027,X17028,X17029] : hAPP(c_Set_Oimage(X17029,X17028,X17027),c_Orderings_Obot__class_Obot(tc_fun(X17029,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X17028,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_image__empty]) ).

fof(i_0_10301,plain,
    ! [X29387,X29388,X29389] :
      ( ~ c_Relation_Orefl__on(X29389,X29388,X29387)
      | c_Relation_Orefl__on(tc_List_Olist(X29389),c_List_Olists(X29389,X29388),c_List_Olistrel(X29389,X29387)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__refl__on])]) ).

fof(i_0_10302,plain,
    ! [X29384,X29385,X29386] :
      ( ~ c_Equiv__Relations_Oequiv(X29386,X29385,X29384)
      | c_Equiv__Relations_Oequiv(tc_List_Olist(X29386),c_List_Olists(X29386,X29385),c_List_Olistrel(X29386,X29384)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__listrel])]) ).

fof(i_0_10303,plain,
    ! [X16891,X16892,X16893] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(X16893),X16892),X16891))
        | hBOOL(hAPP(X16891,X16892)) )
      & ( ~ hBOOL(hAPP(X16891,X16892))
        | hBOOL(hAPP(hAPP(c_member(X16893),X16892),X16891)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).

fof(i_0_10304,plain,
    ! [X33893,X33894,X33895,X33896] :
      ( ~ class_Rings_Odvd(X33896)
      | X33895 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X33896),X33894),X33893)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33896),X33894),X33895)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvdI])]) ).

cnf(i_0_10305,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_6009]) ).

fof(i_0_10306,plain,
    ! [X20781,X20782] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X20782),X20781))
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20782),X20781) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__less])]) ).

fof(i_0_10307,plain,
    ! [X18792,X18793] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18793),X18792))
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18793),X18792) = 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_10308,plain,
    ! [X18790,X18791] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18791),X18790) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18791),X18790)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18791),X18790))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18791),X18790) = 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_10309,plain,
    ! [X26114,X26115] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X26115,tc_HOL_Obool)),X26114),c_Orderings_Otop__class_Otop(tc_fun(X26115,tc_HOL_Obool))) = X26114,
    inference(variable_rename,[status(thm)],[fact_Int__UNIV__right]) ).

fof(i_0_10310,plain,
    ! [X23382,X23383] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23383,tc_HOL_Obool)),X23382),c_Orderings_Obot__class_Obot(tc_fun(X23383,tc_HOL_Obool))) = X23382,
    inference(variable_rename,[status(thm)],[fact_Un__empty__right]) ).

fof(i_0_10311,plain,
    ! [X17371,X17372] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17372,tc_HOL_Obool)),X17371),c_Orderings_Obot__class_Obot(tc_fun(X17372,tc_HOL_Obool))) = X17371,
    inference(variable_rename,[status(thm)],[fact_Diff__empty]) ).

fof(i_0_10312,plain,
    ! [X21488,X21489] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21489,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X21489,tc_HOL_Obool)),X21488)) = X21488,
    inference(variable_rename,[status(thm)],[fact_double__complement]) ).

fof(i_0_10313,plain,
    ! [X28939,X28940] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X28940,X28940),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X28939) = X28939,
    inference(variable_rename,[status(thm)],[fact_rel__pow__1]) ).

fof(i_0_10314,plain,
    ! [X20119] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20119)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20119)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20119)))
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20119)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20119) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6010])]) ).

fof(i_0_10315,plain,
    ! [X29670,X29671,X29672] : hAPP(hAPP(c_List_Olist__update(X29672,X29671),X29670),hAPP(hAPP(c_List_Onth(X29672),X29671),X29670)) = X29671,
    inference(variable_rename,[status(thm)],[fact_list__update__id]) ).

fof(i_0_10316,plain,
    ! [X21177,X21178,X21179] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21179),X21178),X21178) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21179),X21177),X21177)
        | X21178 = X21177
        | X21178 = hAPP(c_Groups_Ouminus__class_Ouminus(X21179),X21177)
        | ~ class_Rings_Oidom(X21179) )
      & ( X21178 != X21177
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21179),X21178),X21178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21179),X21177),X21177)
        | ~ class_Rings_Oidom(X21179) )
      & ( X21178 != hAPP(c_Groups_Ouminus__class_Ouminus(X21179),X21177)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21179),X21178),X21178) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21179),X21177),X21177)
        | ~ class_Rings_Oidom(X21179) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__iff])])]) ).

fof(i_0_10317,plain,
    ! [X17960,X17961] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17961)),X17960) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17961),X17960)),
    inference(variable_rename,[status(thm)],[fact_add__Suc]) ).

fof(i_0_10318,plain,
    ! [X30251,X30252,X30253] : hAPP(hAPP(c_List_Odrop(X30253),X30252),c_List_Obutlast(X30253,X30251)) = c_List_Obutlast(X30253,hAPP(hAPP(c_List_Odrop(X30253),X30252),X30251)),
    inference(variable_rename,[status(thm)],[fact_drop__butlast]) ).

fof(i_0_10319,plain,
    ! [X30248,X30249,X30250] : c_List_Obutlast(X30250,hAPP(hAPP(c_List_Odrop(X30250),X30249),X30248)) = hAPP(hAPP(c_List_Odrop(X30250),X30249),c_List_Obutlast(X30250,X30248)),
    inference(variable_rename,[status(thm)],[fact_butlast__drop]) ).

fof(i_0_10320,plain,
    ! [X30953] :
      ( ( X30953 = 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)),X30953)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X30953))
        | X30953 != 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_10321,plain,
    ! [X28131,X28132,X28133] :
      ( ( hAPP(c_Relation_ODomain(X28133,X28132),X28131) != c_Orderings_Obot__class_Obot(tc_fun(X28133,tc_HOL_Obool))
        | X28131 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28133,X28132),tc_HOL_Obool)) )
      & ( X28131 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28133,X28132),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(X28133,X28132),X28131) = c_Orderings_Obot__class_Obot(tc_fun(X28133,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Domain__empty__iff])]) ).

fof(i_0_10322,plain,
    ! [X27943,X27944,X27945] :
      ( ( hAPP(c_Relation_ORange(X27945,X27944),X27943) != c_Orderings_Obot__class_Obot(tc_fun(X27944,tc_HOL_Obool))
        | X27943 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27945,X27944),tc_HOL_Obool)) )
      & ( X27943 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X27945,X27944),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(X27945,X27944),X27943) = c_Orderings_Obot__class_Obot(tc_fun(X27944,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Range__empty__iff])]) ).

fof(i_0_10323,plain,
    ! [X25969] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25969),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25969) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X25969) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X25969),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25969) = X25969 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6011])]) ).

fof(i_0_10324,plain,
    ! [X25933,X25934] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25934),X25933)) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X25934) = 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_10325,plain,
    ! [X19487,X19488] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19488),X19487))
      | X19488 = X19487
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19487),X19488)) ),
    inference(variable_rename,[status(thm)],[fact_zless__linear]) ).

fof(i_0_10326,plain,
    ! [X17575,X17576] :
      ( X17576 = X17575
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17576),X17575))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17575),X17576)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6012])]) ).

fof(i_0_10327,plain,
    ! [X17558,X17559] :
      ( ( X17559 = X17558
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17559),X17558))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17558),X17559)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17559),X17558))
        | X17559 != X17558 )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17558),X17559))
        | X17559 != X17558 ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__neq__iff])])]) ).

fof(i_0_10328,plain,
    ! [X24187,X24188] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X24188),X24187)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X24187),X24188)),
    inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan__int]) ).

cnf(i_0_10329,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_6013]) ).

fof(i_0_10330,plain,
    ! [X25875,X25876] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25876)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X25876),X25875),hAPP(c_Groups_Oabs__class_Oabs(X25876),X25875))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__ge__self])]) ).

fof(i_0_10331,plain,
    ! [X21708,X21709] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X21709,X21708)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X21708),hAPP(c_Nat_OSuc,X21709)),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanLessThan]) ).

fof(i_0_10332,plain,
    ! [X33058,X33059,X33060] :
      ( ~ hBOOL(hAPP(hAPP(X33059,X33060),X33060))
      | ~ c_Predicate_Osymp(X33058,X33059)
      | ~ c_Predicate_Otransp(X33058,X33059)
      | c_Equiv__Relations_Opart__equivp(X33058,X33059) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_part__equivpI])])]) ).

fof(i_0_10333,plain,
    ! [X19468,X19469] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19469),X19468))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19468),X19469)) ),
    inference(variable_rename,[status(thm)],[fact_zle__linear]) ).

fof(i_0_10334,plain,
    ! [X17211,X17212] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17212),X17211))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17211),X17212)) ),
    inference(variable_rename,[status(thm)],[fact_nat__le__linear]) ).

fof(i_0_10335,plain,
    ! [X21231,X21232] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21232)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21231)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21232),X21231),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus__zminus]) ).

fof(i_0_10336,plain,
    ! [X21229,X21230] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21230),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21229)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21230)),X21229),
    inference(variable_rename,[status(thm)],[fact_zdiv__zminus2]) ).

fof(i_0_10337,plain,
    ! [X30426,X30427,X30428] : hAPP(hAPP(c_List_Odrop(X30428),hAPP(c_Nat_OSuc,X30427)),X30426) = hAPP(hAPP(c_List_Odrop(X30428),X30427),hAPP(c_List_Otl(X30428),X30426)),
    inference(variable_rename,[status(thm)],[fact_drop__Suc]) ).

fof(i_0_10338,plain,
    ! [X18771,X18773,X18774] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18771))
        | X18771 = hAPP(c_Nat_OSuc,esk25_1(X18771)) )
      & ( X18773 != hAPP(c_Nat_OSuc,X18774)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18773)) ) ),
    inference(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_10339,plain,
    ! [X23009,X23010] :
      ( ~ class_Orderings_Olinorder(X23010)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23010),X23009))
      | c_Big__Operators_Olattice_OSup__fin(X23010,c_Orderings_Oord__class_Omax(X23010),X23009) = hAPP(c_Finite__Set_Ofold1(X23010,c_Orderings_Oord__class_Omax(X23010)),X23009) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OSup__fin_OF__eq])]) ).

fof(i_0_10340,plain,
    ! [X21783,X21784] :
      ( ~ class_Orderings_Olinorder(X21784)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21784),X21783))
      | c_Big__Operators_Olattice_OInf__fin(X21784,c_Orderings_Oord__class_Omin(X21784),X21783) = hAPP(c_Finite__Set_Ofold1(X21784,c_Orderings_Oord__class_Omin(X21784)),X21783) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_OInf__fin_OF__eq])]) ).

fof(i_0_10341,plain,
    ! [X30573] :
      ( ~ class_Orderings_Olinorder(X30573)
      | c_Finite__Set_Ofun__left__comm(X30573,tc_List_Olist(X30573),c_List_Olinorder__class_Oinsort__key(X30573,X30573,c_COMBI(X30573))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__insort])]) ).

fof(i_0_10342,plain,
    ! [X25824] :
      ( ( X25824 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X25824) = 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)),X25824))
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X25824) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X25824 = 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)),X25824))
        | c_Groups_Osgn__class_Osgn(tc_Int_Oint,X25824) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | X25824 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6014])])]) ).

fof(i_0_10343,plain,
    ! [X33047,X33048,X33049] :
      ( ( c_Relation_Orefl__on(X33049,X33048,X33047)
        | ~ c_Equiv__Relations_Oequiv(X33049,X33048,X33047) )
      & ( c_Relation_Osym(X33049,X33047)
        | ~ c_Equiv__Relations_Oequiv(X33049,X33048,X33047) )
      & ( c_Relation_Otrans(X33049,X33047)
        | ~ c_Equiv__Relations_Oequiv(X33049,X33048,X33047) )
      & ( ~ c_Relation_Orefl__on(X33049,X33048,X33047)
        | ~ c_Relation_Osym(X33049,X33047)
        | ~ c_Relation_Otrans(X33049,X33047)
        | c_Equiv__Relations_Oequiv(X33049,X33048,X33047) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equiv__def])])]) ).

fof(i_0_10344,plain,
    ! [X33044,X33045,X33046] :
      ( ~ c_Relation_Orefl__on(X33046,X33045,X33044)
      | ~ c_Relation_Osym(X33046,X33044)
      | ~ c_Relation_Otrans(X33046,X33044)
      | c_Equiv__Relations_Oequiv(X33046,X33045,X33044) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivI])]) ).

fof(i_0_10345,plain,
    ! [X30389,X30390] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X30390),X30389))
      | hBOOL(hAPP(c_List_Odistinct(X30390),hAPP(c_List_Otl(X30390),X30389))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__tl])]) ).

fof(i_0_10346,plain,
    ! [X24016,X24017] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X24017),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X24016),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24017,X24016),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThanPlusOne__atLeastAtMost__int]) ).

fof(i_0_10347,plain,
    ! [X19889] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X19889))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19889),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X19889),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,X19889)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__def])]) ).

fof(i_0_10348,plain,
    ! [X29790,X29791] :
      ( hAPP(c_Finite__Set_Ocard(X29791),hAPP(c_List_Oset(X29791),X29790)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29791)),X29790)
      | hBOOL(hAPP(c_List_Odistinct(X29791),X29790)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_card__distinct])]) ).

fof(i_0_10349,plain,
    ! [X20076,X20077] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20077),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20076)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X20077),X20076)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J]) ).

fof(i_0_10350,plain,
    ! [X17126] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X17126),v_U))
      | v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X17126))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_assms_I4_J])]) ).

fof(i_0_10351,plain,
    ! [X31789,X31790,X31791] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(X31791),X31790),c_List_Olist_ONil(X31791)) != hAPP(c_List_Orev(X31791),X31789)
        | X31789 = hAPP(hAPP(c_List_Olist_OCons(X31791),X31790),c_List_Olist_ONil(X31791)) )
      & ( X31789 != hAPP(hAPP(c_List_Olist_OCons(X31791),X31790),c_List_Olist_ONil(X31791))
        | hAPP(hAPP(c_List_Olist_OCons(X31791),X31790),c_List_Olist_ONil(X31791)) = hAPP(c_List_Orev(X31791),X31789) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_singleton__rev__conv])]) ).

fof(i_0_10352,plain,
    ! [X31792,X31793,X31794] :
      ( ( hAPP(c_List_Orev(X31794),X31793) != hAPP(hAPP(c_List_Olist_OCons(X31794),X31792),c_List_Olist_ONil(X31794))
        | X31793 = hAPP(hAPP(c_List_Olist_OCons(X31794),X31792),c_List_Olist_ONil(X31794)) )
      & ( X31793 != hAPP(hAPP(c_List_Olist_OCons(X31794),X31792),c_List_Olist_ONil(X31794))
        | hAPP(c_List_Orev(X31794),X31793) = hAPP(hAPP(c_List_Olist_OCons(X31794),X31792),c_List_Olist_ONil(X31794)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__singleton__conv])]) ).

fof(i_0_10353,plain,
    ! [X29266,X29267] : c_List_Olistrel1(X29267,hAPP(c_Relation_Oconverse(X29267,X29267),X29266)) = hAPP(c_Relation_Oconverse(tc_List_Olist(X29267),tc_List_Olist(X29267)),c_List_Olistrel1(X29267,X29266)),
    inference(variable_rename,[status(thm)],[fact_listrel1__converse]) ).

fof(i_0_10354,plain,
    ! [X21192,X21193,X21194] :
      ( ~ class_Groups_Oab__group__add(X21194)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21194),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21194),X21193),X21192)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21194),X21192),X21193) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__diff__eq])]) ).

cnf(i_0_10355,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_5798]) ).

fof(i_0_10356,plain,
    ! [X32528,X32529,X32530] : hAPP(c_List_Orev(X32530),c_List_Oreplicate(X32530,X32529,X32528)) = c_List_Oreplicate(X32530,X32529,X32528),
    inference(variable_rename,[status(thm)],[fact_rev__replicate]) ).

fof(i_0_10357,plain,
    ! [X28115,X28116,X28117] :
      ( ~ c_Wellfounded_Owf(X28117,X28116)
      | hBOOL(hAPP(hAPP(c_member(X28117),X28115),c_Wellfounded_Oacc(X28117,X28116))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acc__wfD])]) ).

fof(i_0_10358,plain,
    ! [X21275,X21276] :
      ( ~ class_Rings_Ocomm__ring__1(X21276)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21276),X21275) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21276),hAPP(c_Groups_Ouminus__class_Ouminus(X21276),c_Groups_Oone__class_Oone(X21276))),X21275) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J])]) ).

fof(i_0_10359,plain,
    ! [X24001,X24002] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X24002),X24001))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan__int]) ).

fof(i_0_10360,plain,
    ! [X23995,X23996] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X23996),X23995))),
    inference(variable_rename,[status(thm)],[fact_finite__atLeastLessThan]) ).

fof(i_0_10361,plain,
    ! [X32775,X32776,X32777] :
      ( ( ~ c_List_Olist__all(tc_Int_Oint,X32777,c_List_Oupto(X32776,X32775))
        | c_List_Oall__interval__int(X32777,X32776,X32775) )
      & ( ~ c_List_Oall__interval__int(X32777,X32776,X32775)
        | c_List_Olist__all(tc_Int_Oint,X32777,c_List_Oupto(X32776,X32775)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__all__iff__all__interval__int])]) ).

fof(i_0_10362,plain,
    ! [X32215,X32216,X32217] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32216),X32215))
        | hBOOL(hAPP(X32215,X32217))
        | ~ class_Enum_Oenum(X32216) )
      & ( ~ hBOOL(hAPP(X32215,esk463_2(X32215,X32216)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32216),X32215))
        | ~ class_Enum_Oenum(X32216) ) ),
    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_10363,plain,
    ! [X32211,X32212,X32214] :
      ( ( ~ hBOOL(hAPP(X32211,esk462_2(X32211,X32212)))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32212),X32211))
        | ~ class_Enum_Oenum(X32212) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X32212),X32211))
        | hBOOL(hAPP(X32211,X32214))
        | ~ class_Enum_Oenum(X32212) ) ),
    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_10364,plain,
    ! [X19864] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,X19864)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X19864)),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_10365,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_6015]) ).

fof(i_0_10366,plain,
    ! [X17594,X17595,X17596] :
      ( ~ class_Orderings_Oorder(X17596)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17596),X17595),X17594))
      | X17594 != X17595 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq2])]) ).

fof(i_0_10367,plain,
    ! [X17591,X17592,X17593] :
      ( ~ class_Orderings_Oorder(X17593)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17593),X17592),X17591))
      | X17592 != X17591 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__less__imp__not__eq])]) ).

fof(i_0_10368,plain,
    ! [X17582,X17583,X17584] :
      ( ~ class_Orderings_Oorder(X17584)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17584),X17583),X17582))
      | X17583 != X17582 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__imp__neq])]) ).

cnf(i_0_10369,plain,
    c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6016]) ).

fof(i_0_10370,plain,
    ! [X33679,X33680,X33681] :
      ( ~ class_Rings_Olinordered__idom(X33681)
      | hAPP(c_Groups_Oabs__class_Oabs(X33681),X33680) != hAPP(c_Groups_Oabs__class_Oabs(X33681),X33679)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33681),X33680),X33679)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq])]) ).

fof(i_0_10371,plain,
    ! [X32571,X32572,X32573,X32574,X32575] :
      ( ( X32574 = X32572
        | c_List_Oreplicate(X32575,X32574,X32573) != c_List_Oreplicate(X32575,X32572,X32571) )
      & ( X32574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X32573 = X32571
        | c_List_Oreplicate(X32575,X32574,X32573) != c_List_Oreplicate(X32575,X32572,X32571) )
      & ( X32574 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X32574 != X32572
        | c_List_Oreplicate(X32575,X32574,X32573) = c_List_Oreplicate(X32575,X32572,X32571) )
      & ( X32573 != X32571
        | X32574 != X32572
        | c_List_Oreplicate(X32575,X32574,X32573) = c_List_Oreplicate(X32575,X32572,X32571) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__eq__replicate])])]) ).

fof(i_0_10372,plain,
    ! [X17460,X17461,X17462,X17463,X17464] :
      ( ( X17463 != X17462
        | X17461 = X17460
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17464),X17463),X17462) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17464),X17461),X17460)
        | ~ class_Groups_Oab__group__add(X17464) )
      & ( X17461 != X17460
        | X17463 = X17462
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17464),X17463),X17462) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X17464),X17461),X17460)
        | ~ class_Groups_Oab__group__add(X17464) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq])])]) ).

fof(i_0_10373,plain,
    ! [X31804,X31805,X31806] : hAPP(c_List_Orev(X31806),hAPP(c_List_Ofilter(X31806,X31805),X31804)) = hAPP(c_List_Ofilter(X31806,X31805),hAPP(c_List_Orev(X31806),X31804)),
    inference(variable_rename,[status(thm)],[fact_rev__filter]) ).

fof(i_0_10374,plain,
    ! [X21327,X21328] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21328),X21327) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21328,X21327) != 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_10375,plain,
    ! [X21329,X21330] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X21330,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21329)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,X21330,X21329) != 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_10376,plain,
    ! [X17556,X17557] :
      ( ~ class_Orderings_Opreorder(X17557)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X17557),X17556),X17556)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6017])]) ).

fof(i_0_10377,plain,
    ! [X18591] :
      ( ( X18591 = 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)),X18591)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18591))
        | X18591 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neq0__conv])]) ).

fof(i_0_10378,plain,
    ! [X31221,X31222] :
      ( ( X31222 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Enum_On__lists(X31221,X31222,c_List_Olist_ONil(X31221)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31221)),c_List_Olist_ONil(X31221)),c_List_Olist_ONil(tc_List_Olist(X31221))) )
      & ( X31222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Enum_On__lists(X31221,X31222,c_List_Olist_ONil(X31221)) = c_List_Olist_ONil(tc_List_Olist(X31221)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_n__lists__Nil])]) ).

fof(i_0_10379,plain,
    ! [X17847,X17848,X17849,X17850] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17850),X17849),X17848) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17850),X17847),X17848)
        | X17849 = X17847
        | ~ class_Groups_Ocancel__semigroup__add(X17850) )
      & ( X17849 != X17847
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17850),X17849),X17848) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17850),X17847),X17848)
        | ~ class_Groups_Ocancel__semigroup__add(X17850) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__cancel])])]) ).

fof(i_0_10380,plain,
    ! [X17835,X17836,X17837,X17838] :
      ( ~ class_Groups_Ocancel__semigroup__add(X17838)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17838),X17837),X17836) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17838),X17835),X17836)
      | X17837 = X17835 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__right__imp__eq])]) ).

fof(i_0_10381,plain,
    ! [X17839,X17840,X17841,X17842] :
      ( ~ class_Groups_Ocancel__ab__semigroup__add(X17842)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17842),X17841),X17840) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17842),X17841),X17839)
      | X17840 = X17839 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__imp__eq])]) ).

fof(i_0_10382,plain,
    ! [X17851,X17852,X17853,X17854] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17854),X17853),X17852) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17854),X17853),X17851)
        | X17852 = X17851
        | ~ class_Groups_Ocancel__semigroup__add(X17854) )
      & ( X17852 != X17851
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17854),X17853),X17852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17854),X17853),X17851)
        | ~ class_Groups_Ocancel__semigroup__add(X17854) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__cancel])])]) ).

fof(i_0_10383,plain,
    ! [X17843,X17844,X17845,X17846] :
      ( ~ class_Groups_Ocancel__semigroup__add(X17846)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17846),X17845),X17844) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X17846),X17845),X17843)
      | X17844 = X17843 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__left__imp__eq])]) ).

fof(i_0_10384,plain,
    ! [X32659,X32660,X32661,X32662,X32663] :
      ( ( X32662 = X32660
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X32663,X32662,X32661) != c_Lazy__Sequence_Olazy__sequence_OInsert(X32663,X32660,X32659) )
      & ( X32661 = X32659
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X32663,X32662,X32661) != c_Lazy__Sequence_Olazy__sequence_OInsert(X32663,X32660,X32659) )
      & ( X32662 != X32660
        | X32661 != X32659
        | c_Lazy__Sequence_Olazy__sequence_OInsert(X32663,X32662,X32661) = c_Lazy__Sequence_Olazy__sequence_OInsert(X32663,X32660,X32659) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lazy__sequence_Oinject])])]) ).

fof(i_0_10385,plain,
    ! [X20876] :
      ( ( hAPP(c_Int_Onat,X20876) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20876),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20876),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,X20876) = 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_10386,plain,
    ! [X20875] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20875),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | hAPP(c_Int_Onat,X20875) = 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_10387,plain,
    ! [X21765] :
      ( ( ~ c_Nat__Transfer_Ois__nat(X21765)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21765)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X21765))
        | c_Nat__Transfer_Ois__nat(X21765) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_is__nat__def])]) ).

fof(i_0_10388,plain,
    ! [X17962,X17963] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17963),hAPP(c_Nat_OSuc,X17962)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17963),X17962)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__right]) ).

fof(i_0_10389,plain,
    ! [X28234,X28235] : hAPP(c_List_Olexn(X28235,X28234),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(X28235),tc_List_Olist(X28235)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_lexn_Osimps_I1_J]) ).

fof(i_0_10390,plain,
    ! [X20008] : 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),X20008))),
    inference(variable_rename,[status(thm)],[fact_zero__zle__int]) ).

fof(i_0_10391,plain,
    ! [X19995] : 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),X19995))),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J]) ).

fof(i_0_10392,plain,
    ! [X17369,X17370] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X17370,tc_HOL_Obool)),X17369),X17369) = c_Orderings_Obot__class_Obot(tc_fun(X17370,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Diff__cancel]) ).

fof(i_0_10393,plain,
    ! [X32975] : c_Relation_Oantisym(X32975,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X32975,X32975),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_antisym__empty]) ).

fof(i_0_10394,plain,
    ! [X28059] : c_Wellfounded_Owf(X28059,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X28059,X28059),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_wf__empty]) ).

fof(i_0_10395,plain,
    ! [X24106,X24107,X24108] :
      ( ~ class_Orderings_Oorder(X24108)
      | X24107 != X24106
      | c_SetInterval_Oord__class_OatLeastAtMost(X24108,X24107,X24106) = hAPP(hAPP(c_Set_Oinsert(X24108),X24107),c_Orderings_Obot__class_Obot(tc_fun(X24108,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton_H])]) ).

fof(i_0_10396,plain,
    ! [X31753,X31754] :
      ( ( hAPP(c_List_Oset(X31754),c_List_Olinorder__class_Osorted__list__of__set(X31754,X31753)) = X31753
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31754),X31753))
        | ~ class_Orderings_Olinorder(X31754) )
      & ( c_List_Olinorder__class_Osorted(X31754,c_List_Olinorder__class_Osorted__list__of__set(X31754,X31753))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31754),X31753))
        | ~ class_Orderings_Olinorder(X31754) )
      & ( hBOOL(hAPP(c_List_Odistinct(X31754),c_List_Olinorder__class_Osorted__list__of__set(X31754,X31753)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X31754),X31753))
        | ~ class_Orderings_Olinorder(X31754) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set])])]) ).

fof(i_0_10397,plain,
    ! [X20764,X20765,X20766] :
      ( ~ class_Divides_Osemiring__div(X20766)
      | c_Divides_Odiv__class_Omod(X20766,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20766),X20765),X20764),X20765) = c_Groups_Ozero__class_Ozero(X20766) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self1__is__0])]) ).

fof(i_0_10398,plain,
    ! [X20761,X20762,X20763] :
      ( ~ class_Divides_Osemiring__div(X20763)
      | c_Divides_Odiv__class_Omod(X20763,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20763),X20762),X20761),X20761) = c_Groups_Ozero__class_Ozero(X20763) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__mult__self2__is__0])]) ).

fof(i_0_10399,plain,
    ! [X29830,X29831] :
      ( X29831 = c_List_Olist_ONil(X29830)
      | ~ hBOOL(hAPP(c_List_Odistinct(X29830),X29831))
      | hBOOL(hAPP(c_List_Odistinct(X29830),c_List_Obutlast(X29830,X29831))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__butlast])]) ).

fof(i_0_10400,plain,
    ! [X23502,X23503] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X23503,X23502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X23502),X23503),
    inference(variable_rename,[status(thm)],[fact_card__greaterThanAtMost]) ).

fof(i_0_10401,plain,
    ! [X29213,X29214,X29215,X29216,X29217] :
      ( ( X29216 = X29214
        | hAPP(hAPP(c_List_Olist_OCons(X29217),X29216),X29215) != hAPP(hAPP(c_List_Olist_OCons(X29217),X29214),X29213) )
      & ( X29215 = X29213
        | hAPP(hAPP(c_List_Olist_OCons(X29217),X29216),X29215) != hAPP(hAPP(c_List_Olist_OCons(X29217),X29214),X29213) )
      & ( X29216 != X29214
        | X29215 != X29213
        | hAPP(hAPP(c_List_Olist_OCons(X29217),X29216),X29215) = hAPP(hAPP(c_List_Olist_OCons(X29217),X29214),X29213) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list_Oinject])])]) ).

fof(i_0_10402,plain,
    ! [X30055,X30056,X30057,X30058] :
      ( ( hAPP(hAPP(c_List_Oappend(X30058),X30057),X30056) != hAPP(hAPP(c_List_Oappend(X30058),X30055),X30056)
        | X30057 = X30055 )
      & ( X30057 != X30055
        | hAPP(hAPP(c_List_Oappend(X30058),X30057),X30056) = hAPP(hAPP(c_List_Oappend(X30058),X30055),X30056) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__same__eq])]) ).

fof(i_0_10403,plain,
    ! [X30059,X30060,X30061,X30062] :
      ( ( hAPP(hAPP(c_List_Oappend(X30062),X30061),X30060) != hAPP(hAPP(c_List_Oappend(X30062),X30061),X30059)
        | X30060 = X30059 )
      & ( X30060 != X30059
        | hAPP(hAPP(c_List_Oappend(X30062),X30061),X30060) = hAPP(hAPP(c_List_Oappend(X30062),X30061),X30059) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_same__append__eq])]) ).

fof(i_0_10404,plain,
    ! [X24100,X24101] :
      ( ~ class_Orderings_Oorder(X24101)
      | c_SetInterval_Oord__class_OatLeastAtMost(X24101,X24100,X24100) = hAPP(hAPP(c_Set_Oinsert(X24101),X24100),c_Orderings_Obot__class_Obot(tc_fun(X24101,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeastAtMost__singleton])]) ).

fof(i_0_10405,plain,
    ! [X29850,X29851] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X29851),X29850))
      | c_List_Oupto(X29850,X29851) = c_List_Olist_ONil(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_upto__empty])]) ).

fof(i_0_10406,plain,
    ! [X31223,X31224] : c_Enum_On__lists(X31224,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X31223) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31224)),c_List_Olist_ONil(X31224)),c_List_Olist_ONil(tc_List_Olist(X31224))),
    inference(variable_rename,[status(thm)],[fact_n__lists_Osimps_I1_J]) ).

fof(i_0_10407,plain,
    ! [X25310] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25310)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25310)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25310)),
    inference(variable_rename,[status(thm)],[fact_atMost__Suc]) ).

fof(i_0_10408,plain,
    ! [X33232,X33233] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33233),X33232))
        | c_Quickcheck_Obeyond(X33233,X33232) = X33232 )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X33233),X33232))
        | c_Quickcheck_Obeyond(X33233,X33232) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6018])]) ).

fof(i_0_10409,plain,
    ! [X20096] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20096) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20096),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20096),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20096) = 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_10410,plain,
    ! [X19910] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19910)))
      | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X19910) = 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_10411,plain,
    ! [X20097] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20097)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20097),c_Int_OPls)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X20097),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20097) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__0__number__of])]) ).

cnf(i_0_10412,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_6019]) ).

fof(i_0_10413,plain,
    ! [X24922,X24923,X24924] :
      ( ~ class_Lattices_Olattice(X24924)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24924),X24923),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24924),X24923),X24922)) = X24923 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__absorb])]) ).

fof(i_0_10414,plain,
    ! [X24919,X24920,X24921] :
      ( ~ class_Lattices_Olattice(X24921)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X24921),X24920),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24921),X24920),X24919)) = X24920 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__inf__absorb])]) ).

fof(i_0_10415,plain,
    ! [X22455,X22456,X22457] :
      ( ~ class_Orderings_Olinorder(X22457)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22457),X22456),hAPP(hAPP(c_Orderings_Oord__class_Omin(X22457),X22456),X22455)) = X22456 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__inf__absorb])]) ).

fof(i_0_10416,plain,
    ! [X22458,X22459,X22460] :
      ( ~ class_Orderings_Olinorder(X22460)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X22460),X22459),hAPP(hAPP(c_Orderings_Oord__class_Omax(X22460),X22459),X22458)) = X22459 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__sup__absorb])]) ).

fof(i_0_10417,plain,
    ! [X32490,X32491,X32492] : c_Predicate_Oconversep(X32492,X32491,c_Predicate_Oconversep(X32491,X32492,X32490)) = X32490,
    inference(variable_rename,[status(thm)],[fact_conversep__conversep]) ).

fof(i_0_10418,plain,
    ! [X18603] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18603),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | X18603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18603 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X18603),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_10419,plain,
    ! [X33776] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33776),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | X33776 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X33776 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33776),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1])]) ).

fof(i_0_10420,plain,
    ! [X30231,X30232,X30233] : hAPP(hAPP(c_List_Odrop(X30233),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X30233),X30232),X30231)) = X30231,
    inference(variable_rename,[status(thm)],[fact_drop__1__Cons]) ).

fof(i_0_10421,plain,
    ! [X17260,X17261] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17261)),hAPP(c_Nat_OSuc,X17260)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17261),X17260),
    inference(variable_rename,[status(thm)],[fact_diff__Suc__Suc]) ).

fof(i_0_10422,plain,
    ! [X17958,X17959] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17959)),X17958) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17959),hAPP(c_Nat_OSuc,X17958)),
    inference(variable_rename,[status(thm)],[fact_add__Suc__shift]) ).

fof(i_0_10423,plain,
    ! [X19370,X19371,X19372] : hAPP(c_Finite__Set_Ofold1(X19372,X19371),X19370) = c_HOL_OThe(X19372,c_Finite__Set_Ofold1Set(X19372,X19371,X19370)),
    inference(variable_rename,[status(thm)],[fact_fold1__def]) ).

fof(i_0_10424,plain,
    ! [X20816,X20817,X20819,X20820,X20821] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X20817,X20816) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X20817 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20816),esk62_2(X20816,X20817)) )
      & ( X20820 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20819),X20821)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,X20820,X20819) = 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_10425,plain,
    ! [X21284,X21285,X21287,X21288,X21289] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21285,X21284) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X21285 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21284),esk71_2(X21284,X21285)) )
      & ( X21288 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X21287),X21289)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21288,X21287) = 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_10426,plain,
    ! [X21776,X21777] :
      ( ~ c_Nat__Transfer_Onat__set(X21777)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X21776),X21777))
      | c_Nat__Transfer_Ois__nat(X21776) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J])]) ).

fof(i_0_10427,plain,
    ! [X33023,X33024] :
      ( ( ~ c_Relation_Osym(X33024,hAPP(c_Relation_Oconverse(X33024,X33024),X33023))
        | c_Relation_Osym(X33024,X33023) )
      & ( ~ c_Relation_Osym(X33024,X33023)
        | c_Relation_Osym(X33024,hAPP(c_Relation_Oconverse(X33024,X33024),X33023)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__converse])]) ).

fof(i_0_10428,plain,
    ! [X32976,X32977] :
      ( ( ~ c_Relation_Oantisym(X32977,hAPP(c_Relation_Oconverse(X32977,X32977),X32976))
        | c_Relation_Oantisym(X32977,X32976) )
      & ( ~ c_Relation_Oantisym(X32977,X32976)
        | c_Relation_Oantisym(X32977,hAPP(c_Relation_Oconverse(X32977,X32977),X32976)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_antisym__converse])]) ).

fof(i_0_10429,plain,
    ! [X32873,X32874] :
      ( ( ~ c_Relation_Otrans(X32874,hAPP(c_Relation_Oconverse(X32874,X32874),X32873))
        | c_Relation_Otrans(X32874,X32873) )
      & ( ~ c_Relation_Otrans(X32874,X32873)
        | c_Relation_Otrans(X32874,hAPP(c_Relation_Oconverse(X32874,X32874),X32873)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trans__converse])]) ).

fof(i_0_10430,plain,
    ! [X28776,X28777] :
      ( ( ~ c_Wellfounded_Oacyclic(X28777,hAPP(c_Relation_Oconverse(X28777,X28777),X28776))
        | c_Wellfounded_Oacyclic(X28777,X28776) )
      & ( ~ c_Wellfounded_Oacyclic(X28777,X28776)
        | c_Wellfounded_Oacyclic(X28777,hAPP(c_Relation_Oconverse(X28777,X28777),X28776)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__converse])]) ).

fof(i_0_10431,plain,
    ! [X18592] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18592),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6020]) ).

fof(i_0_10432,plain,
    ! [X18590] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18590),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6021]) ).

fof(i_0_10433,plain,
    ! [X18198] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18198),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[i_0_6022]) ).

fof(i_0_10434,plain,
    ! [X29792,X29793] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X29793),X29792))
      | hAPP(c_Finite__Set_Ocard(X29793),hAPP(c_List_Oset(X29793),X29792)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29793)),X29792) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__card])]) ).

fof(i_0_10435,plain,
    ! [X31266,X31267] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31267)),c_List_Oremdups(X31267,X31266)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31267)),X31266)
        | c_List_Oremdups(X31267,X31266) = X31266 )
      & ( c_List_Oremdups(X31267,X31266) != X31266
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31267)),c_List_Oremdups(X31267,X31266)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31267)),X31266) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_length__remdups__eq])]) ).

fof(i_0_10436,plain,
    ! [X28837,X28838,X28839] : hAPP(c_Relation_ODomain(X28839,X28838),hAPP(c_Relation_Oconverse(X28838,X28839),X28837)) = hAPP(c_Relation_ORange(X28838,X28839),X28837),
    inference(variable_rename,[status(thm)],[fact_Domain__converse]) ).

fof(i_0_10437,plain,
    ! [X28834,X28835,X28836] : hAPP(c_Relation_ORange(X28836,X28835),hAPP(c_Relation_Oconverse(X28835,X28836),X28834)) = hAPP(c_Relation_ODomain(X28835,X28836),X28834),
    inference(variable_rename,[status(thm)],[fact_Range__converse]) ).

fof(i_0_10438,plain,
    ! [X31476,X31477,X31478] : c_List_Oremdups(X31478,hAPP(c_List_Ofilter(X31478,X31477),X31476)) = hAPP(c_List_Ofilter(X31478,X31477),c_List_Oremdups(X31478,X31476)),
    inference(variable_rename,[status(thm)],[fact_remdups__filter]) ).

fof(i_0_10439,plain,
    ! [X28767,X28768] : c_Transitive__Closure_Ortrancl(X28768,hAPP(c_Relation_Oconverse(X28768,X28768),X28767)) = hAPP(c_Relation_Oconverse(X28768,X28768),c_Transitive__Closure_Ortrancl(X28768,X28767)),
    inference(variable_rename,[status(thm)],[fact_rtrancl__converse]) ).

fof(i_0_10440,plain,
    ! [X28840,X28841,X28842] : hAPP(c_Relation_ORange(X28842,X28841),X28840) = hAPP(c_Relation_ODomain(X28841,X28842),hAPP(c_Relation_Oconverse(X28842,X28841),X28840)),
    inference(variable_rename,[status(thm)],[fact_Range__def]) ).

fof(i_0_10441,plain,
    ! [X32136,X32137,X32138] :
      ( ( ~ hBOOL(hAPP(X32136,X32138))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32137),X32136))
        | ~ class_Enum_Oenum(X32137) )
      & ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32137),X32136))
        | hBOOL(hAPP(X32136,esk450_2(X32136,X32137)))
        | ~ class_Enum_Oenum(X32137) ) ),
    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_10442,plain,
    ! [X32132,X32133,X32135] :
      ( ( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32133),X32132))
        | hBOOL(hAPP(X32132,esk449_2(X32132,X32133)))
        | ~ class_Enum_Oenum(X32133) )
      & ( ~ hBOOL(hAPP(X32132,X32135))
        | hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X32133),X32132))
        | ~ class_Enum_Oenum(X32133) ) ),
    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_10443,plain,
    ! [X29892,X29893,X29894,X29895] :
      ( ( hAPP(hAPP(c_List_Olist__update(X29895,X29894),X29893),X29892) != c_List_Olist_ONil(X29895)
        | X29894 = c_List_Olist_ONil(X29895) )
      & ( X29894 != c_List_Olist_ONil(X29895)
        | hAPP(hAPP(c_List_Olist__update(X29895,X29894),X29893),X29892) = c_List_Olist_ONil(X29895) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_list__update__nonempty])]) ).

fof(i_0_10444,plain,
    ! [X30722,X30723,X30724,X30725] :
      ( ( hAPP(hAPP(c_List_Omap(X30725,X30724),X30723),X30722) != c_List_Olist_ONil(X30724)
        | X30722 = c_List_Olist_ONil(X30725) )
      & ( X30722 != c_List_Olist_ONil(X30725)
        | hAPP(hAPP(c_List_Omap(X30725,X30724),X30723),X30722) = c_List_Olist_ONil(X30724) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_map__is__Nil__conv])]) ).

fof(i_0_10445,plain,
    ! [X30729,X30730,X30731,X30732] :
      ( ( c_List_Olist_ONil(X30732) != hAPP(hAPP(c_List_Omap(X30731,X30732),X30730),X30729)
        | X30729 = c_List_Olist_ONil(X30731) )
      & ( X30729 != c_List_Olist_ONil(X30731)
        | c_List_Olist_ONil(X30732) = hAPP(hAPP(c_List_Omap(X30731,X30732),X30730),X30729) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__map__conv])]) ).

fof(i_0_10446,plain,
    ! [X18607,X18608] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18608),X18607) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18607),X18608) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | X18608 = X18607 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diffs0__imp__equal])]) ).

fof(i_0_10447,plain,
    ! [X24462,X24463,X24464] :
      ( ~ class_Groups_Ocomm__monoid__add(X24464)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24463,X24464),X24462),c_Orderings_Obot__class_Obot(tc_fun(X24463,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X24464) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum_Oempty])]) ).

fof(i_0_10448,plain,
    ! [X24459,X24460,X24461] :
      ( ~ class_Groups_Ocomm__monoid__add(X24461)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24460,X24461),X24459),c_Orderings_Obot__class_Obot(tc_fun(X24460,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(X24461) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setsum__empty])]) ).

fof(i_0_10449,plain,
    ! [X21899,X21900,X21901] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21901)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21900,X21901),X21899),c_Orderings_Obot__class_Obot(tc_fun(X21900,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X21901) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod__empty])]) ).

fof(i_0_10450,plain,
    ! [X21896,X21897,X21898] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21898)
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21897,X21898),X21896),c_Orderings_Obot__class_Obot(tc_fun(X21897,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(X21898) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_setprod_Oempty])]) ).

fof(i_0_10451,plain,
    ! [X18593,X18594] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X18594),X18593))
      | X18593 != 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_10452,plain,
    ! [X26124] :
      ( ~ class_Finite__Set_Ofinite(X26124)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X26124),c_Orderings_Otop__class_Otop(tc_fun(X26124,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__UNIV])]) ).

fof(i_0_10453,plain,
    ! [X22840,X22841,X22842,X22843] :
      ( ( X22841 = c_Groups_Ozero__class_Ozero(X22843)
        | X22842 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22843),X22840),X22841)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22843),X22842),X22841) != X22840
        | ~ class_Fields_Ofield__inverse__zero(X22843) )
      & ( X22841 != c_Groups_Ozero__class_Ozero(X22843)
        | X22840 = c_Groups_Ozero__class_Ozero(X22843)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22843),X22842),X22841) != X22840
        | ~ class_Fields_Ofield__inverse__zero(X22843) )
      & ( X22841 = c_Groups_Ozero__class_Ozero(X22843)
        | X22841 != c_Groups_Ozero__class_Ozero(X22843)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22843),X22842),X22841) = X22840
        | ~ class_Fields_Ofield__inverse__zero(X22843) )
      & ( X22840 != c_Groups_Ozero__class_Ozero(X22843)
        | X22841 != c_Groups_Ozero__class_Ozero(X22843)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22843),X22842),X22841) = X22840
        | ~ class_Fields_Ofield__inverse__zero(X22843) )
      & ( X22841 = c_Groups_Ozero__class_Ozero(X22843)
        | X22842 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22843),X22840),X22841)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22843),X22842),X22841) = X22840
        | ~ class_Fields_Ofield__inverse__zero(X22843) )
      & ( X22840 != c_Groups_Ozero__class_Ozero(X22843)
        | X22842 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22843),X22840),X22841)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22843),X22842),X22841) = X22840
        | ~ class_Fields_Ofield__inverse__zero(X22843) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__eq])])]) ).

fof(i_0_10454,plain,
    ! [X22844,X22845,X22846,X22847] :
      ( ( X22844 = c_Groups_Ozero__class_Ozero(X22847)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22847),X22846),X22844) = X22845
        | X22846 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22847),X22845),X22844)
        | ~ class_Fields_Ofield__inverse__zero(X22847) )
      & ( X22844 != c_Groups_Ozero__class_Ozero(X22847)
        | X22846 = c_Groups_Ozero__class_Ozero(X22847)
        | X22846 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22847),X22845),X22844)
        | ~ class_Fields_Ofield__inverse__zero(X22847) )
      & ( X22844 = c_Groups_Ozero__class_Ozero(X22847)
        | X22844 != c_Groups_Ozero__class_Ozero(X22847)
        | X22846 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22847),X22845),X22844)
        | ~ class_Fields_Ofield__inverse__zero(X22847) )
      & ( X22846 != c_Groups_Ozero__class_Ozero(X22847)
        | X22844 != c_Groups_Ozero__class_Ozero(X22847)
        | X22846 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22847),X22845),X22844)
        | ~ class_Fields_Ofield__inverse__zero(X22847) )
      & ( X22844 = c_Groups_Ozero__class_Ozero(X22847)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22847),X22846),X22844) != X22845
        | X22846 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22847),X22845),X22844)
        | ~ class_Fields_Ofield__inverse__zero(X22847) )
      & ( X22846 != c_Groups_Ozero__class_Ozero(X22847)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22847),X22846),X22844) != X22845
        | X22846 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22847),X22845),X22844)
        | ~ class_Fields_Ofield__inverse__zero(X22847) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__eq])])]) ).

fof(i_0_10455,plain,
    ! [X20094,X20095] :
      ( ~ class_Rings_Osemiring__1(X20095)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20095),hAPP(c_Nat_OSuc,X20094)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20095),c_Groups_Oone__class_Oone(X20095)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20095),X20094)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__Suc])]) ).

fof(i_0_10456,plain,
    ! [X18203] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X18203))),
    inference(variable_rename,[status(thm)],[fact_zero__less__Suc]) ).

fof(i_0_10457,plain,
    ! [X17580,X17581] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17581),X17580))
      | X17581 != X17580 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl3])]) ).

fof(i_0_10458,plain,
    ! [X17578,X17579] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17579),X17578))
      | X17578 != X17579 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_less__not__refl2])]) ).

cnf(i_0_10459,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_6023]) ).

fof(i_0_10460,plain,
    ! [X24157] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24157),hAPP(c_Nat_OSuc,X24157)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24157),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThan__singleton]) ).

cnf(i_0_10461,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_5524]) ).

fof(i_0_10462,plain,
    ! [X31890,X31891,X31892] :
      ( ~ class_Orderings_Olinorder(X31892)
      | ~ c_List_Olinorder__class_Osorted(X31892,X31891)
      | c_List_Olinorder__class_Osorted(X31892,c_List_OtakeWhile(X31892,X31890,X31891)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__takeWhile])]) ).

fof(i_0_10463,plain,
    ! [X31674,X31675,X31676] :
      ( ~ class_Orderings_Olinorder(X31676)
      | ~ c_List_Olinorder__class_Osorted(X31676,X31675)
      | c_List_Olinorder__class_Osorted(X31676,c_List_Oremove1(X31676,X31674,X31675)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remove1])]) ).

fof(i_0_10464,plain,
    ! [X18362,X18363,X18364] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18364),X18363) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18362),X18363)
        | X18364 = X18362
        | X18363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18364 != X18362
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18364),X18363) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18362),X18363) )
      & ( X18363 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18364),X18363) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18362),X18363) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel2])])]) ).

fof(i_0_10465,plain,
    ! [X18941,X18942,X18943] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18943),X18942) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18943),X18941)
        | X18943 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18942 = X18941 )
      & ( X18943 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18943),X18942) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18943),X18941) )
      & ( X18942 != X18941
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18943),X18942) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18943),X18941) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj])])]) ).

fof(i_0_10466,plain,
    ! [X18359,X18360,X18361] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18361),X18360) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18361),X18359)
        | X18360 = X18359
        | X18361 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18360 != X18359
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18361),X18360) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18361),X18359) )
      & ( X18361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18361),X18360) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18361),X18359) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__cancel1])])]) ).

fof(i_0_10467,plain,
    ! [X30368,X30369,X30370] :
      ( ( X30370 != c_List_Olist_ONil(X30369)
        | hAPP(c_List_Ohd(X30369),hAPP(hAPP(c_List_Oappend(X30369),X30370),X30368)) = hAPP(c_List_Ohd(X30369),X30368) )
      & ( X30370 = c_List_Olist_ONil(X30369)
        | hAPP(c_List_Ohd(X30369),hAPP(hAPP(c_List_Oappend(X30369),X30370),X30368)) = hAPP(c_List_Ohd(X30369),X30370) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append])]) ).

fof(i_0_10468,plain,
    ! [X25935,X25936] :
      ( ~ class_Rings_Olinordered__idom(X25936)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25936),c_Groups_Osgn__class_Osgn(X25936,X25935)),hAPP(c_Groups_Oabs__class_Oabs(X25936),X25935)) = X25935 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs])]) ).

fof(i_0_10469,plain,
    ! [X18637] :
      ( ~ class_Rings_Olinordered__semidom(X18637)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X18637),c_Groups_Ozero__class_Ozero(X18637)),c_Groups_Oone__class_Oone(X18637))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__less__one])]) ).

fof(i_0_10470,plain,
    ! [X20202] :
      ( ~ class_Rings_Osemiring__1(X20202)
      | hBOOL(hAPP(hAPP(c_member(X20202),c_Groups_Ozero__class_Ozero(X20202)),c_Nat_Osemiring__1__class_ONats(X20202))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__0])]) ).

fof(i_0_10471,plain,
    ! [X19198] :
      ( ~ class_Rings_Oring__1(X19198)
      | hBOOL(hAPP(hAPP(c_member(X19198),c_Groups_Ozero__class_Ozero(X19198)),c_Int_Oring__1__class_OInts(X19198))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__0])]) ).

fof(i_0_10472,plain,
    ! [X20209] :
      ( ~ class_Rings_Osemiring__1(X20209)
      | hBOOL(hAPP(hAPP(c_member(X20209),c_Groups_Oone__class_Oone(X20209)),c_Nat_Osemiring__1__class_ONats(X20209))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nats__1])]) ).

fof(i_0_10473,plain,
    ! [X19208] :
      ( ~ class_Rings_Oring__1(X19208)
      | hBOOL(hAPP(hAPP(c_member(X19208),c_Groups_Oone__class_Oone(X19208)),c_Int_Oring__1__class_OInts(X19208))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Ints__1])]) ).

fof(i_0_10474,plain,
    ! [X18636] :
      ( ~ class_Rings_Olinordered__semidom(X18636)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X18636),c_Groups_Ozero__class_Ozero(X18636)),c_Groups_Oone__class_Oone(X18636))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__le__one])]) ).

fof(i_0_10475,plain,
    ! [X22619,X22620,X22621,X22622] :
      ( ~ class_Rings_Odivision__ring(X22622)
      | X22621 = c_Groups_Ozero__class_Ozero(X22622)
      | X22620 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22622),X22619),X22621)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22622),X22620),X22621) = X22619 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__eq__imp])]) ).

fof(i_0_10476,plain,
    ! [X22615,X22616,X22617,X22618] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22618),X22616),X22617) != X22615
        | X22616 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22618),X22615),X22617)
        | X22617 = c_Groups_Ozero__class_Ozero(X22618)
        | ~ class_Rings_Odivision__ring(X22618) )
      & ( X22616 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22618),X22615),X22617)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22618),X22616),X22617) = X22615
        | X22617 = c_Groups_Ozero__class_Ozero(X22618)
        | ~ class_Rings_Odivision__ring(X22618) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__divide__eq__eq])])]) ).

fof(i_0_10477,plain,
    ! [X22611,X22612,X22613,X22614] :
      ( ( X22612 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22614),X22611),X22613)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22614),X22612),X22613) = X22611
        | X22613 = c_Groups_Ozero__class_Ozero(X22614)
        | ~ class_Rings_Odivision__ring(X22614) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22614),X22612),X22613) != X22611
        | X22612 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22614),X22611),X22613)
        | X22613 = c_Groups_Ozero__class_Ozero(X22614)
        | ~ class_Rings_Odivision__ring(X22614) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nonzero__eq__divide__eq])])]) ).

fof(i_0_10478,plain,
    ! [X22623,X22624,X22625,X22626] :
      ( ~ class_Rings_Odivision__ring(X22626)
      | X22625 = c_Groups_Ozero__class_Ozero(X22626)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X22626),X22624),X22625) != X22623
      | X22624 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22626),X22623),X22625) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__divide__imp])]) ).

fof(i_0_10479,plain,
    ! [X21266,X21267,X21268] :
      ( ~ class_Groups_Ogroup__add(X21268)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21268),X21267),hAPP(c_Groups_Ouminus__class_Ouminus(X21268),X21266)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21268),X21267),X21266) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add])]) ).

fof(i_0_10480,plain,
    ! [X25212,X25213,X25214] :
      ( ~ class_Lattices_Oboolean__algebra(X25214)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X25214),X25213),X25212) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25214),X25213),hAPP(c_Groups_Ouminus__class_Ouminus(X25214),X25212)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__eq])]) ).

fof(i_0_10481,plain,
    ! [X21263,X21264,X21265] :
      ( ~ class_Rings_Ocomm__ring__1(X21265)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21265),X21264),X21263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21265),X21264),hAPP(c_Groups_Ouminus__class_Ouminus(X21265),X21263)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J])]) ).

fof(i_0_10482,plain,
    ! [X21272,X21273,X21274] :
      ( ~ class_Groups_Ogroup__add(X21274)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21274),X21273),X21272) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21274),X21273),hAPP(c_Groups_Ouminus__class_Ouminus(X21274),X21272)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__def])]) ).

fof(i_0_10483,plain,
    ! [X21269,X21270,X21271] :
      ( ~ class_Groups_Oab__group__add(X21271)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21271),X21270),X21269) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21271),X21270),hAPP(c_Groups_Ouminus__class_Ouminus(X21271),X21269)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__diff__minus])]) ).

fof(i_0_10484,plain,
    ! [X21349,X21350] :
      ( ~ class_Int_Onumber__ring(X21350)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21350),hAPP(c_Int_Onumber__class_Onumber__of(X21350),c_Int_OMin)),X21349) = hAPP(c_Groups_Ouminus__class_Ouminus(X21350),X21349) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1])]) ).

fof(i_0_10485,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_10486,plain,
    ! [X17577] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17577),X17577)),
    inference(variable_rename,[status(thm)],[i_0_6024]) ).

fof(i_0_10487,plain,
    ! [X17555] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17555),X17555)),
    inference(variable_rename,[status(thm)],[i_0_6025]) ).

fof(i_0_10488,plain,
    ! [X30365,X30366,X30367] :
      ( X30367 = c_List_Olist_ONil(X30366)
      | hAPP(c_List_Ohd(X30366),hAPP(hAPP(c_List_Oappend(X30366),X30367),X30365)) = hAPP(c_List_Ohd(X30366),X30367) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__append2])]) ).

cnf(i_0_10489,plain,
    ( X1 = X2
    | c_Int_OBit0(X1) != c_Int_OBit0(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6026]) ).

fof(i_0_10490,plain,
    ! [X17821,X17822,X17823] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17823),X17822) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17821),X17822)
        | X17823 = X17821 )
      & ( X17823 != X17821
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17823),X17822) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17821),X17822) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__right__cancel])]) ).

fof(i_0_10491,plain,
    ! [X17824,X17825,X17826] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17826),X17825) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17826),X17824)
        | X17825 = X17824 )
      & ( X17825 != X17824
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17826),X17825) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17826),X17824) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__add__left__cancel])]) ).

fof(i_0_10492,plain,
    ! [X27640,X27641] : hAPP(c_Set_OCollect(X27641),hAPP(c_fequal,X27640)) = hAPP(hAPP(c_Set_Oinsert(X27641),X27640),c_Orderings_Obot__class_Obot(tc_fun(X27641,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[fact_singleton__conv2]) ).

fof(i_0_10493,plain,
    ! [X31666,X31667,X31668] :
      ( ~ class_Orderings_Olinorder(X31668)
      | ~ c_List_Olinorder__class_Osorted(X31668,X31667)
      | c_List_Olinorder__class_Osorted(X31668,hAPP(hAPP(c_List_Odrop(X31668),X31666),X31667)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__drop])]) ).

fof(i_0_10494,plain,
    ! [X31671,X31672,X31673] :
      ( ~ class_Orderings_Olinorder(X31673)
      | ~ c_List_Olinorder__class_Osorted(X31673,X31672)
      | c_List_Olinorder__class_Osorted(X31673,hAPP(hAPP(c_List_Otake(X31673),X31671),X31672)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__take])]) ).

fof(i_0_10495,plain,
    ! [X17003] : hBOOL(hAPP(c_Finite__Set_Ofinite(X17003),c_Orderings_Obot__class_Obot(tc_fun(X17003,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_finite_Oequations_I1_J]) ).

fof(i_0_10496,plain,
    ! [X16851] : hBOOL(hAPP(c_Finite__Set_Ofinite(X16851),c_Orderings_Obot__class_Obot(tc_fun(X16851,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[fact_finite_OemptyI]) ).

fof(i_0_10497,plain,
    ! [X23950,X23951] : hAPP(c_Set_OPow(X23951),X23950) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X23951,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pow__not__empty]) ).

fof(i_0_10498,plain,
    ! [X24469,X24470,X24471,X24472] :
      ( ~ class_Groups_Ocomm__monoid__add(X24472)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X24471),X24470))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24471,X24472),X24469),X24470) = c_Groups_Ozero__class_Ozero(X24472) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6027])]) ).

fof(i_0_10499,plain,
    ! [X24465,X24466,X24467,X24468] :
      ( ~ class_Groups_Ocomm__monoid__add(X24468)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X24467),X24466))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X24467,X24468),X24465),X24466) = c_Groups_Ozero__class_Ozero(X24468) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6028])]) ).

fof(i_0_10500,plain,
    ! [X21906,X21907,X21908,X21909] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21909)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X21908),X21907))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21908,X21909),X21906),X21907) = c_Groups_Oone__class_Oone(X21909) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6029])]) ).

fof(i_0_10501,plain,
    ! [X21902,X21903,X21904,X21905] :
      ( ~ class_Groups_Ocomm__monoid__mult(X21905)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X21904),X21903))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X21904,X21905),X21902),X21903) = c_Groups_Oone__class_Oone(X21905) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6030])]) ).

fof(i_0_10502,plain,
    ! [X26185] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26185,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X26185,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X26185,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__UNIV__eq]) ).

fof(i_0_10503,plain,
    ! [X26184] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X26184,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26184,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X26184,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Compl__empty__eq]) ).

fof(i_0_10504,plain,
    ! [X26118] : hAPP(c_Set_OPow(X26118),c_Orderings_Otop__class_Otop(tc_fun(X26118,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X26118,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Pow__UNIV]) ).

fof(i_0_10505,plain,
    ! [X24372] : c_Relation_OId__on(X24372,c_Orderings_Obot__class_Obot(tc_fun(X24372,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X24372,X24372),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Id__on__empty]) ).

fof(i_0_10506,plain,
    ! [X25133,X25134] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X25134,tc_HOL_Obool)),X25133),X25133) = X25133,
    inference(variable_rename,[status(thm)],[fact_Int__absorb]) ).

fof(i_0_10507,plain,
    ! [X23280,X23281] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23281,tc_HOL_Obool)),X23280),X23280) = X23280,
    inference(variable_rename,[status(thm)],[fact_Un__absorb]) ).

fof(i_0_10508,plain,
    ! [X28261,X28262] :
      ( ~ c_Wellfounded_Owf(X28262,X28261)
      | c_Wellfounded_OwfP(X28262,c_FunDef_Oin__rel(X28262,X28262,X28261)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__in__rel])]) ).

fof(i_0_10509,plain,
    ! [X28093,X28094,X28095] :
      ( ~ c_Wellfounded_Owf(X28095,X28094)
      | c_Wellfounded_Owf(X28095,c_Wellfounded_Omlex__prod(X28095,X28093,X28094)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__mlex])]) ).

fof(i_0_10510,plain,
    ! [X19975] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19975))),
    inference(variable_rename,[status(thm)],[i_0_6031]) ).

fof(i_0_10511,plain,
    ! [X33041,X33042,X33043] :
      ( ( c_Relation_Orefl__on(X33043,X33042,X33041)
        | ~ c_Equiv__Relations_Oequiv(X33043,X33042,X33041) )
      & ( c_Relation_Osym(X33043,X33041)
        | ~ c_Equiv__Relations_Oequiv(X33043,X33042,X33041) )
      & ( c_Relation_Otrans(X33043,X33041)
        | ~ c_Equiv__Relations_Oequiv(X33043,X33042,X33041) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6032])])]) ).

fof(i_0_10512,plain,
    ! [X25655,X25656] :
      ( ~ class_Lattices_Olattice(X25656)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X25656),X25655))
      | c_Big__Operators_Olattice__class_OInf__fin(X25656,X25655) = hAPP(c_Finite__Set_Ofold1(X25656,c_Lattices_Osemilattice__inf__class_Oinf(X25656)),X25655) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_OF__eq])]) ).

fof(i_0_10513,plain,
    ! [X23513,X23514] :
      ( ~ class_Lattices_Olattice(X23514)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23514),X23513))
      | c_Big__Operators_Olattice__class_OSup__fin(X23514,X23513) = hAPP(c_Finite__Set_Ofold1(X23514,c_Lattices_Osemilattice__sup__class_Osup(X23514)),X23513) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_OF__eq])]) ).

fof(i_0_10514,plain,
    ! [X23011,X23012] :
      ( ~ class_Orderings_Olinorder(X23012)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X23012),X23011))
      | c_Big__Operators_Olinorder__class_OMax(X23012,X23011) = hAPP(c_Finite__Set_Ofold1(X23012,c_Orderings_Oord__class_Omax(X23012)),X23011) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_OF__eq])]) ).

fof(i_0_10515,plain,
    ! [X21785,X21786] :
      ( ~ class_Orderings_Olinorder(X21786)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X21786),X21785))
      | c_Big__Operators_Olinorder__class_OMin(X21786,X21785) = hAPP(c_Finite__Set_Ofold1(X21786,c_Orderings_Oord__class_Omin(X21786)),X21785) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_OF__eq])]) ).

fof(i_0_10516,plain,
    ! [X17550] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17550),hAPP(c_Nat_OSuc,X17550))),
    inference(variable_rename,[status(thm)],[fact_lessI]) ).

fof(i_0_10517,plain,
    ! [X32514,X32515,X32516] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X32516)),c_List_Oreplicate(X32516,X32515,X32514)) = X32515,
    inference(variable_rename,[status(thm)],[fact_length__replicate]) ).

fof(i_0_10518,plain,
    ! [X25210,X25211] :
      ( ~ class_Lattices_Oboolean__algebra(X25211)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25211),hAPP(c_Groups_Ouminus__class_Ouminus(X25211),X25210)),X25210) = c_Orderings_Obot__class_Obot(X25211) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__inf__bot])]) ).

fof(i_0_10519,plain,
    ! [X26219,X26220] :
      ( ~ class_Lattices_Oboolean__algebra(X26220)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26220),hAPP(c_Groups_Ouminus__class_Ouminus(X26220),X26219)),X26219) = c_Orderings_Otop__class_Otop(X26220) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__sup__top])]) ).

fof(i_0_10520,plain,
    ! [X21254,X21255] :
      ( ~ class_Groups_Ogroup__add(X21255)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21255),hAPP(c_Groups_Ouminus__class_Ouminus(X21255),X21254)),X21254) = c_Groups_Ozero__class_Ozero(X21255) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_left__minus])]) ).

fof(i_0_10521,plain,
    ! [X21256,X21257] :
      ( ~ class_Groups_Oab__group__add(X21257)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21257),hAPP(c_Groups_Ouminus__class_Ouminus(X21257),X21256)),X21256) = c_Groups_Ozero__class_Ozero(X21257) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ab__left__minus])]) ).

fof(i_0_10522,plain,
    ! [X30632,X30633,X30634] :
      ( X30634 != c_List_Olist_ONil(X30633)
      | c_List_Olast(X30633,hAPP(hAPP(c_List_Oappend(X30633),X30632),X30634)) = c_List_Olast(X30633,X30632) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendL])]) ).

fof(i_0_10523,plain,
    ! [X30626,X30627,X30628] :
      ( ( X30628 != c_List_Olist_ONil(X30627)
        | c_List_Olast(X30627,hAPP(hAPP(c_List_Oappend(X30627),X30626),X30628)) = c_List_Olast(X30627,X30626) )
      & ( X30628 = c_List_Olist_ONil(X30627)
        | c_List_Olast(X30627,hAPP(hAPP(c_List_Oappend(X30627),X30626),X30628)) = c_List_Olast(X30627,X30628) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__append])]) ).

fof(i_0_10524,plain,
    ! [X18788,X18789] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18789),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18789),X18788)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__add__0]) ).

fof(i_0_10525,plain,
    ! [X29507,X29508,X29509] : c_List_Osublist(X29509,X29508,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X29507)) = hAPP(hAPP(c_List_Otake(X29509),X29507),X29508),
    inference(variable_rename,[status(thm)],[fact_sublist__upt__eq__take]) ).

fof(i_0_10526,plain,
    ! [X33682,X33683] :
      ( ~ class_Rings_Ocomm__semiring__1(X33683)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33683),c_Groups_Oone__class_Oone(X33683)),X33682)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__dvd])]) ).

fof(i_0_10527,plain,
    ! [X17226,X17227] :
      ( ~ class_Orderings_Obot(X17227)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17227),c_Orderings_Obot__class_Obot(X17227)),X17226)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__least])]) ).

fof(i_0_10528,plain,
    ! [X21766,X21767] :
      ( X21767 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hBOOL(hAPP(c_Divides_Odivmod__int__rel(X21766,X21767),c_Divides_Odivmod__int(X21766,X21767))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divmod__int__correct])]) ).

fof(i_0_10529,plain,
    ! [X26026,X26027] :
      ( ( X26027 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Opdivmod(X26026,X26027) = 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),X26026)) )
      & ( X26027 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Opdivmod(X26026,X26027) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26026),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X26027)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_pdivmod__posDivAlg])]) ).

fof(i_0_10530,plain,
    ! [X31657,X31658] :
      ( ~ class_Orderings_Olinorder(X31658)
      | c_List_Olinorder__class_Osorted(X31658,hAPP(hAPP(c_List_Olist_OCons(X31658),X31657),c_List_Olist_ONil(X31658))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__single])]) ).

fof(i_0_10531,plain,
    ! [X30629,X30630,X30631] :
      ( X30631 = c_List_Olist_ONil(X30630)
      | c_List_Olast(X30630,hAPP(hAPP(c_List_Oappend(X30630),X30629),X30631)) = c_List_Olast(X30630,X30631) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__appendR])]) ).

fof(i_0_10532,plain,
    ! [X30620,X30621,X30622] :
      ( X30622 = c_List_Olist_ONil(X30621)
      | c_List_Olast(X30621,hAPP(hAPP(c_List_Olist_OCons(X30621),X30620),X30622)) = c_List_Olast(X30621,X30622) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsR])]) ).

fof(i_0_10533,plain,
    ! [X30617,X30618,X30619] :
      ( ( X30619 != c_List_Olist_ONil(X30618)
        | c_List_Olast(X30618,hAPP(hAPP(c_List_Olist_OCons(X30618),X30617),X30619)) = X30617 )
      & ( X30619 = c_List_Olist_ONil(X30618)
        | c_List_Olast(X30618,hAPP(hAPP(c_List_Olist_OCons(X30618),X30617),X30619)) = c_List_Olast(X30618,X30619) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last_Osimps])]) ).

fof(i_0_10534,plain,
    ! [X26022,X26023] :
      ( ( X26023 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X26022,X26023) = X26022 )
      & ( X26023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_Nitpick_Onat__gcd(X26022,X26023) = c_Nitpick_Onat__gcd(X26023,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X26022,X26023)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__gcd_Osimps])]) ).

fof(i_0_10535,plain,
    ! [X24125,X24126] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24126)),X24125) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X24126,X24125),
    inference(variable_rename,[status(thm)],[fact_atLeastSucLessThan__greaterThanLessThan]) ).

fof(i_0_10536,plain,
    ! [X24058,X24059] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24059),X24058)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24058),X24059),
    inference(variable_rename,[status(thm)],[fact_card__atLeastLessThan]) ).

fof(i_0_10537,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_10538,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_10539,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_10540,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_10541,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_10542,plain,
    ! [X29871,X29872,X29873] : hAPP(hAPP(c_List_Ozip(X29873,X29872),c_List_Olist_ONil(X29873)),X29871) = c_List_Olist_ONil(tc_prod(X29873,X29872)),
    inference(variable_rename,[status(thm)],[fact_zip__Nil]) ).

fof(i_0_10543,plain,
    ! [X26299,X26300] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X26300,tc_HOL_Obool)),X26299)),
    inference(variable_rename,[status(thm)],[fact_top1I]) ).

fof(i_0_10544,plain,
    ! [X27800,X27801] : hAPP(c_Set_Ovimage(X27801,X27801,c_Fun_Oid(X27801)),X27800) = X27800,
    inference(variable_rename,[status(thm)],[fact_vimage__id]) ).

fof(i_0_10545,plain,
    ! [X26819,X26820] : hAPP(c_Set_Ovimage(X26820,X26820,c_COMBI(X26820)),X26819) = X26819,
    inference(variable_rename,[status(thm)],[fact_vimage__ident]) ).

fof(i_0_10546,plain,
    ! [X27826,X27827] : hAPP(c_Set_Oimage(X27827,X27827,c_Fun_Oid(X27827)),X27826) = X27826,
    inference(variable_rename,[status(thm)],[fact_image__id]) ).

fof(i_0_10547,plain,
    ! [X18187,X18188] : hAPP(c_Set_Oimage(X18188,X18188,c_COMBI(X18188)),X18187) = X18187,
    inference(variable_rename,[status(thm)],[fact_image__ident]) ).

fof(i_0_10548,plain,
    ! [X28656,X28657] : c_Relation_Orefl__on(X28657,c_Orderings_Otop__class_Otop(tc_fun(X28657,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X28657,X28656)),
    inference(variable_rename,[status(thm)],[fact_refl__rtrancl]) ).

fof(i_0_10549,plain,
    ! [X32535,X32536,X32537] :
      ( X32537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(c_List_Ohd(X32536),c_List_Oreplicate(X32536,X32537,X32535)) = X32535 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__replicate])]) ).

cnf(i_0_10550,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_6033]) ).

cnf(i_0_10551,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_6034]) ).

fof(i_0_10552,plain,
    ! [X34052,X34053] :
      ( ~ hBOOL(hAPP(hAPP(c_fimplies,X34053),X34052))
      | ~ hBOOL(X34053)
      | hBOOL(X34052) ),
    inference(variable_rename,[status(thm)],[i_0_6035]) ).

fof(i_0_10553,plain,
    ! [X25784,X25785] :
      ( ~ class_Orderings_Olinorder(X25785)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25785,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X25785),X25784)) = hAPP(c_SetInterval_Oord__class_OatMost(X25785),X25784) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__greaterThan])]) ).

fof(i_0_10554,plain,
    ! [X25740,X25741] :
      ( ~ class_Orderings_Olinorder(X25741)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25741,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(X25741),X25740)) = hAPP(c_SetInterval_Oord__class_OlessThan(X25741),X25740) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atLeast])]) ).

fof(i_0_10555,plain,
    ! [X25786,X25787] :
      ( ~ class_Orderings_Olinorder(X25787)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25787,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(X25787),X25786)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X25787),X25786) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__atMost])]) ).

fof(i_0_10556,plain,
    ! [X25742,X25743] :
      ( ~ class_Orderings_Olinorder(X25743)
      | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X25743,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(X25743),X25742)) = hAPP(c_SetInterval_Oord__class_OatLeast(X25743),X25742) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Compl__lessThan])]) ).

fof(i_0_10557,plain,
    ! [X18847,X18848] :
      ( ( hAPP(c_Finite__Set_Ocard(X18848),X18847) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18847 = c_Orderings_Obot__class_Obot(tc_fun(X18848,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X18848),X18847)) )
      & ( X18847 != c_Orderings_Obot__class_Obot(tc_fun(X18848,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(X18848),X18847) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(X18848),X18847))
        | hAPP(c_Finite__Set_Ocard(X18848),X18847) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6036])])]) ).

fof(i_0_10558,plain,
    ! [X27091,X27092] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X27092)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X27092),X27091))
      | X27091 = c_Orderings_Obot__class_Obot(tc_fun(X27092,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OSup__fin(X27092,X27091) = c_Complete__Lattice_OSup__class_OSup(X27092,X27091) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin__Sup])]) ).

fof(i_0_10559,plain,
    ! [X26966,X26967] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26967)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X26967),X26966))
      | X26966 = c_Orderings_Obot__class_Obot(tc_fun(X26967,tc_HOL_Obool))
      | c_Big__Operators_Olattice__class_OInf__fin(X26967,X26966) = c_Complete__Lattice_OInf__class_OInf(X26967,X26966) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin__Inf])]) ).

fof(i_0_10560,plain,
    ! [X20047,X20048] :
      ( ~ class_Int_Onumber__ring(X20048)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20048),hAPP(c_Int_Onumber__class_Onumber__of(X20048),c_Int_OPls)),X20047) = X20047 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0])]) ).

fof(i_0_10561,plain,
    ! [X18775,X18776] :
      ( ( X18776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18776 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18776),X18775) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18775 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18776 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18776),X18775) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18776),X18775) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18775 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18776),X18775) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18776 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18775 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18776),X18775) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18776 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18775 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18776),X18775) = 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_10562,plain,
    ! [X18777,X18778] :
      ( ( X18778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18778 = 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),X18778),X18777) )
      & ( X18777 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18778 = 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),X18778),X18777) )
      & ( X18778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18777 = 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),X18778),X18777) )
      & ( X18777 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18777 = 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),X18778),X18777) )
      & ( X18778 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18777 != 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),X18778),X18777) )
      & ( X18778 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18777 != 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),X18778),X18777) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__is__add])])]) ).

fof(i_0_10563,plain,
    ! [X28388,X28389,X28390] :
      ( ~ hBOOL(hAPP(X28389,X28390))
      | hBOOL(hAPP(X28389,c_Hilbert__Choice_OEps(X28388,X28389))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_tfl__some])])]) ).

fof(i_0_10564,plain,
    ! [X28385,X28386,X28387] :
      ( ~ hBOOL(hAPP(X28387,X28386))
      | hBOOL(hAPP(X28387,c_Hilbert__Choice_OEps(X28385,X28387))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI])]) ).

fof(i_0_10565,plain,
    ! [X28382,X28383,X28384] :
      ( ~ hBOOL(hAPP(X28383,X28384))
      | hBOOL(hAPP(X28383,c_Hilbert__Choice_OEps(X28382,X28383))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_someI__ex])])]) ).

fof(i_0_10566,plain,
    ! [X34046,X34047] :
      ( ~ hBOOL(hAPP(hAPP(c_fdisj,X34047),X34046))
      | hBOOL(X34047)
      | hBOOL(X34046) ),
    inference(variable_rename,[status(thm)],[i_0_6037]) ).

fof(i_0_10567,plain,
    ! [X24127,X24128] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X24128),X24127) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X24128,X24127),
    inference(variable_rename,[status(thm)],[fact_atLeastSucAtMost__greaterThanAtMost]) ).

fof(i_0_10568,plain,
    ! [X21277,X21278] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21278),X21277),X21277) != c_Groups_Oone__class_Oone(X21278)
        | X21277 = c_Groups_Oone__class_Oone(X21278)
        | X21277 = hAPP(c_Groups_Ouminus__class_Ouminus(X21278),c_Groups_Oone__class_Oone(X21278))
        | ~ class_Rings_Oring__1__no__zero__divisors(X21278) )
      & ( X21277 != c_Groups_Oone__class_Oone(X21278)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21278),X21277),X21277) = c_Groups_Oone__class_Oone(X21278)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21278) )
      & ( X21277 != hAPP(c_Groups_Ouminus__class_Ouminus(X21278),c_Groups_Oone__class_Oone(X21278))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21278),X21277),X21277) = c_Groups_Oone__class_Oone(X21278)
        | ~ class_Rings_Oring__1__no__zero__divisors(X21278) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff])])]) ).

fof(i_0_10569,plain,
    ! [X16828,X16829] :
      ( hAPP(X16829,esk1_2(X16828,X16829)) != hAPP(X16828,esk1_2(X16828,X16829))
      | X16829 = X16828 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_ext])])]) ).

fof(i_0_10570,plain,
    ! [X29874,X29875,X29876] : hAPP(hAPP(c_List_Ozip(X29876,X29875),X29874),c_List_Olist_ONil(X29875)) = c_List_Olist_ONil(tc_prod(X29876,X29875)),
    inference(variable_rename,[status(thm)],[fact_zip_Osimps_I1_J]) ).

fof(i_0_10571,plain,
    ! [X17346,X17347,X17348,X17349] :
      ( ~ c_Finite__Set_Ofolding__one__idem(X17349,X17348,X17347)
      | hAPP(hAPP(X17348,X17346),X17346) = X17346 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_folding__one__idem_Oidem])]) ).

fof(i_0_10572,plain,
    ! [X31207] : c_Enum_Osublists(X31207,c_List_Olist_ONil(X31207)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X31207)),c_List_Olist_ONil(X31207)),c_List_Olist_ONil(tc_List_Olist(X31207))),
    inference(variable_rename,[status(thm)],[fact_sublists_Osimps_I1_J]) ).

fof(i_0_10573,plain,
    ! [X33607,X33608] :
      ( ~ class_Rings_Ocomm__semiring__1(X33608)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33608),X33607),c_Groups_Ozero__class_Ozero(X33608))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__0__right])]) ).

fof(i_0_10574,plain,
    ! [X26149,X26150] :
      ( ~ class_Orderings_Otop(X26150)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X26150),X26149),c_Orderings_Otop__class_Otop(X26150))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__greatest])]) ).

fof(i_0_10575,plain,
    ! [X30623,X30624,X30625] :
      ( X30625 != c_List_Olist_ONil(X30624)
      | c_List_Olast(X30624,hAPP(hAPP(c_List_Olist_OCons(X30624),X30623),X30625)) = X30623 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__ConsL])]) ).

fof(i_0_10576,plain,
    ! [X32538,X32539,X32540] :
      ( X32540 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | c_List_Olast(X32539,c_List_Oreplicate(X32539,X32540,X32538)) = X32538 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__replicate])]) ).

fof(i_0_10577,plain,
    ! [X21294,X21295,X21296] : hAPP(c_Nat_Onat_Onat__rec(X21296,X21295,X21294),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21295,
    inference(variable_rename,[status(thm)],[fact_nat__rec__0]) ).

fof(i_0_10578,plain,
    ! [X17012,X17013,X17014] : hAPP(hAPP(c_Set_Oinsert(X17014),X17013),X17012) != c_Orderings_Obot__class_Obot(tc_fun(X17014,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_insert__not__empty]) ).

fof(i_0_10579,plain,
    ! [X17015,X17016,X17017] : c_Orderings_Obot__class_Obot(tc_fun(X17017,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X17017),X17016),X17015),
    inference(variable_rename,[status(thm)],[fact_empty__not__insert]) ).

fof(i_0_10580,plain,
    ! [X34038,X34039] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X34039),X34038))
      | hBOOL(X34039) ),
    inference(variable_rename,[status(thm)],[i_0_6038]) ).

fof(i_0_10581,plain,
    ! [X34040,X34041] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,X34041),X34040))
      | hBOOL(X34040) ),
    inference(variable_rename,[status(thm)],[i_0_6039]) ).

fof(i_0_10582,plain,
    ! [X20091] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X20091)) = 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),X20091)),
    inference(variable_rename,[status(thm)],[fact_int__Suc]) ).

fof(i_0_10583,plain,
    ! [X21333,X21334] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21334),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21333)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21334),X21333),
    inference(variable_rename,[status(thm)],[fact_diff__int__def__symmetric]) ).

fof(i_0_10584,plain,
    ! [X21331,X21332] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X21332),X21331) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21332),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21331)),
    inference(variable_rename,[status(thm)],[fact_diff__int__def]) ).

fof(i_0_10585,plain,
    ! [X30386,X30387,X30388] : hAPP(c_List_Otl(X30388),hAPP(hAPP(c_List_Olist_OCons(X30388),X30387),X30386)) = X30386,
    inference(variable_rename,[status(thm)],[fact_tl_Osimps_I2_J]) ).

fof(i_0_10586,plain,
    ! [X30362,X30363,X30364] : hAPP(c_List_Ohd(X30364),hAPP(hAPP(c_List_Olist_OCons(X30364),X30363),X30362)) = X30363,
    inference(variable_rename,[status(thm)],[fact_hd_Osimps]) ).

fof(i_0_10587,plain,
    ! [X20281,X20282,X20283] :
      ( ( X20282 = c_Groups_Ozero__class_Ozero(X20283)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20283),X20282),X20281) != c_Groups_Ozero__class_Ozero(X20283)
        | ~ class_Power_Opower(X20283)
        | ~ class_Rings_Omult__zero(X20283)
        | ~ class_Rings_Ono__zero__divisors(X20283)
        | ~ class_Rings_Ozero__neq__one(X20283) )
      & ( X20281 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20283),X20282),X20281) != c_Groups_Ozero__class_Ozero(X20283)
        | ~ class_Power_Opower(X20283)
        | ~ class_Rings_Omult__zero(X20283)
        | ~ class_Rings_Ono__zero__divisors(X20283)
        | ~ class_Rings_Ozero__neq__one(X20283) )
      & ( X20282 != c_Groups_Ozero__class_Ozero(X20283)
        | X20281 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20283),X20282),X20281) = c_Groups_Ozero__class_Ozero(X20283)
        | ~ class_Power_Opower(X20283)
        | ~ class_Rings_Omult__zero(X20283)
        | ~ class_Rings_Ono__zero__divisors(X20283)
        | ~ class_Rings_Ozero__neq__one(X20283) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__eq__0__iff])])]) ).

fof(i_0_10588,plain,
    ! [X21755,X21756] :
      ( ~ c_Nat__Transfer_Ois__nat(X21756)
      | ~ c_Nat__Transfer_Ois__nat(X21755)
      | c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X21756,X21755)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I2_J])]) ).

fof(i_0_10589,plain,
    ! [X27604,X27605,X27606,X27607,X27609] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X27605,tc_HOL_Obool)) != hAPP(c_Set_OCollect(X27605),X27604)
        | ~ hBOOL(hAPP(X27604,X27606)) )
      & ( hBOOL(hAPP(X27607,esk279_1(X27607)))
        | c_Orderings_Obot__class_Obot(tc_fun(X27609,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X27609),X27607) ) ),
    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_6040])])])])]) ).

fof(i_0_10590,plain,
    ! [X27598,X27599,X27600,X27601,X27603] :
      ( ( hAPP(c_Set_OCollect(X27599),X27598) != c_Orderings_Obot__class_Obot(tc_fun(X27599,tc_HOL_Obool))
        | ~ hBOOL(hAPP(X27598,X27600)) )
      & ( hBOOL(hAPP(X27601,esk278_1(X27601)))
        | hAPP(c_Set_OCollect(X27603),X27601) = c_Orderings_Obot__class_Obot(tc_fun(X27603,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_6041])])])])]) ).

fof(i_0_10591,plain,
    ! [X34030,X34031] :
      ( ~ hBOOL(hAPP(hAPP(c_fequal,X34031),X34030))
      | X34031 = X34030 ),
    inference(variable_rename,[status(thm)],[i_0_6042]) ).

fof(i_0_10592,plain,
    ! [X22697,X22698] :
      ( ~ class_Fields_Ofield__inverse__zero(X22698)
      | ~ class_Int_Onumber__ring(X22698)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22698),X22697),hAPP(c_Int_Onumber__class_Onumber__of(X22698),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X22698),X22697) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__minus1])]) ).

fof(i_0_10593,plain,
    ! [X28229,X28230,X28231] :
      ( ~ c_Wellfounded_Owf(X28231,X28230)
      | c_Wellfounded_Owf(tc_List_Olist(X28231),hAPP(c_List_Olexn(X28231,X28230),X28229)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lexn])]) ).

fof(i_0_10594,plain,
    ! [X29889,X29890,X29891] : hAPP(hAPP(c_List_Olist__update(X29891,c_List_Olist_ONil(X29891)),X29890),X29889) = c_List_Olist_ONil(X29891),
    inference(variable_rename,[status(thm)],[fact_list__update_Osimps_I1_J]) ).

fof(i_0_10595,plain,
    ! [X29886,X29887,X29888] : hAPP(hAPP(c_List_Olist__update(X29888,c_List_Olist_ONil(X29888)),X29887),X29886) = c_List_Olist_ONil(X29888),
    inference(variable_rename,[status(thm)],[fact_list__update__code_I1_J]) ).

fof(i_0_10596,plain,
    ! [X20245] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X20245) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_power__Suc__0]) ).

fof(i_0_10597,plain,
    ! [X32071,X32072] : c_List_Oinsert(X32072,X32071,c_List_Olist_ONil(X32072)) = hAPP(hAPP(c_List_Olist_OCons(X32072),X32071),c_List_Olist_ONil(X32072)),
    inference(variable_rename,[status(thm)],[fact_insert__Nil]) ).

fof(i_0_10598,plain,
    ! [X29455,X29456] : hBOOL(hAPP(c_Finite__Set_Ofinite(X29456),hAPP(c_List_Oset(X29456),X29455))),
    inference(variable_rename,[status(thm)],[fact_finite__set]) ).

fof(i_0_10599,plain,
    ! [X28782,X28783,X28784] : hAPP(c_Relation_Oconverse(X28784,X28783),hAPP(c_Relation_Oconverse(X28783,X28784),X28782)) = X28782,
    inference(variable_rename,[status(thm)],[fact_converse__converse]) ).

fof(i_0_10600,plain,
    ! [X24362] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X24362)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X24362),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24362)),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc]) ).

fof(i_0_10601,plain,
    ! [X28785,X28786] : hAPP(c_Relation_OField(X28786),hAPP(c_Relation_Oconverse(X28786,X28786),X28785)) = hAPP(c_Relation_OField(X28786),X28785),
    inference(variable_rename,[status(thm)],[fact_Field__converse]) ).

fof(i_0_10602,plain,
    ! [X21638,X21639] :
      ( ~ class_Rings_Oring__1(X21639)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21639),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21638)) = hAPP(c_Groups_Ouminus__class_Ouminus(X21639),hAPP(c_Int_Oring__1__class_Oof__int(X21639),X21638)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__minus])]) ).

fof(i_0_10603,plain,
    ! [X21124,X21125] :
      ( ~ class_Int_Onumber__ring(X21125)
      | hAPP(c_Int_Onumber__class_Onumber__of(X21125),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21124)) = hAPP(c_Groups_Ouminus__class_Ouminus(X21125),hAPP(c_Int_Onumber__class_Onumber__of(X21125),X21124)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__minus])]) ).

fof(i_0_10604,plain,
    ! [X21122,X21123] :
      ( ~ class_Int_Onumber__ring(X21123)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21123),hAPP(c_Int_Onumber__class_Onumber__of(X21123),X21122)) = hAPP(c_Int_Onumber__class_Onumber__of(X21123),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21122)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I30_J])]) ).

fof(i_0_10605,plain,
    ! [X20246,X20247] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20247),X20246) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X20246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X20247 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X20246 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20247),X20246) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X20247 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X20247),X20246) = 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_10606,plain,
    ! [X17154,X17155,X17156] :
      ( ~ class_Orderings_Opreorder(X17156)
      | X17155 != X17154
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17156),X17155),X17154)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__eq__refl])]) ).

fof(i_0_10607,plain,
    ! [X21258,X21259,X21260] :
      ( ~ class_Groups_Ogroup__add(X21260)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21260),X21259),X21258) != c_Groups_Ozero__class_Ozero(X21260)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21260),X21259) = X21258 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__unique])]) ).

fof(i_0_10608,plain,
    ! [X21251,X21252,X21253] :
      ( ( X21252 != hAPP(c_Groups_Ouminus__class_Ouminus(X21253),X21251)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21253),X21252),X21251) = c_Groups_Ozero__class_Ozero(X21253)
        | ~ class_Groups_Ogroup__add(X21253) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21253),X21252),X21251) != c_Groups_Ozero__class_Ozero(X21253)
        | X21252 = hAPP(c_Groups_Ouminus__class_Ouminus(X21253),X21251)
        | ~ class_Groups_Ogroup__add(X21253) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0])])]) ).

fof(i_0_10609,plain,
    ! [X31301,X31302] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31302)),c_List_Oremdups(X31302,X31301)) = hAPP(c_Finite__Set_Ocard(X31302),hAPP(c_List_Oset(X31302),X31301)),
    inference(variable_rename,[status(thm)],[fact_length__remdups__card__conv]) ).

fof(i_0_10610,plain,
    ! [X27582] : c_Orderings_Otop__class_Otop(tc_fun(X27582,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X27582),hAPP(c_COMBK(tc_HOL_Obool,X27582),c_fTrue)),
    inference(variable_rename,[status(thm)],[fact_UNIV__def]) ).

fof(i_0_10611,plain,
    ! [X27597] : c_Orderings_Obot__class_Obot(tc_fun(X27597,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X27597),hAPP(c_COMBK(tc_HOL_Obool,X27597),c_fFalse)),
    inference(variable_rename,[status(thm)],[fact_empty__def]) ).

fof(i_0_10612,plain,
    ! [X24071,X24072] :
      ( ~ c_Nat__Transfer_Ois__nat(X24072)
      | c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X24072,X24071)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_SetInterval_Otransfer__int__nat__set__function__closures])]) ).

fof(i_0_10613,plain,
    ! [X21347,X21348] :
      ( ~ class_Int_Onumber__ring(X21348)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X21348),X21347),hAPP(c_Int_Onumber__class_Onumber__of(X21348),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(X21348),X21347) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__minus1__right])]) ).

fof(i_0_10614,plain,
    ! [X18393,X18394] :
      ( ( X18394 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18394),X18393) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18393 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18394),X18393) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( X18394 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | X18393 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18394),X18393) = 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_10615,plain,
    ! [X19426] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X19426)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X19426)),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_10616,plain,
    ! [X33744,X33745] :
      ( ~ class_Rings_Ocomm__semiring__1(X33745)
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X33745),X33744),X33744)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd__refl])]) ).

fof(i_0_10617,plain,
    ! [X17129,X17130] :
      ( ~ class_Orderings_Opreorder(X17130)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X17130),X17129),X17129)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_order__refl])]) ).

fof(i_0_10618,plain,
    ! [X24186] : 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)),X24186)) = hAPP(c_Int_Onat,X24186),
    inference(variable_rename,[status(thm)],[fact_card__atLeastZeroLessThan__int]) ).

fof(i_0_10619,plain,
    ! [X21318] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21318)),X21318) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zadd__zminus__inverse2]) ).

fof(i_0_10620,plain,
    ! [X24018,X24019] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24019),hAPP(c_Nat_OSuc,X24018)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X24019,X24018),
    inference(variable_rename,[status(thm)],[fact_atLeastLessThanSuc__atLeastAtMost]) ).

fof(i_0_10621,plain,
    ! [X22380,X22381] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X22381,X22380) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X22381,X22380)),
    inference(variable_rename,[status(thm)],[fact_mod__int__def]) ).

fof(i_0_10622,plain,
    ! [X25104,X25105,X25106] :
      ( ~ class_Lattices_Osemilattice__inf(X25106)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25106),X25105),X25104) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25106),X25104),X25105) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Ocommute])]) ).

fof(i_0_10623,plain,
    ! [X25098,X25099,X25100] :
      ( ~ class_Lattices_Osemilattice__inf(X25100)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25100),X25099),X25098) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25100),X25098),X25099) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__commute])]) ).

fof(i_0_10624,plain,
    ! [X25101,X25102,X25103] :
      ( ~ class_Lattices_Olattice(X25103)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25103),X25102),X25101) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25103),X25101),X25102) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I1_J])]) ).

fof(i_0_10625,plain,
    ! [X23220,X23221,X23222] :
      ( ~ class_Lattices_Olattice(X23222)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23222),X23221),X23220) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23222),X23220),X23221) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__sup__aci_I5_J])]) ).

fof(i_0_10626,plain,
    ! [X23223,X23224,X23225] :
      ( ~ class_Lattices_Osemilattice__sup(X23225)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23225),X23224),X23223) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23225),X23223),X23224) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Ocommute])]) ).

fof(i_0_10627,plain,
    ! [X23217,X23218,X23219] :
      ( ~ class_Lattices_Osemilattice__sup(X23219)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23219),X23218),X23217) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23219),X23217),X23218) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__commute])]) ).

fof(i_0_10628,plain,
    ! [X22516,X22517,X22518] :
      ( ~ class_Orderings_Olinorder(X22518)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22518),X22517),X22516) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22518),X22516),X22517) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Ocommute])]) ).

fof(i_0_10629,plain,
    ! [X22513,X22514,X22515] :
      ( ~ class_Orderings_Olinorder(X22515)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22515),X22514),X22513) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X22515),X22513),X22514) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup__commute])]) ).

fof(i_0_10630,plain,
    ! [X21498,X21499,X21500] :
      ( ~ class_Orderings_Olinorder(X21500)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21500),X21499),X21498) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21500),X21498),X21499) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf__commute])]) ).

fof(i_0_10631,plain,
    ! [X21495,X21496,X21497] :
      ( ~ class_Orderings_Olinorder(X21497)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21497),X21496),X21495) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X21497),X21495),X21496) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Ocommute])]) ).

fof(i_0_10632,plain,
    ! [X19066,X19067,X19068] :
      ( ~ class_Rings_Ocomm__semiring__1(X19068)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19068),X19067),X19066) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19068),X19066),X19067) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J])]) ).

fof(i_0_10633,plain,
    ! [X19032,X19033,X19034] :
      ( ~ class_Rings_Ocomm__semiring__1(X19034)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19034),X19033),X19032) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19034),X19032),X19033) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J])]) ).

fof(i_0_10634,plain,
    ! [X21359] : hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21359))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat__zminus__int]) ).

fof(i_0_10635,plain,
    ! [X18595] :
      ( X18595 = 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)),X18595)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_gr0I])]) ).

fof(i_0_10636,plain,
    ! [X21757,X21758] :
      ( ~ c_Nat__Transfer_Ois__nat(X21758)
      | ~ c_Nat__Transfer_Ois__nat(X21757)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21758),X21757)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Divides_Otransfer__int__nat__function__closures_I1_J])]) ).

fof(i_0_10637,plain,
    ! [X21753,X21754] :
      ( ~ c_Nat__Transfer_Ois__nat(X21754)
      | ~ c_Nat__Transfer_Ois__nat(X21753)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X21754),X21753)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J])]) ).

fof(i_0_10638,plain,
    ! [X21750,X21751] :
      ( ~ c_Nat__Transfer_Ois__nat(X21751)
      | ~ c_Nat__Transfer_Ois__nat(X21750)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X21751),X21750)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J])]) ).

fof(i_0_10639,plain,
    ! [X21319,X21320] :
      ( ( X21320 = 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),X21320)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21319) )
      & ( X21319 = 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),X21320)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21319) )
      & ( X21320 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X21319 != 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),X21320)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21319) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_negative__eq__positive])])]) ).

cnf(i_0_10640,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_6043]) ).

fof(i_0_10641,plain,
    ! [X18602] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18602)),
    inference(variable_rename,[status(thm)],[fact_less__eq__nat_Osimps_I1_J]) ).

fof(i_0_10642,plain,
    ! [X18199] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18199)),
    inference(variable_rename,[status(thm)],[fact_le0]) ).

fof(i_0_10643,plain,
    ! [X28977,X28978] : c_Relation_Ototal__on(X28978,c_Orderings_Obot__class_Obot(tc_fun(X28978,tc_HOL_Obool)),X28977),
    inference(variable_rename,[status(thm)],[fact_total__on__empty]) ).

fof(i_0_10644,plain,
    ! [X18334,X18335,X18336] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18336),X18335),X18334) != c_Groups_Ozero__class_Ozero(X18336)
        | X18335 = c_Groups_Ozero__class_Ozero(X18336)
        | X18334 = c_Groups_Ozero__class_Ozero(X18336)
        | ~ class_Rings_Oring__no__zero__divisors(X18336) )
      & ( X18335 != c_Groups_Ozero__class_Ozero(X18336)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18336),X18335),X18334) = c_Groups_Ozero__class_Ozero(X18336)
        | ~ class_Rings_Oring__no__zero__divisors(X18336) )
      & ( X18334 != c_Groups_Ozero__class_Ozero(X18336)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18336),X18335),X18334) = c_Groups_Ozero__class_Ozero(X18336)
        | ~ class_Rings_Oring__no__zero__divisors(X18336) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__eq__0__iff])])]) ).

fof(i_0_10645,plain,
    ! [X18331,X18332,X18333] :
      ( ~ class_Rings_Ono__zero__divisors(X18333)
      | X18332 = c_Groups_Ozero__class_Ozero(X18333)
      | X18331 = c_Groups_Ozero__class_Ozero(X18333)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18333),X18332),X18331) != c_Groups_Ozero__class_Ozero(X18333) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_no__zero__divisors])]) ).

fof(i_0_10646,plain,
    ! [X18328,X18329,X18330] :
      ( ~ class_Rings_Ono__zero__divisors(X18330)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18330),X18329),X18328) != c_Groups_Ozero__class_Ozero(X18330)
      | X18329 = c_Groups_Ozero__class_Ozero(X18330)
      | X18328 = c_Groups_Ozero__class_Ozero(X18330) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divisors__zero])]) ).

fof(i_0_10647,plain,
    ! [X22190] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22190) = 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_10648,plain,
    ! [X22378,X22379] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X22379),X22378) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(X22379,X22378)),
    inference(variable_rename,[status(thm)],[fact_div__int__def]) ).

fof(i_0_10649,plain,
    ! [X20287,X20288] :
      ( ~ class_Power_Opower(X20288)
      | ~ class_Rings_Osemiring__0(X20288)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20288),c_Groups_Ozero__class_Ozero(X20288)),hAPP(c_Nat_OSuc,X20287)) = c_Groups_Ozero__class_Ozero(X20288) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__Suc])]) ).

fof(i_0_10650,plain,
    ! [X22687,X22688] :
      ( ~ class_Fields_Ofield__inverse__zero(X22688)
      | ~ class_Int_Onumber__ring(X22688)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22688),X22687),hAPP(c_Int_Onumber__class_Onumber__of(X22688),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(X22688) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__Numeral0])]) ).

fof(i_0_10651,plain,
    ! [X25937,X25938] :
      ( ~ class_Rings_Olinordered__idom(X25938)
      | hAPP(c_Groups_Oabs__class_Oabs(X25938),X25937) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X25938),X25937),c_Groups_Osgn__class_Osgn(X25938,X25937)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__sgn])]) ).

fof(i_0_10652,plain,
    ! [X29380] : c_List_Olists(X29380,c_Orderings_Otop__class_Otop(tc_fun(X29380,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X29380),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_lists__UNIV]) ).

fof(i_0_10653,plain,
    ! [X30795,X30796] : hAPP(hAPP(c_List_Omap(X30796,X30796),c_COMBI(X30796)),X30795) = X30795,
    inference(variable_rename,[status(thm)],[fact_map__ident]) ).

fof(i_0_10654,plain,
    ! [X28255,X28256,X28257] :
      ( ~ c_Wellfounded_OwfP(X28257,X28256)
      | hBOOL(hAPP(c_Wellfounded_Oaccp(X28257,X28256),X28255)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_accp__wfPD])]) ).

fof(i_0_10655,plain,
    ! [X27808,X27809,X27810] :
      ( ~ c_Predicate_Oreflp(X27810,X27809)
      | hBOOL(hAPP(hAPP(X27809,X27808),X27808)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_reflpE])]) ).

fof(i_0_10656,plain,
    ! [X26685,X26686,X26687] :
      ( ~ c_Equiv__Relations_Oequivp(X26687,X26686)
      | hBOOL(hAPP(hAPP(X26686,X26685),X26685)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp])]) ).

fof(i_0_10657,plain,
    ! [X29909,X29910] : c_List_Osublist(X29910,X29909,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(X29910),
    inference(variable_rename,[status(thm)],[fact_sublist__empty]) ).

fof(i_0_10658,plain,
    ! [X22631,X22632,X22633] :
      ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22633),X22631),X22632) != c_Groups_Oone__class_Oone(X22633)
        | X22631 = X22632
        | X22632 = c_Groups_Ozero__class_Ozero(X22633)
        | ~ class_Rings_Odivision__ring(X22633) )
      & ( X22631 != X22632
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22633),X22631),X22632) = c_Groups_Oone__class_Oone(X22633)
        | X22632 = c_Groups_Ozero__class_Ozero(X22633)
        | ~ class_Rings_Odivision__ring(X22633) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__inverse__eq])])]) ).

fof(i_0_10659,plain,
    ! [X31833,X31834] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31834)),hAPP(c_List_Orev(X31834),X31833)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X31834)),X31833),
    inference(variable_rename,[status(thm)],[fact_length__rev]) ).

fof(i_0_10660,plain,
    ! [X30273,X30274] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30274)),hAPP(c_List_Orotate1(X30274),X30273)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X30274)),X30273),
    inference(variable_rename,[status(thm)],[fact_length__rotate1]) ).

fof(i_0_10661,plain,
    ! [X28368,X28369,X28370,X28371] :
      ( ~ hBOOL(hAPP(X28370,X28371))
      | X28369 != c_Hilbert__Choice_OEps(X28368,X28370)
      | hBOOL(hAPP(X28370,X28369)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_exE__some])])]) ).

fof(i_0_10662,plain,
    ! [X29008,X29009] : hAPP(hAPP(c_Nat_Ocompow(X29009,X29009),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29008) = c_Fun_Oid(X29009),
    inference(variable_rename,[status(thm)],[fact_funpow_Osimps_I1_J]) ).

fof(i_0_10663,plain,
    ! [X30726,X30727,X30728] : hAPP(hAPP(c_List_Omap(X30728,X30727),X30726),c_List_Olist_ONil(X30728)) = c_List_Olist_ONil(X30727),
    inference(variable_rename,[status(thm)],[fact_map_Osimps_I1_J]) ).

fof(i_0_10664,plain,
    ! [X25208,X25209] :
      ( ~ class_Lattices_Oboolean__algebra(X25209)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25209),X25208),hAPP(c_Groups_Ouminus__class_Ouminus(X25209),X25208)) = c_Orderings_Obot__class_Obot(X25209) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__compl__bot])]) ).

fof(i_0_10665,plain,
    ! [X26221,X26222] :
      ( ~ class_Lattices_Oboolean__algebra(X26222)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26222),X26221),hAPP(c_Groups_Ouminus__class_Ouminus(X26222),X26221)) = c_Orderings_Otop__class_Otop(X26222) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__compl__top])]) ).

fof(i_0_10666,plain,
    ! [X21249,X21250] :
      ( ~ class_Groups_Ogroup__add(X21250)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X21250),X21249),hAPP(c_Groups_Ouminus__class_Ouminus(X21250),X21249)) = c_Groups_Ozero__class_Ozero(X21250) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus])]) ).

fof(i_0_10667,plain,
    ! [X21759,X21760] :
      ( ~ c_Nat__Transfer_Ois__nat(X21760)
      | c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X21760),X21759)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J])]) ).

fof(i_0_10668,plain,
    ! [X20915,X20916] :
      ( ( X20916 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20916 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20916),X20915) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20915 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20916 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20916),X20915) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20916 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20915 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20916),X20915) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20915 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20915 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20916),X20915) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20916 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | X20915 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20916),X20915) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( X20916 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | X20915 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20916),X20915) = 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_10669,plain,
    ! [X26107,X26108,X26109] :
      ( ( X26108 = c_Orderings_Otop__class_Otop(X26109)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26109),X26108),X26107) != c_Orderings_Otop__class_Otop(X26109)
        | ~ class_Lattices_Obounded__lattice__top(X26109) )
      & ( X26107 = c_Orderings_Otop__class_Otop(X26109)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26109),X26108),X26107) != c_Orderings_Otop__class_Otop(X26109)
        | ~ class_Lattices_Obounded__lattice__top(X26109) )
      & ( X26108 != c_Orderings_Otop__class_Otop(X26109)
        | X26107 != c_Orderings_Otop__class_Otop(X26109)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26109),X26108),X26107) = c_Orderings_Otop__class_Otop(X26109)
        | ~ class_Lattices_Obounded__lattice__top(X26109) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__eq__top__iff])])]) ).

fof(i_0_10670,plain,
    ! [X23370,X23371,X23372] :
      ( ( X23371 = c_Orderings_Obot__class_Obot(X23372)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23372),X23371),X23370) != c_Orderings_Obot__class_Obot(X23372)
        | ~ class_Lattices_Obounded__lattice__bot(X23372) )
      & ( X23370 = c_Orderings_Obot__class_Obot(X23372)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23372),X23371),X23370) != c_Orderings_Obot__class_Obot(X23372)
        | ~ class_Lattices_Obounded__lattice__bot(X23372) )
      & ( X23371 != c_Orderings_Obot__class_Obot(X23372)
        | X23370 != c_Orderings_Obot__class_Obot(X23372)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23372),X23371),X23370) = c_Orderings_Obot__class_Obot(X23372)
        | ~ class_Lattices_Obounded__lattice__bot(X23372) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__eq__bot__iff])])]) ).

fof(i_0_10671,plain,
    ! [X20242,X20243,X20244] :
      ( ~ class_Rings_Oring__1__no__zero__divisors(X20244)
      | X20243 = c_Groups_Ozero__class_Ozero(X20244)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20244),X20243),X20242) != c_Groups_Ozero__class_Ozero(X20244) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_field__power__not__zero])]) ).

fof(i_0_10672,plain,
    ! [X19069,X19070] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19070),X19069),X19069) != c_Groups_Ozero__class_Ozero(X19070)
        | X19069 = c_Groups_Ozero__class_Ozero(X19070)
        | ~ class_Groups_Olinordered__ab__group__add(X19070) )
      & ( X19069 != c_Groups_Ozero__class_Ozero(X19070)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19070),X19069),X19069) = c_Groups_Ozero__class_Ozero(X19070)
        | ~ class_Groups_Olinordered__ab__group__add(X19070) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__eq__0__iff])])]) ).

fof(i_0_10673,plain,
    ! [X18556,X18557] :
      ( ( c_Groups_Ozero__class_Ozero(X18557) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18557),X18556),X18556)
        | X18556 = c_Groups_Ozero__class_Ozero(X18557)
        | ~ class_Groups_Olinordered__ab__group__add(X18557) )
      & ( X18556 != c_Groups_Ozero__class_Ozero(X18557)
        | c_Groups_Ozero__class_Ozero(X18557) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18557),X18556),X18556)
        | ~ class_Groups_Olinordered__ab__group__add(X18557) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__zero__sym])])]) ).

fof(i_0_10674,plain,
    ! [X24881] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X24881))),
    inference(variable_rename,[status(thm)],[fact_finite__atMost]) ).

fof(i_0_10675,plain,
    ! [X24354] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24354))),
    inference(variable_rename,[status(thm)],[fact_finite__lessThan]) ).

cnf(i_0_10676,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_5810]) ).

fof(i_0_10677,plain,
    ! [X21219] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21219)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21219)),
    inference(variable_rename,[status(thm)],[fact_minus__numeral__code_I5_J]) ).

fof(i_0_10678,plain,
    ! [X18575,X18576,X18577] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18577),X18576),X18575) != c_Groups_Ozero__class_Ozero(X18577)
        | X18576 = X18575
        | ~ class_Groups_Ogroup__add(X18577) )
      & ( X18576 != X18575
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18577),X18576),X18575) = c_Groups_Ozero__class_Ozero(X18577)
        | ~ class_Groups_Ogroup__add(X18577) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_right__minus__eq])])]) ).

fof(i_0_10679,plain,
    ! [X18572,X18573,X18574] :
      ( ( X18573 != X18572
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18574),X18573),X18572) = c_Groups_Ozero__class_Ozero(X18574)
        | ~ class_Groups_Oab__group__add(X18574) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18574),X18573),X18572) != c_Groups_Ozero__class_Ozero(X18574)
        | X18573 = X18572
        | ~ class_Groups_Oab__group__add(X18574) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__iff__diff__eq__0])])]) ).

fof(i_0_10680,plain,
    ! [X33692,X33693] :
      ( X33693 != X33692
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33693),X33692)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl])]) ).

fof(i_0_10681,plain,
    ! [X17213,X17214] :
      ( X17214 != X17213
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17214),X17213)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__imp__le])]) ).

fof(i_0_10682,plain,
    ! [X29852,X29853,X29854] :
      ( ( hAPP(hAPP(c_List_Otake(X29854),X29853),X29852) != c_List_Olist_ONil(X29854)
        | X29853 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X29852 = c_List_Olist_ONil(X29854) )
      & ( X29853 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(X29854),X29853),X29852) = c_List_Olist_ONil(X29854) )
      & ( X29852 != c_List_Olist_ONil(X29854)
        | hAPP(hAPP(c_List_Otake(X29854),X29853),X29852) = c_List_Olist_ONil(X29854) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_take__eq__Nil])])]) ).

fof(i_0_10683,plain,
    ! [X20917,X20918] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20918),X20917) != c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X20918 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | X20918 = 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_10684,plain,
    ! [X19071,X19072,X19073] :
      ( ( X19072 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19073),X19072),X19071)
        | X19071 = c_Groups_Ozero__class_Ozero(X19073)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19073) )
      & ( X19071 != c_Groups_Ozero__class_Ozero(X19073)
        | X19072 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19073),X19072),X19071)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X19073) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__iff])])]) ).

fof(i_0_10685,plain,
    ! [X32599,X32600,X32601] :
      ( ( c_List_Oreplicate(X32601,X32600,X32599) != c_List_Olist_ONil(X32601)
        | X32600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X32600 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oreplicate(X32601,X32600,X32599) = c_List_Olist_ONil(X32601) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_replicate__empty])]) ).

fof(i_0_10686,plain,
    ! [X32596,X32597,X32598] :
      ( ( c_List_Olist_ONil(X32598) != c_List_Oreplicate(X32598,X32597,X32596)
        | X32597 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X32597 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Olist_ONil(X32598) = c_List_Oreplicate(X32598,X32597,X32596) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_empty__replicate])]) ).

fof(i_0_10687,plain,
    ! [X17765] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17765)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X17765,
    inference(variable_rename,[status(thm)],[fact_diff__Suc__1]) ).

fof(i_0_10688,plain,
    ! [X29636,X29637] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29637,X29636)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X29637,X29636),
    inference(variable_rename,[status(thm)],[fact_set__upto]) ).

fof(i_0_10689,plain,
    ! [X29638,X29639] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X29639,X29638) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X29639,X29638)),
    inference(variable_rename,[status(thm)],[fact_atLeastAtMost__upto]) ).

fof(i_0_10690,plain,
    ! [X32352,X32353] : ~ c_List_Olist__ex1(X32353,X32352,c_List_Olist_ONil(X32353)),
    inference(variable_rename,[status(thm)],[i_0_6044]) ).

fof(i_0_10691,plain,
    ! [X32249,X32250] : ~ c_List_Olist__ex(X32250,X32249,c_List_Olist_ONil(X32250)),
    inference(variable_rename,[status(thm)],[i_0_6045]) ).

fof(i_0_10692,plain,
    ! [X20049,X20050] :
      ( ~ class_Int_Onumber__ring(X20050)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20050),X20049),hAPP(c_Int_Onumber__class_Onumber__of(X20050),c_Int_OPls)) = X20049 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__numeral__0__right])]) ).

fof(i_0_10693,plain,
    ! [X33606] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X33606),X33606)),
    inference(variable_rename,[status(thm)],[fact_dvd_Oorder__refl]) ).

fof(i_0_10694,plain,
    ! [X19467] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19467),X19467)),
    inference(variable_rename,[status(thm)],[fact_zle__refl]) ).

fof(i_0_10695,plain,
    ! [X17210] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X17210),X17210)),
    inference(variable_rename,[status(thm)],[fact_le__refl]) ).

fof(i_0_10696,plain,
    ! [X31020,X31021] : hBOOL(hAPP(c_List_Olistsp(X31021,X31020),c_List_Olist_ONil(X31021))),
    inference(variable_rename,[status(thm)],[fact_listsp_Oequations_I1_J]) ).

fof(i_0_10697,plain,
    ! [X31018,X31019] : hBOOL(hAPP(c_List_Olistsp(X31019,X31018),c_List_Olist_ONil(X31019))),
    inference(variable_rename,[status(thm)],[fact_listsp_ONil]) ).

fof(i_0_10698,plain,
    ! [X31253,X31254] : hBOOL(hAPP(c_List_Odistinct(X31254),c_List_Oremdups(X31254,X31253))),
    inference(variable_rename,[status(thm)],[fact_distinct__remdups]) ).

fof(i_0_10699,plain,
    ! [X30109,X30110,X30111] :
      ( ( X30110 = c_List_Olist_ONil(X30111)
        | hAPP(hAPP(c_List_Oappend(X30111),X30110),X30109) != c_List_Olist_ONil(X30111) )
      & ( X30109 = c_List_Olist_ONil(X30111)
        | hAPP(hAPP(c_List_Oappend(X30111),X30110),X30109) != c_List_Olist_ONil(X30111) )
      & ( X30110 != c_List_Olist_ONil(X30111)
        | X30109 != c_List_Olist_ONil(X30111)
        | hAPP(hAPP(c_List_Oappend(X30111),X30110),X30109) = c_List_Olist_ONil(X30111) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__is__Nil__conv])])]) ).

fof(i_0_10700,plain,
    ! [X30098,X30099,X30100] :
      ( ( X30099 = c_List_Olist_ONil(X30100)
        | c_List_Olist_ONil(X30100) != hAPP(hAPP(c_List_Oappend(X30100),X30099),X30098) )
      & ( X30098 = c_List_Olist_ONil(X30100)
        | c_List_Olist_ONil(X30100) != hAPP(hAPP(c_List_Oappend(X30100),X30099),X30098) )
      & ( X30099 != c_List_Olist_ONil(X30100)
        | X30098 != c_List_Olist_ONil(X30100)
        | c_List_Olist_ONil(X30100) = hAPP(hAPP(c_List_Oappend(X30100),X30099),X30098) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__append__conv])])]) ).

cnf(i_0_10701,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_6046]) ).

cnf(i_0_10702,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_6047]) ).

cnf(i_0_10703,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_6048]) ).

fof(i_0_10704,plain,
    ! [X28679,X28680] : hAPP(c_Relation_ODomain(X28680,X28680),c_Transitive__Closure_Ortrancl(X28680,X28679)) = c_Orderings_Otop__class_Otop(tc_fun(X28680,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Domain__rtrancl]) ).

fof(i_0_10705,plain,
    ! [X28677,X28678] : hAPP(c_Relation_ORange(X28678,X28678),c_Transitive__Closure_Ortrancl(X28678,X28677)) = c_Orderings_Otop__class_Otop(tc_fun(X28678,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_Range__rtrancl]) ).

fof(i_0_10706,plain,
    ! [X34008,X34009,X34010,X34011] : hAPP(hAPP(c_COMBK(X34011,X34010),X34009),X34008) = X34009,
    inference(variable_rename,[status(thm)],[help_c__COMBK__1]) ).

cnf(i_0_10707,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_5979]) ).

fof(i_0_10708,plain,
    ! [X32762,X32763,X32764] : c_Lazy__Sequence_Olazy__sequence_OInsert(X32764,X32763,X32762) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X32764),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I3_J]) ).

fof(i_0_10709,plain,
    ! [X32765,X32766,X32767] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X32767) != c_Lazy__Sequence_Olazy__sequence_OInsert(X32767,X32766,X32765),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osimps_I2_J]) ).

fof(i_0_10710,plain,
    ! [X21367] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X21367),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21367),
    inference(variable_rename,[status(thm)],[fact_zdiv__minus1__right]) ).

fof(i_0_10711,plain,
    ! [X19459,X19460] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19460),X19459) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19459),X19460),
    inference(variable_rename,[status(thm)],[fact_zmult__commute]) ).

fof(i_0_10712,plain,
    ! [X18936,X18937] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18937),X18936) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18936),X18937),
    inference(variable_rename,[status(thm)],[fact_nat__mult__commute]) ).

fof(i_0_10713,plain,
    ! [X19484,X19485] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19485),X19484) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19484),X19485),
    inference(variable_rename,[status(thm)],[fact_zadd__commute]) ).

fof(i_0_10714,plain,
    ! [X17833,X17834] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17834),X17833) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X17833),X17834),
    inference(variable_rename,[status(thm)],[fact_nat__add__commute]) ).

fof(i_0_10715,plain,
    ! [X27096,X27097,X27098] : hAPP(hAPP(c_Nitpick_Ofrac(X27098),X27097),X27096) = c_Nitpick_OAbs__Frac(X27098,c_Nitpick_Onorm__frac(X27097,X27096)),
    inference(variable_rename,[status(thm)],[fact_Nitpick_Ofrac__def]) ).

fof(i_0_10716,plain,
    ! [X21261,X21262] :
      ( ~ class_Groups_Ogroup__add(X21262)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X21262),c_Groups_Ozero__class_Ozero(X21262)),X21261) = hAPP(c_Groups_Ouminus__class_Ouminus(X21262),X21261) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0])]) ).

fof(i_0_10717,plain,
    ! [X34036,X34037] :
      ( ~ hBOOL(X34037)
      | ~ hBOOL(X34036)
      | hBOOL(hAPP(hAPP(c_fconj,X34037),X34036)) ),
    inference(variable_rename,[status(thm)],[i_0_6049]) ).

fof(i_0_10718,plain,
    ! [X30115,X30116,X30117] :
      ( ( hAPP(hAPP(c_List_Oappend(X30117),X30116),X30115) != X30115
        | X30116 = c_List_Olist_ONil(X30117) )
      & ( X30116 != c_List_Olist_ONil(X30117)
        | hAPP(hAPP(c_List_Oappend(X30117),X30116),X30115) = X30115 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv2])]) ).

fof(i_0_10719,plain,
    ! [X30112,X30113,X30114] :
      ( ( hAPP(hAPP(c_List_Oappend(X30114),X30113),X30112) != X30113
        | X30112 = c_List_Olist_ONil(X30114) )
      & ( X30112 != c_List_Olist_ONil(X30114)
        | hAPP(hAPP(c_List_Oappend(X30114),X30113),X30112) = X30113 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_append__self__conv])]) ).

fof(i_0_10720,plain,
    ! [X30103,X30104,X30105] :
      ( ( X30105 != hAPP(hAPP(c_List_Oappend(X30104),X30105),X30103)
        | X30103 = c_List_Olist_ONil(X30104) )
      & ( X30103 != c_List_Olist_ONil(X30104)
        | X30105 = hAPP(hAPP(c_List_Oappend(X30104),X30105),X30103) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv])]) ).

fof(i_0_10721,plain,
    ! [X30106,X30107,X30108] :
      ( ( X30108 != hAPP(hAPP(c_List_Oappend(X30107),X30106),X30108)
        | X30106 = c_List_Olist_ONil(X30107) )
      & ( X30106 != c_List_Olist_ONil(X30107)
        | X30108 = hAPP(hAPP(c_List_Oappend(X30107),X30106),X30108) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_self__append__conv2])]) ).

fof(i_0_10722,plain,
    ! [X20325,X20326] :
      ( ( X20325 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20326),c_Groups_Ozero__class_Ozero(X20326)),X20325) = c_Groups_Oone__class_Oone(X20326)
        | ~ class_Power_Opower(X20326)
        | ~ class_Rings_Osemiring__0(X20326) )
      & ( X20325 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(X20326),c_Groups_Ozero__class_Ozero(X20326)),X20325) = c_Groups_Ozero__class_Ozero(X20326)
        | ~ class_Power_Opower(X20326)
        | ~ class_Rings_Osemiring__0(X20326) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0__left])])]) ).

fof(i_0_10723,plain,
    ! [X29843,X29844,X29845] : hAPP(hAPP(c_List_Olist_OCons(X29845),X29844),X29843) != c_List_Olist_ONil(X29845),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I3_J]) ).

fof(i_0_10724,plain,
    ! [X29840,X29841,X29842] : c_List_Olist_ONil(X29842) != hAPP(hAPP(c_List_Olist_OCons(X29842),X29841),X29840),
    inference(variable_rename,[status(thm)],[fact_list_Osimps_I2_J]) ).

fof(i_0_10725,plain,
    ! [X29771,X29772] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X29772,X29771))),
    inference(variable_rename,[status(thm)],[fact_distinct__upto]) ).

cnf(i_0_10726,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_6050]) ).

fof(i_0_10727,plain,
    ! [X29328,X29329] : c_List_Olistrel(X29329,c_Transitive__Closure_Ortrancl(X29329,X29328)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(X29329),c_List_Olistrel1(X29329,X29328)),
    inference(variable_rename,[status(thm)],[fact_listrel__rtrancl__eq__rtrancl__listrel1]) ).

fof(i_0_10728,plain,
    ! [X28089,X28090] :
      ( ~ c_Wellfounded_Owf(X28090,X28089)
      | c_Wellfounded_Owf(tc_fun(X28090,tc_HOL_Obool),c_Wellfounded_Omax__ext(X28090,X28089)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ext__wf])]) ).

fof(i_0_10729,plain,
    ! [X28080,X28081] :
      ( ~ c_Wellfounded_Owf(X28081,X28080)
      | c_Wellfounded_Owf(tc_fun(X28081,tc_HOL_Obool),c_Wellfounded_Omin__ext(X28081,X28080)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ext__wf])]) ).

fof(i_0_10730,plain,
    ! [X31831,X31832] :
      ( ~ class_Groups_Ocomm__monoid__add(X31832)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X31832),hAPP(c_List_Orev(X31832),X31831)) = hAPP(c_List_Omonoid__add__class_Olistsum(X31832),X31831) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__rev])]) ).

fof(i_0_10731,plain,
    ! [X25858,X25859] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25859)
      | hAPP(c_Groups_Oabs__class_Oabs(X25859),hAPP(c_Groups_Oabs__class_Oabs(X25859),X25858)) = hAPP(c_Groups_Oabs__class_Oabs(X25859),X25858) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__idempotent])]) ).

fof(i_0_10732,plain,
    ! [X25856,X25857] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25857)
      | hAPP(c_Groups_Oabs__class_Oabs(X25857),hAPP(c_Groups_Ouminus__class_Ouminus(X25857),X25856)) = hAPP(c_Groups_Oabs__class_Oabs(X25857),X25856) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel])]) ).

fof(i_0_10733,plain,
    ! [X25866,X25867] :
      ( ~ class_Rings_Olinordered__idom(X25867)
      | hAPP(c_Groups_Oabs__class_Oabs(X25867),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25867),X25866)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X25867),X25866) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__of__nat])]) ).

fof(i_0_10734,plain,
    ! [X21467] :
      ( ~ class_Int_Onumber__ring(X21467)
      | ~ c_Int_Oiszero(X21467,hAPP(c_Int_Onumber__class_Onumber__of(X21467),c_Int_OMin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6051])]) ).

fof(i_0_10735,plain,
    ! [X26134] : c_Orderings_Otop__class_Otop(tc_fun(X26134,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X26134,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_UNIV__not__empty]) ).

fof(i_0_10736,plain,
    ! [X20640] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X20640,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_10737,plain,
    ! [X21281] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,X21281,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_10738,plain,
    ! [X18357,X18358] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18358),X18357) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18358 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18358),X18357) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18357 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18358),X18357) = 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_10739,plain,
    ! [X29210,X29211,X29212] : hAPP(hAPP(c_List_Olist_OCons(X29212),X29211),X29210) != X29210,
    inference(variable_rename,[status(thm)],[fact_not__Cons__self2]) ).

fof(i_0_10740,plain,
    ! [X29207,X29208,X29209] : X29209 != hAPP(hAPP(c_List_Olist_OCons(X29208),X29207),X29209),
    inference(variable_rename,[status(thm)],[fact_not__Cons__self]) ).

fof(i_0_10741,plain,
    ! [X18075] : c_Finite__Set_Ofun__left__comm__idem(X18075,tc_fun(X18075,tc_HOL_Obool),c_Set_Oinsert(X18075)),
    inference(variable_rename,[status(thm)],[fact_fun__left__comm__idem__insert]) ).

fof(i_0_10742,plain,
    ! [X34042,X34043] :
      ( ~ hBOOL(X34043)
      | hBOOL(hAPP(hAPP(c_fdisj,X34043),X34042)) ),
    inference(variable_rename,[status(thm)],[i_0_6052]) ).

fof(i_0_10743,plain,
    ! [X34044,X34045] :
      ( ~ hBOOL(X34045)
      | hBOOL(hAPP(hAPP(c_fdisj,X34044),X34045)) ),
    inference(variable_rename,[status(thm)],[i_0_6053]) ).

fof(i_0_10744,plain,
    ! [X34050,X34051] :
      ( ~ hBOOL(X34051)
      | hBOOL(hAPP(hAPP(c_fimplies,X34050),X34051)) ),
    inference(variable_rename,[status(thm)],[i_0_6054]) ).

fof(i_0_10745,plain,
    ! [X26119,X26120,X26121] :
      ( ~ class_Orderings_Otop(X26121)
      | hAPP(c_Orderings_Otop__class_Otop(tc_fun(X26120,X26121)),X26119) = c_Orderings_Otop__class_Otop(X26121) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_top__apply])]) ).

fof(i_0_10746,plain,
    ! [X17244,X17245,X17246] :
      ( ~ class_Orderings_Obot(X17246)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17245,X17246)),X17244) = c_Orderings_Obot__class_Obot(X17246) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__apply])]) ).

fof(i_0_10747,plain,
    ! [X17131,X17132,X17133] :
      ( ~ class_Orderings_Obot(X17133)
      | hAPP(c_Orderings_Obot__class_Obot(tc_fun(X17132,X17133)),X17131) = c_Orderings_Obot__class_Obot(X17133) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_bot__fun__def])]) ).

fof(i_0_10748,plain,
    ! [X30997,X30998] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X30998),X30997) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,X30998),X30997),
    inference(variable_rename,[status(thm)],[fact_minus__code__numeral__code]) ).

fof(i_0_10749,plain,
    ! [X32947,X32948] :
      ( ~ c_Predicate_Oreflp(X32948,X32947)
      | ~ c_Predicate_Osymp(X32948,X32947)
      | ~ c_Predicate_Otransp(X32948,X32947)
      | c_Equiv__Relations_Oequivp(X32948,X32947) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivpI])]) ).

fof(i_0_10750,plain,
    ! [X32945,X32946] :
      ( ( c_Predicate_Oreflp(X32946,X32945)
        | ~ c_Equiv__Relations_Oequivp(X32946,X32945) )
      & ( c_Predicate_Osymp(X32946,X32945)
        | ~ c_Equiv__Relations_Oequivp(X32946,X32945) )
      & ( c_Predicate_Otransp(X32946,X32945)
        | ~ c_Equiv__Relations_Oequivp(X32946,X32945) )
      & ( ~ c_Predicate_Oreflp(X32946,X32945)
        | ~ c_Predicate_Osymp(X32946,X32945)
        | ~ c_Predicate_Otransp(X32946,X32945)
        | c_Equiv__Relations_Oequivp(X32946,X32945) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__reflp__symp__transp])])]) ).

fof(i_0_10751,plain,
    ! [X31677,X31678] :
      ( ~ class_Orderings_Olinorder(X31678)
      | ~ c_List_Olinorder__class_Osorted(X31678,X31677)
      | c_List_Olinorder__class_Osorted(X31678,hAPP(c_List_Otl(X31678),X31677)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__tl])]) ).

fof(i_0_10752,plain,
    ! [X31262,X31263] :
      ( ( c_List_Oremdups(X31263,X31262) != X31262
        | hBOOL(hAPP(c_List_Odistinct(X31263),X31262)) )
      & ( ~ hBOOL(hAPP(c_List_Odistinct(X31263),X31262))
        | c_List_Oremdups(X31263,X31262) = X31262 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct])]) ).

fof(i_0_10753,plain,
    ! [X31257,X31258] :
      ( ~ hBOOL(hAPP(c_List_Odistinct(X31258),X31257))
      | c_List_Oremdups(X31258,X31257) = X31257 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_distinct__remdups__id])]) ).

cnf(i_0_10754,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_10755,plain,
    ! [X18419,X18420] :
      ( X18420 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18420),X18419)
      | X18419 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | X18420 = 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_10756,plain,
    ! [X30373,X30374] :
      ( X30374 = c_List_Olist_ONil(X30373)
      | hAPP(c_List_Ohd(X30373),X30374) = hAPP(hAPP(c_List_Onth(X30373),X30374),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_10757,plain,
    ! [X34048,X34049] :
      ( hBOOL(X34049)
      | hBOOL(hAPP(hAPP(c_fimplies,X34049),X34048)) ),
    inference(variable_rename,[status(thm)],[help_c__fimplies__1]) ).

fof(i_0_10758,plain,
    ! [X28897,X28898] : c_Relation_Osingle__valued(X28898,X28898,c_Relation_OId__on(X28898,X28897)),
    inference(variable_rename,[status(thm)],[fact_single__valued__Id__on]) ).

fof(i_0_10759,plain,
    ! [X27498,X27499] : c_Relation_Orefl__on(X27499,X27498,c_Relation_OId__on(X27499,X27498)),
    inference(variable_rename,[status(thm)],[fact_refl__on__Id__on]) ).

fof(i_0_10760,plain,
    ! [X18598,X18599] :
      ( ( X18599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18599),X18598) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18599),X18598) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X18599 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X18598 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18599),X18598) = 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_10761,plain,
    ! [X18582,X18583] :
      ( ( X18583 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18583),X18582) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X18582 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18583),X18582) != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( X18583 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X18582 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18583),X18582) = 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_10762,plain,
    ! [X18579,X18580] :
      ( ( X18580 = 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),X18580),X18579) )
      & ( X18579 = 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),X18580),X18579) )
      & ( X18580 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | X18579 != 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),X18580),X18579) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff])])]) ).

fof(i_0_10763,plain,
    ! [X19290,X19291,X19292] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(X19292),X19291) != hAPP(c_Int_Onumber__class_Onumber__of(X19292),X19290)
        | X19291 = X19290
        | ~ class_Int_Onumber__ring(X19292)
        | ~ class_Int_Oring__char__0(X19292) )
      & ( X19291 != X19290
        | hAPP(c_Int_Onumber__class_Onumber__of(X19292),X19291) = hAPP(c_Int_Onumber__class_Onumber__of(X19292),X19290)
        | ~ class_Int_Onumber__ring(X19292)
        | ~ class_Int_Oring__char__0(X19292) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__number__of])])]) ).

fof(i_0_10764,plain,
    ! [X28787,X28788] : hAPP(c_Relation_Oconverse(X28788,X28788),c_Relation_OId__on(X28788,X28787)) = c_Relation_OId__on(X28788,X28787),
    inference(variable_rename,[status(thm)],[fact_converse__Id__on]) ).

fof(i_0_10765,plain,
    ! [X34032,X34033] :
      ( X34033 != X34032
      | hBOOL(hAPP(hAPP(c_fequal,X34033),X34032)) ),
    inference(variable_rename,[status(thm)],[help_c__fequal__2]) ).

fof(i_0_10766,plain,
    ! [X21636,X21637] :
      ( ~ class_Rings_Oring__1(X21637)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21637),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21636)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X21637),X21636) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__of__nat__eq])]) ).

fof(i_0_10767,plain,
    ! [X21627,X21628] :
      ( ~ class_Int_Onumber__ring(X21628)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21628),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21627)) = hAPP(c_Int_Onumber__class_Onumber__of(X21628),X21627) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__number__of__eq])]) ).

fof(i_0_10768,plain,
    ! [X29883,X29884] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(X29884,tc_HOL_Obool)) != hAPP(c_List_Oset(X29884),X29883)
        | X29883 = c_List_Olist_ONil(X29884) )
      & ( X29883 != c_List_Olist_ONil(X29884)
        | c_Orderings_Obot__class_Obot(tc_fun(X29884,tc_HOL_Obool)) = hAPP(c_List_Oset(X29884),X29883) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty2])]) ).

fof(i_0_10769,plain,
    ! [X29881,X29882] :
      ( ( hAPP(c_List_Oset(X29882),X29881) != c_Orderings_Obot__class_Obot(tc_fun(X29882,tc_HOL_Obool))
        | X29881 = c_List_Olist_ONil(X29882) )
      & ( X29881 != c_List_Olist_ONil(X29882)
        | hAPP(c_List_Oset(X29882),X29881) = c_Orderings_Obot__class_Obot(tc_fun(X29882,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_set__empty])]) ).

fof(i_0_10770,plain,
    ! [X33025,X33026] :
      ( ( ~ c_Relation_Osym(X33026,X33025)
        | hAPP(c_Relation_Oconverse(X33026,X33026),X33025) = X33025 )
      & ( hAPP(c_Relation_Oconverse(X33026,X33026),X33025) != X33025
        | c_Relation_Osym(X33026,X33025) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__conv__converse__eq])]) ).

fof(i_0_10771,plain,
    ! [X31811,X31812] : hAPP(c_List_Oset(X31812),hAPP(c_List_Orev(X31812),X31811)) = hAPP(c_List_Oset(X31812),X31811),
    inference(variable_rename,[status(thm)],[fact_set__rev]) ).

fof(i_0_10772,plain,
    ! [X30278,X30279] : hAPP(c_List_Oset(X30279),hAPP(c_List_Orotate1(X30279),X30278)) = hAPP(c_List_Oset(X30279),X30278),
    inference(variable_rename,[status(thm)],[fact_set__rotate1]) ).

fof(i_0_10773,plain,
    ! [X20355] :
      ( ~ class_Power_Opower(X20355)
      | c_Power_Opower__class_Opower(X20355) = c_Power_Opower_Opower(X20355,c_Groups_Oone__class_Oone(X20355),c_Groups_Otimes__class_Otimes(X20355)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__power__power])]) ).

fof(i_0_10774,plain,
    ! [X18600,X18601] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18601),X18600) != X18601
      | X18600 = 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_10775,plain,
    ! [X31852,X31853] :
      ( X31853 = c_List_Olist_ONil(X31852)
      | hAPP(c_List_Ohd(X31852),hAPP(c_List_Orev(X31852),X31853)) = c_List_Olast(X31852,X31853) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_hd__rev])]) ).

fof(i_0_10776,plain,
    ! [X31854,X31855] :
      ( X31855 = c_List_Olist_ONil(X31854)
      | c_List_Olast(X31854,hAPP(c_List_Orev(X31854),X31855)) = hAPP(c_List_Ohd(X31854),X31855) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_last__rev])]) ).

fof(i_0_10777,plain,
    ! [X29996] :
      ( ~ class_Orderings_Olinorder(X29996)
      | c_List_Olinorder__class_Osorted__list__of__set(X29996,c_Orderings_Obot__class_Obot(tc_fun(X29996,tc_HOL_Obool))) = c_List_Olist_ONil(X29996) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__list__of__set__empty])]) ).

fof(i_0_10778,plain,
    ! [X27073] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X27073)
      | c_Complete__Lattice_OSup__class_OSup(X27073,c_Orderings_Otop__class_Otop(tc_fun(X27073,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X27073) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__UNIV])]) ).

fof(i_0_10779,plain,
    ! [X27067] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X27067)
      | c_Complete__Lattice_OSup__class_OSup(X27067,c_Orderings_Obot__class_Obot(tc_fun(X27067,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X27067) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__empty])]) ).

fof(i_0_10780,plain,
    ! [X26892] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26892)
      | c_Complete__Lattice_OInf__class_OInf(X26892,c_Orderings_Otop__class_Otop(tc_fun(X26892,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(X26892) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__UNIV])]) ).

fof(i_0_10781,plain,
    ! [X26891] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X26891)
      | c_Complete__Lattice_OInf__class_OInf(X26891,c_Orderings_Obot__class_Obot(tc_fun(X26891,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(X26891) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__empty])]) ).

fof(i_0_10782,plain,
    ! [X20780] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X20780),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X20780,
    inference(variable_rename,[status(thm)],[fact_div__1]) ).

fof(i_0_10783,plain,
    ! [X27007,X27008] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X27008,tc_HOL_Obool),hAPP(c_Set_OPow(X27008),X27007)) = X27007,
    inference(variable_rename,[status(thm)],[fact_Union__Pow__eq]) ).

fof(i_0_10784,plain,
    ! [X24948,X24949] :
      ( ~ class_Lattices_Obounded__lattice__bot(X24949)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24949),c_Orderings_Obot__class_Obot(X24949)),X24948) = c_Orderings_Obot__class_Obot(X24949) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__left])]) ).

fof(i_0_10785,plain,
    ! [X26105,X26106] :
      ( ~ class_Lattices_Obounded__lattice__top(X26106)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26106),c_Orderings_Otop__class_Otop(X26106)),X26105) = c_Orderings_Otop__class_Otop(X26106) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__left])]) ).

fof(i_0_10786,plain,
    ! [X22547,X22548] :
      ( ~ class_Rings_Odivision__ring(X22548)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22548),c_Groups_Ozero__class_Ozero(X22548)),X22547) = c_Groups_Ozero__class_Ozero(X22548) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero__left])]) ).

fof(i_0_10787,plain,
    ! [X20393,X20394] :
      ( ~ class_Divides_Osemiring__div(X20394)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20394),c_Groups_Ozero__class_Ozero(X20394)),X20393) = c_Groups_Ozero__class_Ozero(X20394) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__0])]) ).

fof(i_0_10788,plain,
    ! [X20260,X20261] :
      ( ~ class_Groups_Omonoid__mult(X20261)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20261),c_Groups_Oone__class_Oone(X20261)),X20260) = c_Groups_Oone__class_Oone(X20261) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one])]) ).

fof(i_0_10789,plain,
    ! [X19080,X19081] :
      ( ~ class_Rings_Ocomm__semiring__1(X19081)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19081),c_Groups_Ozero__class_Ozero(X19081)),X19080) = c_Groups_Ozero__class_Ozero(X19081) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J])]) ).

fof(i_0_10790,plain,
    ! [X18351,X18352] :
      ( ~ class_Rings_Omult__zero(X18352)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18352),c_Groups_Ozero__class_Ozero(X18352)),X18351) = c_Groups_Ozero__class_Ozero(X18352) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__left])]) ).

fof(i_0_10791,plain,
    ! [X31682,X31683] :
      ( ~ class_Orderings_Olinorder(X31683)
      | X31682 = c_List_Olist_ONil(X31683)
      | ~ c_List_Olinorder__class_Osorted(X31683,X31682)
      | c_List_Olinorder__class_Osorted(X31683,c_List_Obutlast(X31683,X31682)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__butlast])]) ).

fof(i_0_10792,plain,
    ! [X21658] :
      ( ~ class_Int_Onumber__ring(X21658)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21658),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(X21658),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__m1])]) ).

fof(i_0_10793,plain,
    ! [X18781] : hAPP(c_Finite__Set_Ocard(X18781),c_Orderings_Obot__class_Obot(tc_fun(X18781,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_card_Oempty]) ).

cnf(i_0_10794,plain,
    ( c_Int_OPls = X1
    | c_Int_OPls != c_Int_OBit0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6055]) ).

cnf(i_0_10795,plain,
    ( X1 = c_Int_OPls
    | c_Int_OBit0(X1) != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_6056]) ).

fof(i_0_10796,plain,
    ! [X25967] :
      ( ~ class_Int_Onumber__ring(X25967)
      | ~ class_Rings_Olinordered__idom(X25967)
      | hAPP(c_Groups_Oabs__class_Oabs(X25967),hAPP(c_Int_Onumber__class_Onumber__of(X25967),c_Int_OMin)) = c_Groups_Oone__class_Oone(X25967) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__minus__one])]) ).

fof(i_0_10797,plain,
    ! [X25307] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X25307) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25307),
    inference(variable_rename,[status(thm)],[fact_atLeast0AtMost]) ).

cnf(i_0_10798,plain,
    c_Int_OBit0(X1) != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[i_0_6057]) ).

cnf(i_0_10799,plain,
    c_Int_OMin != c_Int_OBit0(X1),
    inference(split_conjunct,[status(thm)],[i_0_6058]) ).

fof(i_0_10800,plain,
    ! [X25775,X25776,X25777] :
      ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X25777),X25776) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X25777),X25775)
        | X25776 = X25775
        | ~ class_Orderings_Olinorder(X25777) )
      & ( X25776 != X25775
        | hAPP(c_SetInterval_Oord__class_OgreaterThan(X25777),X25776) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X25777),X25775)
        | ~ class_Orderings_Olinorder(X25777) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_greaterThan__eq__iff])])]) ).

fof(i_0_10801,plain,
    ! [X25731,X25732,X25733] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeast(X25733),X25732) != hAPP(c_SetInterval_Oord__class_OatLeast(X25733),X25731)
        | X25732 = X25731
        | ~ class_Orderings_Olinorder(X25733) )
      & ( X25732 != X25731
        | hAPP(c_SetInterval_Oord__class_OatLeast(X25733),X25732) = hAPP(c_SetInterval_Oord__class_OatLeast(X25733),X25731)
        | ~ class_Orderings_Olinorder(X25733) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atLeast__eq__iff])])]) ).

fof(i_0_10802,plain,
    ! [X25135,X25136,X25137] :
      ( ( hAPP(c_SetInterval_Oord__class_OatMost(X25137),X25136) != hAPP(c_SetInterval_Oord__class_OatMost(X25137),X25135)
        | X25136 = X25135
        | ~ class_Orderings_Olinorder(X25137) )
      & ( X25136 != X25135
        | hAPP(c_SetInterval_Oord__class_OatMost(X25137),X25136) = hAPP(c_SetInterval_Oord__class_OatMost(X25137),X25135)
        | ~ class_Orderings_Olinorder(X25137) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_atMost__eq__iff])])]) ).

fof(i_0_10803,plain,
    ! [X24355,X24356,X24357] :
      ( ( hAPP(c_SetInterval_Oord__class_OlessThan(X24357),X24356) != hAPP(c_SetInterval_Oord__class_OlessThan(X24357),X24355)
        | X24356 = X24355
        | ~ class_Orderings_Olinorder(X24357) )
      & ( X24356 != X24355
        | hAPP(c_SetInterval_Oord__class_OlessThan(X24357),X24356) = hAPP(c_SetInterval_Oord__class_OlessThan(X24357),X24355)
        | ~ class_Orderings_Olinorder(X24357) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lessThan__eq__iff])])]) ).

fof(i_0_10804,plain,
    ! [X21523,X21524,X21525] :
      ( ( hAPP(c_Int_Oring__1__class_Oof__int(X21525),X21524) != hAPP(c_Int_Oring__1__class_Oof__int(X21525),X21523)
        | X21524 = X21523
        | ~ class_Int_Oring__char__0(X21525) )
      & ( X21524 != X21523
        | hAPP(c_Int_Oring__1__class_Oof__int(X21525),X21524) = hAPP(c_Int_Oring__1__class_Oof__int(X21525),X21523)
        | ~ class_Int_Oring__char__0(X21525) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__iff])])]) ).

fof(i_0_10805,plain,
    ! [X21118,X21119,X21120] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X21120),X21119) != hAPP(c_Groups_Ouminus__class_Ouminus(X21120),X21118)
        | X21119 = X21118
        | ~ class_Lattices_Oboolean__algebra(X21120) )
      & ( X21119 != X21118
        | hAPP(c_Groups_Ouminus__class_Ouminus(X21120),X21119) = hAPP(c_Groups_Ouminus__class_Ouminus(X21120),X21118)
        | ~ class_Lattices_Oboolean__algebra(X21120) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff])])]) ).

fof(i_0_10806,plain,
    ! [X21105,X21106,X21107] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X21107),X21106) != hAPP(c_Groups_Ouminus__class_Ouminus(X21107),X21105)
        | X21106 = X21105
        | ~ class_Groups_Ogroup__add(X21107) )
      & ( X21106 != X21105
        | hAPP(c_Groups_Ouminus__class_Ouminus(X21107),X21106) = hAPP(c_Groups_Ouminus__class_Ouminus(X21107),X21105)
        | ~ class_Groups_Ogroup__add(X21107) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal])])]) ).

fof(i_0_10807,plain,
    ! [X19951,X19952,X19953] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19953),X19952) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19953),X19951)
        | X19952 = X19951
        | ~ class_Nat_Osemiring__char__0(X19953) )
      & ( X19952 != X19951
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19953),X19952) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X19953),X19951)
        | ~ class_Nat_Osemiring__char__0(X19953) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__eq__iff])])]) ).

fof(i_0_10808,plain,
    ! [X26112,X26113] :
      ( ~ class_Lattices_Obounded__lattice__top(X26113)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26113),c_Orderings_Otop__class_Otop(X26113)),X26112) = X26112 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__left])]) ).

fof(i_0_10809,plain,
    ! [X23366,X23367] :
      ( ~ class_Lattices_Obounded__lattice__bot(X23367)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23367),c_Orderings_Obot__class_Obot(X23367)),X23366) = X23366 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__left])]) ).

fof(i_0_10810,plain,
    ! [X19106,X19107] :
      ( ~ class_Rings_Ocomm__semiring__1(X19107)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19107),c_Groups_Oone__class_Oone(X19107)),X19106) = X19106 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J])]) ).

fof(i_0_10811,plain,
    ! [X18525,X18526] :
      ( ~ class_Groups_Ocomm__monoid__mult(X18526)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18526),c_Groups_Oone__class_Oone(X18526)),X18525) = X18525 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1])]) ).

fof(i_0_10812,plain,
    ! [X18523,X18524] :
      ( ~ class_Groups_Omonoid__mult(X18524)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18524),c_Groups_Oone__class_Oone(X18524)),X18523) = X18523 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__left])]) ).

fof(i_0_10813,plain,
    ! [X19076,X19077] :
      ( ~ class_Rings_Ocomm__semiring__1(X19077)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19077),c_Groups_Ozero__class_Ozero(X19077)),X19076) = X19076 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J])]) ).

fof(i_0_10814,plain,
    ! [X18554,X18555] :
      ( ~ class_Groups_Ocomm__monoid__add(X18555)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18555),c_Groups_Ozero__class_Ozero(X18555)),X18554) = X18554 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0])]) ).

fof(i_0_10815,plain,
    ! [X18552,X18553] :
      ( ~ class_Groups_Omonoid__add(X18553)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18553),c_Groups_Ozero__class_Ozero(X18553)),X18552) = X18552 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__left])]) ).

fof(i_0_10816,plain,
    ! [X22627,X22628] :
      ( ( X22627 != c_Groups_Ozero__class_Ozero(X22628)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22628),X22627),X22627) = c_Groups_Ozero__class_Ozero(X22628)
        | ~ class_Rings_Odivision__ring__inverse__zero(X22628) )
      & ( X22627 = c_Groups_Ozero__class_Ozero(X22628)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22628),X22627),X22627) = c_Groups_Oone__class_Oone(X22628)
        | ~ class_Rings_Odivision__ring__inverse__zero(X22628) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self__if])])]) ).

fof(i_0_10817,plain,
    ! [X20641,X20642] :
      ( ~ class_Divides_Osemiring__div(X20642)
      | c_Divides_Odiv__class_Omod(X20642,c_Groups_Ozero__class_Ozero(X20642),X20641) = c_Groups_Ozero__class_Ozero(X20642) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__0])]) ).

fof(i_0_10818,plain,
    ! [X20775,X20776] :
      ( ~ class_Divides_Osemiring__div(X20776)
      | c_Divides_Odiv__class_Omod(X20776,X20775,c_Groups_Oone__class_Oone(X20776)) = c_Groups_Ozero__class_Ozero(X20776) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__1])]) ).

fof(i_0_10819,plain,
    ! [X31693,X31694] :
      ( ~ class_Orderings_Olinorder(X31694)
      | ~ c_List_Olinorder__class_Osorted(X31694,X31693)
      | c_List_Olinorder__class_Osorted(X31694,c_List_Oremdups(X31694,X31693)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted__remdups])]) ).

fof(i_0_10820,plain,
    ! [X24950,X24951] :
      ( ~ class_Lattices_Obounded__lattice__bot(X24951)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X24951),X24950),c_Orderings_Obot__class_Obot(X24951)) = c_Orderings_Obot__class_Obot(X24951) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__bot__right])]) ).

fof(i_0_10821,plain,
    ! [X26103,X26104] :
      ( ~ class_Lattices_Obounded__lattice__top(X26104)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X26104),X26103),c_Orderings_Otop__class_Otop(X26104)) = c_Orderings_Otop__class_Otop(X26104) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__top__right])]) ).

fof(i_0_10822,plain,
    ! [X22545,X22546] :
      ( ~ class_Rings_Odivision__ring__inverse__zero(X22546)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22546),X22545),c_Groups_Ozero__class_Ozero(X22546)) = c_Groups_Ozero__class_Ozero(X22546) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__zero])]) ).

fof(i_0_10823,plain,
    ! [X20395,X20396] :
      ( ~ class_Divides_Osemiring__div(X20396)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20396),X20395),c_Groups_Ozero__class_Ozero(X20396)) = c_Groups_Ozero__class_Ozero(X20396) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__0])]) ).

fof(i_0_10824,plain,
    ! [X19078,X19079] :
      ( ~ class_Rings_Ocomm__semiring__1(X19079)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19079),X19078),c_Groups_Ozero__class_Ozero(X19079)) = c_Groups_Ozero__class_Ozero(X19079) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J])]) ).

fof(i_0_10825,plain,
    ! [X18349,X18350] :
      ( ~ class_Rings_Omult__zero(X18350)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18350),X18349),c_Groups_Ozero__class_Ozero(X18350)) = c_Groups_Ozero__class_Ozero(X18350) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__zero__right])]) ).

fof(i_0_10826,plain,
    ! [X33027,X33028] :
      ( ~ c_Relation_Osym(X33028,X33027)
      | c_Relation_Osym(tc_List_Olist(X33028),c_List_Olistrel(X33028,X33027)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__sym])]) ).

fof(i_0_10827,plain,
    ! [X32878,X32879] :
      ( ~ c_Relation_Otrans(X32879,X32878)
      | c_Relation_Otrans(tc_List_Olist(X32879),c_List_Olistrel(X32879,X32878)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listrel__trans])]) ).

fof(i_0_10828,plain,
    ! [X32880,X32881] :
      ( ~ c_Relation_Otrans(X32881,X32880)
      | c_Relation_Otrans(tc_List_Olist(X32881),c_List_Olexord(X32881,X32880)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_lexord__transI])]) ).

fof(i_0_10829,plain,
    ! [X28227,X28228] :
      ( ~ c_Wellfounded_Owf(X28228,X28227)
      | c_Wellfounded_Owf(tc_List_Olist(X28228),c_List_Olex(X28228,X28227)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lex])]) ).

fof(i_0_10830,plain,
    ! [X28205,X28206] :
      ( ~ c_Wellfounded_Owf(X28206,X28205)
      | c_Wellfounded_Owf(tc_List_Olist(X28206),c_List_Olenlex(X28206,X28205)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__lenlex])]) ).

fof(i_0_10831,plain,
    ! [X30118,X30119,X30120] :
      ( X30120 != X30119
      | X30120 = hAPP(hAPP(c_List_Oappend(X30118),c_List_Olist_ONil(X30118)),X30119) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_eq__Nil__appendI])]) ).

fof(i_0_10832,plain,
    ! [X22629,X22630] :
      ( ~ class_Rings_Odivision__ring(X22630)
      | X22629 = c_Groups_Ozero__class_Ozero(X22630)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22630),X22629),X22629) = c_Groups_Oone__class_Oone(X22630) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__self])]) ).

fof(i_0_10833,plain,
    ! [X20451,X20452] :
      ( ~ class_Divides_Osemiring__div(X20452)
      | X20451 = c_Groups_Ozero__class_Ozero(X20452)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20452),X20451),X20451) = c_Groups_Oone__class_Oone(X20452) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__self])]) ).

fof(i_0_10834,plain,
    ! [X20643,X20644] :
      ( ~ class_Divides_Osemiring__div(X20644)
      | c_Divides_Odiv__class_Omod(X20644,X20643,c_Groups_Ozero__class_Ozero(X20644)) = X20643 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__by__0])]) ).

fof(i_0_10835,plain,
    ! [X20835] :
      ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X20835))
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X20835)) = X20835 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6059])]) ).

fof(i_0_10836,plain,
    ! [X19729] :
      ( ~ class_Groups_Oab__semigroup__mult(X19729)
      | c_Finite__Set_Ofun__left__comm(X19729,X19729,c_Groups_Otimes__class_Otimes(X19729)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm])]) ).

fof(i_0_10837,plain,
    ! [X25052] :
      ( ~ class_Lattices_Osemilattice__inf(X25052)
      | c_Finite__Set_Ofun__left__comm__idem(X25052,X25052,c_Lattices_Osemilattice__inf__class_Oinf(X25052)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__inf])]) ).

fof(i_0_10838,plain,
    ! [X23386] :
      ( ~ class_Lattices_Osemilattice__sup(X23386)
      | c_Finite__Set_Ofun__left__comm__idem(X23386,X23386,c_Lattices_Osemilattice__sup__class_Osup(X23386)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem__sup])]) ).

fof(i_0_10839,plain,
    ! [X22610] :
      ( ~ class_Orderings_Olinorder(X22610)
      | c_Finite__Set_Ofun__left__comm__idem(X22610,X22610,c_Orderings_Oord__class_Omax(X22610)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__sup])]) ).

fof(i_0_10840,plain,
    ! [X21609] :
      ( ~ class_Orderings_Olinorder(X21609)
      | c_Finite__Set_Ofun__left__comm__idem(X21609,X21609,c_Orderings_Oord__class_Omin(X21609)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Ofun__left__comm__idem__inf])]) ).

fof(i_0_10841,plain,
    ! [X18639] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X18639)
      | c_Finite__Set_Ofun__left__comm__idem(X18639,X18639,c_Groups_Otimes__class_Otimes(X18639)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_fun__left__comm__idem])]) ).

fof(i_0_10842,plain,
    ! [X28091,X28092] : hAPP(c_Relation_ODomain(X28092,X28092),c_Relation_OId__on(X28092,X28091)) = X28091,
    inference(variable_rename,[status(thm)],[fact_Domain__Id__on]) ).

fof(i_0_10843,plain,
    ! [X27880,X27881] : hAPP(c_Relation_ORange(X27881,X27881),c_Relation_OId__on(X27881,X27880)) = X27880,
    inference(variable_rename,[status(thm)],[fact_Range__Id__on]) ).

fof(i_0_10844,plain,
    ! [X20301,X20302] :
      ( ~ class_Power_Opower(X20302)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20302),X20301),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20302) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__0])]) ).

fof(i_0_10845,plain,
    ! [X20181,X20182] :
      ( ~ class_Rings_Ocomm__semiring__1(X20182)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20182),X20181),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20182) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J])]) ).

fof(i_0_10846,plain,
    ! [X26110,X26111] :
      ( ~ class_Lattices_Obounded__lattice__top(X26111)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X26111),X26110),c_Orderings_Otop__class_Otop(X26111)) = X26110 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__top__right])]) ).

fof(i_0_10847,plain,
    ! [X23368,X23369] :
      ( ~ class_Lattices_Obounded__lattice__bot(X23369)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23369),X23368),c_Orderings_Obot__class_Obot(X23369)) = X23368 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__bot__right])]) ).

fof(i_0_10848,plain,
    ! [X22485,X22486] :
      ( ~ class_Rings_Odivision__ring(X22486)
      | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X22486),X22485),c_Groups_Oone__class_Oone(X22486)) = X22485 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_divide__1])]) ).

fof(i_0_10849,plain,
    ! [X20397,X20398] :
      ( ~ class_Divides_Osemiring__div(X20398)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20398),X20397),c_Groups_Oone__class_Oone(X20398)) = X20397 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_div__by__1])]) ).

fof(i_0_10850,plain,
    ! [X19104,X19105] :
      ( ~ class_Rings_Ocomm__semiring__1(X19105)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X19105),X19104),c_Groups_Oone__class_Oone(X19105)) = X19104 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J])]) ).

fof(i_0_10851,plain,
    ! [X18529,X18530] :
      ( ~ class_Groups_Ocomm__monoid__mult(X18530)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18530),X18529),c_Groups_Oone__class_Oone(X18530)) = X18529 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult_Ocomm__neutral])]) ).

fof(i_0_10852,plain,
    ! [X18527,X18528] :
      ( ~ class_Groups_Omonoid__mult(X18528)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18528),X18527),c_Groups_Oone__class_Oone(X18528)) = X18527 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__1__right])]) ).

fof(i_0_10853,plain,
    ! [X19074,X19075] :
      ( ~ class_Rings_Ocomm__semiring__1(X19075)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X19075),X19074),c_Groups_Ozero__class_Ozero(X19075)) = X19074 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J])]) ).

fof(i_0_10854,plain,
    ! [X18560,X18561] :
      ( ~ class_Groups_Ocomm__monoid__add(X18561)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18561),X18560),c_Groups_Ozero__class_Ozero(X18561)) = X18560 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add_Ocomm__neutral])]) ).

fof(i_0_10855,plain,
    ! [X18558,X18559] :
      ( ~ class_Groups_Omonoid__add(X18559)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X18559),X18558),c_Groups_Ozero__class_Ozero(X18559)) = X18558 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_add__0__right])]) ).

fof(i_0_10856,plain,
    ! [X18568,X18569] :
      ( ~ class_Groups_Ogroup__add(X18569)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18569),X18568),c_Groups_Ozero__class_Ozero(X18569)) = X18568 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__0__right])]) ).

fof(i_0_10857,plain,
    ! [X21112,X21113] :
      ( ~ class_Lattices_Oboolean__algebra(X21113)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21113),hAPP(c_Groups_Ouminus__class_Ouminus(X21113),X21112)) = X21112 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_double__compl])]) ).

fof(i_0_10858,plain,
    ! [X21097,X21098] :
      ( ~ class_Groups_Ogroup__add(X21098)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21098),hAPP(c_Groups_Ouminus__class_Ouminus(X21098),X21097)) = X21097 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__minus])]) ).

fof(i_0_10859,plain,
    ! [X25868] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25868)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X25868),
    inference(variable_rename,[status(thm)],[fact_abs__int__eq]) ).

fof(i_0_10860,plain,
    ! [X21608] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21608)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21608),
    inference(variable_rename,[status(thm)],[fact_of__int__int__eq]) ).

fof(i_0_10861,plain,
    ! [X31264,X31265] : hAPP(c_List_Oset(X31265),c_List_Oremdups(X31265,X31264)) = hAPP(c_List_Oset(X31265),X31264),
    inference(variable_rename,[status(thm)],[fact_set__remdups]) ).

fof(i_0_10862,plain,
    ! [X20645,X20646] :
      ( ~ class_Divides_Osemiring__div(X20646)
      | c_Divides_Odiv__class_Omod(X20646,X20645,X20645) = c_Groups_Ozero__class_Ozero(X20646) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mod__self])]) ).

fof(i_0_10863,plain,
    ! [X31828,X31829,X31830] :
      ( ( hAPP(c_List_Orev(X31830),X31829) != hAPP(c_List_Orev(X31830),X31828)
        | X31829 = X31828 )
      & ( X31829 != X31828
        | hAPP(c_List_Orev(X31830),X31829) = hAPP(c_List_Orev(X31830),X31828) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__rev__conv])]) ).

fof(i_0_10864,plain,
    ! [X18782,X18783] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(X18783),X18782))
      | hAPP(c_Finite__Set_Ocard(X18783),X18782) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6060])]) ).

fof(i_0_10865,plain,
    ! [X28760,X28761] :
      ( ( X28761 != X28760
        | c_Random_Oinc__shift(X28761,X28760) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
      & ( X28761 = X28760
        | c_Random_Oinc__shift(X28761,X28760) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X28760),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_10866,plain,
    ! [X30096,X30097] : hAPP(hAPP(c_List_Oappend(X30097),c_List_Olist_ONil(X30097)),X30096) = X30096,
    inference(variable_rename,[status(thm)],[fact_append__Nil]) ).

fof(i_0_10867,plain,
    ! [X18132] : hAPP(c_Nat_OSuc,X18132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X18132),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1__left]) ).

fof(i_0_10868,plain,
    ! [X29859,X29860] : c_List_Osublist(X29860,c_List_Olist_ONil(X29860),X29859) = c_List_Olist_ONil(X29860),
    inference(variable_rename,[status(thm)],[fact_sublist__nil]) ).

fof(i_0_10869,plain,
    ! [X31932,X31933] : c_List_OtakeWhile(X31933,X31932,c_List_Olist_ONil(X31933)) = c_List_Olist_ONil(X31933),
    inference(variable_rename,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).

fof(i_0_10870,plain,
    ! [X29865,X29866] : c_List_Oremove1(X29866,X29865,c_List_Olist_ONil(X29866)) = c_List_Olist_ONil(X29866),
    inference(variable_rename,[status(thm)],[fact_remove1_Osimps_I1_J]) ).

fof(i_0_10871,plain,
    ! [X24054] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X24054),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_10872,plain,
    ! [X20170,X20171] :
      ( ~ class_Rings_Ocomm__semiring__1(X20171)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20171),X20170),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20170 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J])]) ).

fof(i_0_10873,plain,
    ! [X20269,X20270] :
      ( ~ class_Groups_Omonoid__mult(X20270)
      | hAPP(hAPP(c_Power_Opower__class_Opower(X20270),X20269),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X20269 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_power__one__right])]) ).

fof(i_0_10874,plain,
    ! [X18570,X18571] :
      ( ~ class_Groups_Ogroup__add(X18571)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(X18571),X18570),X18570) = c_Groups_Ozero__class_Ozero(X18571) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_diff__self])]) ).

fof(i_0_10875,plain,
    ! [X29896,X29897] : c_List_Olist_Olist__size(X29897,X29896,c_List_Olist_ONil(X29897)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I1_J]) ).

fof(i_0_10876,plain,
    ! [X33037,X33038] :
      ( ~ c_Relation_Osym(X33038,X33037)
      | c_Relation_Osym(X33038,c_Transitive__Closure_Ortrancl(X33038,X33037)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sym__rtrancl])]) ).

fof(i_0_10877,plain,
    ! [X32992,X32993] :
      ( ~ c_Wellfounded_Oacyclic(X32993,X32992)
      | c_Relation_Oantisym(X32993,c_Transitive__Closure_Ortrancl(X32993,X32992)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_acyclic__impl__antisym__rtrancl])]) ).

fof(i_0_10878,plain,
    ! [X29855,X29856] : hAPP(hAPP(c_List_Otake(X29856),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X29855) = c_List_Olist_ONil(X29856),
    inference(variable_rename,[status(thm)],[fact_take__0]) ).

fof(i_0_10879,plain,
    ! [X30287,X30288] : hAPP(hAPP(c_List_Odrop(X30288),X30287),c_List_Olist_ONil(X30288)) = c_List_Olist_ONil(X30288),
    inference(variable_rename,[status(thm)],[fact_drop__Nil]) ).

fof(i_0_10880,plain,
    ! [X29857,X29858] : hAPP(hAPP(c_List_Otake(X29858),X29857),c_List_Olist_ONil(X29858)) = c_List_Olist_ONil(X29858),
    inference(variable_rename,[status(thm)],[fact_take__Nil]) ).

fof(i_0_10881,plain,
    ! [X21102,X21103,X21104] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X21104),X21103) != X21102
        | hAPP(c_Groups_Ouminus__class_Ouminus(X21104),X21102) = X21103
        | ~ class_Groups_Ogroup__add(X21104) )
      & ( hAPP(c_Groups_Ouminus__class_Ouminus(X21104),X21102) != X21103
        | hAPP(c_Groups_Ouminus__class_Ouminus(X21104),X21103) = X21102
        | ~ class_Groups_Ogroup__add(X21104) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__equation__iff])])]) ).

fof(i_0_10882,plain,
    ! [X21099,X21100,X21101] :
      ( ( X21100 != hAPP(c_Groups_Ouminus__class_Ouminus(X21101),X21099)
        | X21099 = hAPP(c_Groups_Ouminus__class_Ouminus(X21101),X21100)
        | ~ class_Groups_Ogroup__add(X21101) )
      & ( X21099 != hAPP(c_Groups_Ouminus__class_Ouminus(X21101),X21100)
        | X21100 = hAPP(c_Groups_Ouminus__class_Ouminus(X21101),X21099)
        | ~ class_Groups_Ogroup__add(X21101) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equation__minus__iff])])]) ).

fof(i_0_10883,plain,
    ! [X29649] :
      ( ( ~ c_List_Onat__list(X29649)
        | c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X29649)) )
      & ( ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X29649))
        | c_List_Onat__list(X29649) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat__list__def])]) ).

fof(i_0_10884,plain,
    ! [X25309] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25309)) = hAPP(c_Nat_OSuc,X25309),
    inference(variable_rename,[status(thm)],[fact_card__atMost]) ).

fof(i_0_10885,plain,
    ! [X30983] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X30983)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X30983),
    inference(variable_rename,[status(thm)],[fact_nat__of__number]) ).

fof(i_0_10886,plain,
    ! [X20815] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20815)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20815),
    inference(variable_rename,[status(thm)],[fact_nat__number__of]) ).

fof(i_0_10887,plain,
    ! [X20814] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X20814) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X20814)),
    inference(variable_rename,[status(thm)],[fact_nat__number__of__def]) ).

fof(i_0_10888,plain,
    ! [X18133] : hAPP(c_Nat_OSuc,X18133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18133),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(i_0_10889,plain,
    ! [X32594,X32595] : c_List_Oreplicate(X32595,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X32594) = c_List_Olist_ONil(X32595),
    inference(variable_rename,[status(thm)],[fact_replicate__0]) ).

fof(i_0_10890,plain,
    ! [X32760,X32761] : c_Lazy__Sequence_Oappend(X32761,c_Lazy__Sequence_Olazy__sequence_OEmpty(X32761),X32760) = X32760,
    inference(variable_rename,[status(thm)],[fact__02]) ).

fof(i_0_10891,plain,
    ! [X32447,X32448] : c_List_Osplice(X32448,c_List_Olist_ONil(X32448),X32447) = X32447,
    inference(variable_rename,[status(thm)],[fact_splice_Osimps_I1_J]) ).

fof(i_0_10892,plain,
    ! [X32449,X32450] : c_List_Osplice(X32450,X32449,c_List_Olist_ONil(X32450)) = X32449,
    inference(variable_rename,[status(thm)],[fact_splice__Nil2]) ).

fof(i_0_10893,plain,
    ! [X25808,X25809] :
      ( ~ class_Rings_Olinordered__idom(X25809)
      | c_Groups_Osgn__class_Osgn(X25809,c_Groups_Osgn__class_Osgn(X25809,X25808)) = c_Groups_Osgn__class_Osgn(X25809,X25808) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__sgn])]) ).

fof(i_0_10894,plain,
    ! [X32298,X32299] : c_List_Olist__all(X32299,X32298,c_List_Olist_ONil(X32299)),
    inference(variable_rename,[status(thm)],[fact_list__all__simps_I2_J]) ).

fof(i_0_10895,plain,
    ! [X25109,X25110] :
      ( ~ class_Lattices_Osemilattice__inf(X25110)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25110),X25109),X25109) = X25109 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf_Oidem])]) ).

fof(i_0_10896,plain,
    ! [X25107,X25108] :
      ( ~ class_Lattices_Osemilattice__inf(X25108)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25108),X25107),X25107) = X25107 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__idem])]) ).

fof(i_0_10897,plain,
    ! [X25146,X25147] :
      ( ~ class_Lattices_Olattice(X25147)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X25147),X25146),X25146) = X25146 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Inf__fin_Oidem])]) ).

fof(i_0_10898,plain,
    ! [X23290,X23291] :
      ( ~ class_Lattices_Olattice(X23291)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23291),X23290),X23290) = X23290 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Sup__fin_Oidem])]) ).

fof(i_0_10899,plain,
    ! [X23228,X23229] :
      ( ~ class_Lattices_Osemilattice__sup(X23229)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23229),X23228),X23228) = X23228 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup_Oidem])]) ).

fof(i_0_10900,plain,
    ! [X23226,X23227] :
      ( ~ class_Lattices_Osemilattice__sup(X23227)
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23227),X23226),X23226) = X23226 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__idem])]) ).

fof(i_0_10901,plain,
    ! [X22549,X22550] :
      ( ~ class_Orderings_Olinorder(X22550)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22550),X22549),X22549) = X22549 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Max_Oidem])]) ).

fof(i_0_10902,plain,
    ! [X22519,X22520] :
      ( ~ class_Orderings_Olinorder(X22520)
      | hAPP(hAPP(c_Orderings_Oord__class_Omax(X22520),X22519),X22519) = X22519 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oidem])]) ).

fof(i_0_10903,plain,
    ! [X21706,X21707] :
      ( ~ class_Orderings_Olinorder(X21707)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21707),X21706),X21706) = X21706 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Min_Oidem])]) ).

fof(i_0_10904,plain,
    ! [X21493,X21494] :
      ( ~ class_Orderings_Olinorder(X21494)
      | hAPP(hAPP(c_Orderings_Oord__class_Omin(X21494),X21493),X21493) = X21493 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__max_Oinf_Oidem])]) ).

fof(i_0_10905,plain,
    ! [X18367,X18368] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X18368)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18368),X18367),X18367) = X18367 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mult__idem])]) ).

fof(i_0_10906,plain,
    ! [X18365,X18366] :
      ( ~ class_Lattices_Oab__semigroup__idem__mult(X18366)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X18366),X18365),X18365) = X18365 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_times_Oidem])]) ).

fof(i_0_10907,plain,
    ! [X29878,X29879] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29879)),X29878) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | X29878 = c_List_Olist_ONil(X29879) )
      & ( X29878 != c_List_Olist_ONil(X29879)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29879)),X29878) = 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_10908,plain,
    ! [X21337] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X21337) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21337),
    inference(variable_rename,[status(thm)],[fact_mult__Min]) ).

fof(i_0_10909,plain,
    ! [X24361] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X24361) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24361),
    inference(variable_rename,[status(thm)],[fact_atLeast0LessThan]) ).

fof(i_0_10910,plain,
    ! [X32454,X32455,X32456] : hAPP(c_New__DSequence_Opos__single(X32456,X32455),X32454) = hAPP(c_Lazy__Sequence_Osingle(X32456),X32455),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__single__def]) ).

fof(i_0_10911,plain,
    ! [X30266,X30267] : hAPP(hAPP(c_List_Odrop(X30267),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30266) = X30266,
    inference(variable_rename,[status(thm)],[fact_drop__0]) ).

fof(i_0_10912,plain,
    ! [X30101,X30102] : hAPP(hAPP(c_List_Oappend(X30102),X30101),c_List_Olist_ONil(X30102)) = X30101,
    inference(variable_rename,[status(thm)],[fact_append__Nil2]) ).

fof(i_0_10913,plain,
    ! [X31823,X31824] : hAPP(c_List_Orev(X31824),hAPP(c_List_Orev(X31824),X31823)) = X31823,
    inference(variable_rename,[status(thm)],[fact_rev__rev__ident]) ).

fof(i_0_10914,plain,
    ! [X32649] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X32649) = c_Lazy__Sequence_Osmall__lazy_H(X32649,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X32649)),
    inference(variable_rename,[status(thm)],[fact_small__lazy__int__def]) ).

fof(i_0_10915,plain,
    ! [X20735] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20735) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__zero]) ).

fof(i_0_10916,plain,
    ! [X20831] :
      ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X20831))
      | hAPP(c_Int_Onat,X20831) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__nat])]) ).

fof(i_0_10917,plain,
    ! [X25774] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25774)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X25774),
    inference(variable_rename,[status(thm)],[fact_atLeast__Suc__greaterThan]) ).

fof(i_0_10918,plain,
    ! [X25308] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X25308)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X25308),
    inference(variable_rename,[status(thm)],[fact_lessThan__Suc__atMost]) ).

fof(i_0_10919,plain,
    ! [X17772] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17772) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X17772)),
    inference(variable_rename,[status(thm)],[fact_less__eq__Suc__le__raw]) ).

fof(i_0_10920,plain,
    ! [X20822] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20822),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      & c_Divides_Odiv__class_Omod(tc_Int_Oint,X20822,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X20822 ),
    inference(variable_rename,[status(thm)],[fact_DIVISION__BY__ZERO]) ).

fof(i_0_10921,plain,
    ! [X21462] :
      ( ~ class_Int_Onumber__ring(X21462)
      | c_Int_Oiszero(X21462,hAPP(c_Int_Onumber__class_Onumber__of(X21462),c_Int_OPls)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__Numeral0])]) ).

fof(i_0_10922,plain,
    ! [X30857] : hAPP(c_List_Omap(X30857,X30857),c_Fun_Oid(X30857)) = c_Fun_Oid(tc_List_Olist(X30857)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Oid]) ).

fof(i_0_10923,plain,
    ! [X30851] : hAPP(c_List_Omap(X30851,X30851),c_COMBI(X30851)) = c_Fun_Oid(tc_List_Olist(X30851)),
    inference(variable_rename,[status(thm)],[fact_List_Omap_Oidentity]) ).

fof(i_0_10924,plain,
    ! [X20154,X20155] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20155) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20154)
        | X20155 = X20154 )
      & ( X20155 != X20154
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20155) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20154) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_transfer__int__nat__relations_I1_J])]) ).

fof(i_0_10925,plain,
    ! [X20140,X20141] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20141) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20140)
        | X20141 = X20140 )
      & ( X20141 != X20140
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20141) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20140) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_int__int__eq])]) ).

fof(i_0_10926,plain,
    ! [X20736] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X20736,X20736) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zmod__self]) ).

fof(i_0_10927,plain,
    ! [X31825,X31826,X31827] :
      ( ( hAPP(c_List_Orev(X31827),X31826) != X31825
        | X31826 = hAPP(c_List_Orev(X31827),X31825) )
      & ( X31826 != hAPP(c_List_Orev(X31827),X31825)
        | hAPP(c_List_Orev(X31827),X31826) = X31825 ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__swap])]) ).

fof(i_0_10928,plain,
    ! [X21598] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X21598) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_min__0L]) ).

fof(i_0_10929,plain,
    ! [X20371] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20371) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[fact_zdiv__zero]) ).

fof(i_0_10930,plain,
    ! [X18355] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18355) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_mult__0]) ).

fof(i_0_10931,plain,
    ! [X18604] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18604) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__0__eq__0]) ).

fof(i_0_10932,plain,
    ! [X29835] : hBOOL(hAPP(c_List_Odistinct(X29835),c_List_Olist_ONil(X29835))),
    inference(variable_rename,[status(thm)],[fact_distinct_Osimps_I1_J]) ).

fof(i_0_10933,plain,
    ! [X32427,X32428,X32429] : hAPP(c_New__DSequence_Oneg__single(X32429,X32428),X32427) = c_Lazy__Sequence_Ohb__single(X32429,X32428),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Oneg__single__def]) ).

fof(i_0_10934,plain,
    ! [X31268,X31269] : c_List_Oremdups(X31269,c_List_Oremdups(X31269,X31268)) = c_List_Oremdups(X31269,X31268),
    inference(variable_rename,[status(thm)],[fact_remdups__remdups]) ).

fof(i_0_10935,plain,
    ! [X28673,X28674] : c_Transitive__Closure_Ortrancl(X28674,c_Transitive__Closure_Ortrancl(X28674,X28673)) = c_Transitive__Closure_Ortrancl(X28674,X28673),
    inference(variable_rename,[status(thm)],[fact_rtrancl__idemp]) ).

fof(i_0_10936,plain,
    ! [X29885] : hAPP(c_List_Oset(X29885),c_List_Olist_ONil(X29885)) = c_Orderings_Obot__class_Obot(tc_fun(X29885,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[fact_List_Oset_Osimps_I1_J]) ).

fof(i_0_10937,plain,
    ! [X22557] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X22557) = X22557,
    inference(variable_rename,[status(thm)],[fact_max__0L]) ).

fof(i_0_10938,plain,
    ! [X19446] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X19446) = X19446,
    inference(variable_rename,[status(thm)],[fact_zmult__1]) ).

fof(i_0_10939,plain,
    ! [X18578] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X18578) = X18578,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1]) ).

fof(i_0_10940,plain,
    ! [X19448] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19448) = X19448,
    inference(variable_rename,[status(thm)],[fact_zadd__0]) ).

fof(i_0_10941,plain,
    ! [X18596] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X18596) = X18596,
    inference(variable_rename,[status(thm)],[fact_plus__nat_Oadd__0]) ).

fof(i_0_10942,plain,
    ! [X32493] : c_Predicate_Oconversep(X32493,X32493,c_fequal) = c_fequal,
    inference(variable_rename,[status(thm)],[fact_conversep__eq]) ).

fof(i_0_10943,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_10944,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_10945,plain,
    ! [X20407] :
      ( X20407 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X20407),X20407) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zdiv__self])]) ).

fof(i_0_10946,plain,
    ! [X21351] :
      ( ~ class_Int_Onumber__ring(X21351)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21351),c_Groups_Oone__class_Oone(X21351)) = hAPP(c_Int_Onumber__class_Onumber__of(X21351),c_Int_OMin) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_arith__simps_I31_J])]) ).

fof(i_0_10947,plain,
    ! [X21352] :
      ( ~ class_Int_Onumber__ring(X21352)
      | hAPP(c_Int_Onumber__class_Onumber__of(X21352),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X21352),c_Groups_Oone__class_Oone(X21352)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Min])]) ).

fof(i_0_10948,plain,
    ! [X21599] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X21599),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_10949,plain,
    ! [X18356] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18356),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_10950,plain,
    ! [X21148,X21149] :
      ( ( c_Groups_Ozero__class_Ozero(X21149) != hAPP(c_Groups_Ouminus__class_Ouminus(X21149),X21148)
        | c_Groups_Ozero__class_Ozero(X21149) = X21148
        | ~ class_Groups_Ogroup__add(X21149) )
      & ( c_Groups_Ozero__class_Ozero(X21149) != X21148
        | c_Groups_Ozero__class_Ozero(X21149) = hAPP(c_Groups_Ouminus__class_Ouminus(X21149),X21148)
        | ~ class_Groups_Ogroup__add(X21149) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal])])]) ).

fof(i_0_10951,plain,
    ! [X25860,X25861] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(X25861),X25860) != c_Groups_Ozero__class_Ozero(X25861)
        | X25860 = c_Groups_Ozero__class_Ozero(X25861)
        | ~ class_Groups_Oordered__ab__group__add__abs(X25861) )
      & ( X25860 != c_Groups_Ozero__class_Ozero(X25861)
        | hAPP(c_Groups_Oabs__class_Oabs(X25861),X25860) = c_Groups_Ozero__class_Ozero(X25861)
        | ~ class_Groups_Oordered__ab__group__add__abs(X25861) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__eq__0])])]) ).

fof(i_0_10952,plain,
    ! [X21152,X21153] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X21153),X21152) != c_Groups_Ozero__class_Ozero(X21153)
        | X21152 = c_Groups_Ozero__class_Ozero(X21153)
        | ~ class_Groups_Ogroup__add(X21153) )
      & ( X21152 != c_Groups_Ozero__class_Ozero(X21153)
        | hAPP(c_Groups_Ouminus__class_Ouminus(X21153),X21152) = c_Groups_Ozero__class_Ozero(X21153)
        | ~ class_Groups_Ogroup__add(X21153) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal])])]) ).

fof(i_0_10953,plain,
    ! [X34034] :
      ( ~ hBOOL(hAPP(c_fNot,X34034))
      | ~ hBOOL(X34034) ),
    inference(variable_rename,[status(thm)],[i_0_6061]) ).

fof(i_0_10954,plain,
    ! [X22558] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X22558),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X22558,
    inference(variable_rename,[status(thm)],[fact_max__0R]) ).

fof(i_0_10955,plain,
    ! [X19445] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19445),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X19445,
    inference(variable_rename,[status(thm)],[fact_zmult__1__right]) ).

fof(i_0_10956,plain,
    ! [X18581] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18581),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X18581,
    inference(variable_rename,[status(thm)],[fact_nat__mult__1__right]) ).

fof(i_0_10957,plain,
    ! [X19449] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19449),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X19449,
    inference(variable_rename,[status(thm)],[fact_zadd__0__right]) ).

fof(i_0_10958,plain,
    ! [X18597] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X18597),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18597,
    inference(variable_rename,[status(thm)],[fact_Nat_Oadd__0__right]) ).

fof(i_0_10959,plain,
    ! [X18605] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18605),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18605,
    inference(variable_rename,[status(thm)],[fact_minus__nat_Odiff__0]) ).

fof(i_0_10960,plain,
    ! [X21121] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X21121)) = X21121,
    inference(variable_rename,[status(thm)],[fact_zminus__zminus]) ).

fof(i_0_10961,plain,
    ! [X24358] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X24358)) = X24358,
    inference(variable_rename,[status(thm)],[fact_card__lessThan]) ).

fof(i_0_10962,plain,
    ! [X31450,X31451] : hAPP(c_List_Ofilter(X31451,X31450),c_List_Olist_ONil(X31451)) = c_List_Olist_ONil(X31451),
    inference(variable_rename,[status(thm)],[fact_filter_Osimps_I1_J]) ).

fof(i_0_10963,plain,
    ! [X16896,X16897] :
      ( ~ class_Finite__Set_Ofinite(X16897)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X16897),X16896)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite])]) ).

fof(i_0_10964,plain,
    ! [X16894,X16895] :
      ( ~ class_Finite__Set_Ofinite(X16895)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(X16895),X16894)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_finite__code])]) ).

fof(i_0_10965,plain,
    ! [X21613,X21614] :
      ( ( hAPP(c_Int_Oring__1__class_Oof__int(X21614),X21613) != c_Groups_Ozero__class_Ozero(X21614)
        | X21613 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Int_Oring__char__0(X21614) )
      & ( X21613 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(X21614),X21613) = c_Groups_Ozero__class_Ozero(X21614)
        | ~ class_Int_Oring__char__0(X21614) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__eq__0__iff])])]) ).

fof(i_0_10966,plain,
    ! [X21615,X21616] :
      ( ( c_Groups_Ozero__class_Ozero(X21616) != hAPP(c_Int_Oring__1__class_Oof__int(X21616),X21615)
        | X21615 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ class_Int_Oring__char__0(X21616) )
      & ( X21615 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(X21616) = hAPP(c_Int_Oring__1__class_Oof__int(X21616),X21615)
        | ~ class_Int_Oring__char__0(X21616) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0__eq__iff])])]) ).

cnf(i_0_10967,plain,
    ( c_Int_OBit0(X1) = c_Int_OPls
    | X1 != c_Int_OPls ),
    inference(split_conjunct,[status(thm)],[i_0_6056]) ).

cnf(i_0_10968,plain,
    ( c_Int_OPls = c_Int_OBit0(X1)
    | c_Int_OPls != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_6055]) ).

fof(i_0_10969,plain,
    ! [X18606] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X18606),X18606) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_diff__self__eq__0]) ).

fof(i_0_10970,plain,
    ! [X32757,X32758] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X32758,X32757),c_Lazy__Sequence_Olazy__sequence_OEmpty(X32758)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I1_J]) ).

fof(i_0_10971,plain,
    ! [X21605,X21606] :
      ( ~ class_Int_Onumber__ring(X21606)
      | hAPP(c_Int_Onumber__class_Onumber__of(X21606),X21605) = hAPP(c_Int_Oring__1__class_Oof__int(X21606),X21605) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__eq])]) ).

fof(i_0_10972,plain,
    ! [X21154,X21155] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X21155),X21154) != X21154
        | X21154 = c_Groups_Ozero__class_Ozero(X21155)
        | ~ class_Groups_Olinordered__ab__group__add(X21155) )
      & ( X21154 != c_Groups_Ozero__class_Ozero(X21155)
        | hAPP(c_Groups_Ouminus__class_Ouminus(X21155),X21154) = X21154
        | ~ class_Groups_Olinordered__ab__group__add(X21155) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_neg__equal__zero])])]) ).

fof(i_0_10973,plain,
    ! [X21150,X21151] :
      ( ( X21150 != hAPP(c_Groups_Ouminus__class_Ouminus(X21151),X21150)
        | X21150 = c_Groups_Ozero__class_Ozero(X21151)
        | ~ class_Groups_Olinordered__ab__group__add(X21151) )
      & ( X21150 != c_Groups_Ozero__class_Ozero(X21151)
        | X21150 = hAPP(c_Groups_Ouminus__class_Ouminus(X21151),X21150)
        | ~ class_Groups_Olinordered__ab__group__add(X21151) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equal__neg__zero])])]) ).

fof(i_0_10974,plain,
    ! [X19972] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19972),c_Int_OPls) = X19972,
    inference(variable_rename,[status(thm)],[fact_add__Pls__right]) ).

fof(i_0_10975,plain,
    ! [X19976] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19976),c_Int_OPls) = X19976,
    inference(variable_rename,[status(thm)],[fact_diff__bin__simps_I1_J]) ).

fof(i_0_10976,plain,
    ! [X20737] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X20737)) = X20737,
    inference(variable_rename,[status(thm)],[fact_nat__int]) ).

fof(i_0_10977,plain,
    ! [X33997,X33998] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X33998)
      | ~ class_Lazy__Sequence_Osmall__lazy(X33997)
      | class_Lazy__Sequence_Osmall__lazy(tc_prod(X33998,X33997)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Lazy__Sequence_Osmall__lazy])]) ).

fof(i_0_10978,plain,
    ! [X34001,X34002] :
      ( ~ class_Enum_Oenum(X34002)
      | ~ class_Enum_Oenum(X34001)
      | class_Enum_Oenum(tc_prod(X34002,X34001)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Enum_Oenum])]) ).

fof(i_0_10979,plain,
    ! [X33988,X33989] :
      ( ~ class_Enum_Oenum(X33989)
      | ~ class_Enum_Oenum(X33988)
      | class_Enum_Oenum(tc_sum(X33989,X33988)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Enum_Oenum])]) ).

fof(i_0_10980,plain,
    ! [X33982,X33983] :
      ( ~ class_Enum_Oenum(X33983)
      | ~ class_Enum_Oenum(X33982)
      | class_Enum_Oenum(tc_fun(X33983,X33982)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Enum_Oenum])]) ).

fof(i_0_10981,plain,
    ! [X21761,X21762] :
      ( ~ c_Nat__Transfer_Ois__nat(X21762)
      | ~ c_Nat__Transfer_Ois__nat(X21761)
      | c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X21762,X21761)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J])]) ).

fof(i_0_10982,plain,
    ! [X33999,X34000] :
      ( ~ class_Finite__Set_Ofinite(X34000)
      | ~ class_Finite__Set_Ofinite(X33999)
      | class_Finite__Set_Ofinite(tc_prod(X34000,X33999)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_prod__Finite__Set_Ofinite])]) ).

fof(i_0_10983,plain,
    ! [X33986,X33987] :
      ( ~ class_Finite__Set_Ofinite(X33987)
      | ~ class_Finite__Set_Ofinite(X33986)
      | class_Finite__Set_Ofinite(tc_sum(X33987,X33986)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_sum__Finite__Set_Ofinite])]) ).

fof(i_0_10984,plain,
    ! [X33966,X33967] :
      ( ~ class_Finite__Set_Ofinite(X33967)
      | ~ class_Finite__Set_Ofinite(X33966)
      | class_Finite__Set_Ofinite(tc_fun(X33967,X33966)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Finite__Set_Ofinite])]) ).

fof(i_0_10985,plain,
    ! [X19973] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X19973) = X19973,
    inference(variable_rename,[status(thm)],[fact_add__Pls]) ).

fof(i_0_10986,plain,
    ! [X31784,X31785] :
      ( ( hAPP(c_List_Orev(X31785),X31784) != c_List_Olist_ONil(X31785)
        | X31784 = c_List_Olist_ONil(X31785) )
      & ( X31784 != c_List_Olist_ONil(X31785)
        | hAPP(c_List_Orev(X31785),X31784) = c_List_Olist_ONil(X31785) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rev__is__Nil__conv])]) ).

fof(i_0_10987,plain,
    ! [X30289,X30290] :
      ( ( hAPP(c_List_Orotate1(X30290),X30289) != c_List_Olist_ONil(X30290)
        | X30289 = c_List_Olist_ONil(X30290) )
      & ( X30289 != c_List_Olist_ONil(X30290)
        | hAPP(c_List_Orotate1(X30290),X30289) = c_List_Olist_ONil(X30290) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_rotate1__is__Nil__conv])]) ).

fof(i_0_10988,plain,
    ! [X31786,X31787] :
      ( ( c_List_Olist_ONil(X31787) != hAPP(c_List_Orev(X31787),X31786)
        | X31786 = c_List_Olist_ONil(X31787) )
      & ( X31786 != c_List_Olist_ONil(X31787)
        | c_List_Olist_ONil(X31787) = hAPP(c_List_Orev(X31787),X31786) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Nil__is__rev__conv])]) ).

fof(i_0_10989,plain,
    ! [X19974] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X19974) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[fact_mult__Pls]) ).

fof(i_0_10990,plain,
    ! [X32882] : c_Relation_Otrans(tc_fun(X32882,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X32882)),
    inference(variable_rename,[status(thm)],[fact_trans__finite__psubset]) ).

fof(i_0_10991,plain,
    ! [X28082] : c_Wellfounded_Owf(tc_fun(X28082,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X28082)),
    inference(variable_rename,[status(thm)],[fact_wf__finite__psubset]) ).

fof(i_0_10992,plain,
    ! [X31452] : c_List_Otranspose(X31452,c_List_Olist_ONil(tc_List_Olist(X31452))) = c_List_Olist_ONil(tc_List_Olist(X31452)),
    inference(variable_rename,[status(thm)],[fact_transpose_Osimps_I1_J]) ).

cnf(i_0_10993,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_pred__Pls]) ).

cnf(i_0_10994,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_Bit0__Pls]) ).

cnf(i_0_10995,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_succ__Min]) ).

fof(i_0_10996,plain,
    ! [X30976,X30977] :
      ( ( hAPP(c_Code__Numeral_Onat__of,X30977) != hAPP(c_Code__Numeral_Onat__of,X30976)
        | X30977 = X30976 )
      & ( X30977 != X30976
        | hAPP(c_Code__Numeral_Onat__of,X30977) = hAPP(c_Code__Numeral_Onat__of,X30976) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_code__numeral_Onat__of__inject])]) ).

fof(i_0_10997,plain,
    ! [X30974,X30975] :
      ( ( hAPP(c_Code__Numeral_Onat__of,X30975) != hAPP(c_Code__Numeral_Onat__of,X30974)
        | X30975 = X30974 )
      & ( X30975 != X30974
        | hAPP(c_Code__Numeral_Onat__of,X30975) = hAPP(c_Code__Numeral_Onat__of,X30974) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Onat__of__inject])]) ).

fof(i_0_10998,plain,
    ! [X30919,X30920] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,X30920) != hAPP(c_Code__Numeral_Oof__nat,X30919)
        | X30920 = X30919 )
      & ( X30920 != X30919
        | hAPP(c_Code__Numeral_Oof__nat,X30920) = hAPP(c_Code__Numeral_Oof__nat,X30919) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Code__Numeral_Oof__nat__inject])]) ).

fof(i_0_10999,plain,
    ! [X23945,X23946] :
      ( ( hAPP(c_Int_ORep__Integ,X23946) != hAPP(c_Int_ORep__Integ,X23945)
        | X23946 = X23945 )
      & ( X23946 != X23945
        | hAPP(c_Int_ORep__Integ,X23946) = hAPP(c_Int_ORep__Integ,X23945) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Rep__Integ__inject])]) ).

fof(i_0_11000,plain,
    ! [X17200,X17201] :
      ( hAPP(c_Nat_OSuc,X17201) != hAPP(c_Nat_OSuc,X17200)
      | X17201 = X17200 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_Suc__inject])]) ).

fof(i_0_11001,plain,
    ! [X17198,X17199] :
      ( ( hAPP(c_Nat_OSuc,X17199) != hAPP(c_Nat_OSuc,X17198)
        | X17199 = X17198 )
      & ( X17199 != X17198
        | hAPP(c_Nat_OSuc,X17199) = hAPP(c_Nat_OSuc,X17198) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_nat_Oinject])]) ).

fof(i_0_11002,plain,
    ! [X25810,X25811] :
      ( ( c_Groups_Osgn__class_Osgn(X25811,X25810) != c_Groups_Ozero__class_Ozero(X25811)
        | X25810 = c_Groups_Ozero__class_Ozero(X25811)
        | ~ class_Rings_Olinordered__idom(X25811) )
      & ( X25810 != c_Groups_Ozero__class_Ozero(X25811)
        | c_Groups_Osgn__class_Osgn(X25811,X25810) = c_Groups_Ozero__class_Ozero(X25811)
        | ~ class_Rings_Olinordered__idom(X25811) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn__0__0])])]) ).

fof(i_0_11003,plain,
    ! [X32759] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X32759)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X32759)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_lazy__sequence_Osize_I3_J]) ).

fof(i_0_11004,plain,
    ! [X29880] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X29880)),c_List_Olist_ONil(X29880)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_list_Osize_I3_J]) ).

fof(i_0_11005,plain,
    ! [X33035,X33036] : c_Relation_Osym(X33036,c_Relation_OId__on(X33036,X33035)),
    inference(variable_rename,[status(thm)],[fact_sym__Id__on]) ).

fof(i_0_11006,plain,
    ! [X32969,X32970] : c_Relation_Oantisym(X32970,c_Relation_OId__on(X32970,X32969)),
    inference(variable_rename,[status(thm)],[fact_antisym__Id__on]) ).

fof(i_0_11007,plain,
    ! [X32890,X32891] : c_Relation_Otrans(X32891,c_Transitive__Closure_Ortrancl(X32891,X32890)),
    inference(variable_rename,[status(thm)],[fact_trans__rtrancl]) ).

fof(i_0_11008,plain,
    ! [X32888,X32889] : c_Relation_Otrans(X32889,c_Relation_OId__on(X32889,X32888)),
    inference(variable_rename,[status(thm)],[fact_trans__Id__on]) ).

fof(i_0_11009,plain,
    ! [X32099,X32100] : c_Wellfounded_Owf(X32100,c_List_Omeasures(X32100,X32099)),
    inference(variable_rename,[status(thm)],[fact_wf__measures]) ).

fof(i_0_11010,plain,
    ! [X21459] :
      ( ~ class_Rings_Osemiring__1(X21459)
      | ~ c_Int_Oiszero(X21459,c_Groups_Oone__class_Oone(X21459)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6062])]) ).

fof(i_0_11011,plain,
    ! [X31669,X31670] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X31670,X31669)),
    inference(variable_rename,[status(thm)],[fact_sorted__upto]) ).

fof(i_0_11012,plain,
    ! [X28372,X28373] : c_Hilbert__Choice_OEps(X28373,hAPP(c_fequal,X28372)) = X28372,
    inference(variable_rename,[status(thm)],[fact_some__sym__eq__trivial]) ).

fof(i_0_11013,plain,
    ! [X17784,X17785] : c_HOL_OThe(X17785,hAPP(c_fequal,X17784)) = X17784,
    inference(variable_rename,[status(thm)],[fact_the__sym__eq__trivial]) ).

fof(i_0_11014,plain,
    ! [X29877] :
      ( ~ class_Groups_Omonoid__add(X29877)
      | hAPP(c_List_Omonoid__add__class_Olistsum(X29877),c_List_Olist_ONil(X29877)) = c_Groups_Ozero__class_Ozero(X29877) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_listsum__simps_I1_J])]) ).

fof(i_0_11015,plain,
    ! [X25862] :
      ( ~ class_Groups_Oordered__ab__group__add__abs(X25862)
      | hAPP(c_Groups_Oabs__class_Oabs(X25862),c_Groups_Ozero__class_Ozero(X25862)) = c_Groups_Ozero__class_Ozero(X25862) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__zero])]) ).

fof(i_0_11016,plain,
    ! [X25855] :
      ( ~ class_Rings_Olinordered__idom(X25855)
      | hAPP(c_Groups_Oabs__class_Oabs(X25855),c_Groups_Oone__class_Oone(X25855)) = c_Groups_Oone__class_Oone(X25855) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_abs__one])]) ).

fof(i_0_11017,plain,
    ! [X26218] :
      ( ~ class_Lattices_Oboolean__algebra(X26218)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X26218),c_Orderings_Otop__class_Otop(X26218)) = c_Orderings_Obot__class_Obot(X26218) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__top__eq])]) ).

fof(i_0_11018,plain,
    ! [X21147] :
      ( ~ class_Groups_Ogroup__add(X21147)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X21147),c_Groups_Ozero__class_Ozero(X21147)) = c_Groups_Ozero__class_Ozero(X21147) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_minus__zero])]) ).

fof(i_0_11019,plain,
    ! [X26217] :
      ( ~ class_Lattices_Oboolean__algebra(X26217)
      | hAPP(c_Groups_Ouminus__class_Ouminus(X26217),c_Orderings_Obot__class_Obot(X26217)) = c_Orderings_Otop__class_Otop(X26217) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_compl__bot__eq])]) ).

fof(i_0_11020,plain,
    ! [X33948,X33949] :
      ( ~ class_Lattices_Obounded__lattice(X33949)
      | class_Lattices_Obounded__lattice(tc_fun(X33948,X33949)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice])]) ).

fof(i_0_11021,plain,
    ! [X33972,X33973] :
      ( ~ class_Orderings_Otop(X33973)
      | class_Orderings_Otop(tc_fun(X33972,X33973)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Otop])]) ).

fof(i_0_11022,plain,
    ! [X33952,X33953] :
      ( ~ class_Lattices_Obounded__lattice(X33953)
      | class_Lattices_Obounded__lattice__top(tc_fun(X33952,X33953)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__top])]) ).

fof(i_0_11023,plain,
    ! [X33958,X33959] :
      ( ~ class_Lattices_Olattice(X33959)
      | class_Lattices_Osemilattice__inf(tc_fun(X33958,X33959)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__inf])]) ).

fof(i_0_11024,plain,
    ! [X33960,X33961] :
      ( ~ class_Lattices_Odistrib__lattice(X33961)
      | class_Lattices_Odistrib__lattice(tc_fun(X33960,X33961)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Odistrib__lattice])]) ).

fof(i_0_11025,plain,
    ! [X33950,X33951] :
      ( ~ class_Complete__Lattice_Ocomplete__lattice(X33951)
      | class_Complete__Lattice_Ocomplete__lattice(tc_fun(X33950,X33951)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Complete__Lattice_Ocomplete__lattice])]) ).

fof(i_0_11026,plain,
    ! [X33954,X33955] :
      ( ~ class_Lattices_Obounded__lattice(X33955)
      | class_Lattices_Obounded__lattice__bot(tc_fun(X33954,X33955)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Obounded__lattice__bot])]) ).

fof(i_0_11027,plain,
    ! [X33968,X33969] :
      ( ~ class_Lattices_Olattice(X33969)
      | class_Lattices_Olattice(tc_fun(X33968,X33969)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Olattice])]) ).

fof(i_0_11028,plain,
    ! [X33956,X33957] :
      ( ~ class_Lattices_Olattice(X33957)
      | class_Lattices_Osemilattice__sup(tc_fun(X33956,X33957)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Osemilattice__sup])]) ).

fof(i_0_11029,plain,
    ! [X33962,X33963] :
      ( ~ class_Lattices_Oboolean__algebra(X33963)
      | class_Lattices_Oboolean__algebra(tc_fun(X33962,X33963)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra])]) ).

fof(i_0_11030,plain,
    ! [X33978,X33979] :
      ( ~ class_Groups_Ouminus(X33979)
      | class_Groups_Ouminus(tc_fun(X33978,X33979)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus])]) ).

fof(i_0_11031,plain,
    ! [X33980,X33981] :
      ( ~ class_Groups_Ominus(X33981)
      | class_Groups_Ominus(tc_fun(X33980,X33981)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus])]) ).

fof(i_0_11032,plain,
    ! [X33974,X33975] :
      ( ~ class_Orderings_Oord(X33975)
      | class_Orderings_Oord(tc_fun(X33974,X33975)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord])]) ).

fof(i_0_11033,plain,
    ! [X33970,X33971] :
      ( ~ class_Orderings_Oorder(X33971)
      | class_Orderings_Oorder(tc_fun(X33970,X33971)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder])]) ).

fof(i_0_11034,plain,
    ! [X33976,X33977] :
      ( ~ class_Orderings_Obot(X33977)
      | class_Orderings_Obot(tc_fun(X33976,X33977)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Obot])]) ).

fof(i_0_11035,plain,
    ! [X33964,X33965] :
      ( ~ class_Orderings_Opreorder(X33965)
      | class_Orderings_Opreorder(tc_fun(X33964,X33965)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder])]) ).

fof(i_0_11036,plain,
    ! [X33061,X33062] :
      ( ~ c_Equiv__Relations_Oequivp(X33062,X33061)
      | c_Equiv__Relations_Opart__equivp(X33062,X33061) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_equivp__implies__part__equivp])]) ).

fof(i_0_11037,plain,
    ! [X32953,X32954] :
      ( ( c_Predicate_Oreflp(X32954,X32953)
        | ~ c_Equiv__Relations_Oequivp(X32954,X32953) )
      & ( c_Predicate_Osymp(X32954,X32953)
        | ~ c_Equiv__Relations_Oequivp(X32954,X32953) )
      & ( c_Predicate_Otransp(X32954,X32953)
        | ~ c_Equiv__Relations_Oequivp(X32954,X32953) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_6063])])]) ).

fof(i_0_11038,plain,
    ! [X28283,X28284] :
      ( ~ c_Wellfounded_Owf(X28284,X28283)
      | c_Wellfounded_Oacyclic(X28284,X28283) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_wf__acyclic])]) ).

fof(i_0_11039,plain,
    ! [X21752] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X21752)),
    inference(variable_rename,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J]) ).

fof(i_0_11040,plain,
    ! [X33565] : c_Lazy__Sequence_Oflat(X33565,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X33565))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X33565),
    inference(variable_rename,[status(thm)],[fact__04]) ).

fof(i_0_11041,plain,
    ! [X30973] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X30973)) = X30973,
    inference(variable_rename,[status(thm)],[fact_nat__of__of__nat]) ).

fof(i_0_11042,plain,
    ! [X30972] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X30972)) = X30972,
    inference(variable_rename,[status(thm)],[fact_of__nat__nat__of]) ).

fof(i_0_11043,plain,
    ! [X30971] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X30971)) = X30971,
    inference(variable_rename,[status(thm)],[fact_nat__of__inverse]) ).

fof(i_0_11044,plain,
    ! [X24223] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X24223)) = X24223,
    inference(variable_rename,[status(thm)],[fact_Rep__Integ__inverse]) ).

fof(i_0_11045,plain,
    ! [X21457,X21458] :
      ( ( ~ c_Int_Oiszero(X21458,X21457)
        | X21457 = c_Groups_Ozero__class_Ozero(X21458)
        | ~ class_Rings_Osemiring__1(X21458) )
      & ( X21457 != c_Groups_Ozero__class_Ozero(X21458)
        | c_Int_Oiszero(X21458,X21457)
        | ~ class_Rings_Osemiring__1(X21458) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__def])])]) ).

fof(i_0_11046,plain,
    ! [X19994] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19994) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | X19994 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( X19994 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X19994) = 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_11047,plain,
    ! [X21617] :
      ( ~ class_Rings_Oring__1(X21617)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21617),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(X21617) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__0])]) ).

fof(i_0_11048,plain,
    ! [X21632] :
      ( ~ class_Rings_Oring__1(X21632)
      | hAPP(c_Int_Oring__1__class_Oof__int(X21632),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(X21632) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__int__1])]) ).

fof(i_0_11049,plain,
    ! [X20051] :
      ( ~ class_Rings_Osemiring__1(X20051)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20051),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X20051) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__0])]) ).

fof(i_0_11050,plain,
    ! [X20073] :
      ( ~ class_Rings_Osemiring__1(X20073)
      | hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20073),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(X20073) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_of__nat__1])]) ).

fof(i_0_11051,plain,
    ! [X21607] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X21607) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X21607),
    inference(variable_rename,[status(thm)],[fact_int__number__of__def]) ).

fof(i_0_11052,plain,
    ! [X31270,X31271] :
      ( ( c_List_Oremdups(X31271,X31270) != c_List_Olist_ONil(X31271)
        | X31270 = c_List_Olist_ONil(X31271) )
      & ( X31270 != c_List_Olist_ONil(X31271)
        | c_List_Oremdups(X31271,X31270) = c_List_Olist_ONil(X31271) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff])]) ).

fof(i_0_11053,plain,
    ! [X31274,X31275] :
      ( ( c_List_Olist_ONil(X31275) != c_List_Oremdups(X31275,X31274)
        | X31274 = c_List_Olist_ONil(X31275) )
      & ( X31274 != c_List_Olist_ONil(X31275)
        | c_List_Olist_ONil(X31275) = c_List_Oremdups(X31275,X31274) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff])]) ).

fof(i_0_11054,plain,
    ! [X34035] :
      ( hBOOL(X34035)
      | hBOOL(hAPP(c_fNot,X34035)) ),
    inference(variable_rename,[status(thm)],[i_0_6064]) ).

fof(i_0_11055,plain,
    ! [X25812] :
      ( ~ class_Groups_Osgn__if(X25812)
      | c_Groups_Osgn__class_Osgn(X25812,c_Groups_Ozero__class_Ozero(X25812)) = c_Groups_Ozero__class_Ozero(X25812) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sgn0])]) ).

fof(i_0_11056,plain,
    ! [X22699] :
      ( ~ class_Orderings_Oord(X22699)
      | c_Orderings_Oord__class_Omax(X22699) = c_Orderings_Oord_Omax(X22699,c_Orderings_Oord__class_Oless__eq(X22699)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_max__ord__max])]) ).

fof(i_0_11057,plain,
    ! [X21732] :
      ( ~ class_Orderings_Oord(X21732)
      | c_Orderings_Oord__class_Omin(X21732) = c_Orderings_Oord_Omin(X21732,c_Orderings_Oord__class_Oless__eq(X21732)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_min__ord__min])]) ).

fof(i_0_11058,plain,
    ! [X31788] : hAPP(c_List_Orev(X31788),c_List_Olist_ONil(X31788)) = c_List_Olist_ONil(X31788),
    inference(variable_rename,[status(thm)],[fact_rev_Osimps_I1_J]) ).

fof(i_0_11059,plain,
    ! [X30408] : hAPP(c_List_Otl(X30408),c_List_Olist_ONil(X30408)) = c_List_Olist_ONil(X30408),
    inference(variable_rename,[status(thm)],[fact_tl_Osimps_I1_J]) ).

fof(i_0_11060,plain,
    ! [X34003,X34004] : class_Nat_Osize(tc_prod(X34004,X34003)),
    inference(variable_rename,[status(thm)],[arity_prod__Nat_Osize]) ).

fof(i_0_11061,plain,
    ! [X33995,X33996] : class_Nat_Osize(tc_Nitpick_Opair__box(X33996,X33995)),
    inference(variable_rename,[status(thm)],[arity_Nitpick__Opair____box__Nat_Osize]) ).

fof(i_0_11062,plain,
    ! [X33990,X33991] : class_Nat_Osize(tc_sum(X33991,X33990)),
    inference(variable_rename,[status(thm)],[arity_sum__Nat_Osize]) ).

fof(i_0_11063,plain,
    ! [X20038] :
      ( ~ class_Int_Onumber__ring(X20038)
      | hAPP(c_Int_Onumber__class_Onumber__of(X20038),c_Int_OPls) = c_Groups_Ozero__class_Ozero(X20038) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_number__of__Pls])]) ).

fof(i_0_11064,plain,
    ! [X20039] :
      ( ~ class_Int_Onumber__ring(X20039)
      | c_Groups_Ozero__class_Ozero(X20039) = hAPP(c_Int_Onumber__class_Onumber__of(X20039),c_Int_OPls) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_semiring__norm_I112_J])]) ).

fof(i_0_11065,plain,
    ! [X31684] :
      ( ~ class_Orderings_Olinorder(X31684)
      | c_List_Olinorder__class_Osorted(X31684,c_List_Olist_ONil(X31684)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_Oequations_I1_J])]) ).

fof(i_0_11066,plain,
    ! [X31656] :
      ( ~ class_Orderings_Olinorder(X31656)
      | c_List_Olinorder__class_Osorted(X31656,c_List_Olist_ONil(X31656)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sorted_ONil])]) ).

fof(i_0_11067,plain,
    ! [X21456] :
      ( ~ class_Rings_Osemiring__1(X21456)
      | c_Int_Oiszero(X21456,c_Groups_Ozero__class_Ozero(X21456)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_iszero__0])]) ).

fof(i_0_11068,plain,
    ! [X32393,X32394] : hAPP(c_New__DSequence_Opos__empty(X32394),X32393) = c_Lazy__Sequence_Oempty(X32394),
    inference(variable_rename,[status(thm)],[fact_New__DSequence_Opos__empty__def]) ).

fof(i_0_11069,plain,
    ! [X31276] : c_List_Oremdups(X31276,c_List_Olist_ONil(X31276)) = c_List_Olist_ONil(X31276),
    inference(variable_rename,[status(thm)],[fact_remdups_Osimps_I1_J]) ).

fof(i_0_11070,plain,
    ! [X29836] : c_List_Obutlast(X29836,c_List_Olist_ONil(X29836)) = c_List_Olist_ONil(X29836),
    inference(variable_rename,[status(thm)],[fact_butlast_Osimps_I1_J]) ).

fof(i_0_11071,plain,
    ! [X18589] : hAPP(c_Nat_OSuc,X18589) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__neq__Zero]) ).

fof(i_0_11072,plain,
    ! [X18587] : hAPP(c_Nat_OSuc,X18587) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I3_J]) ).

fof(i_0_11073,plain,
    ! [X18586] : hAPP(c_Nat_OSuc,X18586) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[fact_Suc__not__Zero]) ).

fof(i_0_11074,plain,
    ! [X18588] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X18588),
    inference(variable_rename,[status(thm)],[fact_Zero__neq__Suc]) ).

fof(i_0_11075,plain,
    ! [X18585] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X18585),
    inference(variable_rename,[status(thm)],[fact_nat_Osimps_I2_J]) ).

fof(i_0_11076,plain,
    ! [X18584] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X18584),
    inference(variable_rename,[status(thm)],[fact_Zero__not__Suc]) ).

fof(i_0_11077,plain,
    ! [X25148] :
      ( ~ class_Lattices_Osemilattice__inf(X25148)
      | ~ class_Orderings_Olinorder(X25148)
      | c_Lattices_Osemilattice__inf__class_Oinf(X25148) = c_Orderings_Oord__class_Omin(X25148) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_inf__min])]) ).

fof(i_0_11078,plain,
    ! [X23158] :
      ( ~ class_Lattices_Osemilattice__sup(X23158)
      | ~ class_Orderings_Olinorder(X23158)
      | c_Lattices_Osemilattice__sup__class_Osup(X23158) = c_Orderings_Oord__class_Omax(X23158) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_sup__max])]) ).

fof(i_0_11079,plain,
    ! [X17197] : hAPP(c_Nat_OSuc,X17197) != X17197,
    inference(variable_rename,[status(thm)],[fact_Suc__n__not__n]) ).

fof(i_0_11080,plain,
    ! [X17196] : X17196 != hAPP(c_Nat_OSuc,X17196),
    inference(variable_rename,[status(thm)],[fact_n__not__Suc__n]) ).

fof(i_0_11081,plain,
    ! [X27806,X27807] : hAPP(c_Fun_Oid(X27807),X27806) = X27806,
    inference(variable_rename,[status(thm)],[fact_id__apply]) ).

fof(i_0_11082,plain,
    ! [X27804,X27805] : hAPP(c_Fun_Oid(X27805),X27804) = X27804,
    inference(variable_rename,[status(thm)],[fact_id__def]) ).

fof(i_0_11083,plain,
    ! [X27595,X27596] : hAPP(c_Set_OCollect(X27596),X27595) = X27595,
    inference(variable_rename,[status(thm)],[fact_Collect__def]) ).

fof(i_0_11084,plain,
    ! [X34006,X34007] : hAPP(c_COMBI(X34007),X34006) = X34006,
    inference(variable_rename,[status(thm)],[help_c__COMBI__1]) ).

fof(i_0_11085,plain,
    ! [X18431] :
      ( ~ class_Rings_Ozero__neq__one(X18431)
      | c_Groups_Oone__class_Oone(X18431) != c_Groups_Ozero__class_Ozero(X18431) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_one__neq__zero])]) ).

fof(i_0_11086,plain,
    ! [X18430] :
      ( ~ class_Rings_Ozero__neq__one(X18430)
      | c_Groups_Ozero__class_Ozero(X18430) != c_Groups_Oone__class_Oone(X18430) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_zero__neq__one])]) ).

fof(i_0_11087,plain,
    ! [X33234] : c_Quickcheck_Obeyond(X33234,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[fact_beyond__zero]) ).

fof(i_0_11088,plain,
    ! [X28111] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X28111)),
    inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than2]) ).

fof(i_0_11089,plain,
    ! [X28110] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X28110)),
    inference(variable_rename,[status(thm)],[fact_wf__int__ge__less__than]) ).

fof(i_0_11090,plain,
    ! [X19887] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X19887) = X19887,
    inference(variable_rename,[status(thm)],[fact_nat__size]) ).

fof(i_0_11091,plain,
    ! [X19685] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X19685) = X19685,
    inference(variable_rename,[status(thm)],[fact_number__of__is__id]) ).

fof(i_0_11092,plain,
    ! [X33984] :
      ( ~ class_Lazy__Sequence_Osmall__lazy(X33984)
      | class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X33984)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_List__Olist__Lazy__Sequence_Osmall__lazy])]) ).

fof(i_0_11093,plain,
    ! [X33993] :
      ( ~ class_Enum_Oenum(X33993)
      | class_Enum_Oenum(tc_Option_Ooption(X33993)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Enum_Oenum])]) ).

fof(i_0_11094,plain,
    ! [X33992] :
      ( ~ class_Finite__Set_Ofinite(X33992)
      | class_Finite__Set_Ofinite(tc_Option_Ooption(X33992)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[arity_Option__Ooption__Finite__Set_Ofinite])]) ).

fof(i_0_11095,plain,
    ! [X26698] : c_Equiv__Relations_Oequivp(X26698,c_fequal),
    inference(variable_rename,[status(thm)],[fact_identity__equivp]) ).

fof(i_0_11096,plain,
    ! [X34005] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X34005)),
    inference(variable_rename,[status(thm)],[arity_Lazy____Sequence__Olazy____sequence__Nat_Osize]) ).

fof(i_0_11097,plain,
    ! [X33985] : class_Nat_Osize(tc_List_Olist(X33985)),
    inference(variable_rename,[status(thm)],[arity_List__Olist__Nat_Osize]) ).

fof(i_0_11098,plain,
    ! [X33994] : class_Nat_Osize(tc_Option_Ooption(X33994)),
    inference(variable_rename,[status(thm)],[arity_Option__Ooption__Nat_Osize]) ).

fof(i_0_11099,plain,
    ~ hBOOL(c_fFalse),
    inference(fof_simplification,[status(thm)],[help_c__fFalse__1]) ).

cnf(i_0_11100,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,esk192_11(X3,X4,X5,X2,X1,X6,X7,X8,X9,X10,X11)),esk193_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_6065]),
    [final] ).

cnf(i_0_11101,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk193_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_6065]),
    [final] ).

cnf(i_0_11102,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk192_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_6065]),
    [final] ).

cnf(i_0_11103,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),esk546_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk547_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk548_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk549_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))
    | hBOOL(hAPP(hAPP(X3,X6),X5))
    | ~ hBOOL(hAPP(hAPP(X3,X8),X7))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6066]),
    [final] ).

cnf(i_0_11104,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),esk550_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk551_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk552_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk553_8(X3,X4,X5,X6,X7,X8,X2,X1)))),X4))
    | hBOOL(hAPP(hAPP(X3,X8),X7))
    | ~ hBOOL(hAPP(hAPP(X3,X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6067]),
    [final] ).

cnf(i_0_11105,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),esk552_8(X3,X4,X5,X6,X7,X8,X2,X1)),esk553_8(X3,X4,X5,X6,X7,X8,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4)))
    | hBOOL(hAPP(hAPP(X3,X8),X7))
    | ~ hBOOL(hAPP(hAPP(X3,X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X6),X5))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6067]),
    [final] ).

cnf(i_0_11106,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_6068,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11107,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_6072]),
    [final] ).

cnf(i_0_11108,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),esk546_8(X5,X6,X7,X8,X4,X3,X2,X1)),esk547_8(X5,X6,X7,X8,X4,X3,X2,X1)))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6)))
    | hBOOL(hAPP(hAPP(X5,X8),X7))
    | ~ hBOOL(hAPP(hAPP(X5,X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X8),X7))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6066]),
    [final] ).

cnf(i_0_11109,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_6073]),
    [final] ).

cnf(i_0_11110,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_6074]),
    [final] ).

cnf(i_0_11111,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_6075]),
    [final] ).

cnf(i_0_11112,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_6076]),
    [final] ).

cnf(i_0_11113,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_6077]),
    [final] ).

cnf(i_0_11114,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_6078]),
    [final] ).

cnf(i_0_11115,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk265_8(X3,X4,X5,X2,X1,X6,X7,X8)),esk266_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_6079]),
    [final] ).

cnf(i_0_11116,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),esk544_7(X3,X4,X5,X6,X7,X2,X1)),esk545_7(X3,X4,X5,X6,X7,X2,X1))),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3)))
    | hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X4))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6080]),
    [final] ).

cnf(i_0_11117,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_6081,c_0_6082]),
    [final] ).

cnf(i_0_11118,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_6083,c_0_6082]),
    [final] ).

cnf(i_0_11119,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,esk238_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_6084]),
    [final] ).

cnf(i_0_11120,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_6085]),
    [final] ).

cnf(i_0_11121,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_6086]),
    [final] ).

cnf(i_0_11122,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_6087]),
    [final] ).

cnf(i_0_11123,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),esk544_7(X5,X6,X7,X4,X3,X2,X1)),esk545_7(X5,X6,X7,X4,X3,X2,X1)))),X5))
    | hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4) = hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X1,X2),tc_prod(X1,X2))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X1,X2),tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X4)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X7),X6))),c_Transitive__Closure_Ortrancl(tc_prod(X1,X2),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6080]),
    [final] ).

cnf(i_0_11124,plain,
    ( hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(X1,esk548_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk549_8(X1,X2,X3,X4,X5,X6,X7,X8)))
    | ~ hBOOL(hAPP(hAPP(X1,X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6066]),
    [final] ).

cnf(i_0_11125,plain,
    ( hBOOL(hAPP(hAPP(X1,X6),X5))
    | ~ hBOOL(hAPP(hAPP(X1,esk550_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk551_8(X1,X2,X3,X4,X5,X6,X7,X8)))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6067]),
    [final] ).

cnf(i_0_11126,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,esk448_8(X4,X5,X6,X3,X2,X1,X7,X8))),X6) != hAPP(c_Fun_Ocomp(X2,X1,X2,X6),hAPP(X5,esk448_8(X4,X5,X6,X3,X2,X1,X7,X8))) ),
    inference(split_conjunct,[status(thm)],[i_0_6088]),
    [final] ).

cnf(i_0_11127,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_6089,c_0_6090]),c_0_6090]),c_0_6090]),c_0_6090]),c_0_6091]),c_0_6091]),
    [final] ).

cnf(i_0_11128,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_6092]),
    [final] ).

cnf(i_0_11129,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_6093]),
    [final] ).

cnf(i_0_11130,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_6094]),
    [final] ).

cnf(i_0_11131,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_6095,c_0_6096]),
    [final] ).

cnf(i_0_11132,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_6085]),
    [final] ).

cnf(i_0_11133,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_6086]),
    [final] ).

cnf(i_0_11134,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk190_7(X2,X3,X4,X5,X6,X7,X1)),esk191_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_6097]),
    [final] ).

cnf(i_0_11135,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),hAPP(X4,esk265_8(X5,X6,X4,X7,X8,X1,X3,X2))),hAPP(X6,esk266_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_6079]),
    [final] ).

cnf(i_0_11136,plain,
    ( hBOOL(hAPP(hAPP(X1,esk546_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk547_8(X1,X2,X3,X4,X5,X6,X7,X8)))
    | hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X6),X5))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6066]),
    [final] ).

cnf(i_0_11137,plain,
    ( hBOOL(hAPP(hAPP(X1,esk552_8(X1,X2,X3,X4,X5,X6,X7,X8)),esk553_8(X1,X2,X3,X4,X5,X6,X7,X8)))
    | hBOOL(hAPP(hAPP(X1,X6),X5))
    | ~ hBOOL(hAPP(hAPP(X1,X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(X8,X7),tc_prod(X8,X7))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(X8,X7),tc_prod(X8,X7)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X6),X5)),hAPP(hAPP(c_Product__Type_OPair(X8,X7),X4),X3))),c_Transitive__Closure_Ortrancl(tc_prod(X8,X7),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6067]),
    [final] ).

cnf(i_0_11138,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_6092]),
    [final] ).

cnf(i_0_11139,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_6093]),
    [final] ).

cnf(i_0_11140,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_6094]),
    [final] ).

cnf(i_0_11141,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_6098,c_0_6096]),
    [final] ).

cnf(i_0_11142,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_6099,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11143,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_6100]),
    [final] ).

cnf(i_0_11144,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,esk331_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,hAPP(X5,esk331_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_6101]),
    [final] ).

cnf(i_0_11145,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_6102,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11146,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_6104,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11147,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_6105]),
    [final] ).

cnf(i_0_11148,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk448_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_6088]),
    [final] ).

cnf(i_0_11149,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk238_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_6084]),
    [final] ).

cnf(i_0_11150,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk331_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_6101]),
    [final] ).

cnf(i_0_11151,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk125_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_6106]),
    [final] ).

cnf(i_0_11152,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk332_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_6107]),
    [final] ).

cnf(i_0_11153,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_6108]),
    [final] ).

cnf(i_0_11154,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X6,X5,X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(X2,esk498_7(X3,X2,X1,X4,X5,X6,X7)),esk499_7(X3,X2,X1,X4,X5,X6,X7))))
    | ~ hBOOL(hAPP(hAPP(X7,hAPP(c_Product__Type_Osnd(X6,X5),X4)),hAPP(c_Product__Type_Ofst(X6,X5),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6109]),
    [final] ).

cnf(i_0_11155,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_6110]),
    [final] ).

cnf(i_0_11156,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_6111]),
    [final] ).

cnf(i_0_11157,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_6112]),
    [final] ).

cnf(i_0_11158,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,esk125_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(hAPP(c_Fun_Ocomp(X6,X8,X7,X2),X5),esk125_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_6106]),
    [final] ).

cnf(i_0_11159,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,esk332_8(X2,X1,X3,X4,X5,X6,X7,X8)) != hAPP(X2,esk332_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_6107]),
    [final] ).

cnf(i_0_11160,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_6113]),
    [final] ).

cnf(i_0_11161,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_6114]),
    [final] ).

cnf(i_0_11162,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_6105]),
    [final] ).

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(X7,tc_fun(X1,tc_HOL_Obool)),X4),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk194_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_6115]),
    [final] ).

cnf(i_0_11164,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,esk495_7(X2,X3,X4,X5,X1,X6,X7)),X5),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6116]),
    [final] ).

cnf(i_0_11165,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,esk237_7(X2,X3,X1,X4,X5,X6,X7)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6117]),
    [final] ).

cnf(i_0_11166,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_6118]),
    [final] ).

cnf(i_0_11167,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_6119]),
    [final] ).

cnf(i_0_11168,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_6120]),
    [final] ).

cnf(i_0_11169,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_6121]),
    [final] ).

cnf(i_0_11170,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_6122]),
    [final] ).

cnf(i_0_11171,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_6123]),
    [final] ).

cnf(i_0_11172,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)),esk388_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_6124]),
    [final] ).

cnf(i_0_11173,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_6125]),
    [final] ).

cnf(i_0_11174,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_6126]),
    [final] ).

cnf(i_0_11175,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_6127]),
    [final] ).

cnf(i_0_11176,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk332_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_6107]),
    [final] ).

cnf(i_0_11177,plain,
    hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2),X3) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),hAPP(hAPP(c_COMBC(X1,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),X1),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat)),X1),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(X1))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),X1),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(X1),X3)),
    inference(split_conjunct,[status(thm)],[i_0_6128]),
    [final] ).

cnf(i_0_11178,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_6113]),
    [final] ).

cnf(i_0_11179,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),esk20_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk21_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_6129]),
    [final] ).

cnf(i_0_11180,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),esk20_7(X6,X7,X5,X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),esk21_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_6129]),
    [final] ).

cnf(i_0_11181,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,esk494_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_6130]),
    [final] ).

cnf(i_0_11182,plain,
    ( hBOOL(hAPP(hAPP(hAPP(X1,esk129_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_6131]),
    [final] ).

cnf(i_0_11183,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_6132]),
    [final] ).

cnf(i_0_11184,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_6133]),
    [final] ).

cnf(i_0_11185,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_6134,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11186,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_6135,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11187,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_6136,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11188,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_6124]),
    [final] ).

cnf(i_0_11189,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_6125]),
    [final] ).

cnf(i_0_11190,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_6126]),
    [final] ).

cnf(i_0_11191,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_6127]),
    [final] ).

cnf(i_0_11192,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_6137]),
    [final] ).

cnf(i_0_11193,plain,
    ( hBOOL(hAPP(hAPP(X1,esk499_7(X2,X3,X4,X5,X6,X7,X1)),esk498_7(X2,X3,X4,X5,X6,X7,X1)))
    | hBOOL(hAPP(X4,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X6,X2),X3),X5)))
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(c_Product__Type_Osnd(X7,X6),X5)),hAPP(c_Product__Type_Ofst(X7,X6),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6109]),
    [final] ).

cnf(i_0_11194,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_6138,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_11195,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_6140,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_11196,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),esk282_6(X5,X4,X6,X3,X2,X1))))) != hAPP(X5,esk282_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_6141]),
    [final] ).

cnf(i_0_11197,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_6142]),
    [final] ).

cnf(i_0_11198,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_6143]),
    [final] ).

cnf(i_0_11199,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_6144,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11200,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),esk280_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_6145]),
    [final] ).

cnf(i_0_11201,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_6146]),
    [final] ).

cnf(i_0_11202,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4),X1),X5) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(X3),X2),tc_prod(X3,X2),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),X2),c_List_Olist_ONil(X3)),X5),hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,tc_prod(tc_List_Olist(X3),X2)),hAPP(hAPP(c_COMBC(X3,tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2)),tc_fun(tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),X3),c_COMBB(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2),X2)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),tc_fun(tc_prod(tc_List_Olist(X3),X2),tc_prod(tc_List_Olist(X3),X2)),X3),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(X3),X2,tc_prod(tc_List_Olist(X3),X2))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(X3),tc_List_Olist(X3)),tc_fun(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2))),X3),hAPP(c_COMBB(tc_List_Olist(X3),tc_fun(X2,tc_prod(tc_List_Olist(X3),X2)),tc_List_Olist(X3)),c_Product__Type_OPair(tc_List_Olist(X3),X2))),c_List_Olist_OCons(X3))))),hAPP(c_Lazy__Sequence_Oanamorph(X2,X3,X4),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))),hAPP(X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6147]),
    [final] ).

cnf(i_0_11203,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,esk334_5(X3,X4,X5,X2,X1)))),hAPP(X2,esk334_5(X3,X4,X5,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6148]),
    [final] ).

cnf(i_0_11204,plain,
    c_Partial__Function_Ofun__lub(X1,X2,X3,X4,X5,X6) = hAPP(X4,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X3,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X3,X1),tc_HOL_Obool),tc_fun(tc_fun(X3,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X3,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X3,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X3,X1),tc_fun(tc_fun(X3,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X3,X1))),X5)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X3,X1),X1),tc_fun(tc_fun(X3,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X3,X1),X1),tc_fun(tc_fun(X3,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X3,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X3,X1),X3,X1),c_COMBI(tc_fun(X3,X1))),X6)))))),
    inference(split_conjunct,[status(thm)],[i_0_6149]),
    [final] ).

cnf(i_0_11205,plain,
    ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,X1),X3),X4) = c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6150]),
    [final] ).

cnf(i_0_11206,plain,
    ( hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,X1),X3),X4) = c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6151]),
    [final] ).

cnf(i_0_11207,plain,
    ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,X1),X3),X4) = c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6152]),
    [final] ).

cnf(i_0_11208,plain,
    ( hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,X1),X3),X4) = c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X2,X1))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X2,X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X2,X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X2,X1))),X3)))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(X2,X1),X1),tc_fun(tc_fun(X2,X1),tc_HOL_Obool)),X1),c_COMBB(X1,tc_HOL_Obool,tc_fun(X2,X1))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(X2,X1),X2,X1),c_COMBI(tc_fun(X2,X1))),X4))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6153]),
    [final] ).

cnf(i_0_11209,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk556_6(X2,X3,X4,X5,X6,X1)),esk557_6(X2,X3,X4,X5,X6,X1))),X6))
    | c_Equiv__Relations_Ocongruent2(X1,X5,X2,X6,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6154]),
    [final] ).

cnf(i_0_11210,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk558_6(X2,X3,X4,X1,X5,X6)),esk559_6(X2,X3,X4,X1,X5,X6))),X4))
    | c_Equiv__Relations_Ocongruent2(X6,X1,X2,X5,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6154]),
    [final] ).

cnf(i_0_11211,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk367_6(X3,X4,X1,X5,X2,X6)),esk368_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_6155]),
    [final] ).

cnf(i_0_11212,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk366_6(X3,X4,X2,X5,X6,X1)),esk367_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_6155]),
    [final] ).

cnf(i_0_11213,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_6156]),
    [final] ).

cnf(i_0_11214,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_6157]),
    [final] ).

cnf(i_0_11215,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,esk258_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_6158]),
    [final] ).

cnf(i_0_11216,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_6159,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11217,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_6160]),
    [final] ).

cnf(i_0_11218,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_6161]),
    [final] ).

cnf(i_0_11219,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_6162,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11220,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk276_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_6163]),
    [final] ).

cnf(i_0_11221,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk20_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_6129]),
    [final] ).

cnf(i_0_11222,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk20_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_6129]),
    [final] ).

cnf(i_0_11223,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_6164]),
    [final] ).

cnf(i_0_11224,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk494_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_6130]),
    [final] ).

cnf(i_0_11225,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk129_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_6131]),
    [final] ).

cnf(i_0_11226,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk495_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_6116]),
    [final] ).

cnf(i_0_11227,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk237_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_6117]),
    [final] ).

cnf(i_0_11228,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk194_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_6115]),
    [final] ).

cnf(i_0_11229,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk191_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_6097]),
    [final] ).

cnf(i_0_11230,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk190_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_6097]),
    [final] ).

cnf(i_0_11231,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk561_7(X2,X3,X4,X5,X6,X7,X1)),X4))
    | hAPP(hAPP(X5,X3),X4) = hAPP(hAPP(X5,X2),X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ c_Finite__Set_Ofolding__image(X8,X1,X7,X6,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6165]),
    [final] ).

cnf(i_0_11232,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk458_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_6166]),
    [final] ).

cnf(i_0_11233,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk461_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_6167]),
    [final] ).

cnf(i_0_11234,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk358_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),esk357_4(X1,X2,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk357_4(X1,X2,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6168]),
    [final] ).

cnf(i_0_11235,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk358_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),esk357_4(X2,X3,X4,X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X3,esk357_4(X2,X3,X4,X1))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6168]),
    [final] ).

cnf(i_0_11236,plain,
    ( hAPP(X1,esk358_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),esk357_4(X2,X1,X3,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk357_4(X2,X1,X3,X4))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6168]),
    [final] ).

cnf(i_0_11237,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X4),X5))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)))),X4)))))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6169]),
    [final] ).

cnf(i_0_11238,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk258_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_6158]),
    [final] ).

cnf(i_0_11239,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,tc_fun(X1,tc_HOL_Obool)),X4),X2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X6,tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk542_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk542_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_6170]),
    [final] ).

cnf(i_0_11240,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,esk317_6(X3,X2,X1,X4,X5,X6))),hAPP(X3,esk317_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_6171]),
    [final] ).

cnf(i_0_11241,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,esk311_6(X3,X2,X1,X4,X5,X6)),esk312_6(X3,X2,X1,X4,X5,X6)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6172]),
    [final] ).

cnf(i_0_11242,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_6173,c_0_6069]),c_0_6069]),c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11243,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_6174,c_0_6069]),c_0_6069]),c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11244,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6175]),
    [final] ).

cnf(i_0_11245,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6176]),
    [final] ).

cnf(i_0_11246,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6176]),
    [final] ).

cnf(i_0_11247,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6175]),
    [final] ).

cnf(i_0_11248,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_6177]),
    [final] ).

cnf(i_0_11249,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_6178]),
    [final] ).

cnf(i_0_11250,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk524_6(X3,X2,X1,X4,X5,X6))),hAPP(X2,esk525_6(X3,X2,X1,X4,X5,X6))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(X2,esk523_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_6179]),
    [final] ).

cnf(i_0_11251,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X2,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X4))))),
    inference(split_conjunct,[status(thm)],[i_0_6180]),
    [final] ).

cnf(i_0_11252,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X2,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)))),hAPP(hAPP(c_COMBC(tc_fun(X2,tc_HOL_Obool),tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X2,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_fun(X2,tc_HOL_Obool)),c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X4))))),
    inference(split_conjunct,[status(thm)],[i_0_6181]),
    [final] ).

cnf(i_0_11253,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk282_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_6141]),
    [final] ).

cnf(i_0_11254,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk280_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_6145]),
    [final] ).

cnf(i_0_11255,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_6182,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11256,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_6183,c_0_6184]),c_0_6184]),
    [final] ).

cnf(i_0_11257,plain,
    ( hAPP(hAPP(X4,X1),X3) = hAPP(hAPP(X4,X2),X3)
    | hAPP(X1,esk561_7(X2,X1,X3,X4,X5,X6,X7)) != hAPP(X2,esk561_7(X2,X1,X3,X4,X5,X6,X7))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X3))
    | ~ c_Finite__Set_Ofolding__image(X8,X7,X6,X5,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6165]),
    [final] ).

cnf(i_0_11258,plain,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk20_7(X3,X2,X4,X5,X1,X6,X7)),esk21_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_6129]),
    [final] ).

cnf(i_0_11259,plain,
    ( hAPP(hAPP(X1,X2),X3) = hAPP(hAPP(X1,esk20_7(X3,X2,X4,X5,X1,X6,X7)),esk21_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_6129]),
    [final] ).

cnf(i_0_11260,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk520_2(X2,X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_fun(X1,tc_HOL_Obool)),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBS(X1,X1,tc_HOL_Obool),X2),c_COMBI(X1))))),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),tc_fun(X1,tc_HOL_Obool)),c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X1)),c_fequal)),X2)))))
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6185]),
    [final] ).

cnf(i_0_11261,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_6186,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_11262,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_6188]),
    [final] ).

cnf(i_0_11263,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_6189]),
    [final] ).

cnf(i_0_11264,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),esk300_3(X2,X3,X1)),esk300_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))),esk299_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6190]),
    [final] ).

cnf(i_0_11265,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),X3),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)
    | hBOOL(hAPP(hAPP(c_member(X5),esk523_6(X3,X2,X1,X4,X5,X6)),X4))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(X2,esk524_6(X3,X2,X1,X4,X5,X6))),hAPP(X2,esk525_6(X3,X2,X1,X4,X5,X6))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6179]),
    [final] ).

cnf(i_0_11266,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_6191]),
    [final] ).

cnf(i_0_11267,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk300_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))),esk299_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6190]),
    [final] ).

cnf(i_0_11268,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_6192,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11269,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_6193,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11270,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_6194,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11271,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_6195]),
    [final] ).

cnf(i_0_11272,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(X2)),hAPP(hAPP(c_COMBB(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X1),hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X4)))),X3)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3),esk505_4(X3,X1,X4,X2)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6169]),
    [final] ).

cnf(i_0_11273,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_6196]),
    [final] ).

cnf(i_0_11274,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_6197]),
    [final] ).

cnf(i_0_11275,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_6198]),
    [final] ).

cnf(i_0_11276,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_6199]),
    [final] ).

cnf(i_0_11277,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_6200]),
    [final] ).

cnf(i_0_11278,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_6201]),
    [final] ).

cnf(i_0_11279,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk505_4(X2,X3,X4,X1)),X4))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_OCollect(X3),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X3),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X3),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),X2)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6169]),
    [final] ).

cnf(i_0_11280,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(X3,esk309_6(X4,X3,X5,X6,X2,X1)),esk310_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_6202]),
    [final] ).

cnf(i_0_11281,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_6203]),
    [final] ).

cnf(i_0_11282,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk525_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X3,esk523_6(X2,X3,X4,X5,X1,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6179]),
    [final] ).

cnf(i_0_11283,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk524_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(X3,esk523_6(X2,X3,X4,X5,X1,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6179]),
    [final] ).

cnf(i_0_11284,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))))),esk50_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_6204]),
    [final] ).

cnf(i_0_11285,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X2,X3,X4,X5),esk51_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_6205]),
    [final] ).

cnf(i_0_11286,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OlessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6176]),
    [final] ).

cnf(i_0_11287,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6175]),
    [final] ).

cnf(i_0_11288,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_6206]),
    [final] ).

cnf(i_0_11289,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_6207,c_0_6069]),c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11290,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_6208,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11291,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_6209,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11292,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_6210,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11293,plain,
    ( hAPP(X1,esk190_7(X2,X3,X1,X4,X5,X6,X7)) = hAPP(X1,esk191_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_6097]),
    [final] ).

cnf(i_0_11294,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,esk289_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_6211]),
    [final] ).

cnf(i_0_11295,plain,
    ( hBOOL(hAPP(X1,esk458_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_6166]),
    [final] ).

cnf(i_0_11296,plain,
    ( hBOOL(hAPP(X1,esk461_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_6167]),
    [final] ).

cnf(i_0_11297,plain,
    ( c_Equiv__Relations_Ocongruent2(X6,X4,X2,X5,X3,X1)
    | hAPP(hAPP(X1,esk556_6(X2,X1,X3,X4,X5,X6)),esk558_6(X2,X1,X3,X4,X5,X6)) != hAPP(hAPP(X1,esk557_6(X2,X1,X3,X4,X5,X6)),esk559_6(X2,X1,X3,X4,X5,X6)) ),
    inference(split_conjunct,[status(thm)],[i_0_6154]),
    [final] ).

cnf(i_0_11298,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,esk297_4(X3,X2,X1,X4)))),hAPP(X1,esk297_4(X3,X2,X1,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6212]),
    [final] ).

cnf(i_0_11299,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_6213]),
    [final] ).

cnf(i_0_11300,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_6214]),
    [final] ).

cnf(i_0_11301,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)))),esk423_3(X3,X2,X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6215,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_11302,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)))),esk422_3(X2,X3,X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6216,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_11303,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk525_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)
    | hBOOL(hAPP(hAPP(c_member(X1),esk523_6(X2,X3,X4,X5,X1,X6)),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6179]),
    [final] ).

cnf(i_0_11304,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk524_6(X2,X3,X4,X5,X1,X6)),X5))
    | hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X1,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),X6,X1),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X4,c_Groups_Otimes__class_Otimes(X6)),X2),c_Groups_Oone__class_Oone(X6))),X3)),c_Groups_Oone__class_Oone(X6)),X5)
    | hBOOL(hAPP(hAPP(c_member(X1),esk523_6(X2,X3,X4,X5,X1,X6)),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6179]),
    [final] ).

cnf(i_0_11305,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_6217]),
    [final] ).

cnf(i_0_11306,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_6190]),
    [final] ).

cnf(i_0_11307,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_6218,c_0_6219]),
    [final] ).

cnf(i_0_11308,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X3,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)
    | esk524_6(X1,X2,X3,X4,X5,X6) != esk525_6(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(X2,esk523_6(X1,X2,X3,X4,X5,X6))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6179]),
    [final] ).

cnf(i_0_11309,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_6220,c_0_6069]),c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11310,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_6221]),
    [final] ).

cnf(i_0_11311,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_6222,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11312,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,esk276_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_6163]),
    [final] ).

cnf(i_0_11313,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_6223,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11314,plain,
    ( hBOOL(hAPP(X1,esk297_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_6212]),
    [final] ).

cnf(i_0_11315,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_6224]),
    [final] ).

cnf(i_0_11316,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_6225,c_0_6219]),
    [final] ).

cnf(i_0_11317,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_6226,c_0_6219]),
    [final] ).

cnf(i_0_11318,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_6196]),
    [final] ).

cnf(i_0_11319,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_6227]),
    [final] ).

cnf(i_0_11320,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_6228]),
    [final] ).

cnf(i_0_11321,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_6229]),
    [final] ).

cnf(i_0_11322,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_6197]),
    [final] ).

cnf(i_0_11323,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_6230,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11324,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_6231,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11325,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_6232]),
    [final] ).

cnf(i_0_11326,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_6233]),
    [final] ).

cnf(i_0_11327,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_6199]),
    [final] ).

cnf(i_0_11328,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_6200]),
    [final] ).

cnf(i_0_11329,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)),esk303_4(X3,X4,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6234]),
    [final] ).

cnf(i_0_11330,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_6235]),
    [final] ).

cnf(i_0_11331,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,esk261_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_6236]),
    [final] ).

cnf(i_0_11332,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,esk260_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_6237]),
    [final] ).

cnf(i_0_11333,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_6238]),
    [final] ).

cnf(i_0_11334,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_6239]),
    [final] ).

cnf(i_0_11335,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_6239]),
    [final] ).

cnf(i_0_11336,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_6239]),
    [final] ).

cnf(i_0_11337,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_6239]),
    [final] ).

cnf(i_0_11338,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)),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_6240]),
    [final] ).

cnf(i_0_11339,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_6241,c_0_6069]),c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11340,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_6242]),
    [final] ).

cnf(i_0_11341,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_6243,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11342,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_6244,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11343,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_6245,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11344,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_6246,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11345,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_6247,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11346,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_6248]),
    [final] ).

cnf(i_0_11347,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_6249,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11348,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X3,tc_HOL_Obool)),X4),X2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X5,c_Groups_Otimes__class_Otimes(X6)),hAPP(hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),X6,X5),hAPP(hAPP(c_Finite__Set_Ofold__image(X6,X3,c_Groups_Otimes__class_Otimes(X6)),X1),c_Groups_Oone__class_Oone(X6))),X2)),c_Groups_Oone__class_Oone(X6)),X4)
    | hBOOL(hAPP(hAPP(c_member(X5),esk523_6(X1,X2,X3,X4,X5,X6)),X4))
    | esk524_6(X1,X2,X3,X4,X5,X6) != esk525_6(X1,X2,X3,X4,X5,X6)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X4))
    | ~ class_Groups_Ocomm__monoid__mult(X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6179]),
    [final] ).

cnf(i_0_11349,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_6250]),
    [final] ).

cnf(i_0_11350,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_6251]),
    [final] ).

cnf(i_0_11351,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,esk209_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_6252]),
    [final] ).

cnf(i_0_11352,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_6253]),
    [final] ).

cnf(i_0_11353,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_6254]),
    [final] ).

cnf(i_0_11354,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_6255]),
    [final] ).

cnf(i_0_11355,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_6253]),
    [final] ).

cnf(i_0_11356,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_6254]),
    [final] ).

cnf(i_0_11357,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_6255]),
    [final] ).

cnf(i_0_11358,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_6256]),
    [final] ).

cnf(i_0_11359,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_6257]),
    [final] ).

cnf(i_0_11360,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_6258]),
    [final] ).

cnf(i_0_11361,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_6259,c_0_6219]),
    [final] ).

cnf(i_0_11362,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_6260,c_0_6219]),
    [final] ).

cnf(i_0_11363,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_6261,c_0_6262]),c_0_6262]),c_0_6082]),c_0_6082]),
    [final] ).

cnf(i_0_11364,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_6263]),
    [final] ).

cnf(i_0_11365,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),esk281_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_6235]),
    [final] ).

cnf(i_0_11366,plain,
    ( X1 = hAPP(hAPP(X2,X3),esk51_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_6205]),
    [final] ).

cnf(i_0_11367,plain,
    ( X1 = hAPP(hAPP(X2,X3),esk50_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_6204]),
    [final] ).

cnf(i_0_11368,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk407_5(X5,X4,X3,X2,X1)),esk407_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_6264]),
    [final] ).

cnf(i_0_11369,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2) = hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,X1),c_HOL_OEx(tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),X1),hAPP(c_COMBS(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(X1,tc_HOL_Obool))),X2)))),c_member(X1)))),
    inference(split_conjunct,[status(thm)],[i_0_6265]),
    [final] ).

cnf(i_0_11370,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_6266]),
    [final] ).

cnf(i_0_11371,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk349_5(X2,X3,X4,X5,X1)),esk350_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_6267]),
    [final] ).

cnf(i_0_11372,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk348_5(X2,X3,X4,X5,X1)),esk347_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_6268]),
    [final] ).

cnf(i_0_11373,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_6269]),
    [final] ).

cnf(i_0_11374,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_6270,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11375,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_6271,c_0_6219]),
    [final] ).

cnf(i_0_11376,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_6272,c_0_6219]),
    [final] ).

cnf(i_0_11377,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk272_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),esk271_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk271_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6273]),
    [final] ).

cnf(i_0_11378,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk269_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),esk268_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X2,esk268_3(X1,X2,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6274]),
    [final] ).

cnf(i_0_11379,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)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk343_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_6275]),
    [final] ).

cnf(i_0_11380,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)),X4)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk343_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_6275]),
    [final] ).

cnf(i_0_11381,plain,
    ( hAPP(X1,esk272_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),esk271_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk271_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6273]),
    [final] ).

cnf(i_0_11382,plain,
    ( hAPP(X1,esk269_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),esk268_3(X2,X1,X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,esk268_3(X2,X1,X3))))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_6274]),
    [final] ).

cnf(i_0_11383,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_11384,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk261_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_6236]),
    [final] ).

cnf(i_0_11385,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk260_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_6237]),
    [final] ).

cnf(i_0_11386,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_6234]),
    [final] ).

cnf(i_0_11387,plain,
    ( hBOOL(hAPP(X1,esk281_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_6235]),
    [final] ).

cnf(i_0_11388,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_6276]),
    [final] ).

cnf(i_0_11389,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_6277]),
    [final] ).

cnf(i_0_11390,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6278]),
    [final] ).

cnf(i_0_11391,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6279]),
    [final] ).

cnf(i_0_11392,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_11393,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6281]),
    [final] ).

cnf(i_0_11394,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_6282]),
    [final] ).

cnf(i_0_11395,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,X3)),hAPP(X2,X4)))
    | ~ class_Orderings_Oorder(X1)
    | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,X1,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6283]),
    [final] ).

cnf(i_0_11396,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_6284,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11397,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_6285]),
    [final] ).

cnf(i_0_11398,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_6286]),
    [final] ).

cnf(i_0_11399,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_6287]),
    [final] ).

cnf(i_0_11400,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk542_6(X2,X3,X4,X5,X6,X1)),X5))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6170]),
    [final] ).

cnf(i_0_11401,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_6288,c_0_6289]),
    [final] ).

cnf(i_0_11402,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk196_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_6290]),
    [final] ).

cnf(i_0_11403,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk195_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_6290]),
    [final] ).

cnf(i_0_11404,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk317_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_6171]),
    [final] ).

cnf(i_0_11405,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_6291]),
    [final] ).

cnf(i_0_11406,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_6292,c_0_6082]),c_0_6082]),c_0_6082]),
    [final] ).

cnf(i_0_11407,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_6293,c_0_6262]),c_0_6262]),c_0_6262]),
    [final] ).

cnf(i_0_11408,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_6294]),
    [final] ).

cnf(i_0_11409,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk49_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_6295]),
    [final] ).

cnf(i_0_11410,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_6296,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11411,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_6297,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11412,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_6298]),
    [final] ).

cnf(i_0_11413,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk277_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_6299]),
    [final] ).

cnf(i_0_11414,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk209_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_6252]),
    [final] ).

cnf(i_0_11415,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,esk414_5(X3,X2,X4,X5,X1))),hAPP(X3,esk414_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_6300]),
    [final] ).

cnf(i_0_11416,plain,
    ( c_List_Olist__all2(X2,X5,X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk452_5(X1,X4,X5,X3,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk452_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_6301]),
    [final] ).

cnf(i_0_11417,plain,
    ( c_List_Olist__all2(X2,X5,X1,X3,X4)
    | ~ hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk417_5(X4,X3,X1,X5,X2))),hAPP(hAPP(c_List_Onth(X5),X4),esk417_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_6302]),
    [final] ).

cnf(i_0_11418,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,esk218_5(X3,X2,X4,X5,X1))),hAPP(X3,esk218_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_6303]),
    [final] ).

cnf(i_0_11419,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_6304]),
    [final] ).

cnf(i_0_11420,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk347_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_6268]),
    [final] ).

cnf(i_0_11421,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_6305,c_0_6219]),
    [final] ).

cnf(i_0_11422,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_6306,c_0_6219]),
    [final] ).

cnf(i_0_11423,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,esk14_5(X5,X4,X3,X2,X1)),esk15_5(X5,X4,X3,X2,X1))) != hAPP(hAPP(X2,hAPP(X4,esk14_5(X5,X4,X3,X2,X1))),hAPP(X4,esk15_5(X5,X4,X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6307]),
    [final] ).

cnf(i_0_11424,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),esk427_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_6308,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_11425,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),esk427_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_6309,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_11426,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),esk427_3(X3,X1,X2))) != X3 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6310,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_11427,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),esk427_3(X3,X1,X2))) != X3 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6311,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_11428,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_6312,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11429,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk94_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),esk93_3(X1,X2,X3)),esk94_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,esk93_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)))),esk94_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_6313,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11430,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_6314]),
    [final] ).

cnf(i_0_11431,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_6315]),
    [final] ).

cnf(i_0_11432,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_6314]),
    [final] ).

cnf(i_0_11433,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_6315]),
    [final] ).

cnf(i_0_11434,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_6316]),
    [final] ).

cnf(i_0_11435,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_6317]),
    [final] ).

cnf(i_0_11436,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_6318]),
    [final] ).

cnf(i_0_11437,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),esk380_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk380_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_6319]),
    [final] ).

cnf(i_0_11438,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk96_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk95_3(X1,X2,X3)),esk96_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,esk95_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)))),esk96_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_6320,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11439,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)),esk379_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_6321]),
    [final] ).

cnf(i_0_11440,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_6322,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11441,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk378_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_6321]),
    [final] ).

cnf(i_0_11442,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk352_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_6323]),
    [final] ).

cnf(i_0_11443,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk351_5(X2,X3,X4,X5,X1)),X4)),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_6324]),
    [final] ).

cnf(i_0_11444,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_6325,c_0_6090]),c_0_6090]),c_0_6091]),c_0_6091]),
    [final] ).

cnf(i_0_11445,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))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk345_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_6326]),
    [final] ).

cnf(i_0_11446,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))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk345_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_6326]),
    [final] ).

cnf(i_0_11447,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk353_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_6327]),
    [final] ).

cnf(i_0_11448,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_6328,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11449,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_6329,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11450,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)),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_6326]),
    [final] ).

cnf(i_0_11451,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)),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_6326]),
    [final] ).

cnf(i_0_11452,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_6330,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11453,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_6331,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11454,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_6332,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11455,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_6333,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11456,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_6334,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11457,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_6335,c_0_6219]),
    [final] ).

cnf(i_0_11458,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_6336,c_0_6219]),
    [final] ).

cnf(i_0_11459,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_6337,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11460,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_6338]),
    [final] ).

cnf(i_0_11461,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_6339,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11462,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_6340,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11463,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_6341,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11464,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_6342,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11465,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_6343,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11466,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_6344,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11467,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_6345,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11468,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_6346,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11469,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_6347,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11470,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_6348,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11471,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk215_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_6349]),
    [final] ).

cnf(i_0_11472,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk141_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_6350]),
    [final] ).

cnf(i_0_11473,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,esk195_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_6290]),
    [final] ).

cnf(i_0_11474,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,esk10_4(X4,X3,X2,X1)),esk11_4(X4,X3,X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk10_4(X4,X3,X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk11_4(X4,X3,X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6351]),
    [final] ).

cnf(i_0_11475,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_6352,c_0_6139]),
    [final] ).

cnf(i_0_11476,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_6353,c_0_6219]),
    [final] ).

cnf(i_0_11477,plain,
    hAPP(c_Relation_OImage(X1,X2,hAPP(c_Set_OCollect(tc_prod(X1,X2)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,tc_HOL_Obool),X3))),X4) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool,X2),c_HOL_OEx(X1)),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool),X2),hAPP(c_COMBS(X1,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X1),c_fconj),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X4)))),hAPP(c_COMBC(X1,X2,tc_HOL_Obool),X3)))),
    inference(split_conjunct,[status(thm)],[i_0_6354]),
    [final] ).

cnf(i_0_11478,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_6355,c_0_6069]),c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11479,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_6356]),
    [final] ).

cnf(i_0_11480,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,esk49_6(X2,X3,X1,X4,X5,X6)) != hAPP(X3,esk49_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_6295]),
    [final] ).

cnf(i_0_11481,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,esk277_6(X4,X3,X2,X1,X5,X6))) ),
    inference(split_conjunct,[status(thm)],[i_0_6299]),
    [final] ).

cnf(i_0_11482,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_6357]),
    [final] ).

cnf(i_0_11483,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_6358]),
    [final] ).

cnf(i_0_11484,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk309_6(X1,X4,X3,X2,X5,X6)),esk310_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_6202]),
    [final] ).

cnf(i_0_11485,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_6359]),
    [final] ).

cnf(i_0_11486,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk366_6(X4,X5,X6,X1,X3,X2)),esk368_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_6155]),
    [final] ).

cnf(i_0_11487,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_6360,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11488,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_6361,c_0_6082]),c_0_6082]),
    [final] ).

cnf(i_0_11489,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_6362,c_0_6262]),c_0_6262]),
    [final] ).

cnf(i_0_11490,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_6363,c_0_6096]),
    [final] ).

cnf(i_0_11491,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk311_6(X4,X5,X6,X3,X2,X1)),esk312_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_6172]),
    [final] ).

cnf(i_0_11492,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_6364,c_0_6262]),c_0_6082]),
    [final] ).

cnf(i_0_11493,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_6365,c_0_6262]),c_0_6082]),
    [final] ).

cnf(i_0_11494,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_6366]),
    [final] ).

cnf(i_0_11495,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_6367]),
    [final] ).

cnf(i_0_11496,plain,
    ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6278]),
    [final] ).

cnf(i_0_11497,plain,
    ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6368]),
    [final] ).

cnf(i_0_11498,plain,
    ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6279]),
    [final] ).

cnf(i_0_11499,plain,
    ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6369]),
    [final] ).

cnf(i_0_11500,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_11501,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6281]),
    [final] ).

cnf(i_0_11502,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6278]),
    [final] ).

cnf(i_0_11503,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6279]),
    [final] ).

cnf(i_0_11504,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6280]),
    [final] ).

cnf(i_0_11505,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6281]),
    [final] ).

cnf(i_0_11506,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_6286]),
    [final] ).

cnf(i_0_11507,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_6287]),
    [final] ).

cnf(i_0_11508,plain,
    ( c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6370]),
    [final] ).

cnf(i_0_11509,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_6371,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11510,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_6372]),
    [final] ).

cnf(i_0_11511,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_6373,c_0_6219]),
    [final] ).

cnf(i_0_11512,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_6374,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11513,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_6375,c_0_6219]),
    [final] ).

cnf(i_0_11514,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,esk136_5(X3,X2,X4,X5,X1))),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6376]),
    [final] ).

cnf(i_0_11515,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,esk188_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_6377]),
    [final] ).

cnf(i_0_11516,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_6378,c_0_6219]),
    [final] ).

cnf(i_0_11517,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_6379]),
    [final] ).

cnf(i_0_11518,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_6380]),
    [final] ).

cnf(i_0_11519,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,esk137_5(X3,X2,X4,X5,X1))),X3))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6381]),
    [final] ).

cnf(i_0_11520,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_6382,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11521,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_6383,c_0_6069]),c_0_6069]),c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11522,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_6384,c_0_6069]),c_0_6069]),c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11523,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),esk383_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk383_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_6385]),
    [final] ).

cnf(i_0_11524,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),esk383_4(X3,X4,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X4),esk383_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_6385]),
    [final] ).

cnf(i_0_11525,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_6386,c_0_6139]),
    [final] ).

cnf(i_0_11526,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_6387]),
    [final] ).

cnf(i_0_11527,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_6388]),
    [final] ).

cnf(i_0_11528,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_6389]),
    [final] ).

cnf(i_0_11529,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_6390]),
    [final] ).

cnf(i_0_11530,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_6391,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11531,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_6392]),
    [final] ).

cnf(i_0_11532,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_6393]),
    [final] ).

cnf(i_0_11533,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_6394]),
    [final] ).

cnf(i_0_11534,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_6395,c_0_6139]),
    [final] ).

cnf(i_0_11535,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_6396]),
    [final] ).

cnf(i_0_11536,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_6397,c_0_6096]),
    [final] ).

cnf(i_0_11537,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_6398]),
    [final] ).

cnf(i_0_11538,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_6399]),
    [final] ).

cnf(i_0_11539,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_6400]),
    [final] ).

cnf(i_0_11540,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk349_5(X3,X4,X5,X2,X1))),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_6267]),
    [final] ).

cnf(i_0_11541,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_6401]),
    [final] ).

cnf(i_0_11542,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_6402]),
    [final] ).

cnf(i_0_11543,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_6403,c_0_6219]),
    [final] ).

cnf(i_0_11544,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_6404,c_0_6219]),
    [final] ).

cnf(i_0_11545,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_6405]),
    [final] ).

cnf(i_0_11546,plain,
    ( hAPP(X1,esk195_6(X2,X3,X1,X4,X5,X6)) = hAPP(X1,esk196_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_6290]),
    [final] ).

cnf(i_0_11547,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),esk377_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_6406]),
    [final] ).

cnf(i_0_11548,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_6407,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11549,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_6408,c_0_6187]),
    [final] ).

cnf(i_0_11550,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk320_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_6409]),
    [final] ).

cnf(i_0_11551,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk376_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_6406]),
    [final] ).

cnf(i_0_11552,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_6410]),
    [final] ).

cnf(i_0_11553,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_6411]),
    [final] ).

cnf(i_0_11554,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_6412]),
    [final] ).

cnf(i_0_11555,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_6413]),
    [final] ).

cnf(i_0_11556,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk40_5(X3,X4,X5,X2,X1),esk41_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_6414]),
    [final] ).

cnf(i_0_11557,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X1,X1,X2,esk38_5(X3,X4,X5,X2,X1),esk39_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_6415]),
    [final] ).

cnf(i_0_11558,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),esk393_4(X3,X4,X2,X1))),esk392_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_6416]),
    [final] ).

cnf(i_0_11559,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_6417]),
    [final] ).

cnf(i_0_11560,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_6418]),
    [final] ).

cnf(i_0_11561,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_6419,c_0_6082]),c_0_6082]),
    [final] ).

cnf(i_0_11562,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_6420,c_0_6262]),c_0_6262]),
    [final] ).

cnf(i_0_11563,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk353_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_6327]),
    [final] ).

cnf(i_0_11564,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_6421,c_0_6090]),c_0_6091]),
    [final] ).

cnf(i_0_11565,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_6422,c_0_6082]),
    [final] ).

cnf(i_0_11566,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_6423,c_0_6262]),
    [final] ).

cnf(i_0_11567,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_6424]),
    [final] ).

cnf(i_0_11568,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_6425]),
    [final] ).

cnf(i_0_11569,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_6426,c_0_6082]),
    [final] ).

cnf(i_0_11570,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_6427,c_0_6262]),
    [final] ).

cnf(i_0_11571,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk40_5(X2,X3,X4,X5,X1)),esk41_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_6414]),
    [final] ).

cnf(i_0_11572,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk38_5(X2,X3,X4,X5,X1)),esk39_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_6415]),
    [final] ).

cnf(i_0_11573,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),esk375_4(X2,X3,X4,X1)),esk374_4(X2,X3,X4,X1))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6428]),
    [final] ).

cnf(i_0_11574,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),esk374_4(X2,X3,X4,X1)),esk375_4(X2,X3,X4,X1))),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6428]),
    [final] ).

cnf(i_0_11575,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk352_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_6323]),
    [final] ).

cnf(i_0_11576,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk351_5(X3,X4,X5,X2,X1))),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_6324]),
    [final] ).

cnf(i_0_11577,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_6429]),
    [final] ).

cnf(i_0_11578,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_6430]),
    [final] ).

cnf(i_0_11579,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))),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_6275]),
    [final] ).

cnf(i_0_11580,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))),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_6275]),
    [final] ).

cnf(i_0_11581,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_6431,c_0_6219]),
    [final] ).

cnf(i_0_11582,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_6432]),
    [final] ).

cnf(i_0_11583,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_6433,c_0_6219]),
    [final] ).

cnf(i_0_11584,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_6434,c_0_6219]),
    [final] ).

cnf(i_0_11585,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_6435]),
    [final] ).

cnf(i_0_11586,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_6436]),
    [final] ).

cnf(i_0_11587,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_6437]),
    [final] ).

cnf(i_0_11588,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_6438,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11589,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)
    | esk195_6(X1,X2,X3,X4,X5,X6) != esk196_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_6290]),
    [final] ).

cnf(i_0_11590,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_6439]),
    [final] ).

cnf(i_0_11591,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_6440,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11592,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_6441,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11593,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_6442,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11594,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_6443,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11595,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_6444,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11596,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_6445,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11597,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_6446,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11598,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_6447,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11599,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_6448,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11600,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(X2,esk234_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_6449]),
    [final] ).

cnf(i_0_11601,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk132_5(X2,X3,X4,X5,X1)),hAPP(X3,esk131_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_6450]),
    [final] ).

cnf(i_0_11602,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_6451,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11603,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_6452]),
    [final] ).

cnf(i_0_11604,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk264_5(X2,X3,X4,X1,X5)),hAPP(X2,esk263_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_6453]),
    [final] ).

cnf(i_0_11605,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_6454]),
    [final] ).

cnf(i_0_11606,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_6455]),
    [final] ).

cnf(i_0_11607,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_6372]),
    [final] ).

cnf(i_0_11608,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_6456]),
    [final] ).

cnf(i_0_11609,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_6457,c_0_6289]),c_0_6289]),
    [final] ).

cnf(i_0_11610,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_6458]),
    [final] ).

cnf(i_0_11611,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_6458]),
    [final] ).

cnf(i_0_11612,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),esk522_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_6459]),
    [final] ).

cnf(i_0_11613,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_6460]),
    [final] ).

cnf(i_0_11614,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_6461]),
    [final] ).

cnf(i_0_11615,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_6462]),
    [final] ).

cnf(i_0_11616,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_6462]),
    [final] ).

cnf(i_0_11617,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_6463]),
    [final] ).

cnf(i_0_11618,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_6464,c_0_6289]),
    [final] ).

cnf(i_0_11619,plain,
    ( hAPP(X2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk541_3(X3,X2,X1)),X4)) = hAPP(X2,esk541_3(X3,X2,X1))
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X3),c_Transitive__Closure_Ortrancl(X1,X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(X2,hAPP(c_Nat_OSuc,esk540_3(X3,X2,X1)))),hAPP(X2,esk540_3(X3,X2,X1)))),c_Transitive__Closure_Ortrancl(X1,X3))) ),
    inference(rw,[status(thm)],[i_0_6465,c_0_6103]),
    [final] ).

cnf(i_0_11620,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_6466]),
    [final] ).

cnf(i_0_11621,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_6467]),
    [final] ).

cnf(i_0_11622,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_6468]),
    [final] ).

cnf(i_0_11623,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_6469]),
    [final] ).

cnf(i_0_11624,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_6470,c_0_6139]),
    [final] ).

cnf(i_0_11625,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_6471]),
    [final] ).

cnf(i_0_11626,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_6472]),
    [final] ).

cnf(i_0_11627,plain,
    ( c_Fun_Obij__betw(X1,X2,esk532_6(X6,X5,X4,X3,X2,X1),X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
    | ~ c_Fun_Oinj__on(X2,X1,X6,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,X6),X5)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6473]),
    [final] ).

cnf(i_0_11628,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_6474]),
    [final] ).

cnf(i_0_11629,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_6475]),
    [final] ).

cnf(i_0_11630,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)),esk228_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),esk228_4(X2,X3,X4,X1)),X3))),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6476]),
    [final] ).

cnf(i_0_11631,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),esk321_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_6409]),
    [final] ).

cnf(i_0_11632,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),esk245_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_6477]),
    [final] ).

cnf(i_0_11633,plain,
    ( hBOOL(hAPP(hAPP(X1,esk287_4(X2,X3,X1,X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X4,X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6478]),
    [final] ).

cnf(i_0_11634,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,esk330_3(X3,X2,X1)))),hAPP(X3,esk330_3(X3,X2,X1)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6479]),
    [final] ).

cnf(i_0_11635,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,esk291_3(X2,X1,X3)))),hAPP(X3,esk291_3(X2,X1,X3)))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6480]),
    [final] ).

cnf(i_0_11636,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_6481]),
    [final] ).

cnf(i_0_11637,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_6482,c_0_6091]),
    [final] ).

cnf(i_0_11638,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_6483,c_0_6091]),
    [final] ).

cnf(i_0_11639,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_6484]),
    [final] ).

cnf(i_0_11640,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,esk189_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_6485]),
    [final] ).

cnf(i_0_11641,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,esk186_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_6486]),
    [final] ).

cnf(i_0_11642,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_6487]),
    [final] ).

cnf(i_0_11643,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_6488]),
    [final] ).

cnf(i_0_11644,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_6489]),
    [final] ).

cnf(i_0_11645,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_6490]),
    [final] ).

cnf(i_0_11646,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_6129]),
    [final] ).

cnf(i_0_11647,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_6474]),
    [final] ).

cnf(i_0_11648,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_6410]),
    [final] ).

cnf(i_0_11649,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_6491,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11650,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_6492]),
    [final] ).

cnf(i_0_11651,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,esk543_5(X3,X2,X1,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6493]),
    [final] ).

cnf(i_0_11652,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,esk232_5(X3,X4,X5,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6494]),
    [final] ).

cnf(i_0_11653,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,esk485_5(X3,X2,X1,X4,X5)),hAPP(X3,esk485_5(X3,X2,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6495]),
    [final] ).

cnf(i_0_11654,plain,
    ( c_Relation_Orefl__on(X1,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(X1,tc_HOL_Obool)),X4),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X5,tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X4),X3))
    | ~ c_Relation_Orefl__on(X1,hAPP(X2,esk535_5(X3,X2,X1,X4,X5)),hAPP(X3,esk535_5(X3,X2,X1,X4,X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_6496]),
    [final] ).

cnf(i_0_11655,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_6497]),
    [final] ).

cnf(i_0_11656,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_6498,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11657,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk287_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(X5,X6,X7,X1,X4),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6478]),
    [final] ).

cnf(i_0_11658,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,esk231_5(X3,X4,X5,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6499]),
    [final] ).

cnf(i_0_11659,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_6500]),
    [final] ).

cnf(i_0_11660,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_6474]),
    [final] ).

cnf(i_0_11661,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),X2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(X1,tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(X1,tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat),X1),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(X1),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(X1)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_6501]),
    [final] ).

cnf(i_0_11662,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_6502]),
    [final] ).

cnf(i_0_11663,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,esk236_5(X2,X1,X3,X4,X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6503]),
    [final] ).

cnf(i_0_11664,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_6504]),
    [final] ).

cnf(i_0_11665,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_6505]),
    [final] ).

cnf(i_0_11666,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,esk233_5(X3,X4,X5,X2,X1))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6506]),
    [final] ).

cnf(i_0_11667,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,esk455_5(X3,X2,X4,X5,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6507]),
    [final] ).

cnf(i_0_11668,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,esk198_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_6508]),
    [final] ).

cnf(i_0_11669,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_6509,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11670,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_6510]),
    [final] ).

cnf(i_0_11671,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_6511]),
    [final] ).

cnf(i_0_11672,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk456_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_6166]),
    [final] ).

cnf(i_0_11673,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk459_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_6167]),
    [final] ).

cnf(i_0_11674,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_6512,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11675,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk403_4(X2,X3,X4,X1)),esk404_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_6513]),
    [final] ).

cnf(i_0_11676,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_6514]),
    [final] ).

cnf(i_0_11677,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_6515]),
    [final] ).

cnf(i_0_11678,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_6516]),
    [final] ).

cnf(i_0_11679,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_6517]),
    [final] ).

cnf(i_0_11680,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_6474]),
    [final] ).

cnf(i_0_11681,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk320_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_6409]),
    [final] ).

cnf(i_0_11682,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_6502]),
    [final] ).

cnf(i_0_11683,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_11684,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_11685,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_6518]),
    [final] ).

cnf(i_0_11686,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_6519]),
    [final] ).

cnf(i_0_11687,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_6520]),
    [final] ).

cnf(i_0_11688,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_6521]),
    [final] ).

cnf(i_0_11689,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk204_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_6522]),
    [final] ).

cnf(i_0_11690,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_6523]),
    [final] ).

cnf(i_0_11691,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_6524]),
    [final] ).

cnf(i_0_11692,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_6525]),
    [final] ).

cnf(i_0_11693,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_6432]),
    [final] ).

cnf(i_0_11694,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_6526,c_0_6090]),c_0_6091]),
    [final] ).

cnf(i_0_11695,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_6527]),
    [final] ).

cnf(i_0_11696,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_6436]),
    [final] ).

cnf(i_0_11697,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_6528]),
    [final] ).

cnf(i_0_11698,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_6529]),
    [final] ).

cnf(i_0_11699,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_6530]),
    [final] ).

cnf(i_0_11700,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk203_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_6531]),
    [final] ).

cnf(i_0_11701,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_6532]),
    [final] ).

cnf(i_0_11702,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_6533]),
    [final] ).

cnf(i_0_11703,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_6534]),
    [final] ).

cnf(i_0_11704,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_6489]),
    [final] ).

cnf(i_0_11705,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_6490]),
    [final] ).

cnf(i_0_11706,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk369_4(X3,X4,X1,X2)),esk370_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_6535]),
    [final] ).

cnf(i_0_11707,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_6536]),
    [final] ).

cnf(i_0_11708,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_6537]),
    [final] ).

cnf(i_0_11709,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_6538]),
    [final] ).

cnf(i_0_11710,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_6539]),
    [final] ).

cnf(i_0_11711,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_6540]),
    [final] ).

cnf(i_0_11712,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),esk257_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_6541]),
    [final] ).

cnf(i_0_11713,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_6542]),
    [final] ).

cnf(i_0_11714,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_6543]),
    [final] ).

cnf(i_0_11715,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_6544]),
    [final] ).

cnf(i_0_11716,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_6545]),
    [final] ).

cnf(i_0_11717,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_6546]),
    [final] ).

cnf(i_0_11718,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_6547]),
    [final] ).

cnf(i_0_11719,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_6548]),
    [final] ).

cnf(i_0_11720,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_6549]),
    [final] ).

cnf(i_0_11721,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_6550]),
    [final] ).

cnf(i_0_11722,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_6551]),
    [final] ).

cnf(i_0_11723,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk554_4(X2,X3,X4,X1)),esk555_4(X2,X3,X4,X1))),X4))
    | c_Equiv__Relations_Ocongruent(X1,X2,X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6552]),
    [final] ).

cnf(i_0_11724,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),esk373_2(X1,X2)),hAPP(X2,esk373_2(X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6553]),
    [final] ).

cnf(i_0_11725,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_6540]),
    [final] ).

cnf(i_0_11726,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_6458]),
    [final] ).

cnf(i_0_11727,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_6554]),
    [final] ).

cnf(i_0_11728,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_6475]),
    [final] ).

cnf(i_0_11729,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk364_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_6555]),
    [final] ).

cnf(i_0_11730,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_6462]),
    [final] ).

cnf(i_0_11731,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)),esk235_3(X2,X3,X1))),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6556]),
    [final] ).

cnf(i_0_11732,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_6557]),
    [final] ).

cnf(i_0_11733,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_6558]),
    [final] ).

cnf(i_0_11734,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_6558]),
    [final] ).

cnf(i_0_11735,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_6460]),
    [final] ).

cnf(i_0_11736,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_6461]),
    [final] ).

cnf(i_0_11737,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk376_5(X3,X1,X4,X5,X2)),esk377_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_6406]),
    [final] ).

cnf(i_0_11738,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_6559]),
    [final] ).

cnf(i_0_11739,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk354_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_6560,c_0_6103]),
    [final] ).

cnf(i_0_11740,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk414_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_6300]),
    [final] ).

cnf(i_0_11741,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk355_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_6561,c_0_6103]),
    [final] ).

cnf(i_0_11742,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_6562]),
    [final] ).

cnf(i_0_11743,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_6563,c_0_6262]),
    [final] ).

cnf(i_0_11744,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_6564,c_0_6082]),
    [final] ).

cnf(i_0_11745,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_6474]),
    [final] ).

cnf(i_0_11746,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk418_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_6565]),
    [final] ).

cnf(i_0_11747,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),esk416_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_6566]),
    [final] ).

cnf(i_0_11748,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_6518]),
    [final] ).

cnf(i_0_11749,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_6519]),
    [final] ).

cnf(i_0_11750,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk189_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_6485]),
    [final] ).

cnf(i_0_11751,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk186_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_6486]),
    [final] ).

cnf(i_0_11752,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_6487]),
    [final] ).

cnf(i_0_11753,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_6488]),
    [final] ).

cnf(i_0_11754,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_6567]),
    [final] ).

cnf(i_0_11755,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk188_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_6377]),
    [final] ).

cnf(i_0_11756,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk136_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_6376]),
    [final] ).

cnf(i_0_11757,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_6568]),
    [final] ).

cnf(i_0_11758,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk208_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_6569]),
    [final] ).

cnf(i_0_11759,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk207_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_6570]),
    [final] ).

cnf(i_0_11760,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk206_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_6571]),
    [final] ).

cnf(i_0_11761,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk205_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_6572]),
    [final] ).

cnf(i_0_11762,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_6573]),
    [final] ).

cnf(i_0_11763,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_6474]),
    [final] ).

cnf(i_0_11764,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk378_5(X3,X4,X5,X1,X2)),esk379_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_6321]),
    [final] ).

cnf(i_0_11765,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_6574]),
    [final] ).

cnf(i_0_11766,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_6575,c_0_6184]),
    [final] ).

cnf(i_0_11767,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_6576]),
    [final] ).

cnf(i_0_11768,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_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_6301]),
    [final] ).

cnf(i_0_11769,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk417_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_6302]),
    [final] ).

cnf(i_0_11770,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_6574]),
    [final] ).

cnf(i_0_11771,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk6_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_6577]),
    [final] ).

cnf(i_0_11772,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_6578,c_0_6289]),c_0_6289]),
    [final] ).

cnf(i_0_11773,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(X3,esk133_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_6579]),
    [final] ).

cnf(i_0_11774,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_6580]),
    [final] ).

cnf(i_0_11775,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk131_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_6450]),
    [final] ).

cnf(i_0_11776,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_6581]),
    [final] ).

cnf(i_0_11777,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_6582]),
    [final] ).

cnf(i_0_11778,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk234_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_6449]),
    [final] ).

cnf(i_0_11779,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk133_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_6579]),
    [final] ).

cnf(i_0_11780,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk218_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_6303]),
    [final] ).

cnf(i_0_11781,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_6583,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11782,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk217_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_6584]),
    [final] ).

cnf(i_0_11783,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk216_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_6585]),
    [final] ).

cnf(i_0_11784,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk139_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_6586]),
    [final] ).

cnf(i_0_11785,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk126_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_6587]),
    [final] ).

cnf(i_0_11786,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)))
    | esk349_5(X1,X2,X3,X4,X5) != esk350_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_6267]),
    [final] ).

cnf(i_0_11787,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)))
    | esk348_5(X1,X2,X3,X4,X5) != esk347_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_6268]),
    [final] ).

cnf(i_0_11788,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_6588,c_0_6091]),
    [final] ).

cnf(i_0_11789,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_6589,c_0_6091]),
    [final] ).

cnf(i_0_11790,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk535_5(X2,X3,X4,X5,X1)),X5))
    | c_Relation_Orefl__on(X4,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X4,tc_HOL_Obool)),X5),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X5),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6496]),
    [final] ).

cnf(i_0_11791,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk485_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_6495]),
    [final] ).

cnf(i_0_11792,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk128_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_6590]),
    [final] ).

cnf(i_0_11793,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk522_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_6459]),
    [final] ).

cnf(i_0_11794,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_6591]),
    [final] ).

cnf(i_0_11795,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk130_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_6450]),
    [final] ).

cnf(i_0_11796,plain,
    ( hBOOL(hAPP(hAPP(X1,esk128_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_6590]),
    [final] ).

cnf(i_0_11797,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk263_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_6453]),
    [final] ).

cnf(i_0_11798,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk543_5(X2,X3,X4,X5,X1)),X5))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X4,tc_HOL_Obool)),X5),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6493]),
    [final] ).

cnf(i_0_11799,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk232_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_6494]),
    [final] ).

cnf(i_0_11800,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_6592]),
    [final] ).

cnf(i_0_11801,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_6593]),
    [final] ).

cnf(i_0_11802,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_6594]),
    [final] ).

cnf(i_0_11803,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_6595]),
    [final] ).

cnf(i_0_11804,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk215_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_6349]),
    [final] ).

cnf(i_0_11805,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk141_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_6350]),
    [final] ).

cnf(i_0_11806,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_6596]),
    [final] ).

cnf(i_0_11807,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_6597]),
    [final] ).

cnf(i_0_11808,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk137_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_6381]),
    [final] ).

cnf(i_0_11809,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk231_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_6499]),
    [final] ).

cnf(i_0_11810,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(X3,esk138_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_6598]),
    [final] ).

cnf(i_0_11811,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,esk364_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_6555]),
    [final] ).

cnf(i_0_11812,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_6502]),
    [final] ).

cnf(i_0_11813,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_6502]),
    [final] ).

cnf(i_0_11814,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk236_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_6503]),
    [final] ).

cnf(i_0_11815,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk138_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_6598]),
    [final] ).

cnf(i_0_11816,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_6599]),
    [final] ).

cnf(i_0_11817,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_6600,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11818,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_6601,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11819,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_6602,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11820,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk8_4(X1,X3,X4,X2)),esk9_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_6603]),
    [final] ).

cnf(i_0_11821,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,esk391_4(X2,X1,X3,X4))),hAPP(X2,esk391_4(X2,X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6604]),
    [final] ).

cnf(i_0_11822,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_6605]),
    [final] ).

cnf(i_0_11823,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_6606,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11824,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_6607,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11825,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_6608,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11826,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk436_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_6609]),
    [final] ).

cnf(i_0_11827,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_6610,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11828,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_6611,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11829,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk509_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_6612]),
    [final] ).

cnf(i_0_11830,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk241_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_6613]),
    [final] ).

cnf(i_0_11831,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_6614]),
    [final] ).

cnf(i_0_11832,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_6615]),
    [final] ).

cnf(i_0_11833,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_6616]),
    [final] ).

cnf(i_0_11834,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk233_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_6506]),
    [final] ).

cnf(i_0_11835,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk198_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_6508]),
    [final] ).

cnf(i_0_11836,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_6617,c_0_6289]),
    [final] ).

cnf(i_0_11837,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk455_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_6507]),
    [final] ).

cnf(i_0_11838,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_6618]),
    [final] ).

cnf(i_0_11839,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_6619]),
    [final] ).

cnf(i_0_11840,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_6620]),
    [final] ).

cnf(i_0_11841,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_6523]),
    [final] ).

cnf(i_0_11842,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_6524]),
    [final] ).

cnf(i_0_11843,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_6621]),
    [final] ).

cnf(i_0_11844,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,esk7_4(X3,X2,X4,X1))),hAPP(X3,esk7_4(X3,X2,X4,X1))))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6622]),
    [final] ).

cnf(i_0_11845,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_6623]),
    [final] ).

cnf(i_0_11846,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk413_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_6624]),
    [final] ).

cnf(i_0_11847,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_6478]),
    [final] ).

cnf(i_0_11848,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_6625]),
    [final] ).

cnf(i_0_11849,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_6626]),
    [final] ).

cnf(i_0_11850,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk456_5(X1,X3,X4,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X5),esk457_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_6166]),
    [final] ).

cnf(i_0_11851,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk459_5(X3,X4,X1,X5,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X4),esk460_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_6167]),
    [final] ).

cnf(i_0_11852,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_6627]),
    [final] ).

cnf(i_0_11853,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk402_5(X3,X4,X1,X5,X2)),X3)
    | hAPP(hAPP(c_List_Oappend(X2),esk401_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_6628]),
    [final] ).

cnf(i_0_11854,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_6629]),
    [final] ).

cnf(i_0_11855,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk28_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_6630]),
    [final] ).

cnf(i_0_11856,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_6631]),
    [final] ).

cnf(i_0_11857,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_6632]),
    [final] ).

cnf(i_0_11858,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_6633]),
    [final] ).

cnf(i_0_11859,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),esk418_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_6565]),
    [final] ).

cnf(i_0_11860,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),esk416_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_6566]),
    [final] ).

cnf(i_0_11861,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_6634]),
    [final] ).

cnf(i_0_11862,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_6635]),
    [final] ).

cnf(i_0_11863,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_6636]),
    [final] ).

cnf(i_0_11864,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_11865,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_11866,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_6637]),
    [final] ).

cnf(i_0_11867,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_6638]),
    [final] ).

cnf(i_0_11868,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_6618]),
    [final] ).

cnf(i_0_11869,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_6619]),
    [final] ).

cnf(i_0_11870,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_6639]),
    [final] ).

cnf(i_0_11871,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,esk210_3(X2,X3,X1))),hAPP(X3,esk210_3(X2,X3,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6640]),
    [final] ).

cnf(i_0_11872,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X1,esk30_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_6641]),
    [final] ).

cnf(i_0_11873,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk286_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_6642]),
    [final] ).

cnf(i_0_11874,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X1)),hAPP(hAPP(c_Product__Type_OPair(X3,X1),esk285_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_6643]),
    [final] ).

cnf(i_0_11875,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_6644]),
    [final] ).

cnf(i_0_11876,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_6645]),
    [final] ).

cnf(i_0_11877,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_6646]),
    [final] ).

cnf(i_0_11878,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_6647]),
    [final] ).

cnf(i_0_11879,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_6648]),
    [final] ).

cnf(i_0_11880,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_6649]),
    [final] ).

cnf(i_0_11881,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_6650]),
    [final] ).

cnf(i_0_11882,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_6651]),
    [final] ).

cnf(i_0_11883,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_6652]),
    [final] ).

cnf(i_0_11884,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_6653]),
    [final] ).

cnf(i_0_11885,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_6654]),
    [final] ).

cnf(i_0_11886,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_6655]),
    [final] ).

cnf(i_0_11887,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_6656]),
    [final] ).

cnf(i_0_11888,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_6657]),
    [final] ).

cnf(i_0_11889,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_6658]),
    [final] ).

cnf(i_0_11890,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_6659]),
    [final] ).

cnf(i_0_11891,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_6660]),
    [final] ).

cnf(i_0_11892,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_6661]),
    [final] ).

cnf(i_0_11893,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_6662]),
    [final] ).

cnf(i_0_11894,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_6663]),
    [final] ).

cnf(i_0_11895,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_6664]),
    [final] ).

cnf(i_0_11896,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_6665]),
    [final] ).

cnf(i_0_11897,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_6666]),
    [final] ).

cnf(i_0_11898,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_6667]),
    [final] ).

cnf(i_0_11899,plain,
    ( hBOOL(hAPP(X1,X6))
    | ~ hBOOL(hAPP(X1,esk132_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_6450]),
    [final] ).

cnf(i_0_11900,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_6385]),
    [final] ).

cnf(i_0_11901,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_6668,c_0_6103]),c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11902,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_6669]),
    [final] ).

cnf(i_0_11903,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_6670]),
    [final] ).

cnf(i_0_11904,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_6671]),
    [final] ).

cnf(i_0_11905,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_6672]),
    [final] ).

cnf(i_0_11906,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_6673]),
    [final] ).

cnf(i_0_11907,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_6674,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11908,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_6675,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11909,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_6676]),
    [final] ).

cnf(i_0_11910,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_6677]),
    [final] ).

cnf(i_0_11911,plain,
    ( c_Fun_Obij__betw(X1,X3,X5,X6,X8)
    | ~ c_Fun_Obij__betw(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6,X7)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X3,X5),X6)),X8))
    | ~ c_Fun_Obij__betw(X3,X2,X4,X8,X7) ),
    inference(split_conjunct,[status(thm)],[i_0_6678]),
    [final] ).

cnf(i_0_11912,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_6414]),
    [final] ).

cnf(i_0_11913,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_6645]),
    [final] ).

cnf(i_0_11914,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_6646]),
    [final] ).

cnf(i_0_11915,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_6647]),
    [final] ).

cnf(i_0_11916,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),esk270_3(X2,X3,X1)),esk270_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_6679]),
    [final] ).

cnf(i_0_11917,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),esk267_3(X2,X3,X1)),esk267_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_6680]),
    [final] ).

cnf(i_0_11918,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_6681]),
    [final] ).

cnf(i_0_11919,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_6682]),
    [final] ).

cnf(i_0_11920,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk355_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_6683,c_0_6103]),
    [final] ).

cnf(i_0_11921,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_6665]),
    [final] ).

cnf(i_0_11922,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_6666]),
    [final] ).

cnf(i_0_11923,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_6684]),
    [final] ).

cnf(i_0_11924,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk263_5(X4,X5,X1,X3,X2)),esk264_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_6453]),
    [final] ).

cnf(i_0_11925,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk354_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_6685,c_0_6103]),
    [final] ).

cnf(i_0_11926,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_6686]),
    [final] ).

cnf(i_0_11927,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_6687,c_0_6289]),c_0_6289]),
    [final] ).

cnf(i_0_11928,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk40_5(X4,X3,X2,X5,X1)),esk41_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_6414]),
    [final] ).

cnf(i_0_11929,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Set_Oinsert(X1),esk38_5(X4,X3,X2,X5,X1)),esk39_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_6415]),
    [final] ).

cnf(i_0_11930,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,esk204_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_6522]),
    [final] ).

cnf(i_0_11931,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_6660]),
    [final] ).

cnf(i_0_11932,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_6688,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11933,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_6689,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [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_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_6658]),
    [final] ).

cnf(i_0_11935,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,esk436_5(X2,X1,X3,X4,X5)))
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6609]),
    [final] ).

cnf(i_0_11936,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_6690]),
    [final] ).

cnf(i_0_11937,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_6691]),
    [final] ).

cnf(i_0_11938,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_6692]),
    [final] ).

cnf(i_0_11939,plain,
    ( hBOOL(hAPP(X1,X7))
    | ~ hBOOL(hAPP(X1,esk130_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_6450]),
    [final] ).

cnf(i_0_11940,plain,
    ( c_Fun_Obij__betw(X1,X6,hAPP(c_Fun_Ocomp(X2,X6,X1,X7),X3),X4,X8)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4)),X5))
    | ~ c_Fun_Obij__betw(X2,X6,X7,X5,X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6678]),
    [final] ).

cnf(i_0_11941,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_6693]),
    [final] ).

cnf(i_0_11942,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_6694]),
    [final] ).

cnf(i_0_11943,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_6695]),
    [final] ).

cnf(i_0_11944,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_6696]),
    [final] ).

cnf(i_0_11945,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_6697]),
    [final] ).

cnf(i_0_11946,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_6696]),
    [final] ).

cnf(i_0_11947,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_6697]),
    [final] ).

cnf(i_0_11948,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,esk223_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk223_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_6698]),
    [final] ).

cnf(i_0_11949,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,esk220_5(X2,X1,X3,X4,X5)) != hAPP(X2,esk220_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_6699]),
    [final] ).

cnf(i_0_11950,plain,
    ( hAPP(hAPP(c_List_Omap(X5,X4),X1),X3) = hAPP(hAPP(c_List_Omap(X5,X4),X2),X3)
    | hAPP(X1,esk413_5(X2,X3,X1,X4,X5)) != hAPP(X2,esk413_5(X2,X3,X1,X4,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6624]),
    [final] ).

cnf(i_0_11951,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_6700]),
    [final] ).

cnf(i_0_11952,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_6701]),
    [final] ).

cnf(i_0_11953,plain,
    ( hBOOL(hAPP(X1,esk364_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_6555]),
    [final] ).

cnf(i_0_11954,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_6702,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11955,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_6703,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_11956,plain,
    ( c_Hilbert__Choice_Oinv__into(X4,X2,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(X1,X2,X4,X3),X5)) = hAPP(c_Fun_Ocomp(X1,X4,X2,c_Hilbert__Choice_Oinv__into(X4,X1,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X5)),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X4,X1,X5,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6704]),
    [final] ).

cnf(i_0_11957,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_6705,c_0_6706]),c_0_6706]),c_0_6706]),
    [final] ).

cnf(i_0_11958,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_6707]),
    [final] ).

cnf(i_0_11959,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_6708]),
    [final] ).

cnf(i_0_11960,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_6709]),
    [final] ).

cnf(i_0_11961,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_6710]),
    [final] ).

cnf(i_0_11962,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_6711]),
    [final] ).

cnf(i_0_11963,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_6712]),
    [final] ).

cnf(i_0_11964,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_6713]),
    [final] ).

cnf(i_0_11965,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_6714]),
    [final] ).

cnf(i_0_11966,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_6715]),
    [final] ).

cnf(i_0_11967,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_6716]),
    [final] ).

cnf(i_0_11968,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_6717]),
    [final] ).

cnf(i_0_11969,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_6718]),
    [final] ).

cnf(i_0_11970,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_6658]),
    [final] ).

cnf(i_0_11971,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_6659]),
    [final] ).

cnf(i_0_11972,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_6660]),
    [final] ).

cnf(i_0_11973,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_6719]),
    [final] ).

cnf(i_0_11974,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk402_5(X3,X4,X5,X2,X1)) = X4
    | hAPP(hAPP(c_List_Oappend(X1),esk401_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_6628]),
    [final] ).

cnf(i_0_11975,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk402_5(X3,X4,X1,X5,X2)),X3)
    | X5 = hAPP(hAPP(c_List_Oappend(X2),X4),esk401_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_6628]),
    [final] ).

cnf(i_0_11976,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_6720]),
    [final] ).

cnf(i_0_11977,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_6721]),
    [final] ).

cnf(i_0_11978,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_6722]),
    [final] ).

cnf(i_0_11979,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_6723]),
    [final] ).

cnf(i_0_11980,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_6724]),
    [final] ).

cnf(i_0_11981,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_6725,c_0_6726]),c_0_6726]),
    [final] ).

cnf(i_0_11982,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_6727]),
    [final] ).

cnf(i_0_11983,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_6728,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11984,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_6729,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11985,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_6574]),
    [final] ).

cnf(i_0_11986,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_6591]),
    [final] ).

cnf(i_0_11987,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_6730]),
    [final] ).

cnf(i_0_11988,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_6731]),
    [final] ).

cnf(i_0_11989,plain,
    ( X1 = X2
    | c_Fun_Ofun__upd(X3,X4,c_Fun_Ofun__upd(X3,X4,X5,X1,X6),X2,X7) = c_Fun_Ofun__upd(X3,X4,c_Fun_Ofun__upd(X3,X4,X5,X2,X7),X1,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6732]),
    [final] ).

cnf(i_0_11990,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_6733]),
    [final] ).

cnf(i_0_11991,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_6734,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11992,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_6735,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_11993,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_6736]),
    [final] ).

cnf(i_0_11994,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_6737]),
    [final] ).

cnf(i_0_11995,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_6738]),
    [final] ).

cnf(i_0_11996,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_6737]),
    [final] ).

cnf(i_0_11997,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_6739]),
    [final] ).

cnf(i_0_11998,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_6740]),
    [final] ).

cnf(i_0_11999,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_6741]),
    [final] ).

cnf(i_0_12000,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X5)),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X3)),c_List_Olexord(X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X5)),c_List_Olexord(X1,X4)))
    | ~ c_Relation_Otrans(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6742]),
    [final] ).

cnf(i_0_12001,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_6743]),
    [final] ).

cnf(i_0_12002,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_6744]),
    [final] ).

cnf(i_0_12003,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,esk363_2(X2,X1)))
    | ~ hBOOL(hAPP(X2,esk363_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6745]),
    [final] ).

cnf(i_0_12004,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_6746,c_0_6184]),c_0_6184]),
    [final] ).

cnf(i_0_12005,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_6747]),
    [final] ).

cnf(i_0_12006,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_6748]),
    [final] ).

cnf(i_0_12007,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_6596]),
    [final] ).

cnf(i_0_12008,plain,
    ( hBOOL(hAPP(X1,esk363_2(X2,X1)))
    | hBOOL(hAPP(X2,esk363_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_6745]),
    [final] ).

cnf(i_0_12009,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk363_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_6745]),
    [final] ).

cnf(i_0_12010,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_6749]),
    [final] ).

cnf(i_0_12011,plain,
    ( hAPP(c_Set_Oimage(X1,X4,c_Fun_Ofun__upd(X1,X4,X5,X2,X6)),X3) = hAPP(hAPP(c_Set_Oinsert(X4),X6),hAPP(c_Set_Oimage(X1,X4,X5),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6750]),
    [final] ).

cnf(i_0_12012,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_6751]),
    [final] ).

cnf(i_0_12013,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_6751]),
    [final] ).

cnf(i_0_12014,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_6658]),
    [final] ).

cnf(i_0_12015,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_6659]),
    [final] ).

cnf(i_0_12016,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_6660]),
    [final] ).

cnf(i_0_12017,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_6752]),
    [final] ).

cnf(i_0_12018,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_6753]),
    [final] ).

cnf(i_0_12019,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk405_4(X3,X1,X4,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk404_4(X3,X1,X4,X2)),esk406_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_6513]),
    [final] ).

cnf(i_0_12020,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk405_4(X3,X4,X1,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),esk403_4(X3,X4,X1,X2)),esk406_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_6513]),
    [final] ).

cnf(i_0_12021,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_6754,c_0_6103]),
    [final] ).

cnf(i_0_12022,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_6755]),
    [final] ).

cnf(i_0_12023,plain,
    ( c_Fun_Obij__betw(X3,X2,X4,X8,X7)
    | ~ c_Fun_Obij__betw(X1,X2,hAPP(c_Fun_Ocomp(X3,X2,X1,X4),X5),X6,X7)
    | ~ c_Fun_Obij__betw(X1,X3,X5,X6,X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6756]),
    [final] ).

cnf(i_0_12024,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_6660]),
    [final] ).

cnf(i_0_12025,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_6757]),
    [final] ).

cnf(i_0_12026,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_6758]),
    [final] ).

cnf(i_0_12027,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)),esk13_3(X1,X3,X2)),hAPP(hAPP(c_Set_Oinsert(X2),esk12_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_6759]),
    [final] ).

cnf(i_0_12028,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_6658]),
    [final] ).

cnf(i_0_12029,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_6319]),
    [final] ).

cnf(i_0_12030,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_6760]),
    [final] ).

cnf(i_0_12031,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk299_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),esk300_3(X2,X3,X1)),esk300_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6190]),
    [final] ).

cnf(i_0_12032,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_6761,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12033,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_6762]),
    [final] ).

cnf(i_0_12034,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_6763]),
    [final] ).

cnf(i_0_12035,plain,
    ( c_Fun_Obij__betw(X1,X4,hAPP(c_Fun_Ocomp(X2,X4,X1,X5),X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X2,X4,X5,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6764]),
    [final] ).

cnf(i_0_12036,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_6765]),
    [final] ).

cnf(i_0_12037,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),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_6416]),
    [final] ).

cnf(i_0_12038,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_6766]),
    [final] ).

cnf(i_0_12039,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_6767,c_0_6184]),c_0_6184]),c_0_6184]),
    [final] ).

cnf(i_0_12040,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_6768]),
    [final] ).

cnf(i_0_12041,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_6769]),
    [final] ).

cnf(i_0_12042,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_6770]),
    [final] ).

cnf(i_0_12043,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_6771]),
    [final] ).

cnf(i_0_12044,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_6772]),
    [final] ).

cnf(i_0_12045,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_6773]),
    [final] ).

cnf(i_0_12046,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_6774]),
    [final] ).

cnf(i_0_12047,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk381_3(X2,X3,X1)),esk381_3(X2,X3,X1))),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X2),X2)),c_List_Olexord(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6775]),
    [final] ).

cnf(i_0_12048,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_6776]),
    [final] ).

cnf(i_0_12049,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_6129]),
    [final] ).

cnf(i_0_12050,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_6777,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6219]),c_0_6219]),
    [final] ).

cnf(i_0_12051,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_6778]),
    [final] ).

cnf(i_0_12052,plain,
    ( hAPP(X1,esk203_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_6531]),
    [final] ).

cnf(i_0_12053,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_6779]),
    [final] ).

cnf(i_0_12054,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk383_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_6385]),
    [final] ).

cnf(i_0_12055,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_6780]),
    [final] ).

cnf(i_0_12056,plain,
    ( c_Fun_Obij__betw(X1,X4,X7,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X5),X6))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X5),X6) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X4,X7,X2,X5)
    | ~ c_Fun_Obij__betw(X1,X4,X7,X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_6781]),
    [final] ).

cnf(i_0_12057,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_6782]),
    [final] ).

cnf(i_0_12058,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk491_4(X2,X3,X1,X4)),esk490_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)),esk488_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_6783]),
    [final] ).

cnf(i_0_12059,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk491_4(X2,X3,X1,X4)),esk489_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)),esk488_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_6783]),
    [final] ).

cnf(i_0_12060,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_6784]),
    [final] ).

cnf(i_0_12061,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_6785]),
    [final] ).

cnf(i_0_12062,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_6786]),
    [final] ).

cnf(i_0_12063,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_6787,c_0_6262]),
    [final] ).

cnf(i_0_12064,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_6788]),
    [final] ).

cnf(i_0_12065,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_6789]),
    [final] ).

cnf(i_0_12066,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_6790,c_0_6082]),
    [final] ).

cnf(i_0_12067,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_6791]),
    [final] ).

cnf(i_0_12068,plain,
    ( c_Fun_Obij__betw(X1,X6,hAPP(c_Fun_Ocomp(X2,X6,X1,X7),X3),X4,X8)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ c_Fun_Obij__betw(X2,X6,X7,X5,X8) ),
    inference(split_conjunct,[status(thm)],[i_0_6792]),
    [final] ).

cnf(i_0_12069,plain,
    ( c_Fun_Obij__betw(X6,X2,hAPP(c_Fun_Ocomp(X1,X2,X6,X3),X7),X8,X5)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ c_Fun_Obij__betw(X6,X1,X7,X8,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6756]),
    [final] ).

cnf(i_0_12070,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_6793,c_0_6082]),
    [final] ).

cnf(i_0_12071,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_6794]),
    [final] ).

cnf(i_0_12072,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_6774]),
    [final] ).

cnf(i_0_12073,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_6795]),
    [final] ).

cnf(i_0_12074,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_6796]),
    [final] ).

cnf(i_0_12075,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_6797]),
    [final] ).

cnf(i_0_12076,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_6798]),
    [final] ).

cnf(i_0_12077,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_6799]),
    [final] ).

cnf(i_0_12078,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_6774]),
    [final] ).

cnf(i_0_12079,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_6800]),
    [final] ).

cnf(i_0_12080,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_6801]),
    [final] ).

cnf(i_0_12081,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_6802]),
    [final] ).

cnf(i_0_12082,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_6660]),
    [final] ).

cnf(i_0_12083,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),esk329_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_6803]),
    [final] ).

cnf(i_0_12084,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),esk322_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_6804]),
    [final] ).

cnf(i_0_12085,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X5),X7))
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X6,X7)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X5),X7) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_6805]),
    [final] ).

cnf(i_0_12086,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk383_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_6385]),
    [final] ).

cnf(i_0_12087,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_6806,c_0_6096]),c_0_6103]),
    [final] ).

cnf(i_0_12088,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_6807]),
    [final] ).

cnf(i_0_12089,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_6658]),
    [final] ).

cnf(i_0_12090,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_6808]),
    [final] ).

cnf(i_0_12091,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_6659]),
    [final] ).

cnf(i_0_12092,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_6809,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12093,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_6810,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12094,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_6733]),
    [final] ).

cnf(i_0_12095,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_6811]),
    [final] ).

cnf(i_0_12096,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_6812]),
    [final] ).

cnf(i_0_12097,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_6813]),
    [final] ).

cnf(i_0_12098,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),esk341_3(X2,X3,X1)),esk340_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_12099,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),esk340_3(X2,X3,X1)),esk341_3(X2,X3,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_12100,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_6815]),
    [final] ).

cnf(i_0_12101,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_6816]),
    [final] ).

cnf(i_0_12102,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_6817]),
    [final] ).

cnf(i_0_12103,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_6818]),
    [final] ).

cnf(i_0_12104,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_6819]),
    [final] ).

cnf(i_0_12105,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_6820]),
    [final] ).

cnf(i_0_12106,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_6821]),
    [final] ).

cnf(i_0_12107,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_6774]),
    [final] ).

cnf(i_0_12108,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk8_4(X2,X3,X4,X1)),esk9_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_6603]),
    [final] ).

cnf(i_0_12109,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]),
    [final] ).

cnf(i_0_12110,plain,
    ( c_List_OtakeWhile(X1,X3,X2) = hAPP(c_List_Ofilter(X1,X3),X2)
    | hBOOL(hAPP(hAPP(c_member(X1),esk439_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_6822,c_0_6289]),
    [final] ).

cnf(i_0_12111,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk321_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_6409]),
    [final] ).

cnf(i_0_12112,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk245_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_6477]),
    [final] ).

cnf(i_0_12113,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_6823,c_0_6103]),
    [final] ).

cnf(i_0_12114,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_6824,c_0_6103]),
    [final] ).

cnf(i_0_12115,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_6825]),
    [final] ).

cnf(i_0_12116,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_6807]),
    [final] ).

cnf(i_0_12117,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]),
    [final] ).

cnf(i_0_12118,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]),
    [final] ).

cnf(i_0_12119,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_6826]),
    [final] ).

cnf(i_0_12120,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk509_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_6612]),
    [final] ).

cnf(i_0_12121,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),esk241_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_6613]),
    [final] ).

cnf(i_0_12122,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_6827,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12123,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_6828,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12124,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]),
    [final] ).

cnf(i_0_12125,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_6829,c_0_6103]),
    [final] ).

cnf(i_0_12126,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk491_4(X2,X3,X1,X4)),esk490_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),esk488_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_6783]),
    [final] ).

cnf(i_0_12127,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk491_4(X2,X3,X1,X4)),esk489_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),esk488_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_6783]),
    [final] ).

cnf(i_0_12128,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_6830]),
    [final] ).

cnf(i_0_12129,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_6831]),
    [final] ).

cnf(i_0_12130,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk294_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_6832]),
    [final] ).

cnf(i_0_12131,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X3)),hAPP(hAPP(c_Product__Type_OPair(X1,X3),X2),esk293_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_6833]),
    [final] ).

cnf(i_0_12132,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_6834]),
    [final] ).

cnf(i_0_12133,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_6835]),
    [final] ).

cnf(i_0_12134,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_6836]),
    [final] ).

cnf(i_0_12135,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_6837,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12136,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_6838]),
    [final] ).

cnf(i_0_12137,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]),
    [final] ).

cnf(i_0_12138,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6839]),
    [final] ).

cnf(i_0_12139,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]),
    [final] ).

cnf(i_0_12140,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_6839]),
    [final] ).

cnf(i_0_12141,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_6840]),
    [final] ).

cnf(i_0_12142,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_6841]),
    [final] ).

cnf(i_0_12143,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_6842]),
    [final] ).

cnf(i_0_12144,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk111_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),esk110_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_6843]),
    [final] ).

cnf(i_0_12145,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_6844,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12146,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk109_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(X1),esk108_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_6845]),
    [final] ).

cnf(i_0_12147,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_6846,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12148,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_6847,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12149,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_6848,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12150,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk490_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)),esk488_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_6783]),
    [final] ).

cnf(i_0_12151,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk489_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)),esk488_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_6783]),
    [final] ).

cnf(i_0_12152,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk345_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_6326]),
    [final] ).

cnf(i_0_12153,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk343_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_6275]),
    [final] ).

cnf(i_0_12154,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk345_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_6326]),
    [final] ).

cnf(i_0_12155,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk343_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_6275]),
    [final] ).

cnf(i_0_12156,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_6117]),
    [final] ).

cnf(i_0_12157,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_6849]),
    [final] ).

cnf(i_0_12158,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_6850]),
    [final] ).

cnf(i_0_12159,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_6851,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12160,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_6852,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12161,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_6409]),
    [final] ).

cnf(i_0_12162,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_6853,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12163,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_6854,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12164,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_6409]),
    [final] ).

cnf(i_0_12165,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_6409]),
    [final] ).

cnf(i_0_12166,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_6855,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12167,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_6856,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12168,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_6782]),
    [final] ).

cnf(i_0_12169,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_6857]),
    [final] ).

cnf(i_0_12170,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_6858,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12171,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X4)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]),
    [final] ).

cnf(i_0_12172,plain,
    ( hAPP(hAPP(c_List_Otake(X1),esk383_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk383_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_6385]),
    [final] ).

cnf(i_0_12173,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(hAPP(c_List_Omap(X1,X4),c_Fun_Ofun__upd(X1,X4,X5,X2,X6)),X3) = hAPP(hAPP(c_List_Omap(X1,X4),X5),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6859]),
    [final] ).

cnf(i_0_12174,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_6696]),
    [final] ).

cnf(i_0_12175,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_6697]),
    [final] ).

cnf(i_0_12176,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(c_Set_Oimage(X1,X4,c_Fun_Ofun__upd(X1,X4,X5,X2,X6)),X3) = hAPP(c_Set_Oimage(X1,X4,X5),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6750]),
    [final] ).

cnf(i_0_12177,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X3,X4),c_Fun_Ofun__upd(X3,X1,X5,X6,X7)) = c_Fun_Ofun__upd(X3,X2,hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6,hAPP(X4,X7)),
    inference(split_conjunct,[status(thm)],[i_0_6860]),
    [final] ).

cnf(i_0_12178,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),X2)),c_Wellfounded_Ofinite__psubset(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6831]),
    [final] ).

cnf(i_0_12179,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_6861,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12180,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_6862]),
    [final] ).

cnf(i_0_12181,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_6863]),
    [final] ).

cnf(i_0_12182,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk223_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_6698]),
    [final] ).

cnf(i_0_12183,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk220_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_6699]),
    [final] ).

cnf(i_0_12184,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_6864]),
    [final] ).

cnf(i_0_12185,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_6864]),
    [final] ).

cnf(i_0_12186,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk402_5(X3,X4,X5,X2,X1)) = X4
    | X2 = hAPP(hAPP(c_List_Oappend(X1),X4),esk401_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_6628]),
    [final] ).

cnf(i_0_12187,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk400_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_6865]),
    [final] ).

cnf(i_0_12188,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk399_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_6866]),
    [final] ).

cnf(i_0_12189,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk388_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_6124]),
    [final] ).

cnf(i_0_12190,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_6867]),
    [final] ).

cnf(i_0_12191,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),esk99_2(X2,X1)),esk100_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk99_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk100_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6868]),
    [final] ).

cnf(i_0_12192,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),esk79_2(X2,X1)),esk80_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk79_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk80_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6869]),
    [final] ).

cnf(i_0_12193,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,esk262_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6870]),
    [final] ).

cnf(i_0_12194,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_6871]),
    [final] ).

cnf(i_0_12195,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_6872]),
    [final] ).

cnf(i_0_12196,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_6873]),
    [final] ).

cnf(i_0_12197,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk399_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_6866]),
    [final] ).

cnf(i_0_12198,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk400_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_6865]),
    [final] ).

cnf(i_0_12199,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),esk44_2(X2,X1)),esk45_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk44_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk45_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6874]),
    [final] ).

cnf(i_0_12200,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_6875,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12201,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_6876]),
    [final] ).

cnf(i_0_12202,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_6727]),
    [final] ).

cnf(i_0_12203,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_6877]),
    [final] ).

cnf(i_0_12204,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_6878]),
    [final] ).

cnf(i_0_12205,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,esk208_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_6569]),
    [final] ).

cnf(i_0_12206,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,esk207_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_6570]),
    [final] ).

cnf(i_0_12207,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,esk206_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_6571]),
    [final] ).

cnf(i_0_12208,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,esk205_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_6572]),
    [final] ).

cnf(i_0_12209,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_6879]),
    [final] ).

cnf(i_0_12210,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_6880]),
    [final] ).

cnf(i_0_12211,plain,
    ( hAPP(hAPP(c_List_Otake(X1),esk383_4(X2,X3,X4,X1)),X4) = hAPP(hAPP(c_List_Otake(X1),esk383_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_6385]),
    [final] ).

cnf(i_0_12212,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_6881]),
    [final] ).

cnf(i_0_12213,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_6882]),
    [final] ).

cnf(i_0_12214,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_6883]),
    [final] ).

cnf(i_0_12215,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_6884]),
    [final] ).

cnf(i_0_12216,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6885]),
    [final] ).

cnf(i_0_12217,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5))),X6)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X5))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6886]),
    [final] ).

cnf(i_0_12218,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_6887]),
    [final] ).

cnf(i_0_12219,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk393_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_6416]),
    [final] ).

cnf(i_0_12220,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk358_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk357_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_6168]),
    [final] ).

cnf(i_0_12221,plain,
    c_Fun_Ofun__upd(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4,X6) = c_Fun_Ofun__upd(X1,X2,X3,X4,X6),
    inference(split_conjunct,[status(thm)],[i_0_6888]),
    [final] ).

cnf(i_0_12222,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_6889]),
    [final] ).

cnf(i_0_12223,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X1,X2,X3),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X1,X2,X3),X4)),X5))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6890]),
    [final] ).

cnf(i_0_12224,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_6891,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_12225,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_6892]),
    [final] ).

cnf(i_0_12226,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),esk108_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,esk109_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_6845]),
    [final] ).

cnf(i_0_12227,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk109_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,X5))
    | ~ hBOOL(hAPP(X2,esk108_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_6845]),
    [final] ).

cnf(i_0_12228,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_6893]),
    [final] ).

cnf(i_0_12229,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_6894]),
    [final] ).

cnf(i_0_12230,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_6895]),
    [final] ).

cnf(i_0_12231,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_6896]),
    [final] ).

cnf(i_0_12232,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_6897]),
    [final] ).

cnf(i_0_12233,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_6897]),
    [final] ).

cnf(i_0_12234,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),esk211_2(X2,X1)),esk212_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk211_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk212_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6898]),
    [final] ).

cnf(i_0_12235,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),esk116_2(X2,X1)),esk117_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk116_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk117_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6899]),
    [final] ).

cnf(i_0_12236,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),esk101_2(X2,X1)),esk102_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk101_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk102_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6900]),
    [final] ).

cnf(i_0_12237,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),esk81_2(X2,X1)),esk82_2(X2,X1))),hAPP(hAPP(c_Set_Oinsert(X1),esk81_2(X2,X1)),hAPP(hAPP(c_Set_Oinsert(X1),esk82_2(X2,X1)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))) ),
    inference(split_conjunct,[status(thm)],[i_0_6901]),
    [final] ).

cnf(i_0_12238,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_6902]),
    [final] ).

cnf(i_0_12239,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_6903]),
    [final] ).

cnf(i_0_12240,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk329_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_6803]),
    [final] ).

cnf(i_0_12241,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk322_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_6804]),
    [final] ).

cnf(i_0_12242,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_6904]),
    [final] ).

cnf(i_0_12243,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_6905]),
    [final] ).

cnf(i_0_12244,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_6906]),
    [final] ).

cnf(i_0_12245,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk490_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),esk488_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_6783]),
    [final] ).

cnf(i_0_12246,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk489_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),esk488_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_6783]),
    [final] ).

cnf(i_0_12247,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_6907,c_0_6103]),
    [final] ).

cnf(i_0_12248,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_6908]),
    [final] ).

cnf(i_0_12249,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_6909]),
    [final] ).

cnf(i_0_12250,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_6910]),
    [final] ).

cnf(i_0_12251,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_6911]),
    [final] ).

cnf(i_0_12252,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,esk217_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_6584]),
    [final] ).

cnf(i_0_12253,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,esk216_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_6585]),
    [final] ).

cnf(i_0_12254,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,esk139_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_6586]),
    [final] ).

cnf(i_0_12255,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,esk126_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_6587]),
    [final] ).

cnf(i_0_12256,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),hAPP(c_Set_Ovimage(X3,X1,X4),X2)),X5))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X3,X1,X4),X5)))
    | ~ c_Fun_Obij__betw(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6890]),
    [final] ).

cnf(i_0_12257,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_6912,c_0_6103]),
    [final] ).

cnf(i_0_12258,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_6913,c_0_6103]),
    [final] ).

cnf(i_0_12259,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_6914]),
    [final] ).

cnf(i_0_12260,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_6915]),
    [final] ).

cnf(i_0_12261,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_6566]),
    [final] ).

cnf(i_0_12262,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_6916]),
    [final] ).

cnf(i_0_12263,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_6916]),
    [final] ).

cnf(i_0_12264,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_6917]),
    [final] ).

cnf(i_0_12265,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_6918]),
    [final] ).

cnf(i_0_12266,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk423_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_6919,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_12267,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),esk422_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_6920,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_12268,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),esk441_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_6921]),
    [final] ).

cnf(i_0_12269,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_6922,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12270,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_6923,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12271,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_6924,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12272,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_6925,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12273,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_6760]),
    [final] ).

cnf(i_0_12274,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_6926]),
    [final] ).

cnf(i_0_12275,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_6927]),
    [final] ).

cnf(i_0_12276,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_6928]),
    [final] ).

cnf(i_0_12277,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_6929]),
    [final] ).

cnf(i_0_12278,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_6930,c_0_6706]),
    [final] ).

cnf(i_0_12279,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_6931]),
    [final] ).

cnf(i_0_12280,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_6932]),
    [final] ).

cnf(i_0_12281,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_6933]),
    [final] ).

cnf(i_0_12282,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_6934]),
    [final] ).

cnf(i_0_12283,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_6935]),
    [final] ).

cnf(i_0_12284,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,esk307_3(X3,X2,X1)))),c_Predicate_ORangeP(X1,X1,hAPP(X2,esk308_3(X3,X2,X1)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Wellfounded_OwfP(X1,hAPP(X2,esk306_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6936]),
    [final] ).

cnf(i_0_12285,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_6937]),
    [final] ).

cnf(i_0_12286,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_6938,c_0_6706]),c_0_6706]),
    [final] ).

cnf(i_0_12287,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_6359]),
    [final] ).

cnf(i_0_12288,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,esk436_5(X1,X2,X3,X4,X5)) != c_Groups_Ozero__class_Ozero(X5)
    | ~ class_Groups_Omonoid__add(X5) ),
    inference(split_conjunct,[status(thm)],[i_0_6609]),
    [final] ).

cnf(i_0_12289,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk397_3(X1,X2,X3)),c_Groups_Oone__class_Oone(tc_Int_Oint))),esk398_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk397_3(X1,X2,X3)),esk398_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_6939]),
    [final] ).

cnf(i_0_12290,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_6940]),
    [final] ).

cnf(i_0_12291,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_6941,c_0_6103]),
    [final] ).

cnf(i_0_12292,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_6942]),
    [final] ).

cnf(i_0_12293,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X2))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6943]),
    [final] ).

cnf(i_0_12294,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X5)),X2))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6944]),
    [final] ).

cnf(i_0_12295,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_6945]),
    [final] ).

cnf(i_0_12296,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_6934]),
    [final] ).

cnf(i_0_12297,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_6946,c_0_6289]),c_0_6289]),
    [final] ).

cnf(i_0_12298,plain,
    ( hBOOL(hAPP(X1,X5))
    | ~ hBOOL(hAPP(X1,esk109_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X1,esk108_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_6845]),
    [final] ).

cnf(i_0_12299,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_6947]),
    [final] ).

cnf(i_0_12300,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),esk451_4(X2,X3,X4,X1)),hAPP(c_List_Oset(X1),X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_6948,c_0_6289]),c_0_6289]),
    [final] ).

cnf(i_0_12301,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_6786]),
    [final] ).

cnf(i_0_12302,plain,
    ( X1 = hAPP(hAPP(c_List_Olist__update(X2,X3),esk393_4(X4,X1,X3,X2)),esk392_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_6416]),
    [final] ).

cnf(i_0_12303,plain,
    ( hBOOL(hAPP(X1,esk111_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(hAPP(c_member(X4),esk110_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_6843]),
    [final] ).

cnf(i_0_12304,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk111_4(X2,X3,X4,X1)),X3))
    | hBOOL(hAPP(X2,esk110_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_6843]),
    [final] ).

cnf(i_0_12305,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_6949,c_0_6706]),c_0_6706]),
    [final] ).

cnf(i_0_12306,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_6950]),
    [final] ).

cnf(i_0_12307,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_6951,c_0_6184]),
    [final] ).

cnf(i_0_12308,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk339_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_6952,c_0_6103]),
    [final] ).

cnf(i_0_12309,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)))
    | esk374_4(X1,X2,X3,X4) != esk375_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6428]),
    [final] ).

cnf(i_0_12310,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_6774]),
    [final] ).

cnf(i_0_12311,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_6953]),
    [final] ).

cnf(i_0_12312,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_6954]),
    [final] ).

cnf(i_0_12313,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_6955,c_0_6139]),c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_12314,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,esk305_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6956]),
    [final] ).

cnf(i_0_12315,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,esk127_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6957]),
    [final] ).

cnf(i_0_12316,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_6958]),
    [final] ).

cnf(i_0_12317,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_6940]),
    [final] ).

cnf(i_0_12318,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_6959]),
    [final] ).

cnf(i_0_12319,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_6960]),
    [final] ).

cnf(i_0_12320,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_6807]),
    [final] ).

cnf(i_0_12321,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X1,tc_HOL_Obool)),X5),X6)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_fun(X2,tc_HOL_Obool)),X5),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool),X4),c_Set_Oimage(X1,X2,X3)),X6))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6961]),
    [final] ).

cnf(i_0_12322,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_6962]),
    [final] ).

cnf(i_0_12323,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),hAPP(c_Relation_Oconverse(X1,X1),X2)),X2)),X2))
    | ~ c_Relation_Osym(X1,X2)
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6963]),
    [final] ).

cnf(i_0_12324,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_6964]),
    [final] ).

cnf(i_0_12325,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_6884]),
    [final] ).

cnf(i_0_12326,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_6965]),
    [final] ).

cnf(i_0_12327,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_6966]),
    [final] ).

cnf(i_0_12328,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_6967]),
    [final] ).

cnf(i_0_12329,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_6968]),
    [final] ).

cnf(i_0_12330,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk380_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_6319]),
    [final] ).

cnf(i_0_12331,plain,
    ( c_Fun_Obij__betw(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6969]),
    [final] ).

cnf(i_0_12332,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_6970]),
    [final] ).

cnf(i_0_12333,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_6971]),
    [final] ).

cnf(i_0_12334,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_6972]),
    [final] ).

cnf(i_0_12335,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Set_OCollect(X1),X4)) = hAPP(c_Set_OCollect(X2),hAPP(hAPP(c_COMBB(X1,tc_HOL_Obool,X2),X4),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_6973]),
    [final] ).

cnf(i_0_12336,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_6974]),
    [final] ).

cnf(i_0_12337,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_6975]),
    [final] ).

cnf(i_0_12338,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,esk371_4(X2,X3,X4,X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6976]),
    [final] ).

cnf(i_0_12339,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,esk372_4(X2,X3,X4,X1))))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6977]),
    [final] ).

cnf(i_0_12340,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk262_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_6870]),
    [final] ).

cnf(i_0_12341,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_6978]),
    [final] ).

cnf(i_0_12342,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_6979,c_0_6103]),
    [final] ).

cnf(i_0_12343,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_6980,c_0_6103]),
    [final] ).

cnf(i_0_12344,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_6981]),
    [final] ).

cnf(i_0_12345,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_6962]),
    [final] ).

cnf(i_0_12346,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_6982]),
    [final] ).

cnf(i_0_12347,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk358_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk357_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_6168]),
    [final] ).

cnf(i_0_12348,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk358_4(X1,X2,X3,X4)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk357_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_6168]),
    [final] ).

cnf(i_0_12349,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,esk259_4(X2,X1,X3,X4))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_6983]),
    [final] ).

cnf(i_0_12350,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_6984]),
    [final] ).

cnf(i_0_12351,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_6985]),
    [final] ).

cnf(i_0_12352,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk152_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_6986]),
    [final] ).

cnf(i_0_12353,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),esk440_4(X1,X3,X2,X4)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6987]),
    [final] ).

cnf(i_0_12354,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6)) = hAPP(hAPP(hAPP(X4,X5),X6),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X2,X3,X4,X6)),
    inference(split_conjunct,[status(thm)],[i_0_6988]),
    [final] ).

cnf(i_0_12355,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,esk510_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_6612]),
    [final] ).

cnf(i_0_12356,plain,
    ( c_Wellfounded_Omax__extp(X1,X4,X5,X3)
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(X4,esk508_4(X4,X3,X5,X1)),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6989]),
    [final] ).

cnf(i_0_12357,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,esk242_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_6613]),
    [final] ).

cnf(i_0_12358,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_6990]),
    [final] ).

cnf(i_0_12359,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_6991]),
    [final] ).

cnf(i_0_12360,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk539_4(X2,X3,X4,X1)),c_Quotient_ORespects(X1,X4)))
    | ~ hBOOL(hAPP(X3,X5))
    | ~ hBOOL(hAPP(X2,esk538_4(X2,X3,X4,X1)))
    | ~ c_Equiv__Relations_Oequivp(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6992]),
    [final] ).

cnf(i_0_12361,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),esk440_4(X4,X3,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_6987]),
    [final] ).

cnf(i_0_12362,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_6993,c_0_6103]),
    [final] ).

cnf(i_0_12363,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_6884]),
    [final] ).

cnf(i_0_12364,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)),esk488_4(X1,X2,X3,X4)),X2))
    | hAPP(X1,esk491_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_6783]),
    [final] ).

cnf(i_0_12365,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk419_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_6994]),
    [final] ).

cnf(i_0_12366,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(cn,[status(thm)],[i_0_6995]),
    [final] ).

cnf(i_0_12367,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X4,X1)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(cn,[status(thm)],[i_0_6996]),
    [final] ).

cnf(i_0_12368,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk328_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_6997]),
    [final] ).

cnf(i_0_12369,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk323_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_6998]),
    [final] ).

cnf(i_0_12370,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_6831]),
    [final] ).

cnf(i_0_12371,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)),esk488_4(X1,X2,X3,X4)),X2))
    | esk489_4(X1,X2,X3,X4) != esk490_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_6783]),
    [final] ).

cnf(i_0_12372,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_6999]),
    [final] ).

cnf(i_0_12373,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,X6,X7)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X6),X4))
    | hAPP(c_Set_Oimage(X1,X2,X3),X6) != X7 ),
    inference(split_conjunct,[status(thm)],[i_0_7000]),
    [final] ).

cnf(i_0_12374,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_7001]),
    [final] ).

cnf(i_0_12375,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_7001]),
    [final] ).

cnf(i_0_12376,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_7002]),
    [final] ).

cnf(i_0_12377,plain,
    ( X1 = hAPP(c_Set_Oimage(X2,X3,X4),esk6_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_6577]),
    [final] ).

cnf(i_0_12378,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,esk451_4(X2,X1,X3,X4))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_7003,c_0_6289]),c_0_6289]),
    [final] ).

cnf(i_0_12379,plain,
    ( X1 = hAPP(X2,esk225_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_7004]),
    [final] ).

cnf(i_0_12380,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_7005]),
    [final] ).

cnf(i_0_12381,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_7006]),
    [final] ).

cnf(i_0_12382,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(X2),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Finite__Set_Ocard(X2),esk564_4(X1,X3,X4,X2))))
    | ~ c_Equiv__Relations_Oequiv(X2,X4,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7007]),
    [final] ).

cnf(i_0_12383,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_7008,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12384,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_7009,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12385,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_7010]),
    [final] ).

cnf(i_0_12386,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_7011]),
    [final] ).

cnf(i_0_12387,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_7012]),
    [final] ).

cnf(i_0_12388,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk335_3(X3,X2,X1)),esk337_3(X3,X2,X1))),X3))
    | c_Relation_Osingle__valued(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7013]),
    [final] ).

cnf(i_0_12389,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),esk335_3(X3,X2,X1)),esk336_3(X3,X2,X1))),X3))
    | c_Relation_Osingle__valued(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7013]),
    [final] ).

cnf(i_0_12390,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),hAPP(esk292_2(X2,X1),hAPP(c_Nat_OSuc,X3))),hAPP(esk292_2(X2,X1),X3))),X2))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6480]),
    [final] ).

cnf(i_0_12391,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_7014]),
    [final] ).

cnf(i_0_12392,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_7015]),
    [final] ).

cnf(i_0_12393,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_7016]),
    [final] ).

cnf(i_0_12394,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_7017]),
    [final] ).

cnf(i_0_12395,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk150_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_7018]),
    [final] ).

cnf(i_0_12396,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_7019]),
    [final] ).

cnf(i_0_12397,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_Set_Oimage(X1,X2,X3),X4)))
    | c_Fun_Oinj__on(X1,X2,c_Fun_Ofun__upd(X1,X2,X3,X6,X5),X4)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7020]),
    [final] ).

cnf(i_0_12398,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_7021]),
    [final] ).

cnf(i_0_12399,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_7022]),
    [final] ).

cnf(i_0_12400,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),esk219_3(X2,X3,X1)),X3)),X2))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7023]),
    [final] ).

cnf(i_0_12401,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_7024]),
    [final] ).

cnf(i_0_12402,plain,
    ( hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7025]),
    [final] ).

cnf(i_0_12403,plain,
    ( hBOOL(hAPP(X3,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,tc_HOL_Obool,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_7026]),
    [final] ).

cnf(i_0_12404,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_7027]),
    [final] ).

cnf(i_0_12405,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_7028]),
    [final] ).

cnf(i_0_12406,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk153_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_6986]),
    [final] ).

cnf(i_0_12407,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_7029]),
    [final] ).

cnf(i_0_12408,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_7030]),
    [final] ).

cnf(i_0_12409,plain,
    ( c_Fun_Obij__betw(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3),X5,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7031]),
    [final] ).

cnf(i_0_12410,plain,
    ( c_Fun_Obij__betw(X2,X1,c_Fun_Othe__inv__into(X1,X2,X4,X3),X5,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7032]),
    [final] ).

cnf(i_0_12411,plain,
    ( hAPP(c_Hilbert__Choice_Oinv__into(X2,X1,X5,c_Hilbert__Choice_Oinv__into(X1,X2,X4,X3)),X6) = hAPP(X3,X6)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7033]),
    [final] ).

cnf(i_0_12412,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_6131]),
    [final] ).

cnf(i_0_12413,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_7034]),
    [final] ).

cnf(i_0_12414,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X3)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6839]),
    [final] ).

cnf(i_0_12415,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_7035]),
    [final] ).

cnf(i_0_12416,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_7011]),
    [final] ).

cnf(i_0_12417,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_7012]),
    [final] ).

cnf(i_0_12418,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_7036]),
    [final] ).

cnf(i_0_12419,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_6842]),
    [final] ).

cnf(i_0_12420,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_6842]),
    [final] ).

cnf(i_0_12421,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_7037]),
    [final] ).

cnf(i_0_12422,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_7038]),
    [final] ).

cnf(i_0_12423,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_7039]),
    [final] ).

cnf(i_0_12424,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_7040]),
    [final] ).

cnf(i_0_12425,plain,
    ( hAPP(c_Set_Ovimage(X1,X2,X3),X4) = hAPP(c_Set_Oimage(X2,X1,c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)),X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7041]),
    [final] ).

cnf(i_0_12426,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_7042]),
    [final] ).

cnf(i_0_12427,plain,
    ( hAPP(c_Set_Oimage(X2,X1,esk29_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_6641]),
    [final] ).

cnf(i_0_12428,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_5492]),
    [final] ).

cnf(i_0_12429,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_7043]),
    [final] ).

cnf(i_0_12430,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_7044]),
    [final] ).

cnf(i_0_12431,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_7045]),
    [final] ).

cnf(i_0_12432,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_6880]),
    [final] ).

cnf(i_0_12433,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk445_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),esk446_2(X2,X1))),hAPP(c_List_Oset(X1),esk447_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_7046,c_0_6139]),
    [final] ).

cnf(i_0_12434,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_6830]),
    [final] ).

cnf(i_0_12435,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_7047]),
    [final] ).

cnf(i_0_12436,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_7048]),
    [final] ).

cnf(i_0_12437,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6885]),
    [final] ).

cnf(i_0_12438,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X5),X6))),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X6))
    | ~ class_Rings_Ocomm__ring(X1)
    | ~ class_Rings_Odvd(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6886]),
    [final] ).

cnf(i_0_12439,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_7049]),
    [final] ).

cnf(i_0_12440,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_7050]),
    [final] ).

cnf(i_0_12441,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_7051]),
    [final] ).

cnf(i_0_12442,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_7049]),
    [final] ).

cnf(i_0_12443,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),esk328_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_6997]),
    [final] ).

cnf(i_0_12444,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),esk323_4(X3,X2,X4,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_6998]),
    [final] ).

cnf(i_0_12445,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_7052,c_0_6726]),
    [final] ).

cnf(i_0_12446,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk151_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_7018]),
    [final] ).

cnf(i_0_12447,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_7053,c_0_6103]),
    [final] ).

cnf(i_0_12448,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_7054]),
    [final] ).

cnf(i_0_12449,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_7055]),
    [final] ).

cnf(i_0_12450,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_7055]),
    [final] ).

cnf(i_0_12451,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_7056]),
    [final] ).

cnf(i_0_12452,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_7057]),
    [final] ).

cnf(i_0_12453,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_7058]),
    [final] ).

cnf(i_0_12454,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_7014]),
    [final] ).

cnf(i_0_12455,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_7015]),
    [final] ).

cnf(i_0_12456,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_7059]),
    [final] ).

cnf(i_0_12457,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_7060,c_0_6706]),c_0_6706]),
    [final] ).

cnf(i_0_12458,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_7061]),
    [final] ).

cnf(i_0_12459,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_7062]),
    [final] ).

cnf(i_0_12460,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_7063]),
    [final] ).

cnf(i_0_12461,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_7064]),
    [final] ).

cnf(i_0_12462,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_7065]),
    [final] ).

cnf(i_0_12463,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_7066,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_12464,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_7067]),
    [final] ).

cnf(i_0_12465,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_7013]),
    [final] ).

cnf(i_0_12466,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_7068]),
    [final] ).

cnf(i_0_12467,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_7069]),
    [final] ).

cnf(i_0_12468,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),esk359_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_7070]),
    [final] ).

cnf(i_0_12469,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_7071,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12470,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_7072,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12471,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_7073,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12472,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_7074,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12473,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_6839]),
    [final] ).

cnf(i_0_12474,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk270_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_6679]),
    [final] ).

cnf(i_0_12475,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk267_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_6680]),
    [final] ).

cnf(i_0_12476,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_7051]),
    [final] ).

cnf(i_0_12477,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_7075,c_0_7076]),
    [final] ).

cnf(i_0_12478,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_7077,c_0_6184]),c_0_6184]),
    [final] ).

cnf(i_0_12479,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_6376]),
    [final] ).

cnf(i_0_12480,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_7078]),
    [final] ).

cnf(i_0_12481,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_7079]),
    [final] ).

cnf(i_0_12482,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_12483,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_7080]),
    [final] ).

cnf(i_0_12484,plain,
    ( X3 = X4
    | ~ c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7081]),
    [final] ).

cnf(i_0_12485,plain,
    ( X3 = X4
    | ~ c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7082]),
    [final] ).

cnf(i_0_12486,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_7083]),
    [final] ).

cnf(i_0_12487,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_7084]),
    [final] ).

cnf(i_0_12488,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_7085]),
    [final] ).

cnf(i_0_12489,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_7086]),
    [final] ).

cnf(i_0_12490,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_7087]),
    [final] ).

cnf(i_0_12491,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_7088]),
    [final] ).

cnf(i_0_12492,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_7089]),
    [final] ).

cnf(i_0_12493,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_7090]),
    [final] ).

cnf(i_0_12494,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_7091,c_0_6103]),
    [final] ).

cnf(i_0_12495,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_7092]),
    [final] ).

cnf(i_0_12496,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_7093,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6219]),c_0_6219]),
    [final] ).

cnf(i_0_12497,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_7094]),
    [final] ).

cnf(i_0_12498,plain,
    ( hAPP(X1,esk358_4(X2,X1,X3,X4)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk357_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_6168]),
    [final] ).

cnf(i_0_12499,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_7095]),
    [final] ).

cnf(i_0_12500,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_7087]),
    [final] ).

cnf(i_0_12501,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_7054]),
    [final] ).

cnf(i_0_12502,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk539_4(X2,X3,X4,X1)),c_Quotient_ORespects(X1,X4)))
    | hBOOL(hAPP(X3,esk538_4(X2,X3,X4,X1)))
    | ~ hBOOL(hAPP(X3,X5))
    | ~ c_Equiv__Relations_Oequivp(X1,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6992]),
    [final] ).

cnf(i_0_12503,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_7096]),
    [final] ).

cnf(i_0_12504,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_6894]),
    [final] ).

cnf(i_0_12505,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),esk446_2(X2,X1))),hAPP(c_List_Oset(X1),esk447_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),esk445_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7097,c_0_6139]),
    [final] ).

cnf(i_0_12506,plain,
    ( hBOOL(hAPP(hAPP(X1,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk97_3(X1,X2,X3))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),esk98_3(X1,X2,X3))))
    | hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk98_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_7098]),
    [final] ).

cnf(i_0_12507,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk164_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_7099]),
    [final] ).

cnf(i_0_12508,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_7100]),
    [final] ).

cnf(i_0_12509,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_7101]),
    [final] ).

cnf(i_0_12510,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_7101]),
    [final] ).

cnf(i_0_12511,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)))))
    | esk225_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_7004]),
    [final] ).

cnf(i_0_12512,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_7096]),
    [final] ).

cnf(i_0_12513,plain,
    ( X2 = hAPP(hAPP(c_List_Olist_OCons(X1),esk409_3(X3,X2,X1)),esk410_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_7102]),
    [final] ).

cnf(i_0_12514,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_7103]),
    [final] ).

cnf(i_0_12515,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_7104]),
    [final] ).

cnf(i_0_12516,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_7105]),
    [final] ).

cnf(i_0_12517,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_7106]),
    [final] ).

cnf(i_0_12518,plain,
    ( hBOOL(hAPP(X1,esk111_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(X1,esk110_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_6843]),
    [final] ).

cnf(i_0_12519,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,esk491_4(X1,X2,X3,X4)) != c_Groups_Ozero__class_Ozero(X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk488_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_6783]),
    [final] ).

cnf(i_0_12520,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_7107]),
    [final] ).

cnf(i_0_12521,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk445_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk447_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_7108,c_0_6139]),
    [final] ).

cnf(i_0_12522,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk445_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2)))
    | hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk446_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_7109,c_0_6139]),
    [final] ).

cnf(i_0_12523,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_7110]),
    [final] ).

cnf(i_0_12524,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)
    | esk489_4(X1,X2,X3,X4) != esk490_4(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),esk488_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_6783]),
    [final] ).

cnf(i_0_12525,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk483_3(X1,X2,X3)),esk484_3(X1,X2,X3)))
    | hBOOL(hAPP(hAPP(X1,esk483_3(X1,X2,X3)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk484_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_7111]),
    [final] ).

cnf(i_0_12526,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_7112]),
    [final] ).

cnf(i_0_12527,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_7113]),
    [final] ).

cnf(i_0_12528,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_7114,c_0_6103]),
    [final] ).

cnf(i_0_12529,plain,
    ( X1 = hAPP(c_Relation_OImage(X2,X2,X3),hAPP(hAPP(c_Set_Oinsert(X2),esk187_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_7115]),
    [final] ).

cnf(i_0_12530,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_7116,c_0_7117]),c_0_7117]),
    [final] ).

cnf(i_0_12531,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_7118,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12532,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_7119]),
    [final] ).

cnf(i_0_12533,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_7089]),
    [final] ).

cnf(i_0_12534,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_7090]),
    [final] ).

cnf(i_0_12535,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk441_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_6921]),
    [final] ).

cnf(i_0_12536,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk176_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_7120]),
    [final] ).

cnf(i_0_12537,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk168_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_7121]),
    [final] ).

cnf(i_0_12538,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk153_4(X2,X3,X4,X1)),esk152_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_6986]),
    [final] ).

cnf(i_0_12539,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_7122]),
    [final] ).

cnf(i_0_12540,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_7123]),
    [final] ).

cnf(i_0_12541,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_7124]),
    [final] ).

cnf(i_0_12542,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_7125]),
    [final] ).

cnf(i_0_12543,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_7126,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12544,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_7127,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12545,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_7128,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12546,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_7129,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12547,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_7130,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12548,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_7131]),
    [final] ).

cnf(i_0_12549,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_7095]),
    [final] ).

cnf(i_0_12550,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_7132]),
    [final] ).

cnf(i_0_12551,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk162_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_7133]),
    [final] ).

cnf(i_0_12552,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_7134]),
    [final] ).

cnf(i_0_12553,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_7022]),
    [final] ).

cnf(i_0_12554,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_7135]),
    [final] ).

cnf(i_0_12555,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_7136]),
    [final] ).

cnf(i_0_12556,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk362_3(X2,X1,X3)),X3)),X2))
    | c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk360_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7070]),
    [final] ).

cnf(i_0_12557,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_6897]),
    [final] ).

cnf(i_0_12558,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),esk170_1(X1)),esk171_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_7137]),
    [final] ).

cnf(i_0_12559,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk5_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_7138]),
    [final] ).

cnf(i_0_12560,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk165_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_7099]),
    [final] ).

cnf(i_0_12561,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_7139]),
    [final] ).

cnf(i_0_12562,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_7140]),
    [final] ).

cnf(i_0_12563,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_7141]),
    [final] ).

cnf(i_0_12564,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_7142,c_0_6139]),
    [final] ).

cnf(i_0_12565,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_7143]),
    [final] ).

cnf(i_0_12566,plain,
    ( c_Hilbert__Choice_Oinv__into(X2,X1,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X3)) = X3
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7144]),
    [final] ).

cnf(i_0_12567,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_7145,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12568,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_7146,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12569,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_7147]),
    [final] ).

cnf(i_0_12570,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_7148]),
    [final] ).

cnf(i_0_12571,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk289_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_6211]),
    [final] ).

cnf(i_0_12572,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),esk103_3(X3,X2,X1)),esk104_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk103_3(X3,X2,X1))),hAPP(X2,esk104_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7149]),
    [final] ).

cnf(i_0_12573,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),esk105_3(X3,X2,X1)),esk106_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk105_3(X3,X2,X1))),hAPP(X2,esk106_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7150]),
    [final] ).

cnf(i_0_12574,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_6945]),
    [final] ).

cnf(i_0_12575,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_7151]),
    [final] ).

cnf(i_0_12576,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_7152]),
    [final] ).

cnf(i_0_12577,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_6302]),
    [final] ).

cnf(i_0_12578,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_7153]),
    [final] ).

cnf(i_0_12579,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_7154,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12580,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_7155,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12581,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_7156,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12582,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_7157,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12583,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_7158]),
    [final] ).

cnf(i_0_12584,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_7159]),
    [final] ).

cnf(i_0_12585,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_7139]),
    [final] ).

cnf(i_0_12586,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_7160]),
    [final] ).

cnf(i_0_12587,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_7161]),
    [final] ).

cnf(i_0_12588,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_Set_Ovimage(X1,X2,X3),X4)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7162]),
    [final] ).

cnf(i_0_12589,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk305_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_6956]),
    [final] ).

cnf(i_0_12590,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk127_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_6957]),
    [final] ).

cnf(i_0_12591,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_7163]),
    [final] ).

cnf(i_0_12592,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_7164]),
    [final] ).

cnf(i_0_12593,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_7165]),
    [final] ).

cnf(i_0_12594,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_7164]),
    [final] ).

cnf(i_0_12595,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_7166]),
    [final] ).

cnf(i_0_12596,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_7167]),
    [final] ).

cnf(i_0_12597,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_7168]),
    [final] ).

cnf(i_0_12598,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),esk46_3(X3,X2,X1)),esk47_3(X3,X2,X1))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X2,esk46_3(X3,X2,X1))),hAPP(X2,esk47_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7169]),
    [final] ).

cnf(i_0_12599,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_7170]),
    [final] ).

cnf(i_0_12600,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_7171]),
    [final] ).

cnf(i_0_12601,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk319_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_7172]),
    [final] ).

cnf(i_0_12602,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk318_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_7173]),
    [final] ).

cnf(i_0_12603,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk226_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_7174]),
    [final] ).

cnf(i_0_12604,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_7175]),
    [final] ).

cnf(i_0_12605,hypothesis,
    ( v_P(X1,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
    | hAPP(c_Finite__Set_Ocard(t_a),X1) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),v_n)
    | ~ v_wt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7176]),
    [final] ).

cnf(i_0_12606,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk447_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),esk445_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7177,c_0_6139]),
    [final] ).

cnf(i_0_12607,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk446_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),esk445_2(X2,X1))) ),
    inference(rw,[status(thm)],[i_0_7178,c_0_6139]),
    [final] ).

cnf(i_0_12608,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_7179]),
    [final] ).

cnf(i_0_12609,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk391_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_6604]),
    [final] ).

cnf(i_0_12610,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_7180]),
    [final] ).

cnf(i_0_12611,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk178_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_7181]),
    [final] ).

cnf(i_0_12612,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk166_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_7182]),
    [final] ).

cnf(i_0_12613,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk151_4(X2,X3,X4,X1)),esk150_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_7018]),
    [final] ).

cnf(i_0_12614,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_7183]),
    [final] ).

cnf(i_0_12615,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk112_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_6843]),
    [final] ).

cnf(i_0_12616,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk112_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_6843]),
    [final] ).

cnf(i_0_12617,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk396_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_7184]),
    [final] ).

cnf(i_0_12618,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_7185]),
    [final] ).

cnf(i_0_12619,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_12620,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_12621,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_7186]),
    [final] ).

cnf(i_0_12622,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_7187]),
    [final] ).

cnf(i_0_12623,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk187_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_7115]),
    [final] ).

cnf(i_0_12624,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_7188]),
    [final] ).

cnf(i_0_12625,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk358_4(X2,X3,X4,X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),esk357_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_6168]),
    [final] ).

cnf(i_0_12626,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_7189]),
    [final] ).

cnf(i_0_12627,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk107_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_6845]),
    [final] ).

cnf(i_0_12628,plain,
    ( hBOOL(hAPP(X4,X2))
    | hBOOL(hAPP(hAPP(c_member(X1),esk107_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_6845]),
    [final] ).

cnf(i_0_12629,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_7190]),
    [final] ).

cnf(i_0_12630,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_7191]),
    [final] ).

cnf(i_0_12631,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_7192]),
    [final] ).

cnf(i_0_12632,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_7193]),
    [final] ).

cnf(i_0_12633,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk8_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_6603]),
    [final] ).

cnf(i_0_12634,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk177_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_7120]),
    [final] ).

cnf(i_0_12635,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk169_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_7121]),
    [final] ).

cnf(i_0_12636,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_7194]),
    [final] ).

cnf(i_0_12637,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_7194]),
    [final] ).

cnf(i_0_12638,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_7011]),
    [final] ).

cnf(i_0_12639,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_7012]),
    [final] ).

cnf(i_0_12640,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_7195]),
    [final] ).

cnf(i_0_12641,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_7161]),
    [final] ).

cnf(i_0_12642,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_7196]),
    [final] ).

cnf(i_0_12643,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_6630]),
    [final] ).

cnf(i_0_12644,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_7197,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12645,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk163_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_7133]),
    [final] ).

cnf(i_0_12646,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_7198]),
    [final] ).

cnf(i_0_12647,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_7199]),
    [final] ).

cnf(i_0_12648,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),esk213_3(X3,X2,X1)),esk214_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(X2,esk213_3(X3,X2,X1))),hAPP(X2,esk214_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7200]),
    [final] ).

cnf(i_0_12649,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),esk121_3(X3,X2,X1)),esk122_3(X3,X2,X1))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(X2,esk121_3(X3,X2,X1))),hAPP(X2,esk122_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7201]),
    [final] ).

cnf(i_0_12650,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),esk113_3(X3,X2,X1)),esk114_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(X2,esk113_3(X3,X2,X1))),hAPP(X2,esk114_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7202]),
    [final] ).

cnf(i_0_12651,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),esk118_3(X3,X2,X1)),esk119_3(X3,X2,X1))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(X2,esk118_3(X3,X2,X1))),hAPP(X2,esk119_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7203]),
    [final] ).

cnf(i_0_12652,plain,
    ( hBOOL(hAPP(X3,esk175_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,esk172_2(X3,X2)))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_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_7204]),
    [final] ).

cnf(i_0_12653,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_7205]),
    [final] ).

cnf(i_0_12654,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),esk445_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)))
    | esk447_2(X1,X2) != esk446_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1)) ),
    inference(rw,[status(thm)],[i_0_7206,c_0_6139]),
    [final] ).

cnf(i_0_12655,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_7207]),
    [final] ).

cnf(i_0_12656,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_7014]),
    [final] ).

cnf(i_0_12657,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_7015]),
    [final] ).

cnf(i_0_12658,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk346_2(X2,X1)),esk346_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_7208,c_0_6103]),
    [final] ).

cnf(i_0_12659,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk333_2(X2,X1)),esk333_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_7209,c_0_6103]),
    [final] ).

cnf(i_0_12660,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_7210]),
    [final] ).

cnf(i_0_12661,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_7211]),
    [final] ).

cnf(i_0_12662,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk564_4(X2,X3,X4,X1)),hAPP(hAPP(c_Equiv__Relations_Oquotient(X1),X4),X3)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),hAPP(c_Finite__Set_Ocard(X1),X4)))
    | ~ c_Equiv__Relations_Oequiv(X1,X4,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7007]),
    [final] ).

cnf(i_0_12663,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_7113]),
    [final] ).

cnf(i_0_12664,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_7212]),
    [final] ).

cnf(i_0_12665,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_7213]),
    [final] ).

cnf(i_0_12666,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_7214]),
    [final] ).

cnf(i_0_12667,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_7215]),
    [final] ).

cnf(i_0_12668,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_7216]),
    [final] ).

cnf(i_0_12669,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_7217]),
    [final] ).

cnf(i_0_12670,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_7218]),
    [final] ).

cnf(i_0_12671,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_7219]),
    [final] ).

cnf(i_0_12672,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_7089]),
    [final] ).

cnf(i_0_12673,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_7089]),
    [final] ).

cnf(i_0_12674,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_7090]),
    [final] ).

cnf(i_0_12675,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_7090]),
    [final] ).

cnf(i_0_12676,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_7220]),
    [final] ).

cnf(i_0_12677,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_7221]),
    [final] ).

cnf(i_0_12678,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2)),X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7222]),
    [final] ).

cnf(i_0_12679,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_7223]),
    [final] ).

cnf(i_0_12680,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_7224]),
    [final] ).

cnf(i_0_12681,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_7225]),
    [final] ).

cnf(i_0_12682,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_7226]),
    [final] ).

cnf(i_0_12683,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk48_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_7227]),
    [final] ).

cnf(i_0_12684,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk464_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_7228]),
    [final] ).

cnf(i_0_12685,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_7229]),
    [final] ).

cnf(i_0_12686,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_7230]),
    [final] ).

cnf(i_0_12687,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_7231]),
    [final] ).

cnf(i_0_12688,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_7232]),
    [final] ).

cnf(i_0_12689,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_7233]),
    [final] ).

cnf(i_0_12690,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_7234]),
    [final] ).

cnf(i_0_12691,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_7235]),
    [final] ).

cnf(i_0_12692,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk185_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_7236]),
    [final] ).

cnf(i_0_12693,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk90_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_7237]),
    [final] ).

cnf(i_0_12694,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_6124]),
    [final] ).

cnf(i_0_12695,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_6319]),
    [final] ).

cnf(i_0_12696,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_7238]),
    [final] ).

cnf(i_0_12697,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_7239]),
    [final] ).

cnf(i_0_12698,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_6934]),
    [final] ).

cnf(i_0_12699,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
    | ~ c_Relation_Osym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7240]),
    [final] ).

cnf(i_0_12700,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
    | ~ c_Relation_Osym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X4)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7241]),
    [final] ).

cnf(i_0_12701,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_7242,c_0_6184]),
    [final] ).

cnf(i_0_12702,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_6385]),
    [final] ).

cnf(i_0_12703,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_7243,c_0_6096]),
    [final] ).

cnf(i_0_12704,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_7011]),
    [final] ).

cnf(i_0_12705,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_7012]),
    [final] ).

cnf(i_0_12706,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X2),esk16_3(X1,X3,X2)),esk17_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_7244]),
    [final] ).

cnf(i_0_12707,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_7245]),
    [final] ).

cnf(i_0_12708,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_7158]),
    [final] ).

cnf(i_0_12709,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_7159]),
    [final] ).

cnf(i_0_12710,plain,
    ( hBOOL(hAPP(X1,esk539_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X2,X5))
    | ~ hBOOL(hAPP(X1,esk538_4(X1,X2,X3,X4)))
    | ~ c_Equiv__Relations_Oequivp(X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6992]),
    [final] ).

cnf(i_0_12711,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_7246]),
    [final] ).

cnf(i_0_12712,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk160_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_7247]),
    [final] ).

cnf(i_0_12713,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk158_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_7248]),
    [final] ).

cnf(i_0_12714,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk400_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_6865]),
    [final] ).

cnf(i_0_12715,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk399_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_6866]),
    [final] ).

cnf(i_0_12716,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_7249]),
    [final] ).

cnf(i_0_12717,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk87_3(X3,X2,X1)),esk88_3(X3,X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7250]),
    [final] ).

cnf(i_0_12718,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(X2,X3,tc_HOL_Obool,X1),X4),X5))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[i_0_7251]),
    [final] ).

cnf(i_0_12719,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk179_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_7181]),
    [final] ).

cnf(i_0_12720,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk167_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_7182]),
    [final] ).

cnf(i_0_12721,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk259_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_6983]),
    [final] ).

cnf(i_0_12722,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_7252]),
    [final] ).

cnf(i_0_12723,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk255_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_7253]),
    [final] ).

cnf(i_0_12724,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_7045]),
    [final] ).

cnf(i_0_12725,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_7254,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12726,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Ovimage(X3,X1,X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Fun_Obij__betw(X3,X1,X4,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7162]),
    [final] ).

cnf(i_0_12727,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk174_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,esk172_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_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_7204]),
    [final] ).

cnf(i_0_12728,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk480_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_7255]),
    [final] ).

cnf(i_0_12729,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_7256,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12730,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk514_2(X2,X1)),esk513_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7241]),
    [final] ).

cnf(i_0_12731,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk500_2(X2,X1)),esk502_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_6944]),
    [final] ).

cnf(i_0_12732,plain,
    ( c_Nitpick_Orefl_H(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk89_2(X2,X1)),esk89_2(X2,X1))),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7257]),
    [final] ).

cnf(i_0_12733,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),esk124_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_7258]),
    [final] ).

cnf(i_0_12734,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),esk120_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_7259]),
    [final] ).

cnf(i_0_12735,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk400_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_6865]),
    [final] ).

cnf(i_0_12736,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk399_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_6866]),
    [final] ).

cnf(i_0_12737,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_6884]),
    [final] ).

cnf(i_0_12738,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_7260]),
    [final] ).

cnf(i_0_12739,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_7261,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12740,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_7262]),
    [final] ).

cnf(i_0_12741,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_7263]),
    [final] ).

cnf(i_0_12742,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk481_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_7264]),
    [final] ).

cnf(i_0_12743,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_7265]),
    [final] ).

cnf(i_0_12744,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_7266]),
    [final] ).

cnf(i_0_12745,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_7267,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12746,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_7268,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12747,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X4)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X1,X2,X3),X4))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7269]),
    [final] ).

cnf(i_0_12748,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_7270,c_0_6706]),
    [final] ).

cnf(i_0_12749,plain,
    ( X1 = hAPP(c_List_Ofilter(X2,X3),esk457_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_6166]),
    [final] ).

cnf(i_0_12750,plain,
    ( X1 = hAPP(c_List_Ofilter(X2,X3),esk460_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_6167]),
    [final] ).

cnf(i_0_12751,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_7271,c_0_7117]),
    [final] ).

cnf(i_0_12752,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_7272]),
    [final] ).

cnf(i_0_12753,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk372_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_6977]),
    [final] ).

cnf(i_0_12754,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk371_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_6976]),
    [final] ).

cnf(i_0_12755,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_7273]),
    [final] ).

cnf(i_0_12756,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),esk483_3(X1,X2,X3)),esk484_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_7111]),
    [final] ).

cnf(i_0_12757,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),esk397_3(X1,X2,X3)),esk398_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_6939]),
    [final] ).

cnf(i_0_12758,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),esk97_3(X1,X2,X3)),esk98_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_7098]),
    [final] ).

cnf(i_0_12759,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),esk95_3(X1,X2,X3)),esk96_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_5315]),
    [final] ).

cnf(i_0_12760,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),esk93_3(X1,X2,X3)),esk94_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_5312]),
    [final] ).

cnf(i_0_12761,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),esk221_3(X1,X2,X3)),esk222_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_7274]),
    [final] ).

cnf(i_0_12762,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_7275]),
    [final] ).

cnf(i_0_12763,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_7276]),
    [final] ).

cnf(i_0_12764,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_7277]),
    [final] ).

cnf(i_0_12765,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_7278]),
    [final] ).

cnf(i_0_12766,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_7279,c_0_6184]),
    [final] ).

cnf(i_0_12767,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk339_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_7280,c_0_6103]),
    [final] ).

cnf(i_0_12768,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)))
    | esk447_2(X1,X2) != esk446_2(X1,X2)
    | ~ hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),X1))
    | ~ hBOOL(hAPP(c_List_Odistinct(X2),esk445_2(X1,X2))) ),
    inference(rw,[status(thm)],[i_0_7281,c_0_6139]),
    [final] ).

cnf(i_0_12769,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),esk521_3(X1,X3,X2))) != esk521_3(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7282]),
    [final] ).

cnf(i_0_12770,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,esk185_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7236]),
    [final] ).

cnf(i_0_12771,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,esk90_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7237]),
    [final] ).

cnf(i_0_12772,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk487_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_7283]),
    [final] ).

cnf(i_0_12773,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk479_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_7284]),
    [final] ).

cnf(i_0_12774,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_7285]),
    [final] ).

cnf(i_0_12775,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_7089]),
    [final] ).

cnf(i_0_12776,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_7090]),
    [final] ).

cnf(i_0_12777,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_7286]),
    [final] ).

cnf(i_0_12778,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_7287]),
    [final] ).

cnf(i_0_12779,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk303_4(X2,X3,X4,X1)),X3))
    | c_Equiv__Relations_Ocongruent(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6234]),
    [final] ).

cnf(i_0_12780,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),esk440_4(X1,X3,X2,X4)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6987]),
    [final] ).

cnf(i_0_12781,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_7087]),
    [final] ).

cnf(i_0_12782,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_7288]),
    [final] ).

cnf(i_0_12783,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_7289,c_0_6289]),
    [final] ).

cnf(i_0_12784,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_7290,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12785,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_7291]),
    [final] ).

cnf(i_0_12786,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_7292]),
    [final] ).

cnf(i_0_12787,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),esk440_4(X4,X3,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6987]),
    [final] ).

cnf(i_0_12788,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_7293]),
    [final] ).

cnf(i_0_12789,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk419_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_6994]),
    [final] ).

cnf(i_0_12790,plain,
    ( hAPP(hAPP(c_List_Otake(X1),X4),X2) = hAPP(hAPP(c_List_Otake(X1),X4),X3)
    | hAPP(hAPP(c_List_Onth(X1),X2),esk396_4(X3,X2,X1,X4)) != hAPP(hAPP(c_List_Onth(X1),X3),esk396_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_7184]),
    [final] ).

cnf(i_0_12791,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_6814]),
    [final] ).

cnf(i_0_12792,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_7294]),
    [final] ).

cnf(i_0_12793,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_7295]),
    [final] ).

cnf(i_0_12794,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),X2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),esk338_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_7296]),
    [final] ).

cnf(i_0_12795,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_7297]),
    [final] ).

cnf(i_0_12796,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_7298]),
    [final] ).

cnf(i_0_12797,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_7235]),
    [final] ).

cnf(i_0_12798,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk510_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_6612]),
    [final] ).

cnf(i_0_12799,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk242_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_6613]),
    [final] ).

cnf(i_0_12800,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk508_4(X2,X3,X4,X1)),X4))
    | c_Wellfounded_Omax__extp(X1,X2,X4,X3)
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6989]),
    [final] ).

cnf(i_0_12801,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_7299]),
    [final] ).

cnf(i_0_12802,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_7300]),
    [final] ).

cnf(i_0_12803,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_7087]),
    [final] ).

cnf(i_0_12804,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk454_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_7301]),
    [final] ).

cnf(i_0_12805,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_7302]),
    [final] ).

cnf(i_0_12806,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk182_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_7303]),
    [final] ).

cnf(i_0_12807,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_7304]),
    [final] ).

cnf(i_0_12808,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk161_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_7247]),
    [final] ).

cnf(i_0_12809,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk159_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_7248]),
    [final] ).

cnf(i_0_12810,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_7305]),
    [final] ).

cnf(i_0_12811,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_7087]),
    [final] ).

cnf(i_0_12812,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_7014]),
    [final] ).

cnf(i_0_12813,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_7015]),
    [final] ).

cnf(i_0_12814,plain,
    ( esk222_3(X1,X2,X3) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(X1,esk222_3(X1,X2,X3)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,esk221_3(X1,X2,X3),esk222_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_7274]),
    [final] ).

cnf(i_0_12815,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_7306]),
    [final] ).

cnf(i_0_12816,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_7307]),
    [final] ).

cnf(i_0_12817,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk165_4(X2,X3,X4,X1)),esk164_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_7099]),
    [final] ).

cnf(i_0_12818,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7308]),
    [final] ).

cnf(i_0_12819,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7309]),
    [final] ).

cnf(i_0_12820,plain,
    ( X1 = X2
    | hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = hAPP(X5,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7310]),
    [final] ).

cnf(i_0_12821,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_7040]),
    [final] ).

cnf(i_0_12822,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk184_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_7311]),
    [final] ).

cnf(i_0_12823,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_7312]),
    [final] ).

cnf(i_0_12824,plain,
    ( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7308]),
    [final] ).

cnf(i_0_12825,plain,
    ( hAPP(c_Fun_Ofun__upd(X3,X4,X5,X2,X6),X1) = X6
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7309]),
    [final] ).

cnf(i_0_12826,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_7198]),
    [final] ).

cnf(i_0_12827,plain,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
    inference(split_conjunct,[status(thm)],[i_0_7313]),
    [final] ).

cnf(i_0_12828,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_7314]),
    [final] ).

cnf(i_0_12829,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_7187]),
    [final] ).

cnf(i_0_12830,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),esk440_4(X1,X3,X2,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6987]),
    [final] ).

cnf(i_0_12831,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_7087]),
    [final] ).

cnf(i_0_12832,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_7315]),
    [final] ).

cnf(i_0_12833,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_7316,c_0_7317]),
    [final] ).

cnf(i_0_12834,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),esk440_4(X4,X3,X2,X1)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_6987]),
    [final] ).

cnf(i_0_12835,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_7318]),
    [final] ).

cnf(i_0_12836,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_7011]),
    [final] ).

cnf(i_0_12837,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_7012]),
    [final] ).

cnf(i_0_12838,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_6350]),
    [final] ).

cnf(i_0_12839,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_7319]),
    [final] ).

cnf(i_0_12840,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_7320]),
    [final] ).

cnf(i_0_12841,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_7321]),
    [final] ).

cnf(i_0_12842,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_7322]),
    [final] ).

cnf(i_0_12843,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_7323]),
    [final] ).

cnf(i_0_12844,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_7324]),
    [final] ).

cnf(i_0_12845,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_7298]),
    [final] ).

cnf(i_0_12846,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_7325]),
    [final] ).

cnf(i_0_12847,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_7326]),
    [final] ).

cnf(i_0_12848,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_7327]),
    [final] ).

cnf(i_0_12849,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_7328]),
    [final] ).

cnf(i_0_12850,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_7329]),
    [final] ).

cnf(i_0_12851,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_7330]),
    [final] ).

cnf(i_0_12852,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7331]),
    [final] ).

cnf(i_0_12853,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7332]),
    [final] ).

cnf(i_0_12854,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_7333,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_12855,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_7334]),
    [final] ).

cnf(i_0_12856,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_7335]),
    [final] ).

cnf(i_0_12857,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_7336]),
    [final] ).

cnf(i_0_12858,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_7054]),
    [final] ).

cnf(i_0_12859,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_7337]),
    [final] ).

cnf(i_0_12860,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_7338]),
    [final] ).

cnf(i_0_12861,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_7339,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12862,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_7340,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12863,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_7341]),
    [final] ).

cnf(i_0_12864,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_7342]),
    [final] ).

cnf(i_0_12865,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_7343]),
    [final] ).

cnf(i_0_12866,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_7344]),
    [final] ).

cnf(i_0_12867,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk23_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7345]),
    [final] ).

cnf(i_0_12868,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk22_4(X2,X3,X4,X1)),X2))
    | c_Fun_Oinj__on(X1,X4,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7345]),
    [final] ).

cnf(i_0_12869,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_7346]),
    [final] ).

cnf(i_0_12870,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_7347]),
    [final] ).

cnf(i_0_12871,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_7122]),
    [final] ).

cnf(i_0_12872,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_7326]),
    [final] ).

cnf(i_0_12873,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_7327]),
    [final] ).

cnf(i_0_12874,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_7348]),
    [final] ).

cnf(i_0_12875,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk83_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_7349]),
    [final] ).

cnf(i_0_12876,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X3),esk370_4(X4,X1,X3,X2)),esk369_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_6535]),
    [final] ).

cnf(i_0_12877,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_7350]),
    [final] ).

cnf(i_0_12878,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_7351]),
    [final] ).

cnf(i_0_12879,plain,
    ( hBOOL(hAPP(X1,esk174_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk172_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_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_7204]),
    [final] ).

cnf(i_0_12880,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_7352,c_0_6096]),
    [final] ).

cnf(i_0_12881,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk177_4(X2,X3,X4,X1)),esk176_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_7120]),
    [final] ).

cnf(i_0_12882,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk169_4(X2,X3,X4,X1)),esk168_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_7121]),
    [final] ).

cnf(i_0_12883,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_7049]),
    [final] ).

cnf(i_0_12884,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk229_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_7353]),
    [final] ).

cnf(i_0_12885,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk134_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_7354]),
    [final] ).

cnf(i_0_12886,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk230_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_7355]),
    [final] ).

cnf(i_0_12887,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk135_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_7356]),
    [final] ).

cnf(i_0_12888,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(X1,esk313_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_7357]),
    [final] ).

cnf(i_0_12889,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_7358]),
    [final] ).

cnf(i_0_12890,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_7359]),
    [final] ).

cnf(i_0_12891,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_7360]),
    [final] ).

cnf(i_0_12892,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_7361]),
    [final] ).

cnf(i_0_12893,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk444_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_7362]),
    [final] ).

cnf(i_0_12894,plain,
    ( hAPP(X1,esk358_4(X2,X1,X3,X4)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),esk357_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_6168]),
    [final] ).

cnf(i_0_12895,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_7363]),
    [final] ).

cnf(i_0_12896,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_7364]),
    [final] ).

cnf(i_0_12897,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_7365,c_0_6706]),c_0_6706]),
    [final] ).

cnf(i_0_12898,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_7366]),
    [final] ).

cnf(i_0_12899,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_7367]),
    [final] ).

cnf(i_0_12900,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk163_4(X2,X3,X4,X1)),esk162_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_7133]),
    [final] ).

cnf(i_0_12901,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_7368,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12902,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_7369]),
    [final] ).

cnf(i_0_12903,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)),esk252_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),esk253_3(X2,X3,X1)),esk254_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_7370]),
    [final] ).

cnf(i_0_12904,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_7061]),
    [final] ).

cnf(i_0_12905,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7331]),
    [final] ).

cnf(i_0_12906,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7371]),
    [final] ).

cnf(i_0_12907,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_7372]),
    [final] ).

cnf(i_0_12908,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_7373]),
    [final] ).

cnf(i_0_12909,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_7374]),
    [final] ).

cnf(i_0_12910,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_7375,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12911,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_7376]),
    [final] ).

cnf(i_0_12912,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_7377]),
    [final] ).

cnf(i_0_12913,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_7378]),
    [final] ).

cnf(i_0_12914,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_7379]),
    [final] ).

cnf(i_0_12915,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk313_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_7357]),
    [final] ).

cnf(i_0_12916,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_7380]),
    [final] ).

cnf(i_0_12917,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_7381,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12918,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_7382]),
    [final] ).

cnf(i_0_12919,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_7158]),
    [final] ).

cnf(i_0_12920,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_7159]),
    [final] ).

cnf(i_0_12921,plain,
    ( X1 = hAPP(X2,esk224_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_7004]),
    [final] ).

cnf(i_0_12922,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_7383,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_12923,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_7384]),
    [final] ).

cnf(i_0_12924,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_7385]),
    [final] ).

cnf(i_0_12925,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_7386,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12926,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_7387,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12927,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_7388,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12928,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_7389,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12929,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_7390,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12930,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_7391,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12931,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_7392,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12932,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_7393,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12933,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_7394]),
    [final] ).

cnf(i_0_12934,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_7395]),
    [final] ).

cnf(i_0_12935,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk254_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)),esk252_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_7370]),
    [final] ).

cnf(i_0_12936,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk253_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)),esk252_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_7370]),
    [final] ).

cnf(i_0_12937,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_7396]),
    [final] ).

cnf(i_0_12938,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_7397]),
    [final] ).

cnf(i_0_12939,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))))) ),
    inference(rw,[status(thm)],[i_0_7398,c_0_6096]),
    [final] ).

cnf(i_0_12940,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_7399]),
    [final] ).

cnf(i_0_12941,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_7400]),
    [final] ).

cnf(i_0_12942,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_7401]),
    [final] ).

cnf(i_0_12943,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_7402]),
    [final] ).

cnf(i_0_12944,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_7403]),
    [final] ).

cnf(i_0_12945,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_7404]),
    [final] ).

cnf(i_0_12946,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_7405]),
    [final] ).

cnf(i_0_12947,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_7406,c_0_6289]),c_0_6289]),
    [final] ).

cnf(i_0_12948,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,esk464_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_7228]),
    [final] ).

cnf(i_0_12949,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_7407]),
    [final] ).

cnf(i_0_12950,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_7141]),
    [final] ).

cnf(i_0_12951,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7408]),
    [final] ).

cnf(i_0_12952,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_7409]),
    [final] ).

cnf(i_0_12953,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_7410]),
    [final] ).

cnf(i_0_12954,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_7411]),
    [final] ).

cnf(i_0_12955,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_7064]),
    [final] ).

cnf(i_0_12956,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_7065]),
    [final] ).

cnf(i_0_12957,plain,
    ( c_Wellfounded_Owf(tc_prod(X3,X1),c_Recdef_Osame__fst(X3,X1,X4,X2))
    | ~ c_Wellfounded_Owf(X1,hAPP(X2,esk296_4(X3,X2,X1,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7412]),
    [final] ).

cnf(i_0_12958,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_7413]),
    [final] ).

cnf(i_0_12959,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7414]),
    [final] ).

cnf(i_0_12960,plain,
    ( c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7415]),
    [final] ).

cnf(i_0_12961,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_7416,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_12962,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_7417]),
    [final] ).

cnf(i_0_12963,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_7418,c_0_6103]),
    [final] ).

cnf(i_0_12964,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_7419]),
    [final] ).

cnf(i_0_12965,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_7420]),
    [final] ).

cnf(i_0_12966,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_7147]),
    [final] ).

cnf(i_0_12967,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_7148]),
    [final] ).

cnf(i_0_12968,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_7421]),
    [final] ).

cnf(i_0_12969,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk179_4(X2,X3,X4,X1)),esk178_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_7181]),
    [final] ).

cnf(i_0_12970,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk167_4(X2,X3,X4,X1)),esk166_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_7182]),
    [final] ).

cnf(i_0_12971,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_7422,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_12972,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_6494]),
    [final] ).

cnf(i_0_12973,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_7423]),
    [final] ).

cnf(i_0_12974,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_7424]),
    [final] ).

cnf(i_0_12975,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_7425]),
    [final] ).

cnf(i_0_12976,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_7426]),
    [final] ).

cnf(i_0_12977,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_7427]),
    [final] ).

cnf(i_0_12978,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_7428]),
    [final] ).

cnf(i_0_12979,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_7429]),
    [final] ).

cnf(i_0_12980,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_7430]),
    [final] ).

cnf(i_0_12981,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_7431]),
    [final] ).

cnf(i_0_12982,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_7432]),
    [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_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_7433]),
    [final] ).

cnf(i_0_12984,plain,
    ( hBOOL(hAPP(X1,esk539_4(X1,X2,X3,X4)))
    | hBOOL(hAPP(X2,esk538_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(X2,X5))
    | ~ c_Equiv__Relations_Oequivp(X4,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6992]),
    [final] ).

cnf(i_0_12985,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_7434]),
    [final] ).

cnf(i_0_12986,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_7435]),
    [final] ).

cnf(i_0_12987,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_7436]),
    [final] ).

cnf(i_0_12988,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_7158]),
    [final] ).

cnf(i_0_12989,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_7089]),
    [final] ).

cnf(i_0_12990,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_7159]),
    [final] ).

cnf(i_0_12991,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_7090]),
    [final] ).

cnf(i_0_12992,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,esk324_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_7437]),
    [final] ).

cnf(i_0_12993,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7438]),
    [final] ).

cnf(i_0_12994,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(X1,X2,X3),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7331]),
    [final] ).

cnf(i_0_12995,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_7439]),
    [final] ).

cnf(i_0_12996,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_7440]),
    [final] ).

cnf(i_0_12997,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_7441]),
    [final] ).

cnf(i_0_12998,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_7442]),
    [final] ).

cnf(i_0_12999,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_7443]),
    [final] ).

cnf(i_0_13000,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_7444,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_13001,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_7445]),
    [final] ).

cnf(i_0_13002,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_7446]),
    [final] ).

cnf(i_0_13003,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_7447]),
    [final] ).

cnf(i_0_13004,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_7448]),
    [final] ).

cnf(i_0_13005,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_7449]),
    [final] ).

cnf(i_0_13006,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_7450]),
    [final] ).

cnf(i_0_13007,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_7451]),
    [final] ).

cnf(i_0_13008,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_7452]),
    [final] ).

cnf(i_0_13009,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_7453]),
    [final] ).

cnf(i_0_13010,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_7454]),
    [final] ).

cnf(i_0_13011,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_7455,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13012,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_7456,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13013,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_7014]),
    [final] ).

cnf(i_0_13014,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_7015]),
    [final] ).

cnf(i_0_13015,plain,
    ( hBOOL(hAPP(X3,esk175_2(X3,X2)))
    | hBOOL(hAPP(X3,esk172_2(X3,X2)))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X3,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_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_7204]),
    [final] ).

cnf(i_0_13016,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X4) = hAPP(c_Finite__Set_Ocard(X2),X5)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X5))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7457]),
    [final] ).

cnf(i_0_13017,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_7458]),
    [final] ).

cnf(i_0_13018,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_7459]),
    [final] ).

cnf(i_0_13019,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_7460]),
    [final] ).

cnf(i_0_13020,negated_conjecture,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,v_pn)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))),v_G)),
    inference(split_conjunct,[status(thm)],[i_0_7461]),
    [final] ).

cnf(i_0_13021,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_7462]),
    [final] ).

cnf(i_0_13022,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),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_7463,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13023,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_7464,c_0_6103]),
    [final] ).

cnf(i_0_13024,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_7122]),
    [final] ).

cnf(i_0_13025,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_7296]),
    [final] ).

cnf(i_0_13026,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_7465]),
    [final] ).

cnf(i_0_13027,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_7466]),
    [final] ).

cnf(i_0_13028,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_7174]),
    [final] ).

cnf(i_0_13029,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_7467]),
    [final] ).

cnf(i_0_13030,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_7089]),
    [final] ).

cnf(i_0_13031,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_7090]),
    [final] ).

cnf(i_0_13032,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_7468]),
    [final] ).

cnf(i_0_13033,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_7469]),
    [final] ).

cnf(i_0_13034,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_7470]),
    [final] ).

cnf(i_0_13035,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_7471]),
    [final] ).

cnf(i_0_13036,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_7472]),
    [final] ).

cnf(i_0_13037,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_7473]),
    [final] ).

cnf(i_0_13038,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_7364]),
    [final] ).

cnf(i_0_13039,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_7474]),
    [final] ).

cnf(i_0_13040,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_7475]),
    [final] ).

cnf(i_0_13041,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_7476]),
    [final] ).

cnf(i_0_13042,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_7477]),
    [final] ).

cnf(i_0_13043,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_7478]),
    [final] ).

cnf(i_0_13044,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_7212]),
    [final] ).

cnf(i_0_13045,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_7213]),
    [final] ).

cnf(i_0_13046,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_7479,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13047,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_7480,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13048,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_7481,c_0_6069]),c_0_6070]),c_0_6071]),
    [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),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_7482,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13050,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_7483,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13051,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_7484,c_0_6726]),
    [final] ).

cnf(i_0_13052,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_7485]),
    [final] ).

cnf(i_0_13053,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_7486]),
    [final] ).

cnf(i_0_13054,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_7487]),
    [final] ).

cnf(i_0_13055,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_7011]),
    [final] ).

cnf(i_0_13056,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_7012]),
    [final] ).

cnf(i_0_13057,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_7488]),
    [final] ).

cnf(i_0_13058,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_7489]),
    [final] ).

cnf(i_0_13059,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_7490]),
    [final] ).

cnf(i_0_13060,plain,
    ( hAPP(c_Set_Oimage(X1,X2,X3),X4) = X5
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7414]),
    [final] ).

cnf(i_0_13061,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_7491]),
    [final] ).

cnf(i_0_13062,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_7474]),
    [final] ).

cnf(i_0_13063,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_7475]),
    [final] ).

cnf(i_0_13064,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_7492]),
    [final] ).

cnf(i_0_13065,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_7014]),
    [final] ).

cnf(i_0_13066,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_7015]),
    [final] ).

cnf(i_0_13067,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Fun_Obij__betw(X1,X3,X5,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7493]),
    [final] ).

cnf(i_0_13068,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Fun_Obij__betw(X3,X1,X5,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7493]),
    [final] ).

cnf(i_0_13069,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7494]),
    [final] ).

cnf(i_0_13070,plain,
    ( X4 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_7495]),
    [final] ).

cnf(i_0_13071,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_7496]),
    [final] ).

cnf(i_0_13072,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_7497]),
    [final] ).

cnf(i_0_13073,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_7498,c_0_6096]),
    [final] ).

cnf(i_0_13074,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_7499]),
    [final] ).

cnf(i_0_13075,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_7500]),
    [final] ).

cnf(i_0_13076,plain,
    ( X3 = esk224_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_7004]),
    [final] ).

cnf(i_0_13077,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_7384]),
    [final] ).

cnf(i_0_13078,plain,
    ( ~ c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))
    | ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3) ),
    inference(rw,[status(thm)],[i_0_7501,c_0_6187]),
    [final] ).

cnf(i_0_13079,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_7502]),
    [final] ).

cnf(i_0_13080,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_7503,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_13081,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_7291]),
    [final] ).

cnf(i_0_13082,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_7504]),
    [final] ).

cnf(i_0_13083,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_7505]),
    [final] ).

cnf(i_0_13084,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_7506]),
    [final] ).

cnf(i_0_13085,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_7507]),
    [final] ).

cnf(i_0_13086,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_7508]),
    [final] ).

cnf(i_0_13087,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_7509]),
    [final] ).

cnf(i_0_13088,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_7510]),
    [final] ).

cnf(i_0_13089,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_7511]),
    [final] ).

cnf(i_0_13090,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_7512]),
    [final] ).

cnf(i_0_13091,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_7513]),
    [final] ).

cnf(i_0_13092,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_7514]),
    [final] ).

cnf(i_0_13093,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_7515,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13094,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk483_3(X1,X2,X3)),esk484_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_7111]),
    [final] ).

cnf(i_0_13095,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk397_3(X1,X2,X3)),esk398_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_6939]),
    [final] ).

cnf(i_0_13096,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk221_3(X1,X2,X3)),esk222_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_7274]),
    [final] ).

cnf(i_0_13097,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk97_3(X1,X2,X3)),esk98_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_7098]),
    [final] ).

cnf(i_0_13098,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk95_3(X1,X2,X3)),esk96_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_5315]),
    [final] ).

cnf(i_0_13099,plain,
    ( hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ hBOOL(hAPP(hAPP(X1,esk93_3(X1,X2,X3)),esk94_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_5312]),
    [final] ).

cnf(i_0_13100,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_6302]),
    [final] ).

cnf(i_0_13101,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_6566]),
    [final] ).

cnf(i_0_13102,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_7516]),
    [final] ).

cnf(i_0_13103,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_7517]),
    [final] ).

cnf(i_0_13104,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_7518]),
    [final] ).

cnf(i_0_13105,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,esk69_3(X2,X1,X3)),esk70_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_7519]),
    [final] ).

cnf(i_0_13106,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_7520]),
    [final] ).

cnf(i_0_13107,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_7521]),
    [final] ).

cnf(i_0_13108,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_7522]),
    [final] ).

cnf(i_0_13109,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_7523]),
    [final] ).

cnf(i_0_13110,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_7524]),
    [final] ).

cnf(i_0_13111,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_7525]),
    [final] ).

cnf(i_0_13112,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_7519]),
    [final] ).

cnf(i_0_13113,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,esk67_3(X2,X1,X3)),esk68_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_7526]),
    [final] ).

cnf(i_0_13114,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_7527]),
    [final] ).

cnf(i_0_13115,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_7528]),
    [final] ).

cnf(i_0_13116,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_7529]),
    [final] ).

cnf(i_0_13117,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_7530]),
    [final] ).

cnf(i_0_13118,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_7531]),
    [final] ).

cnf(i_0_13119,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_7532]),
    [final] ).

cnf(i_0_13120,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_7533]),
    [final] ).

cnf(i_0_13121,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_7534]),
    [final] ).

cnf(i_0_13122,plain,
    ( hAPP(X4,hAPP(X3,X6)) = X6
    | ~ c_Typedef_Otype__definition(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7535]),
    [final] ).

cnf(i_0_13123,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),X4) = hAPP(c_Finite__Set_Ocard(X2),X5)
    | ~ c_Fun_Obij__betw(X1,X2,X3,X4,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_7536]),
    [final] ).

cnf(i_0_13124,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_7526]),
    [final] ).

cnf(i_0_13125,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_7537,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13126,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_7538]),
    [final] ).

cnf(i_0_13127,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_7539]),
    [final] ).

cnf(i_0_13128,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_7540,c_0_6103]),
    [final] ).

cnf(i_0_13129,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk161_4(X2,X3,X4,X1)),esk160_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_7247]),
    [final] ).

cnf(i_0_13130,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk159_4(X2,X3,X4,X1)),esk158_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_7248]),
    [final] ).

cnf(i_0_13131,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_7089]),
    [final] ).

cnf(i_0_13132,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_7090]),
    [final] ).

cnf(i_0_13133,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,esk454_4(X2,X1,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7301]),
    [final] ).

cnf(i_0_13134,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_7541]),
    [final] ).

cnf(i_0_13135,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk174_2(X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X2)))
    | hBOOL(hAPP(X1,esk172_2(X1,X2)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_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_7204]),
    [final] ).

cnf(i_0_13136,plain,
    ( hAPP(X3,X4) = X5
    | c_Fun_Ofun__upd(X1,X2,X3,X4,X5) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7542]),
    [final] ).

cnf(i_0_13137,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_7543]),
    [final] ).

cnf(i_0_13138,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_7544]),
    [final] ).

cnf(i_0_13139,plain,
    ( X2 = X3
    | ~ c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7545]),
    [final] ).

cnf(i_0_13140,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_6833]),
    [final] ).

cnf(i_0_13141,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_7546]),
    [final] ).

cnf(i_0_13142,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_6643]),
    [final] ).

cnf(i_0_13143,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_7547]),
    [final] ).

cnf(i_0_13144,plain,
    ( c_Fun_Obij__betw(X1,X3,esk530_4(X4,X3,X2,X1),X2,X4)
    | hAPP(c_Finite__Set_Ocard(X1),X2) != hAPP(c_Finite__Set_Ocard(X3),X4)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7457]),
    [final] ).

cnf(i_0_13145,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_7548]),
    [final] ).

cnf(i_0_13146,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_7549]),
    [final] ).

cnf(i_0_13147,plain,
    ( X2 = X3
    | ~ c_List_Olist__all2(X1,X1,c_fequal,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7550]),
    [final] ).

cnf(i_0_13148,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_7089]),
    [final] ).

cnf(i_0_13149,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_7158]),
    [final] ).

cnf(i_0_13150,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_7090]),
    [final] ).

cnf(i_0_13151,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_7159]),
    [final] ).

cnf(i_0_13152,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_7394]),
    [final] ).

cnf(i_0_13153,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_7395]),
    [final] ).

cnf(i_0_13154,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_7551]),
    [final] ).

cnf(i_0_13155,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_7552]),
    [final] ).

cnf(i_0_13156,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_7553,c_0_6139]),c_0_6139]),
    [final] ).

cnf(i_0_13157,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_7554]),
    [final] ).

cnf(i_0_13158,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_7555]),
    [final] ).

cnf(i_0_13159,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_7556]),
    [final] ).

cnf(i_0_13160,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_7557]),
    [final] ).

cnf(i_0_13161,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_7558,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13162,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_7102]),
    [final] ).

cnf(i_0_13163,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_7559]),
    [final] ).

cnf(i_0_13164,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk389_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_7273]),
    [final] ).

cnf(i_0_13165,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_7560]),
    [final] ).

cnf(i_0_13166,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_7561]),
    [final] ).

cnf(i_0_13167,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_7562]),
    [final] ).

cnf(i_0_13168,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_7563]),
    [final] ).

cnf(i_0_13169,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_7564]),
    [final] ).

cnf(i_0_13170,plain,
    ( c_List_Olinorder__class_Osorted(X1,X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk444_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_7362]),
    [final] ).

cnf(i_0_13171,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_7565]),
    [final] ).

cnf(i_0_13172,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_7158]),
    [final] ).

cnf(i_0_13173,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_7158]),
    [final] ).

cnf(i_0_13174,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_7159]),
    [final] ).

cnf(i_0_13175,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_7159]),
    [final] ).

cnf(i_0_13176,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_7413]),
    [final] ).

cnf(i_0_13177,plain,
    ( c_Equiv__Relations_Ocongruent(X4,X2,X3,X1)
    | hAPP(X1,esk554_4(X2,X1,X3,X4)) != hAPP(X1,esk555_4(X2,X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_6552]),
    [final] ).

cnf(i_0_13178,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_7566]),
    [final] ).

cnf(i_0_13179,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4))
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7567]),
    [final] ).

cnf(i_0_13180,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_6680]),
    [final] ).

cnf(i_0_13181,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_7568]),
    [final] ).

cnf(i_0_13182,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_7569]),
    [final] ).

cnf(i_0_13183,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_7570]),
    [final] ).

cnf(i_0_13184,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_7298]),
    [final] ).

cnf(i_0_13185,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_7298]),
    [final] ).

cnf(i_0_13186,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_7571]),
    [final] ).

cnf(i_0_13187,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_7572]),
    [final] ).

cnf(i_0_13188,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_7573,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_13189,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_7574]),
    [final] ).

cnf(i_0_13190,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_7575]),
    [final] ).

cnf(i_0_13191,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_7576]),
    [final] ).

cnf(i_0_13192,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_7577]),
    [final] ).

cnf(i_0_13193,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_7577]),
    [final] ).

cnf(i_0_13194,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_7578]),
    [final] ).

cnf(i_0_13195,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_7579]),
    [final] ).

cnf(i_0_13196,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_5321]),
    [final] ).

cnf(i_0_13197,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_7327]),
    [final] ).

cnf(i_0_13198,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_7580]),
    [final] ).

cnf(i_0_13199,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk251_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_7581]),
    [final] ).

cnf(i_0_13200,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk250_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_7581]),
    [final] ).

cnf(i_0_13201,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_7582]),
    [final] ).

cnf(i_0_13202,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_7583]),
    [final] ).

cnf(i_0_13203,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_7584,c_0_6096]),c_0_6103]),
    [final] ).

cnf(i_0_13204,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_7585]),
    [final] ).

cnf(i_0_13205,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_7586]),
    [final] ).

cnf(i_0_13206,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_7587]),
    [final] ).

cnf(i_0_13207,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_7441]),
    [final] ).

cnf(i_0_13208,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_7442]),
    [final] ).

cnf(i_0_13209,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_7588]),
    [final] ).

cnf(i_0_13210,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_7588]),
    [final] ).

cnf(i_0_13211,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_7589]),
    [final] ).

cnf(i_0_13212,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_7589]),
    [final] ).

cnf(i_0_13213,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_7590]),
    [final] ).

cnf(i_0_13214,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_7591]),
    [final] ).

cnf(i_0_13215,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_7592]),
    [final] ).

cnf(i_0_13216,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_7591]),
    [final] ).

cnf(i_0_13217,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_7592]),
    [final] ).

cnf(i_0_13218,plain,
    c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4),hAPP(c_Lazy__Sequence_Oyield(X2),c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X5,X6))) = hAPP(hAPP(X4,X5),X6),
    inference(rw,[status(thm)],[i_0_7593,c_0_7594]),
    [final] ).

cnf(i_0_13219,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,esk107_4(X4,X3,X5,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6845]),
    [final] ).

cnf(i_0_13220,plain,
    ( hBOOL(hAPP(X4,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | ~ hBOOL(hAPP(X4,esk107_4(X4,X5,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_6845]),
    [final] ).

cnf(i_0_13221,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_7595]),
    [final] ).

cnf(i_0_13222,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk9_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_6603]),
    [final] ).

cnf(i_0_13223,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_7596]),
    [final] ).

cnf(i_0_13224,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_7597]),
    [final] ).

cnf(i_0_13225,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_7598]),
    [final] ).

cnf(i_0_13226,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_7599]),
    [final] ).

cnf(i_0_13227,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,X4,X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | hAPP(c_Set_Oimage(X1,X2,X3),X4) != X5 ),
    inference(split_conjunct,[status(thm)],[i_0_7414]),
    [final] ).

cnf(i_0_13228,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_7600]),
    [final] ).

cnf(i_0_13229,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_7601]),
    [final] ).

cnf(i_0_13230,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_7602]),
    [final] ).

cnf(i_0_13231,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_7011]),
    [final] ).

cnf(i_0_13232,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_7012]),
    [final] ).

cnf(i_0_13233,plain,
    ( hBOOL(hAPP(X1,esk9_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_6603]),
    [final] ).

cnf(i_0_13234,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_7603,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13235,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)),esk256_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7604]),
    [final] ).

cnf(i_0_13236,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_7605]),
    [final] ).

cnf(i_0_13237,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_7606]),
    [final] ).

cnf(i_0_13238,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_7011]),
    [final] ).

cnf(i_0_13239,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_7012]),
    [final] ).

cnf(i_0_13240,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_7014]),
    [final] ).

cnf(i_0_13241,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_7015]),
    [final] ).

cnf(i_0_13242,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_7607]),
    [final] ).

cnf(i_0_13243,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_7608]),
    [final] ).

cnf(i_0_13244,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_7609,c_0_7317]),
    [final] ).

cnf(i_0_13245,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,esk307_3(X2,X1,X3)) != hAPP(X1,esk308_3(X2,X1,X3))
    | ~ c_Wellfounded_OwfP(X3,hAPP(X1,esk306_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_6936]),
    [final] ).

cnf(i_0_13246,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_7610]),
    [final] ).

cnf(i_0_13247,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_7611]),
    [final] ).

cnf(i_0_13248,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_7612]),
    [final] ).

cnf(i_0_13249,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_7613]),
    [final] ).

cnf(i_0_13250,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_7614]),
    [final] ).

cnf(i_0_13251,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)),esk253_3(X2,X3,X1)),esk254_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(X1),esk252_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_7370]),
    [final] ).

cnf(i_0_13252,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_7615,c_0_6726]),c_0_6726]),c_0_6726]),
    [final] ).

cnf(i_0_13253,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_7562]),
    [final] ).

cnf(i_0_13254,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_7616]),
    [final] ).

cnf(i_0_13255,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_7562]),
    [final] ).

cnf(i_0_13256,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_7616]),
    [final] ).

cnf(i_0_13257,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_7617]),
    [final] ).

cnf(i_0_13258,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_7618]),
    [final] ).

cnf(i_0_13259,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_7619]),
    [final] ).

cnf(i_0_13260,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_7620]),
    [final] ).

cnf(i_0_13261,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_7621]),
    [final] ).

cnf(i_0_13262,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_7622]),
    [final] ).

cnf(i_0_13263,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_7623]),
    [final] ).

cnf(i_0_13264,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_7624]),
    [final] ).

cnf(i_0_13265,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ class_Rings_Odvd(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7625]),
    [final] ).

cnf(i_0_13266,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_7626]),
    [final] ).

cnf(i_0_13267,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_7627,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13268,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_7628,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13269,plain,
    ( X2 = hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk356_2(X2,X1)),esk356_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_7629,c_0_6096]),
    [final] ).

cnf(i_0_13270,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_7630,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_13271,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_7631]),
    [final] ).

cnf(i_0_13272,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_7576]),
    [final] ).

cnf(i_0_13273,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_7632,c_0_6096]),
    [final] ).

cnf(i_0_13274,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_7633,c_0_6096]),
    [final] ).

cnf(i_0_13275,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_7634]),
    [final] ).

cnf(i_0_13276,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_7635]),
    [final] ).

cnf(i_0_13277,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_7636]),
    [final] ).

cnf(i_0_13278,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_7637]),
    [final] ).

cnf(i_0_13279,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_7638]),
    [final] ).

cnf(i_0_13280,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk156_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_7639]),
    [final] ).

cnf(i_0_13281,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk154_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_7640]),
    [final] ).

cnf(i_0_13282,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_7641]),
    [final] ).

cnf(i_0_13283,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk202_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_7642]),
    [final] ).

cnf(i_0_13284,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_7643,c_0_6139]),
    [final] ).

cnf(i_0_13285,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_7520]),
    [final] ).

cnf(i_0_13286,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_7644,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_13287,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_7645]),
    [final] ).

cnf(i_0_13288,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_6381]),
    [final] ).

cnf(i_0_13289,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_7646]),
    [final] ).

cnf(i_0_13290,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_7647]),
    [final] ).

cnf(i_0_13291,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_7648]),
    [final] ).

cnf(i_0_13292,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_7649]),
    [final] ).

cnf(i_0_13293,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk254_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),esk252_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_7370]),
    [final] ).

cnf(i_0_13294,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk253_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),esk252_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_7370]),
    [final] ).

cnf(i_0_13295,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_7650]),
    [final] ).

cnf(i_0_13296,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_7014]),
    [final] ).

cnf(i_0_13297,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_7015]),
    [final] ).

cnf(i_0_13298,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_7651]),
    [final] ).

cnf(i_0_13299,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk513_2(X2,X1)),esk514_2(X2,X1))),X2))
    | c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7241]),
    [final] ).

cnf(i_0_13300,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk512_2(X2,X1)),esk511_2(X2,X1))),X2))
    | c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7082]),
    [final] ).

cnf(i_0_13301,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk511_2(X2,X1)),esk512_2(X2,X1))),X2))
    | c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7082]),
    [final] ).

cnf(i_0_13302,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk501_2(X2,X1)),esk502_2(X2,X1))),X2))
    | c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6944]),
    [final] ).

cnf(i_0_13303,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk500_2(X2,X1)),esk501_2(X2,X1))),X2))
    | c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6944]),
    [final] ).

cnf(i_0_13304,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),esk115_2(X2,X1)),esk115_2(X2,X1))),X2))
    | c_Relation_Oirrefl(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7652]),
    [final] ).

cnf(i_0_13305,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_7653]),
    [final] ).

cnf(i_0_13306,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk66_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_7654]),
    [final] ).

cnf(i_0_13307,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_7655]),
    [final] ).

cnf(i_0_13308,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_7656]),
    [final] ).

cnf(i_0_13309,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_7657]),
    [final] ).

cnf(i_0_13310,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_7658]),
    [final] ).

cnf(i_0_13311,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_7474]),
    [final] ).

cnf(i_0_13312,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_7475]),
    [final] ).

cnf(i_0_13313,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_7659]),
    [final] ).

cnf(i_0_13314,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_7660]),
    [final] ).

cnf(i_0_13315,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_7064]),
    [final] ).

cnf(i_0_13316,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_7065]),
    [final] ).

cnf(i_0_13317,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_7661]),
    [final] ).

cnf(i_0_13318,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_7662]),
    [final] ).

cnf(i_0_13319,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_7122]),
    [final] ).

cnf(i_0_13320,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)),esk252_3(X1,X2,X3)),X2))
    | esk253_3(X1,X2,X3) != esk254_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_7370]),
    [final] ).

cnf(i_0_13321,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_7663]),
    [final] ).

cnf(i_0_13322,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_7664]),
    [final] ).

cnf(i_0_13323,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_7665]),
    [final] ).

cnf(i_0_13324,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_7666]),
    [final] ).

cnf(i_0_13325,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_7652]),
    [final] ).

cnf(i_0_13326,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_7667]),
    [final] ).

cnf(i_0_13327,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_7668]),
    [final] ).

cnf(i_0_13328,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_7474]),
    [final] ).

cnf(i_0_13329,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_7474]),
    [final] ).

cnf(i_0_13330,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_7475]),
    [final] ).

cnf(i_0_13331,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_7475]),
    [final] ).

cnf(i_0_13332,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_7669,c_0_6096]),
    [final] ).

cnf(i_0_13333,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_7670]),
    [final] ).

cnf(i_0_13334,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_7671]),
    [final] ).

cnf(i_0_13335,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_7672]),
    [final] ).

cnf(i_0_13336,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_7423]),
    [final] ).

cnf(i_0_13337,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_7424]),
    [final] ).

cnf(i_0_13338,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_7425]),
    [final] ).

cnf(i_0_13339,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),esk66_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_7654]),
    [final] ).

cnf(i_0_13340,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),esk437_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk438_2(X2,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7673]),
    [final] ).

cnf(i_0_13341,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),esk433_2(X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk432_2(X2,X1))))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7674]),
    [final] ).

cnf(i_0_13342,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_6499]),
    [final] ).

cnf(i_0_13343,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_7675]),
    [final] ).

cnf(i_0_13344,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_7676]),
    [final] ).

cnf(i_0_13345,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_7677]),
    [final] ).

cnf(i_0_13346,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_7678]),
    [final] ).

cnf(i_0_13347,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_7679]),
    [final] ).

cnf(i_0_13348,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_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),esk565_3(X1,X2,X3))),esk566_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_7680]),
    [final] ).

cnf(i_0_13349,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_7681]),
    [final] ).

cnf(i_0_13350,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_7682,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13351,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_7683,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13352,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_7684,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13353,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_7685,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13354,plain,
    ( hBOOL(hAPP(X1,X2))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(X1,esk481_4(X1,X2,X3,X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_7264]),
    [final] ).

cnf(i_0_13355,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_7686]),
    [final] ).

cnf(i_0_13356,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_7687]),
    [final] ).

cnf(i_0_13357,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_7688]),
    [final] ).

cnf(i_0_13358,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_7689]),
    [final] ).

cnf(i_0_13359,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_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),esk569_3(X1,X2,X3))),esk570_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13360,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_7691]),
    [final] ).

cnf(i_0_13361,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_7692]),
    [final] ).

cnf(i_0_13362,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk272_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk271_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_6273]),
    [final] ).

cnf(i_0_13363,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk269_3(X1,X2,X3)),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk268_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_6274]),
    [final] ).

cnf(i_0_13364,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_7693]),
    [final] ).

cnf(i_0_13365,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_7694]),
    [final] ).

cnf(i_0_13366,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_7695,c_0_6070]),
    [final] ).

cnf(i_0_13367,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_7696]),
    [final] ).

cnf(i_0_13368,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_7697]),
    [final] ).

cnf(i_0_13369,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_7698]),
    [final] ).

cnf(i_0_13370,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_7699]),
    [final] ).

cnf(i_0_13371,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_7700]),
    [final] ).

cnf(i_0_13372,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_7701]),
    [final] ).

cnf(i_0_13373,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_7702]),
    [final] ).

cnf(i_0_13374,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_7562]),
    [final] ).

cnf(i_0_13375,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_7562]),
    [final] ).

cnf(i_0_13376,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_7703]),
    [final] ).

cnf(i_0_13377,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_7704]),
    [final] ).

cnf(i_0_13378,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_7705,c_0_6289]),
    [final] ).

cnf(i_0_13379,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_7706]),
    [final] ).

cnf(i_0_13380,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_7158]),
    [final] ).

cnf(i_0_13381,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_7159]),
    [final] ).

cnf(i_0_13382,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_7707,c_0_6184]),
    [final] ).

cnf(i_0_13383,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_7445]),
    [final] ).

cnf(i_0_13384,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_7708]),
    [final] ).

cnf(i_0_13385,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_7709,c_0_6187]),
    [final] ).

cnf(i_0_13386,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,esk66_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_7654]),
    [final] ).

cnf(i_0_13387,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_7710]),
    [final] ).

cnf(i_0_13388,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_7711]),
    [final] ).

cnf(i_0_13389,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_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),esk569_3(X1,X2,X3))),esk570_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_7690]),
    [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),esk567_3(X1,X2,X3))),esk568_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),esk565_3(X1,X2,X3))),esk566_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_7680]),
    [final] ).

cnf(i_0_13391,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7712]),
    [final] ).

cnf(i_0_13392,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_7713,c_0_6726]),c_0_6726]),c_0_6726]),
    [final] ).

cnf(i_0_13393,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk69_3(X1,X3,X2))),esk70_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_7519]),
    [final] ).

cnf(i_0_13394,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_7562]),
    [final] ).

cnf(i_0_13395,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_7299]),
    [final] ).

cnf(i_0_13396,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_7299]),
    [final] ).

cnf(i_0_13397,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_7714,c_0_6184]),
    [final] ).

cnf(i_0_13398,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),esk562_3(X2,X3,X1)),c_Groups_Ozero__class_Ozero(X1))))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7715]),
    [final] ).

cnf(i_0_13399,plain,
    ( hBOOL(hAPP(X1,esk174_2(X1,X2)))
    | hBOOL(hAPP(X1,esk172_2(X1,X2)))
    | hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk172_2(X1,X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),esk173_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_7204]),
    [final] ).

cnf(i_0_13400,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_7716]),
    [final] ).

cnf(i_0_13401,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_7717]),
    [final] ).

cnf(i_0_13402,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk67_3(X1,X3,X2))),esk68_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_7526]),
    [final] ).

cnf(i_0_13403,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_7718]),
    [final] ).

cnf(i_0_13404,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_7719]),
    [final] ).

cnf(i_0_13405,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_7720]),
    [final] ).

cnf(i_0_13406,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_7721]),
    [final] ).

cnf(i_0_13407,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_7722]),
    [final] ).

cnf(i_0_13408,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_7723]),
    [final] ).

cnf(i_0_13409,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,esk255_4(X3,X2,X1,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_7253]),
    [final] ).

cnf(i_0_13410,plain,
    c_Option_Ooption_Ooption__case(X1,tc_prod(X2,tc_Lazy__Sequence_Olazy__sequence(X2)),X3,hAPP(c_Product__Type_Oprod_Oprod__case(X2,tc_Lazy__Sequence_Olazy__sequence(X2),X1),X4),hAPP(c_Lazy__Sequence_Oyield(X2),c_Lazy__Sequence_Olazy__sequence_OEmpty(X2))) = X3,
    inference(rw,[status(thm)],[i_0_7724,c_0_7594]),
    [final] ).

cnf(i_0_13411,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_7725]),
    [final] ).

cnf(i_0_13412,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_7725]),
    [final] ).

cnf(i_0_13413,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,esk66_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_7654]),
    [final] ).

cnf(i_0_13414,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_7726]),
    [final] ).

cnf(i_0_13415,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_7727]),
    [final] ).

cnf(i_0_13416,plain,
    ( hBOOL(hAPP(X1,esk296_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_7412]),
    [final] ).

cnf(i_0_13417,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_7654]),
    [final] ).

cnf(i_0_13418,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_7728]),
    [final] ).

cnf(i_0_13419,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_7282]),
    [final] ).

cnf(i_0_13420,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_6957]),
    [final] ).

cnf(i_0_13421,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_7729]),
    [final] ).

cnf(i_0_13422,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_7730]),
    [final] ).

cnf(i_0_13423,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_7731]),
    [final] ).

cnf(i_0_13424,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_7732]),
    [final] ).

cnf(i_0_13425,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_7733]),
    [final] ).

cnf(i_0_13426,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_7734]),
    [final] ).

cnf(i_0_13427,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_7735,c_0_6726]),c_0_6726]),
    [final] ).

cnf(i_0_13428,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_7505]),
    [final] ).

cnf(i_0_13429,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_7736]),
    [final] ).

cnf(i_0_13430,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_7737]),
    [final] ).

cnf(i_0_13431,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_7738]),
    [final] ).

cnf(i_0_13432,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_7739]),
    [final] ).

cnf(i_0_13433,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_7740]),
    [final] ).

cnf(i_0_13434,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_7436]),
    [final] ).

cnf(i_0_13435,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_7089]),
    [final] ).

cnf(i_0_13436,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_7090]),
    [final] ).

cnf(i_0_13437,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_7741]),
    [final] ).

cnf(i_0_13438,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_7741]),
    [final] ).

cnf(i_0_13439,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_7742]),
    [final] ).

cnf(i_0_13440,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_7742]),
    [final] ).

cnf(i_0_13441,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_7743,c_0_6096]),
    [final] ).

cnf(i_0_13442,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_7744]),
    [final] ).

cnf(i_0_13443,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_6774]),
    [final] ).

cnf(i_0_13444,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_7745]),
    [final] ).

cnf(i_0_13445,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_7746]),
    [final] ).

cnf(i_0_13446,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_7747]),
    [final] ).

cnf(i_0_13447,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_7748]),
    [final] ).

cnf(i_0_13448,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_7749,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13449,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_7750]),
    [final] ).

cnf(i_0_13450,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_7751,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13451,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_7752,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13452,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_7753,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13453,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_7754,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13454,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_7755]),
    [final] ).

cnf(i_0_13455,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_7756,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6219]),c_0_6219]),c_0_6219]),
    [final] ).

cnf(i_0_13456,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_7757]),
    [final] ).

cnf(i_0_13457,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_7758]),
    [final] ).

cnf(i_0_13458,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_7759,c_0_6103]),
    [final] ).

cnf(i_0_13459,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk157_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_7639]),
    [final] ).

cnf(i_0_13460,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk155_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_7640]),
    [final] ).

cnf(i_0_13461,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_7706]),
    [final] ).

cnf(i_0_13462,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_7760]),
    [final] ).

cnf(i_0_13463,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_7761]),
    [final] ).

cnf(i_0_13464,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_7762]),
    [final] ).

cnf(i_0_13465,plain,
    ( hBOOL(hAPP(X2,X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk16_3(X2,X3,X1)),esk17_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_7244]),
    [final] ).

cnf(i_0_13466,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_7763]),
    [final] ).

cnf(i_0_13467,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X5)),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)),X4))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7764]),
    [final] ).

cnf(i_0_13468,plain,
    ( c_Fun_Obij__betw(tc_Nat_Onat,X1,esk531_2(X2,X1),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7765]),
    [final] ).

cnf(i_0_13469,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_7766,c_0_6096]),
    [final] ).

cnf(i_0_13470,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_7767]),
    [final] ).

cnf(i_0_13471,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_7768]),
    [final] ).

cnf(i_0_13472,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_7769]),
    [final] ).

cnf(i_0_13473,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_7770]),
    [final] ).

cnf(i_0_13474,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_7771]),
    [final] ).

cnf(i_0_13475,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_7772]),
    [final] ).

cnf(i_0_13476,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_7773]),
    [final] ).

cnf(i_0_13477,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_7774]),
    [final] ).

cnf(i_0_13478,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_7775]),
    [final] ).

cnf(i_0_13479,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_7776]),
    [final] ).

cnf(i_0_13480,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_7777,c_0_6289]),
    [final] ).

cnf(i_0_13481,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_7778]),
    [final] ).

cnf(i_0_13482,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_7779]),
    [final] ).

cnf(i_0_13483,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_7780]),
    [final] ).

cnf(i_0_13484,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_7781]),
    [final] ).

cnf(i_0_13485,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_7782,c_0_6139]),
    [final] ).

cnf(i_0_13486,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,esk48_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_7227]),
    [final] ).

cnf(i_0_13487,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_7762]),
    [final] ).

cnf(i_0_13488,plain,
    ( c_Fun_Obij__betw(tc_Nat_Onat,X1,esk533_2(X2,X1),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)),X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7783]),
    [final] ).

cnf(i_0_13489,plain,
    ( c_Fun_Obij__betw(X1,tc_Nat_Onat,esk534_2(X2,X1),X2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7784]),
    [final] ).

cnf(i_0_13490,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_7785]),
    [final] ).

cnf(i_0_13491,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_7786]),
    [final] ).

cnf(i_0_13492,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_7787]),
    [final] ).

cnf(i_0_13493,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_7788]),
    [final] ).

cnf(i_0_13494,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_7789]),
    [final] ).

cnf(i_0_13495,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_7790]),
    [final] ).

cnf(i_0_13496,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_7791]),
    [final] ).

cnf(i_0_13497,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_7792]),
    [final] ).

cnf(i_0_13498,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_7793]),
    [final] ).

cnf(i_0_13499,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_7794]),
    [final] ).

cnf(i_0_13500,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_7795]),
    [final] ).

cnf(i_0_13501,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_7796]),
    [final] ).

cnf(i_0_13502,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_7797,c_0_6139]),
    [final] ).

cnf(i_0_13503,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_7798]),
    [final] ).

cnf(i_0_13504,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_7762]),
    [final] ).

cnf(i_0_13505,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk75_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_7799]),
    [final] ).

cnf(i_0_13506,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk78_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_7800]),
    [final] ).

cnf(i_0_13507,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk75_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_7799]),
    [final] ).

cnf(i_0_13508,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk78_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_7800]),
    [final] ).

cnf(i_0_13509,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_6503]),
    [final] ).

cnf(i_0_13510,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_7801]),
    [final] ).

cnf(i_0_13511,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_7802]),
    [final] ).

cnf(i_0_13512,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_7803]),
    [final] ).

cnf(i_0_13513,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_7804]),
    [final] ).

cnf(i_0_13514,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_7805]),
    [final] ).

cnf(i_0_13515,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_7806]),
    [final] ).

cnf(i_0_13516,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_7807]),
    [final] ).

cnf(i_0_13517,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_7808]),
    [final] ).

cnf(i_0_13518,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_7588]),
    [final] ).

cnf(i_0_13519,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_7589]),
    [final] ).

cnf(i_0_13520,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(rw,[status(thm)],[i_0_7809,c_0_6096]),
    [final] ).

cnf(i_0_13521,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_7810]),
    [final] ).

cnf(i_0_13522,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_7380]),
    [final] ).

cnf(i_0_13523,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_7811]),
    [final] ).

cnf(i_0_13524,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,esk273_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7812]),
    [final] ).

cnf(i_0_13525,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,esk85_3(X1,X2,X3))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7813]),
    [final] ).

cnf(i_0_13526,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_7814]),
    [final] ).

cnf(i_0_13527,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_7815]),
    [final] ).

cnf(i_0_13528,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_7816]),
    [final] ).

cnf(i_0_13529,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_7817]),
    [final] ).

cnf(i_0_13530,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_7818]),
    [final] ).

cnf(i_0_13531,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_7819]),
    [final] ).

cnf(i_0_13532,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_7087]),
    [final] ).

cnf(i_0_13533,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_5322]),
    [final] ).

cnf(i_0_13534,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_7820]),
    [final] ).

cnf(i_0_13535,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_7821]),
    [final] ).

cnf(i_0_13536,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_7822]),
    [final] ).

cnf(i_0_13537,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_7823]),
    [final] ).

cnf(i_0_13538,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_7824]),
    [final] ).

cnf(i_0_13539,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_7825]),
    [final] ).

cnf(i_0_13540,plain,
    ( X1 = hAPP(X2,esk5_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_7138]),
    [final] ).

cnf(i_0_13541,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_7826]),
    [final] ).

cnf(i_0_13542,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_7530]),
    [final] ).

cnf(i_0_13543,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_7827]),
    [final] ).

cnf(i_0_13544,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_6577]),
    [final] ).

cnf(i_0_13545,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_7828]),
    [final] ).

cnf(i_0_13546,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_7829]),
    [final] ).

cnf(i_0_13547,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_7830,c_0_6184]),
    [final] ).

cnf(i_0_13548,plain,
    ( c_Relation_Oantisym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(rw,[status(thm)],[i_0_7831,c_0_6096]),
    [final] ).

cnf(i_0_13549,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(rw,[status(thm)],[i_0_7832,c_0_6096]),
    [final] ).

cnf(i_0_13550,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_7833]),
    [final] ).

cnf(i_0_13551,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_7834]),
    [final] ).

cnf(i_0_13552,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_7835]),
    [final] ).

cnf(i_0_13553,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_7835]),
    [final] ).

cnf(i_0_13554,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_7836]),
    [final] ).

cnf(i_0_13555,plain,
    ( hBOOL(hAPP(X1,esk487_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_7283]),
    [final] ).

cnf(i_0_13556,plain,
    ( hBOOL(hAPP(X1,esk479_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_7284]),
    [final] ).

cnf(i_0_13557,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_7837,c_0_6096]),
    [final] ).

cnf(i_0_13558,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_7838,c_0_6096]),
    [final] ).

cnf(i_0_13559,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_7011]),
    [final] ).

cnf(i_0_13560,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_7012]),
    [final] ).

cnf(i_0_13561,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_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),esk565_3(X1,X2,X3))),esk566_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_7680]),
    [final] ).

cnf(i_0_13562,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_7839,c_0_6289]),
    [final] ).

cnf(i_0_13563,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_7840]),
    [final] ).

cnf(i_0_13564,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_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_7680]),
    [final] ).

cnf(i_0_13565,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_7122]),
    [final] ).

cnf(i_0_13566,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_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),esk569_3(X1,X2,X3))),esk570_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13567,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_7841]),
    [final] ).

cnf(i_0_13568,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_7842]),
    [final] ).

cnf(i_0_13569,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_7843]),
    [final] ).

cnf(i_0_13570,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_7844]),
    [final] ).

cnf(i_0_13571,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_7845]),
    [final] ).

cnf(i_0_13572,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_7846,c_0_6096]),
    [final] ).

cnf(i_0_13573,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_7847]),
    [final] ).

cnf(i_0_13574,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_7848]),
    [final] ).

cnf(i_0_13575,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_7849]),
    [final] ).

cnf(i_0_13576,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_7850]),
    [final] ).

cnf(i_0_13577,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_7851]),
    [final] ).

cnf(i_0_13578,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X1,X2,X3)),X2))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13579,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_7852]),
    [final] ).

cnf(i_0_13580,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_7853]),
    [final] ).

cnf(i_0_13581,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_7854]),
    [final] ).

cnf(i_0_13582,plain,
    ( c_Fun_Oinj__on(X1,X2,esk28_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_6630]),
    [final] ).

cnf(i_0_13583,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_7855]),
    [final] ).

cnf(i_0_13584,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_7856]),
    [final] ).

cnf(i_0_13585,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_7857,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13586,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_7858]),
    [final] ).

cnf(i_0_13587,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_7859]),
    [final] ).

cnf(i_0_13588,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_7860]),
    [final] ).

cnf(i_0_13589,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_7848]),
    [final] ).

cnf(i_0_13590,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_7847]),
    [final] ).

cnf(i_0_13591,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_7861]),
    [final] ).

cnf(i_0_13592,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_7862]),
    [final] ).

cnf(i_0_13593,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_7863]),
    [final] ).

cnf(i_0_13594,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_7864]),
    [final] ).

cnf(i_0_13595,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_7865]),
    [final] ).

cnf(i_0_13596,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_7866]),
    [final] ).

cnf(i_0_13597,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk256_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_7604]),
    [final] ).

cnf(i_0_13598,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_7867,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13599,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_7847]),
    [final] ).

cnf(i_0_13600,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_7848]),
    [final] ).

cnf(i_0_13601,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_7868]),
    [final] ).

cnf(i_0_13602,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_7869]),
    [final] ).

cnf(i_0_13603,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_7706]),
    [final] ).

cnf(i_0_13604,plain,
    ( v_P(X2,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X1)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
    | ~ v_P(hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,X1)),X2),hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X1)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7870]),
    [final] ).

cnf(i_0_13605,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_7871]),
    [final] ).

cnf(i_0_13606,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_7872]),
    [final] ).

cnf(i_0_13607,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk385_3(X1,X3,X2))))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7873]),
    [final] ).

cnf(i_0_13608,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_7874]),
    [final] ).

cnf(i_0_13609,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_7502]),
    [final] ).

cnf(i_0_13610,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_7875,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13611,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_7876,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13612,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_7848]),
    [final] ).

cnf(i_0_13613,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_7847]),
    [final] ).

cnf(i_0_13614,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_7591]),
    [final] ).

cnf(i_0_13615,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_7592]),
    [final] ).

cnf(i_0_13616,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_7877,c_0_6103]),
    [final] ).

cnf(i_0_13617,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_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),esk569_3(X1,X2,X3))),esk570_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_7690]),
    [final] ).

cnf(i_0_13618,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_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),esk565_3(X1,X2,X3))),esk566_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_7680]),
    [final] ).

cnf(i_0_13619,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_6449]),
    [final] ).

cnf(i_0_13620,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),esk429_3(X2,X3,X1)),esk430_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_7878]),
    [final] ).

cnf(i_0_13621,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_7879]),
    [final] ).

cnf(i_0_13622,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_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_7690]),
    [final] ).

cnf(i_0_13623,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_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_7680]),
    [final] ).

cnf(i_0_13624,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_7158]),
    [final] ).

cnf(i_0_13625,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_7159]),
    [final] ).

cnf(i_0_13626,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_7880]),
    [final] ).

cnf(i_0_13627,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_7881]),
    [final] ).

cnf(i_0_13628,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk70_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_7519]),
    [final] ).

cnf(i_0_13629,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_7882]),
    [final] ).

cnf(i_0_13630,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_7474]),
    [final] ).

cnf(i_0_13631,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_7475]),
    [final] ).

cnf(i_0_13632,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_7883]),
    [final] ).

cnf(i_0_13633,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_7884]),
    [final] ).

cnf(i_0_13634,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk68_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_7526]),
    [final] ).

cnf(i_0_13635,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),esk157_3(X2,X1,X3)),esk156_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_7639]),
    [final] ).

cnf(i_0_13636,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),esk155_3(X2,X1,X3)),esk154_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_7640]),
    [final] ).

cnf(i_0_13637,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_7885]),
    [final] ).

cnf(i_0_13638,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_7886]),
    [final] ).

cnf(i_0_13639,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_7887]),
    [final] ).

cnf(i_0_13640,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_7588]),
    [final] ).

cnf(i_0_13641,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_7474]),
    [final] ).

cnf(i_0_13642,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_7888]),
    [final] ).

cnf(i_0_13643,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_7889]),
    [final] ).

cnf(i_0_13644,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_7890]),
    [final] ).

cnf(i_0_13645,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_7589]),
    [final] ).

cnf(i_0_13646,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_7475]),
    [final] ).

cnf(i_0_13647,plain,
    ( X2 = hAPP(c_Set_Oimage(tc_Nat_Onat,X1,esk284_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)),esk283_2(X2,X1))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7598]),
    [final] ).

cnf(i_0_13648,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_7833]),
    [final] ).

cnf(i_0_13649,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_7891]),
    [final] ).

cnf(i_0_13650,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_7517]),
    [final] ).

cnf(i_0_13651,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_7518]),
    [final] ).

cnf(i_0_13652,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk300_3(X2,X3,X1)),X3))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk299_3(X2,X3,X1)),X2))
    | c_Relation_Orefl__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6190]),
    [final] ).

cnf(i_0_13653,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_7892]),
    [final] ).

cnf(i_0_13654,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_7893]),
    [final] ).

cnf(i_0_13655,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_7662]),
    [final] ).

cnf(i_0_13656,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_7894,c_0_6726]),
    [final] ).

cnf(i_0_13657,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_7895,c_0_6139]),
    [final] ).

cnf(i_0_13658,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_7896,c_0_6139]),
    [final] ).

cnf(i_0_13659,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_7897]),
    [final] ).

cnf(i_0_13660,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_7898]),
    [final] ).

cnf(i_0_13661,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_7899]),
    [final] ).

cnf(i_0_13662,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_7900]),
    [final] ).

cnf(i_0_13663,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_7901]),
    [final] ).

cnf(i_0_13664,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_7902]),
    [final] ).

cnf(i_0_13665,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_7849]),
    [final] ).

cnf(i_0_13666,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_7903]),
    [final] ).

cnf(i_0_13667,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_7904]),
    [final] ).

cnf(i_0_13668,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_7905]),
    [final] ).

cnf(i_0_13669,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_7906]),
    [final] ).

cnf(i_0_13670,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_7907,c_0_6187]),c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_13671,plain,
    c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_7908]),
    [final] ).

cnf(i_0_13672,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_7909]),
    [final] ).

cnf(i_0_13673,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_5323]),
    [final] ).

cnf(i_0_13674,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_7520]),
    [final] ).

cnf(i_0_13675,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_7910]),
    [final] ).

cnf(i_0_13676,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_7911]),
    [final] ).

cnf(i_0_13677,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)),esk250_3(X2,X3,X1)),esk251_3(X2,X3,X1)) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7581]),
    [final] ).

cnf(i_0_13678,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_7912]),
    [final] ).

cnf(i_0_13679,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_7913]),
    [final] ).

cnf(i_0_13680,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_7914]),
    [final] ).

cnf(i_0_13681,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_6190]),
    [final] ).

cnf(i_0_13682,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_6680]),
    [final] ).

cnf(i_0_13683,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_7915]),
    [final] ).

cnf(i_0_13684,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_7916]),
    [final] ).

cnf(i_0_13685,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_7917]),
    [final] ).

cnf(i_0_13686,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_7918]),
    [final] ).

cnf(i_0_13687,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_7919]),
    [final] ).

cnf(i_0_13688,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_6774]),
    [final] ).

cnf(i_0_13689,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_7667]),
    [final] ).

cnf(i_0_13690,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_7920]),
    [final] ).

cnf(i_0_13691,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_7921]),
    [final] ).

cnf(i_0_13692,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_7922]),
    [final] ).

cnf(i_0_13693,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_7923,c_0_6289]),
    [final] ).

cnf(i_0_13694,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),esk482_3(X3,X2,X1))))
    | ~ class_Fields_Olinordered__field(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7924]),
    [final] ).

cnf(i_0_13695,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_7616]),
    [final] ).

cnf(i_0_13696,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_7925]),
    [final] ).

cnf(i_0_13697,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_7926]),
    [final] ).

cnf(i_0_13698,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_7927]),
    [final] ).

cnf(i_0_13699,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_7928]),
    [final] ).

cnf(i_0_13700,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_7929]),
    [final] ).

cnf(i_0_13701,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_7930]),
    [final] ).

cnf(i_0_13702,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_7931]),
    [final] ).

cnf(i_0_13703,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_7932]),
    [final] ).

cnf(i_0_13704,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_7933]),
    [final] ).

cnf(i_0_13705,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_7934]),
    [final] ).

cnf(i_0_13706,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_7935]),
    [final] ).

cnf(i_0_13707,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_7936,c_0_6289]),
    [final] ).

cnf(i_0_13708,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_7937]),
    [final] ).

cnf(i_0_13709,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_7938]),
    [final] ).

cnf(i_0_13710,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_7939]),
    [final] ).

cnf(i_0_13711,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_7577]),
    [final] ).

cnf(i_0_13712,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_7014]),
    [final] ).

cnf(i_0_13713,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_7015]),
    [final] ).

cnf(i_0_13714,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_7940,c_0_6706]),
    [final] ).

cnf(i_0_13715,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_7941]),
    [final] ).

cnf(i_0_13716,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_7576]),
    [final] ).

cnf(i_0_13717,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_7942]),
    [final] ).

cnf(i_0_13718,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,esk274_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_7943]),
    [final] ).

cnf(i_0_13719,plain,
    ( c_List_Olist__ex(tc_Nat_Onat,X1,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))
    | c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),X1),X2,X3) ),
    inference(rw,[status(thm)],[i_0_7944,c_0_6187]),
    [final] ).

cnf(i_0_13720,plain,
    ( hAPP(X1,esk22_4(X2,X1,X3,X4)) = hAPP(X1,esk23_4(X2,X1,X3,X4))
    | c_Fun_Oinj__on(X4,X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7345]),
    [final] ).

cnf(i_0_13721,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_7585]),
    [final] ).

cnf(i_0_13722,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_7945]),
    [final] ).

cnf(i_0_13723,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_13724,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7946]),
    [final] ).

cnf(i_0_13725,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7947]),
    [final] ).

cnf(i_0_13726,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_7948]),
    [final] ).

cnf(i_0_13727,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_7949]),
    [final] ).

cnf(i_0_13728,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_7950]),
    [final] ).

cnf(i_0_13729,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_7951]),
    [final] ).

cnf(i_0_13730,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_7952]),
    [final] ).

cnf(i_0_13731,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7953]),
    [final] ).

cnf(i_0_13732,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_7954]),
    [final] ).

cnf(i_0_13733,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_7955]),
    [final] ).

cnf(i_0_13734,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_7956]),
    [final] ).

cnf(i_0_13735,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_3(X1,X2,X3))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk565_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_13736,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk565_3(X2,X3,X1))),esk566_3(X2,X3,X1))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_13737,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_7957]),
    [final] ).

cnf(i_0_13738,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_7958]),
    [final] ).

cnf(i_0_13739,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_6579]),
    [final] ).

cnf(i_0_13740,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_7959]),
    [final] ).

cnf(i_0_13741,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_7960]),
    [final] ).

cnf(i_0_13742,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_7961]),
    [final] ).

cnf(i_0_13743,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_7962]),
    [final] ).

cnf(i_0_13744,plain,
    ( hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),esk563_3(X2,X4,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),c_Groups_Ozero__class_Ozero(X1))))
    | ~ hBOOL(hAPP(X4,X3))
    | ~ class_Rings_Odvd(X1)
    | ~ class_Rings_Osemiring__0(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7715]),
    [final] ).

cnf(i_0_13745,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_7963,c_0_6289]),
    [final] ).

cnf(i_0_13746,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7964]),
    [final] ).

cnf(i_0_13747,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7965]),
    [final] ).

cnf(i_0_13748,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_7966]),
    [final] ).

cnf(i_0_13749,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk570_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13750,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk569_3(X2,X3,X1))),esk570_3(X2,X3,X1))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13751,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk473_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7967]),
    [final] ).

cnf(i_0_13752,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk470_3(X3,X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7968]),
    [final] ).

cnf(i_0_13753,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_7969,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_13754,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_7970]),
    [final] ).

cnf(i_0_13755,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_7971]),
    [final] ).

cnf(i_0_13756,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_7972]),
    [final] ).

cnf(i_0_13757,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_7973]),
    [final] ).

cnf(i_0_13758,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_7974]),
    [final] ).

cnf(i_0_13759,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_7975]),
    [final] ).

cnf(i_0_13760,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_7976]),
    [final] ).

cnf(i_0_13761,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_7977]),
    [final] ).

cnf(i_0_13762,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_7978]),
    [final] ).

cnf(i_0_13763,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_7674]),
    [final] ).

cnf(i_0_13764,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_13765,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_7979]),
    [final] ).

cnf(i_0_13766,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_7980]),
    [final] ).

cnf(i_0_13767,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_7981]),
    [final] ).

cnf(i_0_13768,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_7982]),
    [final] ).

cnf(i_0_13769,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_7859]),
    [final] ).

cnf(i_0_13770,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_7983,c_0_6070]),
    [final] ).

cnf(i_0_13771,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_7984,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13772,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_7985]),
    [final] ).

cnf(i_0_13773,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_6774]),
    [final] ).

cnf(i_0_13774,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_7986]),
    [final] ).

cnf(i_0_13775,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_7987]),
    [final] ).

cnf(i_0_13776,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_7988]),
    [final] ).

cnf(i_0_13777,plain,
    ( hBOOL(hAPP(X1,esk112_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6843]),
    [final] ).

cnf(i_0_13778,plain,
    ( hBOOL(hAPP(X1,esk112_4(X1,X2,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X3))
    | ~ hBOOL(hAPP(X1,X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_6843]),
    [final] ).

cnf(i_0_13779,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7712]),
    [final] ).

cnf(i_0_13780,plain,
    c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_7989]),
    [final] ).

cnf(i_0_13781,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_7990,c_0_6706]),
    [final] ).

cnf(i_0_13782,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_7991,c_0_7992]),c_0_7993]),c_0_7993]),
    [final] ).

cnf(i_0_13783,plain,
    ( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7542]),
    [final] ).

cnf(i_0_13784,plain,
    ( c_Fun_Ofun__upd(X4,X5,X1,X2,X3) = X1
    | hAPP(X1,X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_7994]),
    [final] ).

cnf(i_0_13785,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),esk35_3(X2,X3,X1)),esk36_3(X2,X3,X1)))
    | hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7995]),
    [final] ).

cnf(i_0_13786,plain,
    ( hAPP(X1,esk272_3(X2,X1,X3)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk271_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_6273]),
    [final] ).

cnf(i_0_13787,plain,
    ( hAPP(X1,esk269_3(X2,X1,X3)) = X2
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk268_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_6274]),
    [final] ).

cnf(i_0_13788,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_7996]),
    [final] ).

cnf(i_0_13789,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_7997]),
    [final] ).

cnf(i_0_13790,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_7998]),
    [final] ).

cnf(i_0_13791,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_7999]),
    [final] ).

cnf(i_0_13792,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_8000]),
    [final] ).

cnf(i_0_13793,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_8001]),
    [final] ).

cnf(i_0_13794,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),
    inference(split_conjunct,[status(thm)],[i_0_8002]),
    [final] ).

cnf(i_0_13795,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(hAPP(c_Product__Type_OPair(X1,X2),X5),X6)),
    inference(split_conjunct,[status(thm)],[i_0_8003]),
    [final] ).

cnf(i_0_13796,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_8004]),
    [final] ).

cnf(i_0_13797,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),esk435_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2))) ),
    inference(rw,[status(thm)],[i_0_8005,c_0_6289]),
    [final] ).

cnf(i_0_13798,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_7543]),
    [final] ).

cnf(i_0_13799,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_7544]),
    [final] ).

cnf(i_0_13800,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_7886]),
    [final] ).

cnf(i_0_13801,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_8006]),
    [final] ).

cnf(i_0_13802,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_7474]),
    [final] ).

cnf(i_0_13803,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_7885]),
    [final] ).

cnf(i_0_13804,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_7588]),
    [final] ).

cnf(i_0_13805,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_7889]),
    [final] ).

cnf(i_0_13806,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_8007]),
    [final] ).

cnf(i_0_13807,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_7475]),
    [final] ).

cnf(i_0_13808,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_7888]),
    [final] ).

cnf(i_0_13809,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_7589]),
    [final] ).

cnf(i_0_13810,plain,
    ( c_Fun_Obij__betw(X3,X3,c_Fun_Oid(X3),X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7545]),
    [final] ).

cnf(i_0_13811,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_8008]),
    [final] ).

cnf(i_0_13812,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_8009]),
    [final] ).

cnf(i_0_13813,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_7562]),
    [final] ).

cnf(i_0_13814,plain,
    ( X3 = X2
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),c_fequal),esk389_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_7273]),
    [final] ).

cnf(i_0_13815,plain,
    c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X2,X3,X4,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_8010]),
    [final] ).

cnf(i_0_13816,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_8011]),
    [final] ).

cnf(i_0_13817,plain,
    c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X2),
    inference(split_conjunct,[status(thm)],[i_0_8012]),
    [final] ).

cnf(i_0_13818,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_8013]),
    [final] ).

cnf(i_0_13819,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_8014]),
    [final] ).

cnf(i_0_13820,plain,
    ( c_List_Olist__all2(X3,X3,c_fequal,X1,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_7550]),
    [final] ).

cnf(i_0_13821,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_7849]),
    [final] ).

cnf(i_0_13822,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk570_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13823,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_3(X1,X2,X3))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk565_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_13824,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk569_3(X2,X3,X1))),esk570_3(X2,X3,X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13825,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X3),esk565_3(X2,X3,X1))),esk566_3(X2,X3,X1))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_13826,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_8015,c_0_6706]),
    [final] ).

cnf(i_0_13827,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_8016]),
    [final] ).

cnf(i_0_13828,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_8017]),
    [final] ).

cnf(i_0_13829,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_8018]),
    [final] ).

cnf(i_0_13830,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_8019]),
    [final] ).

cnf(i_0_13831,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_7474]),
    [final] ).

cnf(i_0_13832,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_7475]),
    [final] ).

cnf(i_0_13833,plain,
    ( hBOOL(hAPP(X1,esk124_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_7258]),
    [final] ).

cnf(i_0_13834,plain,
    ( hBOOL(hAPP(X1,esk120_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_7259]),
    [final] ).

cnf(i_0_13835,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_8020]),
    [final] ).

cnf(i_0_13836,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_8021]),
    [final] ).

cnf(i_0_13837,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_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_7680]),
    [final] ).

cnf(i_0_13838,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_8022,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_13839,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk384_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_7873]),
    [final] ).

cnf(i_0_13840,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_8023]),
    [final] ).

cnf(i_0_13841,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_8024]),
    [final] ).

cnf(i_0_13842,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_8025]),
    [final] ).

cnf(i_0_13843,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_8026,c_0_6726]),c_0_6726]),
    [final] ).

cnf(i_0_13844,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_8027,c_0_6103]),c_0_6103]),
    [final] ).

cnf(i_0_13845,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13846,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,esk182_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_7303]),
    [final] ).

cnf(i_0_13847,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_8028]),
    [final] ).

cnf(i_0_13848,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_8029]),
    [final] ).

cnf(i_0_13849,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_8030]),
    [final] ).

cnf(i_0_13850,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_7011]),
    [final] ).

cnf(i_0_13851,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_7012]),
    [final] ).

cnf(i_0_13852,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_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),esk565_3(X2,X1,X3))),esk566_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_7680]),
    [final] ).

cnf(i_0_13853,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_8031]),
    [final] ).

cnf(i_0_13854,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_8032]),
    [final] ).

cnf(i_0_13855,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_8033]),
    [final] ).

cnf(i_0_13856,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_8034]),
    [final] ).

cnf(i_0_13857,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_7935]),
    [final] ).

cnf(i_0_13858,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_7935]),
    [final] ).

cnf(i_0_13859,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_8035]),
    [final] ).

cnf(i_0_13860,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_6807]),
    [final] ).

cnf(i_0_13861,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_8036]),
    [final] ).

cnf(i_0_13862,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_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),esk569_3(X2,X1,X3))),esk570_3(X2,X1,X3))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13863,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_8037]),
    [final] ).

cnf(i_0_13864,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_8038]),
    [final] ).

cnf(i_0_13865,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_8039]),
    [final] ).

cnf(i_0_13866,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_8040]),
    [final] ).

cnf(i_0_13867,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_8039]),
    [final] ).

cnf(i_0_13868,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_8040]),
    [final] ).

cnf(i_0_13869,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_7986]),
    [final] ).

cnf(i_0_13870,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_13871,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_7987]),
    [final] ).

cnf(i_0_13872,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_8042]),
    [final] ).

cnf(i_0_13873,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_7859]),
    [final] ).

cnf(i_0_13874,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_8043]),
    [final] ).

cnf(i_0_13875,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_8044]),
    [final] ).

cnf(i_0_13876,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_6650]),
    [final] ).

cnf(i_0_13877,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_6774]),
    [final] ).

cnf(i_0_13878,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_8045]),
    [final] ).

cnf(i_0_13879,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_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_7680]),
    [final] ).

cnf(i_0_13880,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_8046]),
    [final] ).

cnf(i_0_13881,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_8047,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13882,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_7183]),
    [final] ).

cnf(i_0_13883,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_8048]),
    [final] ).

cnf(i_0_13884,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_8049]),
    [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(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_7014]),
    [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(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_7015]),
    [final] ).

cnf(i_0_13887,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_8050]),
    [final] ).

cnf(i_0_13888,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_8051]),
    [final] ).

cnf(i_0_13889,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X1,X2,X3)),X2))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_13890,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,esk184_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_7311]),
    [final] ).

cnf(i_0_13891,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_8052]),
    [final] ).

cnf(i_0_13892,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_8053,c_0_6184]),
    [final] ).

cnf(i_0_13893,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_8054]),
    [final] ).

cnf(i_0_13894,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_8055]),
    [final] ).

cnf(i_0_13895,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_8056,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13896,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Oantisym(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8057]),
    [final] ).

cnf(i_0_13897,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_8058]),
    [final] ).

cnf(i_0_13898,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_8059]),
    [final] ).

cnf(i_0_13899,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_8060]),
    [final] ).

cnf(i_0_13900,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_7158]),
    [final] ).

cnf(i_0_13901,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_7159]),
    [final] ).

cnf(i_0_13902,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))
    | esk253_3(X1,X2,X3) != esk254_3(X1,X2,X3)
    | hAPP(c_Finite__Set_Ocard(X3),esk252_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_7370]),
    [final] ).

cnf(i_0_13903,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_8061]),
    [final] ).

cnf(i_0_13904,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_8062]),
    [final] ).

cnf(i_0_13905,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_8063]),
    [final] ).

cnf(i_0_13906,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_8064]),
    [final] ).

cnf(i_0_13907,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_8065]),
    [final] ).

cnf(i_0_13908,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_8066]),
    [final] ).

cnf(i_0_13909,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_8067]),
    [final] ).

cnf(i_0_13910,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_8068]),
    [final] ).

cnf(i_0_13911,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_8069]),
    [final] ).

cnf(i_0_13912,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_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_7690]),
    [final] ).

cnf(i_0_13913,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_3(X1,X2,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_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_7680]),
    [final] ).

cnf(i_0_13914,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_8070]),
    [final] ).

cnf(i_0_13915,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_8071]),
    [final] ).

cnf(i_0_13916,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_8072,c_0_6187]),
    [final] ).

cnf(i_0_13917,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_8073]),
    [final] ).

cnf(i_0_13918,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_5322]),
    [final] ).

cnf(i_0_13919,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk70_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_7519]),
    [final] ).

cnf(i_0_13920,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_8074]),
    [final] ).

cnf(i_0_13921,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_8075,c_0_6070]),
    [final] ).

cnf(i_0_13922,plain,
    ( hBOOL(hAPP(X1,esk492_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_8076]),
    [final] ).

cnf(i_0_13923,plain,
    c_Fun_Oinj__on(X1,tc_prod(X2,X1),esk257_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_6541]),
    [final] ).

cnf(i_0_13924,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_8077]),
    [final] ).

cnf(i_0_13925,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_8078]),
    [final] ).

cnf(i_0_13926,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_8079]),
    [final] ).

cnf(i_0_13927,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_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),esk569_3(X2,X1,X3))),esk570_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_7690]),
    [final] ).

cnf(i_0_13928,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_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),esk565_3(X2,X1,X3))),esk566_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_7680]),
    [final] ).

cnf(i_0_13929,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_7588]),
    [final] ).

cnf(i_0_13930,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_7588]),
    [final] ).

cnf(i_0_13931,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_7589]),
    [final] ).

cnf(i_0_13932,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_7589]),
    [final] ).

cnf(i_0_13933,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_7588]),
    [final] ).

cnf(i_0_13934,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_7589]),
    [final] ).

cnf(i_0_13935,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_8080]),
    [final] ).

cnf(i_0_13936,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_8081]),
    [final] ).

cnf(i_0_13937,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_8082]),
    [final] ).

cnf(i_0_13938,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_8083]),
    [final] ).

cnf(i_0_13939,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_8084,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13940,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_8085,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13941,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_8086,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13942,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_8087,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_13943,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_7607]),
    [final] ).

cnf(i_0_13944,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_8088]),
    [final] ).

cnf(i_0_13945,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_8089]),
    [final] ).

cnf(i_0_13946,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_6774]),
    [final] ).

cnf(i_0_13947,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_8090]),
    [final] ).

cnf(i_0_13948,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_8091]),
    [final] ).

cnf(i_0_13949,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_8092]),
    [final] ).

cnf(i_0_13950,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk68_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_7526]),
    [final] ).

cnf(i_0_13951,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_8093]),
    [final] ).

cnf(i_0_13952,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_8094]),
    [final] ).

cnf(i_0_13953,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_8095]),
    [final] ).

cnf(i_0_13954,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_8096]),
    [final] ).

cnf(i_0_13955,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_8097]),
    [final] ).

cnf(i_0_13956,hypothesis,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,v_n)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))),
    inference(split_conjunct,[status(thm)],[conj_3]),
    [final] ).

cnf(i_0_13957,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_8035]),
    [final] ).

cnf(i_0_13958,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk365_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_8098]),
    [final] ).

cnf(i_0_13959,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_8099]),
    [final] ).

cnf(i_0_13960,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk197_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_8100]),
    [final] ).

cnf(i_0_13961,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_8101]),
    [final] ).

cnf(i_0_13962,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_8102]),
    [final] ).

cnf(i_0_13963,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_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_7690]),
    [final] ).

cnf(i_0_13964,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_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_7680]),
    [final] ).

cnf(i_0_13965,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_8103]),
    [final] ).

cnf(i_0_13966,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_8104]),
    [final] ).

cnf(i_0_13967,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_8105]),
    [final] ).

cnf(i_0_13968,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_8106]),
    [final] ).

cnf(i_0_13969,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_8107]),
    [final] ).

cnf(i_0_13970,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_8108]),
    [final] ).

cnf(i_0_13971,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_8109]),
    [final] ).

cnf(i_0_13972,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_7660]),
    [final] ).

cnf(i_0_13973,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_8110]),
    [final] ).

cnf(i_0_13974,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_7847]),
    [final] ).

cnf(i_0_13975,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_8111]),
    [final] ).

cnf(i_0_13976,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_7848]),
    [final] ).

cnf(i_0_13977,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_8112]),
    [final] ).

cnf(i_0_13978,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_8113]),
    [final] ).

cnf(i_0_13979,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_7793]),
    [final] ).

cnf(i_0_13980,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_8114]),
    [final] ).

cnf(i_0_13981,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_8115]),
    [final] ).

cnf(i_0_13982,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_8116]),
    [final] ).

cnf(i_0_13983,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_8117]),
    [final] ).

cnf(i_0_13984,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_8118]),
    [final] ).

cnf(i_0_13985,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_7796]),
    [final] ).

cnf(i_0_13986,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_8119]),
    [final] ).

cnf(i_0_13987,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_8120]),
    [final] ).

cnf(i_0_13988,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_8121]),
    [final] ).

cnf(i_0_13989,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_8122]),
    [final] ).

cnf(i_0_13990,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_8123]),
    [final] ).

cnf(i_0_13991,plain,
    ( c_Big__Operators_Olinorder__class_OMax(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk327_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_8124]),
    [final] ).

cnf(i_0_13992,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_5470]),
    [final] ).

cnf(i_0_13993,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8125]),
    [final] ).

cnf(i_0_13994,plain,
    ( c_List_Olist__all(X2,X1,X3)
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk474_3(X3,X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8126]),
    [final] ).

cnf(i_0_13995,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_7813]),
    [final] ).

cnf(i_0_13996,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_8127]),
    [final] ).

cnf(i_0_13997,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_8128]),
    [final] ).

cnf(i_0_13998,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_8129]),
    [final] ).

cnf(i_0_13999,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_8130]),
    [final] ).

cnf(i_0_14000,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_8131,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14001,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_8132,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14002,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_8108]),
    [final] ).

cnf(i_0_14003,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_8107]),
    [final] ).

cnf(i_0_14004,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_8133]),
    [final] ).

cnf(i_0_14005,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_8134,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14006,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_8135,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14007,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_8136]),
    [final] ).

cnf(i_0_14008,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_8137]),
    [final] ).

cnf(i_0_14009,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_8138]),
    [final] ).

cnf(i_0_14010,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_8139,c_0_6706]),
    [final] ).

cnf(i_0_14011,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_7926]),
    [final] ).

cnf(i_0_14012,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_8140]),
    [final] ).

cnf(i_0_14013,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_8141]),
    [final] ).

cnf(i_0_14014,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_8142]),
    [final] ).

cnf(i_0_14015,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_8143]),
    [final] ).

cnf(i_0_14016,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_8120]),
    [final] ).

cnf(i_0_14017,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_8120]),
    [final] ).

cnf(i_0_14018,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_8121]),
    [final] ).

cnf(i_0_14019,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_8121]),
    [final] ).

cnf(i_0_14020,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_8122]),
    [final] ).

cnf(i_0_14021,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_8122]),
    [final] ).

cnf(i_0_14022,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_6830]),
    [final] ).

cnf(i_0_14023,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_6830]),
    [final] ).

cnf(i_0_14024,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_7719]),
    [final] ).

cnf(i_0_14025,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_8144]),
    [final] ).

cnf(i_0_14026,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_7804]),
    [final] ).

cnf(i_0_14027,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_8145]),
    [final] ).

cnf(i_0_14028,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_7806]),
    [final] ).

cnf(i_0_14029,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_8146]),
    [final] ).

cnf(i_0_14030,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_7847]),
    [final] ).

cnf(i_0_14031,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_8147]),
    [final] ).

cnf(i_0_14032,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_7848]),
    [final] ).

cnf(i_0_14033,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_7815]),
    [final] ).

cnf(i_0_14034,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_8148]),
    [final] ).

cnf(i_0_14035,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_8149]),
    [final] ).

cnf(i_0_14036,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_8150]),
    [final] ).

cnf(i_0_14037,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_8151]),
    [final] ).

cnf(i_0_14038,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_7816]),
    [final] ).

cnf(i_0_14039,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_7122]),
    [final] ).

cnf(i_0_14040,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_7844]),
    [final] ).

cnf(i_0_14041,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_7845]),
    [final] ).

cnf(i_0_14042,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_7758]),
    [final] ).

cnf(i_0_14043,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_8152,c_0_6289]),
    [final] ).

cnf(i_0_14044,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk319_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7172]),
    [final] ).

cnf(i_0_14045,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk318_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7173]),
    [final] ).

cnf(i_0_14046,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk226_3(X2,X3,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7174]),
    [final] ).

cnf(i_0_14047,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_8153]),
    [final] ).

cnf(i_0_14048,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_8154]),
    [final] ).

cnf(i_0_14049,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_8035]),
    [final] ).

cnf(i_0_14050,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_8120]),
    [final] ).

cnf(i_0_14051,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_8121]),
    [final] ).

cnf(i_0_14052,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_8122]),
    [final] ).

cnf(i_0_14053,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_8155]),
    [final] ).

cnf(i_0_14054,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_8156,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_14055,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_6506]),
    [final] ).

cnf(i_0_14056,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_7650]),
    [final] ).

cnf(i_0_14057,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_8157]),
    [final] ).

cnf(i_0_14058,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_8158]),
    [final] ).

cnf(i_0_14059,plain,
    ( hBOOL(hAPP(X1,esk480_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_7255]),
    [final] ).

cnf(i_0_14060,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_8159]),
    [final] ).

cnf(i_0_14061,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8160]),
    [final] ).

cnf(i_0_14062,plain,
    hAPP(hAPP(c_Fun_Ocomp(X1,X2,X3,X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_8161]),
    [final] ).

cnf(i_0_14063,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_7257]),
    [final] ).

cnf(i_0_14064,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8162]),
    [final] ).

cnf(i_0_14065,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_8163]),
    [final] ).

cnf(i_0_14066,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_8164]),
    [final] ).

cnf(i_0_14067,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_8165]),
    [final] ).

cnf(i_0_14068,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_8166]),
    [final] ).

cnf(i_0_14069,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_8167]),
    [final] ).

cnf(i_0_14070,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_8168]),
    [final] ).

cnf(i_0_14071,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_8169]),
    [final] ).

cnf(i_0_14072,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_8170]),
    [final] ).

cnf(i_0_14073,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_7778]),
    [final] ).

cnf(i_0_14074,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_8171]),
    [final] ).

cnf(i_0_14075,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_8172]),
    [final] ).

cnf(i_0_14076,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X4)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8173]),
    [final] ).

cnf(i_0_14077,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_8174]),
    [final] ).

cnf(i_0_14078,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_8175]),
    [final] ).

cnf(i_0_14079,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_8176]),
    [final] ).

cnf(i_0_14080,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_8177]),
    [final] ).

cnf(i_0_14081,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_8178]),
    [final] ).

cnf(i_0_14082,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_8179]),
    [final] ).

cnf(i_0_14083,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_8180]),
    [final] ).

cnf(i_0_14084,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_8181]),
    [final] ).

cnf(i_0_14085,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_6590]),
    [final] ).

cnf(i_0_14086,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_8182]),
    [final] ).

cnf(i_0_14087,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),esk247_3(X2,X3,X1)),X2))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8183]),
    [final] ).

cnf(i_0_14088,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_6807]),
    [final] ).

cnf(i_0_14089,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_8036]),
    [final] ).

cnf(i_0_14090,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_8184]),
    [final] ).

cnf(i_0_14091,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_8185]),
    [final] ).

cnf(i_0_14092,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_8186]),
    [final] ).

cnf(i_0_14093,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_8187]),
    [final] ).

cnf(i_0_14094,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_8188]),
    [final] ).

cnf(i_0_14095,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,esk229_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7353]),
    [final] ).

cnf(i_0_14096,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,esk134_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7354]),
    [final] ).

cnf(i_0_14097,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,esk230_4(X1,X2,X3,X4)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7355]),
    [final] ).

cnf(i_0_14098,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,esk135_4(X1,X2,X3,X4)) != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7356]),
    [final] ).

cnf(i_0_14099,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_8189]),
    [final] ).

cnf(i_0_14100,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_8190]),
    [final] ).

cnf(i_0_14101,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk72_3(X2,X1,X3))),esk73_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_8191]),
    [final] ).

cnf(i_0_14102,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk273_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_7812]),
    [final] ).

cnf(i_0_14103,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk85_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_7813]),
    [final] ).

cnf(i_0_14104,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),c_List_Olists(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk386_3(X2,X3,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8192]),
    [final] ).

cnf(i_0_14105,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_8193]),
    [final] ).

cnf(i_0_14106,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_7833]),
    [final] ).

cnf(i_0_14107,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_7616]),
    [final] ).

cnf(i_0_14108,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X5)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8194]),
    [final] ).

cnf(i_0_14109,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_8195]),
    [final] ).

cnf(i_0_14110,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_7755]),
    [final] ).

cnf(i_0_14111,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_8196]),
    [final] ).

cnf(i_0_14112,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_8197]),
    [final] ).

cnf(i_0_14113,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_7255]),
    [final] ).

cnf(i_0_14114,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_7264]),
    [final] ).

cnf(i_0_14115,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_8198,c_0_6184]),
    [final] ).

cnf(i_0_14116,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_8074]),
    [final] ).

cnf(i_0_14117,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_8199]),
    [final] ).

cnf(i_0_14118,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_8200,c_0_6139]),
    [final] ).

cnf(i_0_14119,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_8201,c_0_6139]),
    [final] ).

cnf(i_0_14120,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_8202]),
    [final] ).

cnf(i_0_14121,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_8203]),
    [final] ).

cnf(i_0_14122,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_8204]),
    [final] ).

cnf(i_0_14123,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_8205]),
    [final] ).

cnf(i_0_14124,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk248_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_8088]),
    [final] ).

cnf(i_0_14125,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_8206]),
    [final] ).

cnf(i_0_14126,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_8207]),
    [final] ).

cnf(i_0_14127,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk63_3(X2,X1,X3))),esk64_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_8208]),
    [final] ).

cnf(i_0_14128,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_8209]),
    [final] ).

cnf(i_0_14129,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_8210]),
    [final] ).

cnf(i_0_14130,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_8211,c_0_6726]),c_0_6726]),
    [final] ).

cnf(i_0_14131,plain,
    ( c_Fun_Oinj__on(X4,X3,X2,X1)
    | esk22_4(X1,X2,X3,X4) != esk23_4(X1,X2,X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_7345]),
    [final] ).

cnf(i_0_14132,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_8212]),
    [final] ).

cnf(i_0_14133,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred1_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk565_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14134,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_8083]),
    [final] ).

cnf(i_0_14135,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_8213,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_14136,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_8214]),
    [final] ).

cnf(i_0_14137,hypothesis,
    hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Nat_OSuc,v_n)),
    inference(split_conjunct,[status(thm)],[conj_4]),
    [final] ).

cnf(i_0_14138,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X2,X3,X1)),X3))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14139,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_3(X1,X2,X3)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,esk570_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14140,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_8039]),
    [final] ).

cnf(i_0_14141,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_8215]),
    [final] ).

cnf(i_0_14142,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_7255]),
    [final] ).

cnf(i_0_14143,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_8216]),
    [final] ).

cnf(i_0_14144,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X2,X3,X1)),X3))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14145,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_8217]),
    [final] ).

cnf(i_0_14146,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_8217]),
    [final] ).

cnf(i_0_14147,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_8218]),
    [final] ).

cnf(i_0_14148,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_8219]),
    [final] ).

cnf(i_0_14149,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_8220]),
    [final] ).

cnf(i_0_14150,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_8220]),
    [final] ).

cnf(i_0_14151,plain,
    ( v_P(X1,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
    | ~ v_P(X1,hAPP(hAPP(c_Set_Oinsert(t_a),hAPP(v_mgt__call,esk2_2(X1,X2))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
    | ~ v_wt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8221]),
    [final] ).

cnf(i_0_14152,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_8222]),
    [final] ).

cnf(i_0_14153,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk72_3(X2,X1,X3))),esk73_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_8191]),
    [final] ).

cnf(i_0_14154,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_8223]),
    [final] ).

cnf(i_0_14155,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_8224]),
    [final] ).

cnf(i_0_14156,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_8225]),
    [final] ).

cnf(i_0_14157,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk12_3(X2,X3,X1)),esk13_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_6759]),
    [final] ).

cnf(i_0_14158,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_5324]),
    [final] ).

cnf(i_0_14159,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_7264]),
    [final] ).

cnf(i_0_14160,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_8079]),
    [final] ).

cnf(i_0_14161,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_8226]),
    [final] ).

cnf(i_0_14162,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_8226]),
    [final] ).

cnf(i_0_14163,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_8227]),
    [final] ).

cnf(i_0_14164,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_8227]),
    [final] ).

cnf(i_0_14165,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8228]),
    [final] ).

cnf(i_0_14166,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8229]),
    [final] ).

cnf(i_0_14167,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_8230]),
    [final] ).

cnf(i_0_14168,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_8231]),
    [final] ).

cnf(i_0_14169,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,esk435_3(X2,X1,X3))) ),
    inference(rw,[status(thm)],[i_0_8232,c_0_6289]),
    [final] ).

cnf(i_0_14170,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_8233]),
    [final] ).

cnf(i_0_14171,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_8234]),
    [final] ).

cnf(i_0_14172,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),esk316_2(X2,X1)),hAPP(c_Relation_OImage(X1,X1,X2),esk316_2(X2,X1))))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8235]),
    [final] ).

cnf(i_0_14173,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_8236]),
    [final] ).

cnf(i_0_14174,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_8237]),
    [final] ).

cnf(i_0_14175,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_8065]),
    [final] ).

cnf(i_0_14176,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_8238]),
    [final] ).

cnf(i_0_14177,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_8239]),
    [final] ).

cnf(i_0_14178,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_8240]),
    [final] ).

cnf(i_0_14179,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_6766]),
    [final] ).

cnf(i_0_14180,plain,
    ( X1 = hAPP(hAPP(c_Product__Type_OPair(X2,X2),esk197_3(X3,X1,X2)),esk197_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_8100]),
    [final] ).

cnf(i_0_14181,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_8241]),
    [final] ).

cnf(i_0_14182,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_8242]),
    [final] ).

cnf(i_0_14183,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_5324]),
    [final] ).

cnf(i_0_14184,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_8243,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6219]),
    [final] ).

cnf(i_0_14185,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_8244]),
    [final] ).

cnf(i_0_14186,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_8245,c_0_6103]),
    [final] ).

cnf(i_0_14187,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_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_7680]),
    [final] ).

cnf(i_0_14188,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_8246,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_14189,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_8247,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_14190,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_7474]),
    [final] ).

cnf(i_0_14191,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_7475]),
    [final] ).

cnf(i_0_14192,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_8248]),
    [final] ).

cnf(i_0_14193,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_8249]),
    [final] ).

cnf(i_0_14194,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_8250]),
    [final] ).

cnf(i_0_14195,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk63_3(X2,X1,X3))),esk64_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_8208]),
    [final] ).

cnf(i_0_14196,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_7869]),
    [final] ).

cnf(i_0_14197,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_8251]),
    [final] ).

cnf(i_0_14198,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_8251]),
    [final] ).

cnf(i_0_14199,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_8252]),
    [final] ).

cnf(i_0_14200,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_8253]),
    [final] ).

cnf(i_0_14201,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),esk565_3(X2,X1,X3))),esk566_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_7680]),
    [final] ).

cnf(i_0_14202,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_8254,c_0_6726]),c_0_6726]),
    [final] ).

cnf(i_0_14203,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_8255]),
    [final] ).

cnf(i_0_14204,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_8256]),
    [final] ).

cnf(i_0_14205,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_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_7690]),
    [final] ).

cnf(i_0_14206,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_8257,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_14207,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_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,esk570_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14208,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_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,esk565_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14209,plain,
    ( X1 = hAPP(c_Int_ORep__Integ,esk275_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_8258]),
    [final] ).

cnf(i_0_14210,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk325_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_8259]),
    [final] ).

cnf(i_0_14211,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk412_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_8260]),
    [final] ).

cnf(i_0_14212,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk385_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_7873]),
    [final] ).

cnf(i_0_14213,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_8261]),
    [final] ).

cnf(i_0_14214,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),esk569_3(X2,X1,X3))),esk570_3(X2,X1,X3))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14215,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X2,X3,X1)),X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14216,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_3(X2,X3,X1)),X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14217,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X3),X2),X4)))
    | ~ hBOOL(hAPP(X1,esk384_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_7873]),
    [final] ).

cnf(i_0_14218,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_8262]),
    [final] ).

cnf(i_0_14219,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_8263]),
    [final] ).

cnf(i_0_14220,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_8264]),
    [final] ).

cnf(i_0_14221,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_8265]),
    [final] ).

cnf(i_0_14222,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_8261]),
    [final] ).

cnf(i_0_14223,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_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)),esk566_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_7680]),
    [final] ).

cnf(i_0_14224,plain,
    ( c_Fun_Oinj__on(X1,X2,esk30_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_6641]),
    [final] ).

cnf(i_0_14225,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_8255]),
    [final] ).

cnf(i_0_14226,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X2))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8266]),
    [final] ).

cnf(i_0_14227,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_7690]),
    [final] ).

cnf(i_0_14228,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_7680]),
    [final] ).

cnf(i_0_14229,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_8267]),
    [final] ).

cnf(i_0_14230,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_8268]),
    [final] ).

cnf(i_0_14231,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_8269]),
    [final] ).

cnf(i_0_14232,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_8270]),
    [final] ).

cnf(i_0_14233,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),esk42_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8271]),
    [final] ).

cnf(i_0_14234,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_8272]),
    [final] ).

cnf(i_0_14235,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_8273]),
    [final] ).

cnf(i_0_14236,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_7799]),
    [final] ).

cnf(i_0_14237,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_7800]),
    [final] ).

cnf(i_0_14238,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_8274]),
    [final] ).

cnf(i_0_14239,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_8275]),
    [final] ).

cnf(i_0_14240,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_8276]),
    [final] ).

cnf(i_0_14241,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_8277]),
    [final] ).

cnf(i_0_14242,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_7986]),
    [final] ).

cnf(i_0_14243,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_8278]),
    [final] ).

cnf(i_0_14244,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7947]),
    [final] ).

cnf(i_0_14245,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_8279]),
    [final] ).

cnf(i_0_14246,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_8107]),
    [final] ).

cnf(i_0_14247,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_8280]),
    [final] ).

cnf(i_0_14248,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_8108]),
    [final] ).

cnf(i_0_14249,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_7949]),
    [final] ).

cnf(i_0_14250,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_8281]),
    [final] ).

cnf(i_0_14251,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_8282]),
    [final] ).

cnf(i_0_14252,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_8283]),
    [final] ).

cnf(i_0_14253,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_7951]),
    [final] ).

cnf(i_0_14254,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_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)),esk570_3(X1,X2,X3)))
    | epred2_3(X3,X2,X1)
    | ~ hBOOL(hAPP(X3,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14255,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_8284]),
    [final] ).

cnf(i_0_14256,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_8285]),
    [final] ).

cnf(i_0_14257,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_8286]),
    [final] ).

cnf(i_0_14258,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_8287]),
    [final] ).

cnf(i_0_14259,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_8288]),
    [final] ).

cnf(i_0_14260,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_8289]),
    [final] ).

cnf(i_0_14261,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_6766]),
    [final] ).

cnf(i_0_14262,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_6766]),
    [final] ).

cnf(i_0_14263,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk201_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_8290]),
    [final] ).

cnf(i_0_14264,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk77_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_8291]),
    [final] ).

cnf(i_0_14265,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk76_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_8292]),
    [final] ).

cnf(i_0_14266,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_7087]),
    [final] ).

cnf(i_0_14267,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_8293]),
    [final] ).

cnf(i_0_14268,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)),esk420_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_8294,c_0_6139]),
    [final] ).

cnf(i_0_14269,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)),esk421_2(X2,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X2))) ),
    inference(rw,[status(thm)],[i_0_8295,c_0_6139]),
    [final] ).

cnf(i_0_14270,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_8296]),
    [final] ).

cnf(i_0_14271,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_8297]),
    [final] ).

cnf(i_0_14272,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_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_7680]),
    [final] ).

cnf(i_0_14273,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_8298]),
    [final] ).

cnf(i_0_14274,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_8299,c_0_8300]),
    [final] ).

cnf(i_0_14275,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_7690]),
    [final] ).

cnf(i_0_14276,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_7680]),
    [final] ).

cnf(i_0_14277,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_8301]),
    [final] ).

cnf(i_0_14278,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_8302]),
    [final] ).

cnf(i_0_14279,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_8303]),
    [final] ).

cnf(i_0_14280,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_8304]),
    [final] ).

cnf(i_0_14281,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_8305]),
    [final] ).

cnf(i_0_14282,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_8306]),
    [final] ).

cnf(i_0_14283,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_8307]),
    [final] ).

cnf(i_0_14284,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_8308]),
    [final] ).

cnf(i_0_14285,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk387_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_8309]),
    [final] ).

cnf(i_0_14286,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_3(X2,X1,X3)),X1))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14287,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_8310]),
    [final] ).

cnf(i_0_14288,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_8311]),
    [final] ).

cnf(i_0_14289,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_8312]),
    [final] ).

cnf(i_0_14290,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_8313]),
    [final] ).

cnf(i_0_14291,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_8314]),
    [final] ).

cnf(i_0_14292,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_8315]),
    [final] ).

cnf(i_0_14293,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_8030]),
    [final] ).

cnf(i_0_14294,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_8316]),
    [final] ).

cnf(i_0_14295,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_8317]),
    [final] ).

cnf(i_0_14296,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_8318]),
    [final] ).

cnf(i_0_14297,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_8319]),
    [final] ).

cnf(i_0_14298,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_8320]),
    [final] ).

cnf(i_0_14299,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_8321]),
    [final] ).

cnf(i_0_14300,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_8322,c_0_6096]),
    [final] ).

cnf(i_0_14301,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_7409]),
    [final] ).

cnf(i_0_14302,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_8323]),
    [final] ).

cnf(i_0_14303,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_8324]),
    [final] ).

cnf(i_0_14304,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_8120]),
    [final] ).

cnf(i_0_14305,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_8120]),
    [final] ).

cnf(i_0_14306,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_8325]),
    [final] ).

cnf(i_0_14307,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_8326]),
    [final] ).

cnf(i_0_14308,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_8327]),
    [final] ).

cnf(i_0_14309,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_8328]),
    [final] ).

cnf(i_0_14310,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_8329]),
    [final] ).

cnf(i_0_14311,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_8121]),
    [final] ).

cnf(i_0_14312,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_8121]),
    [final] ).

cnf(i_0_14313,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_8330]),
    [final] ).

cnf(i_0_14314,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_8331]),
    [final] ).

cnf(i_0_14315,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_8330]),
    [final] ).

cnf(i_0_14316,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_8332]),
    [final] ).

cnf(i_0_14317,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_8122]),
    [final] ).

cnf(i_0_14318,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_8122]),
    [final] ).

cnf(i_0_14319,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_8333]),
    [final] ).

cnf(i_0_14320,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_8334]),
    [final] ).

cnf(i_0_14321,plain,
    c_Lazy__Sequence_Omap(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X4,X5)) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,hAPP(X3,X4),c_Lazy__Sequence_Omap(X1,X2,X3,X5)),
    inference(split_conjunct,[status(thm)],[i_0_8335]),
    [final] ).

cnf(i_0_14322,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk571_3(X1,X2,X3))),esk572_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_7690]),
    [final] ).

cnf(i_0_14323,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk567_3(X1,X2,X3))),esk568_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_7680]),
    [final] ).

cnf(i_0_14324,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_8336]),
    [final] ).

cnf(i_0_14325,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_8337,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_14326,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_8338,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_14327,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8339]),
    [final] ).

cnf(i_0_14328,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8340]),
    [final] ).

cnf(i_0_14329,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_8341]),
    [final] ).

cnf(i_0_14330,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_8341]),
    [final] ).

cnf(i_0_14331,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_8342]),
    [final] ).

cnf(i_0_14332,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_8343]),
    [final] ).

cnf(i_0_14333,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_8342]),
    [final] ).

cnf(i_0_14334,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_8343]),
    [final] ).

cnf(i_0_14335,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_8344]),
    [final] ).

cnf(i_0_14336,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_8345]),
    [final] ).

cnf(i_0_14337,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8344]),
    [final] ).

cnf(i_0_14338,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X4),X2)),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8345]),
    [final] ).

cnf(i_0_14339,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_8346]),
    [final] ).

cnf(i_0_14340,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_8347]),
    [final] ).

cnf(i_0_14341,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_8348]),
    [final] ).

cnf(i_0_14342,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk42_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_8271]),
    [final] ).

cnf(i_0_14343,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_8349]),
    [final] ).

cnf(i_0_14344,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_8350]),
    [final] ).

cnf(i_0_14345,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_8348]),
    [final] ).

cnf(i_0_14346,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),esk569_3(X2,X1,X3))),esk570_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_7690]),
    [final] ).

cnf(i_0_14347,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),esk565_3(X2,X1,X3))),esk566_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_7680]),
    [final] ).

cnf(i_0_14348,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_8351]),
    [final] ).

cnf(i_0_14349,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_8352,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_14350,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_8353,c_0_8354]),c_0_8354]),
    [final] ).

cnf(i_0_14351,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_8355]),
    [final] ).

cnf(i_0_14352,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_6648]),
    [final] ).

cnf(i_0_14353,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_6649]),
    [final] ).

cnf(i_0_14354,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)),esk248_3(X2,X3,X1)),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8088]),
    [final] ).

cnf(i_0_14355,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_8356]),
    [final] ).

cnf(i_0_14356,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_8357]),
    [final] ).

cnf(i_0_14357,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_8358]),
    [final] ).

cnf(i_0_14358,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_8359]),
    [final] ).

cnf(i_0_14359,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),esk76_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8292]),
    [final] ).

cnf(i_0_14360,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),esk201_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8290]),
    [final] ).

cnf(i_0_14361,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),esk77_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8291]),
    [final] ).

cnf(i_0_14362,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_8360]),
    [final] ).

cnf(i_0_14363,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_8078]),
    [final] ).

cnf(i_0_14364,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_8361,c_0_6726]),
    [final] ).

cnf(i_0_14365,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_5325]),
    [final] ).

cnf(i_0_14366,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_8362]),
    [final] ).

cnf(i_0_14367,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_8191]),
    [final] ).

cnf(i_0_14368,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_8363]),
    [final] ).

cnf(i_0_14369,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_8364]),
    [final] ).

cnf(i_0_14370,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_8365]),
    [final] ).

cnf(i_0_14371,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_8366]),
    [final] ).

cnf(i_0_14372,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_8154]),
    [final] ).

cnf(i_0_14373,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_8367]),
    [final] ).

cnf(i_0_14374,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_8368]),
    [final] ).

cnf(i_0_14375,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_8369]),
    [final] ).

cnf(i_0_14376,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_8370]),
    [final] ).

cnf(i_0_14377,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_8371]),
    [final] ).

cnf(i_0_14378,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_8372]),
    [final] ).

cnf(i_0_14379,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_8373]),
    [final] ).

cnf(i_0_14380,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_8374]),
    [final] ).

cnf(i_0_14381,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_8375]),
    [final] ).

cnf(i_0_14382,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_8376]),
    [final] ).

cnf(i_0_14383,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_8377]),
    [final] ).

cnf(i_0_14384,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_8378]),
    [final] ).

cnf(i_0_14385,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_8379]),
    [final] ).

cnf(i_0_14386,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_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)),esk570_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_7690]),
    [final] ).

cnf(i_0_14387,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_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)),esk566_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_7680]),
    [final] ).

cnf(i_0_14388,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_8380]),
    [final] ).

cnf(i_0_14389,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_8052]),
    [final] ).

cnf(i_0_14390,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_6598]),
    [final] ).

cnf(i_0_14391,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_8381]),
    [final] ).

cnf(i_0_14392,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_8060]),
    [final] ).

cnf(i_0_14393,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_7762]),
    [final] ).

cnf(i_0_14394,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_8196]),
    [final] ).

cnf(i_0_14395,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_8382]),
    [final] ).

cnf(i_0_14396,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_8383]),
    [final] ).

cnf(i_0_14397,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_8384]),
    [final] ).

cnf(i_0_14398,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_8385]),
    [final] ).

cnf(i_0_14399,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_8386]),
    [final] ).

cnf(i_0_14400,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_7376]),
    [final] ).

cnf(i_0_14401,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_7377]),
    [final] ).

cnf(i_0_14402,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_8387]),
    [final] ).

cnf(i_0_14403,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_8388]),
    [final] ).

cnf(i_0_14404,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_8389]),
    [final] ).

cnf(i_0_14405,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_8390]),
    [final] ).

cnf(i_0_14406,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8391]),
    [final] ).

cnf(i_0_14407,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7965]),
    [final] ).

cnf(i_0_14408,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Oidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7964]),
    [final] ).

cnf(i_0_14409,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_8392]),
    [final] ).

cnf(i_0_14410,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_7970]),
    [final] ).

cnf(i_0_14411,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_8393]),
    [final] ).

cnf(i_0_14412,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_7972]),
    [final] ).

cnf(i_0_14413,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_8394]),
    [final] ).

cnf(i_0_14414,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_7974]),
    [final] ).

cnf(i_0_14415,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_8395]),
    [final] ).

cnf(i_0_14416,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_7976]),
    [final] ).

cnf(i_0_14417,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_8396]),
    [final] ).

cnf(i_0_14418,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_8397]),
    [final] ).

cnf(i_0_14419,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_8398]),
    [final] ).

cnf(i_0_14420,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_8205]),
    [final] ).

cnf(i_0_14421,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_8399]),
    [final] ).

cnf(i_0_14422,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_8400]),
    [final] ).

cnf(i_0_14423,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_8401]),
    [final] ).

cnf(i_0_14424,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_8402]),
    [final] ).

cnf(i_0_14425,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_8403]),
    [final] ).

cnf(i_0_14426,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk570_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_7690]),
    [final] ).

cnf(i_0_14427,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),esk566_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_7680]),
    [final] ).

cnf(i_0_14428,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_8404]),
    [final] ).

cnf(i_0_14429,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_8405]),
    [final] ).

cnf(i_0_14430,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_8406]),
    [final] ).

cnf(i_0_14431,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_8239]),
    [final] ).

cnf(i_0_14432,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_8240]),
    [final] ).

cnf(i_0_14433,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_8407]),
    [final] ).

cnf(i_0_14434,plain,
    ( X2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),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_8408]),
    [final] ).

cnf(i_0_14435,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_8409]),
    [final] ).

cnf(i_0_14436,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_8284]),
    [final] ).

cnf(i_0_14437,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_8410]),
    [final] ).

cnf(i_0_14438,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_8411]),
    [final] ).

cnf(i_0_14439,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_8412]),
    [final] ).

cnf(i_0_14440,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_8413]),
    [final] ).

cnf(i_0_14441,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_8414]),
    [final] ).

cnf(i_0_14442,plain,
    ( hBOOL(hAPP(hAPP(X3,X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(X1,X2,X3),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_8415]),
    [final] ).

cnf(i_0_14443,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_8416]),
    [final] ).

cnf(i_0_14444,plain,
    ( epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk565_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14445,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk244_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_8417]),
    [final] ).

cnf(i_0_14446,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk244_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_8417]),
    [final] ).

cnf(i_0_14447,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_8418]),
    [final] ).

cnf(i_0_14448,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_8419]),
    [final] ).

cnf(i_0_14449,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_8420]),
    [final] ).

cnf(i_0_14450,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_8421]),
    [final] ).

cnf(i_0_14451,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_8422]),
    [final] ).

cnf(i_0_14452,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X2)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X4),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8423]),
    [final] ).

cnf(i_0_14453,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_8424]),
    [final] ).

cnf(i_0_14454,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_8425]),
    [final] ).

cnf(i_0_14455,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_7878]),
    [final] ).

cnf(i_0_14456,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_8426]),
    [final] ).

cnf(i_0_14457,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_8427]),
    [final] ).

cnf(i_0_14458,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_8208]),
    [final] ).

cnf(i_0_14459,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk472_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk473_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7967]),
    [final] ).

cnf(i_0_14460,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),esk470_3(X1,X3,X2)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),esk471_3(X1,X3,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7968]),
    [final] ).

cnf(i_0_14461,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X1),esk467_3(X3,X2,X1)),hAPP(hAPP(c_List_Olist_OCons(X1),X2),esk468_3(X3,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8428]),
    [final] ).

cnf(i_0_14462,plain,
    c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Relation_Oconverse(X1,X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8429]),
    [final] ).

cnf(i_0_14463,plain,
    c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),hAPP(c_Relation_Oconverse(X1,X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_8430]),
    [final] ).

cnf(i_0_14464,plain,
    ( epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk570_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14465,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_8431]),
    [final] ).

cnf(i_0_14466,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_8432]),
    [final] ).

cnf(i_0_14467,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_8292]),
    [final] ).

cnf(i_0_14468,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_8290]),
    [final] ).

cnf(i_0_14469,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_8291]),
    [final] ).

cnf(i_0_14470,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_8433]),
    [final] ).

cnf(i_0_14471,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_8358]),
    [final] ).

cnf(i_0_14472,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_8358]),
    [final] ).

cnf(i_0_14473,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_8434]),
    [final] ).

cnf(i_0_14474,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_7588]),
    [final] ).

cnf(i_0_14475,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_7589]),
    [final] ).

cnf(i_0_14476,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk411_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_8260]),
    [final] ).

cnf(i_0_14477,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_8435]),
    [final] ).

cnf(i_0_14478,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_8436]),
    [final] ).

cnf(i_0_14479,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8437]),
    [final] ).

cnf(i_0_14480,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_8438]),
    [final] ).

cnf(i_0_14481,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_7429]),
    [final] ).

cnf(i_0_14482,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_8439]),
    [final] ).

cnf(i_0_14483,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_8440]),
    [final] ).

cnf(i_0_14484,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_8441]),
    [final] ).

cnf(i_0_14485,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_8442]),
    [final] ).

cnf(i_0_14486,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_8443]),
    [final] ).

cnf(i_0_14487,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_8444]),
    [final] ).

cnf(i_0_14488,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_5332]),
    [final] ).

cnf(i_0_14489,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_8445]),
    [final] ).

cnf(i_0_14490,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_8446]),
    [final] ).

cnf(i_0_14491,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(X1,X3)),c_Sum__Type_OPlus(X1,X3,X2,X4)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X3),X4))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8447]),
    [final] ).

cnf(i_0_14492,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_8341]),
    [final] ).

cnf(i_0_14493,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_8342]),
    [final] ).

cnf(i_0_14494,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_8448]),
    [final] ).

cnf(i_0_14495,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X4)),X3))
    | ~ class_Lattices_Osemilattice__sup(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8449]),
    [final] ).

cnf(i_0_14496,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_8344]),
    [final] ).

cnf(i_0_14497,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_8450]),
    [final] ).

cnf(i_0_14498,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X4)),X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8451]),
    [final] ).

cnf(i_0_14499,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_8452]),
    [final] ).

cnf(i_0_14500,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_8453]),
    [final] ).

cnf(i_0_14501,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_8454]),
    [final] ).

cnf(i_0_14502,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_8455]),
    [final] ).

cnf(i_0_14503,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_8456,c_0_6726]),
    [final] ).

cnf(i_0_14504,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_8457]),
    [final] ).

cnf(i_0_14505,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_8458]),
    [final] ).

cnf(i_0_14506,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_8459]),
    [final] ).

cnf(i_0_14507,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_8460]),
    [final] ).

cnf(i_0_14508,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_8461]),
    [final] ).

cnf(i_0_14509,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_8462]),
    [final] ).

cnf(i_0_14510,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_8463]),
    [final] ).

cnf(i_0_14511,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_8464]),
    [final] ).

cnf(i_0_14512,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_8020]),
    [final] ).

cnf(i_0_14513,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_8044]),
    [final] ).

cnf(i_0_14514,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk362_3(X2,X1,X3)),esk360_2(X2,X1)))
    | c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X3),esk360_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7070]),
    [final] ).

cnf(i_0_14515,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_7430]),
    [final] ).

cnf(i_0_14516,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_7431]),
    [final] ).

cnf(i_0_14517,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_7432]),
    [final] ).

cnf(i_0_14518,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_7433]),
    [final] ).

cnf(i_0_14519,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_8465]),
    [final] ).

cnf(i_0_14520,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_8181]),
    [final] ).

cnf(i_0_14521,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_8466]),
    [final] ).

cnf(i_0_14522,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_8467]),
    [final] ).

cnf(i_0_14523,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_8468]),
    [final] ).

cnf(i_0_14524,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_8469]),
    [final] ).

cnf(i_0_14525,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_8470]),
    [final] ).

cnf(i_0_14526,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_8471]),
    [final] ).

cnf(i_0_14527,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_7921]),
    [final] ).

cnf(i_0_14528,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_8472]),
    [final] ).

cnf(i_0_14529,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_8473]),
    [final] ).

cnf(i_0_14530,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_7921]),
    [final] ).

cnf(i_0_14531,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8474]),
    [final] ).

cnf(i_0_14532,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8473]),
    [final] ).

cnf(i_0_14533,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_8475]),
    [final] ).

cnf(i_0_14534,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_8476]),
    [final] ).

cnf(i_0_14535,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_8477]),
    [final] ).

cnf(i_0_14536,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_8478]),
    [final] ).

cnf(i_0_14537,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_8479]),
    [final] ).

cnf(i_0_14538,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_8480]),
    [final] ).

cnf(i_0_14539,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_8481]),
    [final] ).

cnf(i_0_14540,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_8482]),
    [final] ).

cnf(i_0_14541,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_8483]),
    [final] ).

cnf(i_0_14542,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_8484]),
    [final] ).

cnf(i_0_14543,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_8485]),
    [final] ).

cnf(i_0_14544,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_8486]),
    [final] ).

cnf(i_0_14545,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_8487]),
    [final] ).

cnf(i_0_14546,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_8488]),
    [final] ).

cnf(i_0_14547,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_8489]),
    [final] ).

cnf(i_0_14548,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_7403]),
    [final] ).

cnf(i_0_14549,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_7404]),
    [final] ).

cnf(i_0_14550,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_8490]),
    [final] ).

cnf(i_0_14551,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_8491]),
    [final] ).

cnf(i_0_14552,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_8492]),
    [final] ).

cnf(i_0_14553,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_8196]),
    [final] ).

cnf(i_0_14554,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_8493]),
    [final] ).

cnf(i_0_14555,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_8494]),
    [final] ).

cnf(i_0_14556,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_8495]),
    [final] ).

cnf(i_0_14557,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_8496]),
    [final] ).

cnf(i_0_14558,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk570_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14559,plain,
    ( X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,esk565_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14560,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_8497]),
    [final] ).

cnf(i_0_14561,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_8498]),
    [final] ).

cnf(i_0_14562,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_8499]),
    [final] ).

cnf(i_0_14563,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_8500,c_0_6070]),
    [final] ).

cnf(i_0_14564,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_8501,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14565,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_8187]),
    [final] ).

cnf(i_0_14566,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_8187]),
    [final] ).

cnf(i_0_14567,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8502]),
    [final] ).

cnf(i_0_14568,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8503]),
    [final] ).

cnf(i_0_14569,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,hAPP(hAPP(c_COMBC(X1,X1,X1),c_Groups_Oplus__class_Oplus(X1)),c_Groups_Oone__class_Oone(X1)),X2,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8504]),
    [final] ).

cnf(i_0_14570,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_6436]),
    [final] ).

cnf(i_0_14571,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)))
    | X2 != hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8505]),
    [final] ).

cnf(i_0_14572,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_8205]),
    [final] ).

cnf(i_0_14573,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8437]),
    [final] ).

cnf(i_0_14574,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Set_OPow(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8506]),
    [final] ).

cnf(i_0_14575,plain,
    hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),hAPP(c_Nat_OSuc,X5)) = hAPP(hAPP(X3,X4),hAPP(hAPP(c_Power_Opower_Opower(X1,X2,X3),X4),X5)),
    inference(split_conjunct,[status(thm)],[i_0_8507]),
    [final] ).

cnf(i_0_14576,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_8508]),
    [final] ).

cnf(i_0_14577,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_8509]),
    [final] ).

cnf(i_0_14578,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_8510]),
    [final] ).

cnf(i_0_14579,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_8199]),
    [final] ).

cnf(i_0_14580,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk386_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_8192]),
    [final] ).

cnf(i_0_14581,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_8511]),
    [final] ).

cnf(i_0_14582,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
    inference(split_conjunct,[status(thm)],[i_0_8512]),
    [final] ).

cnf(i_0_14583,plain,
    ( hBOOL(hAPP(hAPP(c_member(X4),X1),hAPP(c_Set_Oimage(X5,X4,X2),c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)))))
    | X1 != hAPP(X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8513]),
    [final] ).

cnf(i_0_14584,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_3(X2,X3,X1)))
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14585,plain,
    ( hAPP(c_Set_Oimage(tc_prod(X2,X3),X3,c_Product__Type_Osnd(X2,X3)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8514]),
    [final] ).

cnf(i_0_14586,plain,
    ( hAPP(c_Set_Oimage(tc_prod(X3,X2),X3,c_Product__Type_Ofst(X3,X2)),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1))) = c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8515]),
    [final] ).

cnf(i_0_14587,plain,
    ( X1 = X2
    | X1 = X3
    | hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_14588,plain,
    ( X1 = X2
    | X1 = X3
    | hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_14589,plain,
    ( X1 = X2
    | X3 = X2
    | hAPP(hAPP(c_Set_Oinsert(X4),X1),hAPP(hAPP(c_Set_Oinsert(X4),X3),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X2),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_14590,plain,
    ( X1 = X2
    | X3 = X2
    | hAPP(hAPP(c_Set_Oinsert(X4),X3),hAPP(hAPP(c_Set_Oinsert(X4),X1),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(X4),X2),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_14591,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8517]),
    [final] ).

cnf(i_0_14592,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_8079]),
    [final] ).

cnf(i_0_14593,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_8518]),
    [final] ).

cnf(i_0_14594,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_7122]),
    [final] ).

cnf(i_0_14595,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_8519]),
    [final] ).

cnf(i_0_14596,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_8520]),
    [final] ).

cnf(i_0_14597,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_8520]),
    [final] ).

cnf(i_0_14598,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_8521]),
    [final] ).

cnf(i_0_14599,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_8522]),
    [final] ).

cnf(i_0_14600,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk73_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_8191]),
    [final] ).

cnf(i_0_14601,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X2,X3,X1)))
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14602,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_8523]),
    [final] ).

cnf(i_0_14603,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_8185]),
    [final] ).

cnf(i_0_14604,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_3(X2,X1,X3)))
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk565_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14605,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_8524]),
    [final] ).

cnf(i_0_14606,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_8525]),
    [final] ).

cnf(i_0_14607,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_8526]),
    [final] ).

cnf(i_0_14608,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_8527,c_0_6070]),
    [final] ).

cnf(i_0_14609,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_8528,c_0_6070]),
    [final] ).

cnf(i_0_14610,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_8529,c_0_6070]),
    [final] ).

cnf(i_0_14611,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_8530,c_0_6070]),
    [final] ).

cnf(i_0_14612,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_8531,c_0_6070]),
    [final] ).

cnf(i_0_14613,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_8532,c_0_6070]),
    [final] ).

cnf(i_0_14614,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_8533]),
    [final] ).

cnf(i_0_14615,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_8534]),
    [final] ).

cnf(i_0_14616,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_6786]),
    [final] ).

cnf(i_0_14617,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk246_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_8535]),
    [final] ).

cnf(i_0_14618,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_8536]),
    [final] ).

cnf(i_0_14619,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_8537,c_0_6096]),
    [final] ).

cnf(i_0_14620,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_8538]),
    [final] ).

cnf(i_0_14621,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_8539]),
    [final] ).

cnf(i_0_14622,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_3(X2,X1,X3)))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk570_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14623,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_8255]),
    [final] ).

cnf(i_0_14624,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_8540]),
    [final] ).

cnf(i_0_14625,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_8541]),
    [final] ).

cnf(i_0_14626,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_8123]),
    [final] ).

cnf(i_0_14627,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk327_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_8124]),
    [final] ).

cnf(i_0_14628,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk326_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_8542]),
    [final] ).

cnf(i_0_14629,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_8543]),
    [final] ).

cnf(i_0_14630,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),esk249_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_8544]),
    [final] ).

cnf(i_0_14631,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8545]),
    [final] ).

cnf(i_0_14632,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_8546]),
    [final] ).

cnf(i_0_14633,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_8547]),
    [final] ).

cnf(i_0_14634,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_8548]),
    [final] ).

cnf(i_0_14635,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk64_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_8208]),
    [final] ).

cnf(i_0_14636,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_8549,c_0_6219]),
    [final] ).

cnf(i_0_14637,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_8550,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_14638,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_8551]),
    [final] ).

cnf(i_0_14639,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_8552]),
    [final] ).

cnf(i_0_14640,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8231]),
    [final] ).

cnf(i_0_14641,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),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_8238]),
    [final] ).

cnf(i_0_14642,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_8553]),
    [final] ).

cnf(i_0_14643,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),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_8554]),
    [final] ).

cnf(i_0_14644,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_8260]),
    [final] ).

cnf(i_0_14645,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8555]),
    [final] ).

cnf(i_0_14646,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8556]),
    [final] ).

cnf(i_0_14647,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_8557]),
    [final] ).

cnf(i_0_14648,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_8558]),
    [final] ).

cnf(i_0_14649,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14650,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),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_8558]),
    [final] ).

cnf(i_0_14651,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8558]),
    [final] ).

cnf(i_0_14652,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_8559]),
    [final] ).

cnf(i_0_14653,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8559]),
    [final] ).

cnf(i_0_14654,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8560]),
    [final] ).

cnf(i_0_14655,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8560]),
    [final] ).

cnf(i_0_14656,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),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_8559]),
    [final] ).

cnf(i_0_14657,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)))
    | ~ class_Fields_Olinordered__field__inverse__zero(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8559]),
    [final] ).

cnf(i_0_14658,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8560]),
    [final] ).

cnf(i_0_14659,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ class_Rings_Olinordered__ring__strict(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8560]),
    [final] ).

cnf(i_0_14660,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk497_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_8561]),
    [final] ).

cnf(i_0_14661,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_7468]),
    [final] ).

cnf(i_0_14662,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_7469]),
    [final] ).

cnf(i_0_14663,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_7470]),
    [final] ).

cnf(i_0_14664,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = X3
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7471]),
    [final] ).

cnf(i_0_14665,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8125]),
    [final] ).

cnf(i_0_14666,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_8562,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14667,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8563,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14668,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),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_8564]),
    [final] ).

cnf(i_0_14669,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_8565]),
    [final] ).

cnf(i_0_14670,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),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_8133]),
    [final] ).

cnf(i_0_14671,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_8566,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14672,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8567,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_14673,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),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_8568]),
    [final] ).

cnf(i_0_14674,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_8569]),
    [final] ).

cnf(i_0_14675,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_8570]),
    [final] ).

cnf(i_0_14676,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7950]),
    [final] ).

cnf(i_0_14677,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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_8571]),
    [final] ).

cnf(i_0_14678,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7952]),
    [final] ).

cnf(i_0_14679,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_8572]),
    [final] ).

cnf(i_0_14680,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),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_8136]),
    [final] ).

cnf(i_0_14681,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_8573]),
    [final] ).

cnf(i_0_14682,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),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_8574]),
    [final] ).

cnf(i_0_14683,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_8575]),
    [final] ).

cnf(i_0_14684,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_8576]),
    [final] ).

cnf(i_0_14685,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_8577]),
    [final] ).

cnf(i_0_14686,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3))) = hAPP(c_List_Ofoldl(X1,X1,c_Orderings_Oord__class_Omin(X1),X2),X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8578]),
    [final] ).

cnf(i_0_14687,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_8579]),
    [final] ).

cnf(i_0_14688,plain,
    ( c_List_Olist__ex1(X3,X2,X1)
    | esk487_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_7283]),
    [final] ).

cnf(i_0_14689,plain,
    ( c_List_Olist__ex1(X3,X2,X1)
    | esk479_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_7284]),
    [final] ).

cnf(i_0_14690,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_8580]),
    [final] ).

cnf(i_0_14691,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_8581,c_0_6071]),
    [final] ).

cnf(i_0_14692,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_8582]),
    [final] ).

cnf(i_0_14693,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_8583]),
    [final] ).

cnf(i_0_14694,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_8583]),
    [final] ).

cnf(i_0_14695,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk430_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_7878]),
    [final] ).

cnf(i_0_14696,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk429_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_7878]),
    [final] ).

cnf(i_0_14697,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk408_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_8185]),
    [final] ).

cnf(i_0_14698,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_8584]),
    [final] ).

cnf(i_0_14699,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_8585]),
    [final] ).

cnf(i_0_14700,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_7138]),
    [final] ).

cnf(i_0_14701,plain,
    ( hBOOL(hAPP(hAPP(c_member(X6),X4),hAPP(c_Set_Oimage(X1,X6,X5),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | X4 != hAPP(X5,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8586]),
    [final] ).

cnf(i_0_14702,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X3,X2),X4),X5)))
    | ~ hBOOL(hAPP(X1,esk86_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7250]),
    [final] ).

cnf(i_0_14703,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_6191]),
    [final] ).

cnf(i_0_14704,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(tc_prod(X2,X3),X3,c_Product__Type_Osnd(X2,X3)),hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4))) = X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8514]),
    [final] ).

cnf(i_0_14705,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(tc_prod(X3,X2),X3,c_Product__Type_Ofst(X3,X2)),hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1))) = X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8515]),
    [final] ).

cnf(i_0_14706,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 != esk182_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_7303]),
    [final] ).

cnf(i_0_14707,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_8587]),
    [final] ).

cnf(i_0_14708,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_8588]),
    [final] ).

cnf(i_0_14709,plain,
    ( X5 = X6
    | ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X6),X4))
    | hAPP(X3,X5) != hAPP(X3,X6) ),
    inference(split_conjunct,[status(thm)],[i_0_8589]),
    [final] ).

cnf(i_0_14710,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_7345]),
    [final] ).

cnf(i_0_14711,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_8590]),
    [final] ).

cnf(i_0_14712,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_8591]),
    [final] ).

cnf(i_0_14713,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_8592]),
    [final] ).

cnf(i_0_14714,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_8593]),
    [final] ).

cnf(i_0_14715,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_8594]),
    [final] ).

cnf(i_0_14716,plain,
    ( c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,esk517_1(X1)),esk518_1(X1)))
    | ~ hBOOL(hAPP(hAPP(X1,esk517_1(X1)),esk517_1(X1)))
    | ~ hBOOL(hAPP(hAPP(X1,esk518_1(X1)),esk518_1(X1)))
    | hAPP(X1,esk517_1(X1)) != hAPP(X1,esk518_1(X1))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_14717,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_8518]),
    [final] ).

cnf(i_0_14718,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_8596]),
    [final] ).

cnf(i_0_14719,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_8597]),
    [final] ).

cnf(i_0_14720,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk73_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_8191]),
    [final] ).

cnf(i_0_14721,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(X3,X5)),hAPP(X4,X5)))
    | ~ class_Orderings_Oord(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,X1)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8598]),
    [final] ).

cnf(i_0_14722,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_8599]),
    [final] ).

cnf(i_0_14723,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_6622]),
    [final] ).

cnf(i_0_14724,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X2,X3,X1)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14725,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_3(X2,X3,X1)))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14726,plain,
    ( X4 = X5
    | hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) != hAPP(hAPP(c_List_Omap(X1,X2),X3),X5)
    | ~ c_Fun_Oinj__on(X1,X2,X3,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_8600]),
    [final] ).

cnf(i_0_14727,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_8601]),
    [final] ).

cnf(i_0_14728,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_8602]),
    [final] ).

cnf(i_0_14729,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_8603]),
    [final] ).

cnf(i_0_14730,plain,
    ( c_Big__Operators_Olinorder__class_OMin(X1,X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),esk326_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_8542]),
    [final] ).

cnf(i_0_14731,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk181_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_7303]),
    [final] ).

cnf(i_0_14732,plain,
    ( c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8604]),
    [final] ).

cnf(i_0_14733,plain,
    ( c_Relation_Osym(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8605]),
    [final] ).

cnf(i_0_14734,plain,
    ( c_Relation_Otrans(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X2),X3))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Otrans(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8606]),
    [final] ).

cnf(i_0_14735,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_8607]),
    [final] ).

cnf(i_0_14736,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_8424]),
    [final] ).

cnf(i_0_14737,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_8608]),
    [final] ).

cnf(i_0_14738,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_8609]),
    [final] ).

cnf(i_0_14739,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_8610]),
    [final] ).

cnf(i_0_14740,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_8611]),
    [final] ).

cnf(i_0_14741,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk465_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_8612]),
    [final] ).

cnf(i_0_14742,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk431_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
    | ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8613]),
    [final] ).

cnf(i_0_14743,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk428_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_8614]),
    [final] ).

cnf(i_0_14744,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_8615]),
    [final] ).

cnf(i_0_14745,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_7588]),
    [final] ).

cnf(i_0_14746,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_7589]),
    [final] ).

cnf(i_0_14747,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_8616]),
    [final] ).

cnf(i_0_14748,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_8558]),
    [final] ).

cnf(i_0_14749,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_8617]),
    [final] ).

cnf(i_0_14750,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_8618]),
    [final] ).

cnf(i_0_14751,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_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_8619]),
    [final] ).

cnf(i_0_14752,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)))
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8620]),
    [final] ).

cnf(i_0_14753,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_8621]),
    [final] ).

cnf(i_0_14754,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_8622]),
    [final] ).

cnf(i_0_14755,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_8559]),
    [final] ).

cnf(i_0_14756,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X3))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8623]),
    [final] ).

cnf(i_0_14757,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_8624]),
    [final] ).

cnf(i_0_14758,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ 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_8560]),
    [final] ).

cnf(i_0_14759,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_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_8625]),
    [final] ).

cnf(i_0_14760,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk324_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_7437]),
    [final] ).

cnf(i_0_14761,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_8626]),
    [final] ).

cnf(i_0_14762,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_8627]),
    [final] ).

cnf(i_0_14763,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_8628]),
    [final] ).

cnf(i_0_14764,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_8629,c_0_6096]),
    [final] ).

cnf(i_0_14765,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_8630]),
    [final] ).

cnf(i_0_14766,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),esk325_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8259]),
    [final] ).

cnf(i_0_14767,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X2))) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2))),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X2),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8631,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_14768,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_8632,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_14769,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_8633]),
    [final] ).

cnf(i_0_14770,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk247_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_8183]),
    [final] ).

cnf(i_0_14771,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8634]),
    [final] ).

cnf(i_0_14772,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_8635]),
    [final] ).

cnf(i_0_14773,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk382_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_8636]),
    [final] ).

cnf(i_0_14774,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_3(X2,X1,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk570_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14775,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_3(X2,X1,X3)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,esk565_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_14776,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_8637]),
    [final] ).

cnf(i_0_14777,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_8638]),
    [final] ).

cnf(i_0_14778,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_List_Onth(X2),X3),esk466_3(X3,X1,X2))))
    | ~ c_List_Olist__ex(X2,X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8593]),
    [final] ).

cnf(i_0_14779,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_8639]),
    [final] ).

cnf(i_0_14780,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_8640]),
    [final] ).

cnf(i_0_14781,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_8641]),
    [final] ).

cnf(i_0_14782,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_8642]),
    [final] ).

cnf(i_0_14783,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_8643]),
    [final] ).

cnf(i_0_14784,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_8644]),
    [final] ).

cnf(i_0_14785,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_8645]),
    [final] ).

cnf(i_0_14786,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_8220]),
    [final] ).

cnf(i_0_14787,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_8646]),
    [final] ).

cnf(i_0_14788,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_8155]),
    [final] ).

cnf(i_0_14789,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_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_7680]),
    [final] ).

cnf(i_0_14790,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_8647]),
    [final] ).

cnf(i_0_14791,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),esk496_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_8648]),
    [final] ).

cnf(i_0_14792,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_8649]),
    [final] ).

cnf(i_0_14793,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_8650]),
    [final] ).

cnf(i_0_14794,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_8651]),
    [final] ).

cnf(i_0_14795,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_8652]),
    [final] ).

cnf(i_0_14796,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_8644]),
    [final] ).

cnf(i_0_14797,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8645]),
    [final] ).

cnf(i_0_14798,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_8653]),
    [final] ).

cnf(i_0_14799,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_8654]),
    [final] ).

cnf(i_0_14800,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_8655]),
    [final] ).

cnf(i_0_14801,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_8656]),
    [final] ).

cnf(i_0_14802,plain,
    ( hAPP(X1,esk83_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_7349]),
    [final] ).

cnf(i_0_14803,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_8657]),
    [final] ).

cnf(i_0_14804,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8658]),
    [final] ).

cnf(i_0_14805,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8659]),
    [final] ).

cnf(i_0_14806,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_7952]),
    [final] ).

cnf(i_0_14807,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_7950]),
    [final] ).

cnf(i_0_14808,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_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_7680]),
    [final] ).

cnf(i_0_14809,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 != esk184_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_7311]),
    [final] ).

cnf(i_0_14810,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk143_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_8660]),
    [final] ).

cnf(i_0_14811,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk183_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_7311]),
    [final] ).

cnf(i_0_14812,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_8661]),
    [final] ).

cnf(i_0_14813,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk301_2(X1,X2)),c_Int_OInteg))
    | hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8662]),
    [final] ).

cnf(i_0_14814,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_8073]),
    [final] ).

cnf(i_0_14815,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_8663,c_0_6070]),
    [final] ).

cnf(i_0_14816,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_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_7690]),
    [final] ).

cnf(i_0_14817,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_8664]),
    [final] ).

cnf(i_0_14818,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_8665]),
    [final] ).

cnf(i_0_14819,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_8666]),
    [final] ).

cnf(i_0_14820,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_8627]),
    [final] ).

cnf(i_0_14821,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_8667]),
    [final] ).

cnf(i_0_14822,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk64_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_8208]),
    [final] ).

cnf(i_0_14823,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_8668]),
    [final] ).

cnf(i_0_14824,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_8669]),
    [final] ).

cnf(i_0_14825,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X4)))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7964]),
    [final] ).

cnf(i_0_14826,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X4),X1)))
    | X1 != c_Groups_Ozero__class_Ozero(X2)
    | ~ class_Rings_Oidom(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7965]),
    [final] ).

cnf(i_0_14827,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_8670]),
    [final] ).

cnf(i_0_14828,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),esk566_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_7680]),
    [final] ).

cnf(i_0_14829,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_8671]),
    [final] ).

cnf(i_0_14830,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk466_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_8593]),
    [final] ).

cnf(i_0_14831,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_8672]),
    [final] ).

cnf(i_0_14832,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_8673]),
    [final] ).

cnf(i_0_14833,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_3(X2,X1,X3)))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14834,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_8674]),
    [final] ).

cnf(i_0_14835,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_8675]),
    [final] ).

cnf(i_0_14836,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_8676]),
    [final] ).

cnf(i_0_14837,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_8677]),
    [final] ).

cnf(i_0_14838,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_8678]),
    [final] ).

cnf(i_0_14839,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_8679]),
    [final] ).

cnf(i_0_14840,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_8680]),
    [final] ).

cnf(i_0_14841,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8681]),
    [final] ).

cnf(i_0_14842,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8682]),
    [final] ).

cnf(i_0_14843,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_8683]),
    [final] ).

cnf(i_0_14844,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_8684]),
    [final] ).

cnf(i_0_14845,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_8685]),
    [final] ).

cnf(i_0_14846,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_8070]),
    [final] ).

cnf(i_0_14847,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_8071]),
    [final] ).

cnf(i_0_14848,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_8686]),
    [final] ).

cnf(i_0_14849,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_8687]),
    [final] ).

cnf(i_0_14850,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_8592]),
    [final] ).

cnf(i_0_14851,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_8688]),
    [final] ).

cnf(i_0_14852,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),esk570_3(X2,X1,X3)),X1))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_14853,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_8689]),
    [final] ).

cnf(i_0_14854,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_8690]),
    [final] ).

cnf(i_0_14855,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_8691]),
    [final] ).

cnf(i_0_14856,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_8692]),
    [final] ).

cnf(i_0_14857,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_8693]),
    [final] ).

cnf(i_0_14858,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk359_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_7070]),
    [final] ).

cnf(i_0_14859,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_8694]),
    [final] ).

cnf(i_0_14860,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_8695]),
    [final] ).

cnf(i_0_14861,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk144_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_8696]),
    [final] ).

cnf(i_0_14862,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_8268]),
    [final] ).

cnf(i_0_14863,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_8269]),
    [final] ).

cnf(i_0_14864,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_8697]),
    [final] ).

cnf(i_0_14865,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_8270]),
    [final] ).

cnf(i_0_14866,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_8698]),
    [final] ).

cnf(i_0_14867,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_8699]),
    [final] ).

cnf(i_0_14868,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_8192]),
    [final] ).

cnf(i_0_14869,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk560_3(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X1)))
    | c_List_Oall__interval__nat(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8700]),
    [final] ).

cnf(i_0_14870,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_8701]),
    [final] ).

cnf(i_0_14871,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_8702]),
    [final] ).

cnf(i_0_14872,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_8558]),
    [final] ).

cnf(i_0_14873,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_8703]),
    [final] ).

cnf(i_0_14874,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_8704]),
    [final] ).

cnf(i_0_14875,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_8559]),
    [final] ).

cnf(i_0_14876,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Oordered__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8623]),
    [final] ).

cnf(i_0_14877,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_8705]),
    [final] ).

cnf(i_0_14878,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_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_8560]),
    [final] ).

cnf(i_0_14879,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_8538]),
    [final] ).

cnf(i_0_14880,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_8539]),
    [final] ).

cnf(i_0_14881,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_8706]),
    [final] ).

cnf(i_0_14882,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_8707]),
    [final] ).

cnf(i_0_14883,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_8708]),
    [final] ).

cnf(i_0_14884,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),esk365_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_8098]),
    [final] ).

cnf(i_0_14885,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_8709]),
    [final] ).

cnf(i_0_14886,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_8592]),
    [final] ).

cnf(i_0_14887,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_8710]),
    [final] ).

cnf(i_0_14888,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_6372]),
    [final] ).

cnf(i_0_14889,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_8711]),
    [final] ).

cnf(i_0_14890,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_8712]),
    [final] ).

cnf(i_0_14891,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_8713,c_0_6219]),
    [final] ).

cnf(i_0_14892,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_8714]),
    [final] ).

cnf(i_0_14893,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_8715]),
    [final] ).

cnf(i_0_14894,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_8716]),
    [final] ).

cnf(i_0_14895,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_8717]),
    [final] ).

cnf(i_0_14896,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_8718]),
    [final] ).

cnf(i_0_14897,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_8719]),
    [final] ).

cnf(i_0_14898,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_8720]),
    [final] ).

cnf(i_0_14899,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_8721,c_0_6069]),c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_14900,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_8722]),
    [final] ).

cnf(i_0_14901,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk411_3(X3,X1,X2)),esk412_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_8260]),
    [final] ).

cnf(i_0_14902,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_8723]),
    [final] ).

cnf(i_0_14903,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk200_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_8724]),
    [final] ).

cnf(i_0_14904,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk199_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_8724]),
    [final] ).

cnf(i_0_14905,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))
    | esk250_3(X1,X2,X3) != esk251_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7581]),
    [final] ).

cnf(i_0_14906,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_8725]),
    [final] ).

cnf(i_0_14907,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_8726]),
    [final] ).

cnf(i_0_14908,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_8296]),
    [final] ).

cnf(i_0_14909,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_8297]),
    [final] ).

cnf(i_0_14910,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_8727]),
    [final] ).

cnf(i_0_14911,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_8728]),
    [final] ).

cnf(i_0_14912,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_8729]),
    [final] ).

cnf(i_0_14913,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_8730]),
    [final] ).

cnf(i_0_14914,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk474_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_8126]),
    [final] ).

cnf(i_0_14915,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_8731]),
    [final] ).

cnf(i_0_14916,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_8732]),
    [final] ).

cnf(i_0_14917,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk243_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_8733]),
    [final] ).

cnf(i_0_14918,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_8734]),
    [final] ).

cnf(i_0_14919,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_8735]),
    [final] ).

cnf(i_0_14920,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_7747]),
    [final] ).

cnf(i_0_14921,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),esk443_2(X3,X1)),X2))
    | X3 = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),esk442_2(X3,X1))))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_7362]),
    [final] ).

cnf(i_0_14922,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk507_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8736]),
    [final] ).

cnf(i_0_14923,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk506_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | ~ c_List_Olist__ex(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8737]),
    [final] ).

cnf(i_0_14924,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk486_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex1(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7283]),
    [final] ).

cnf(i_0_14925,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk478_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex1(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7284]),
    [final] ).

cnf(i_0_14926,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk469_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | ~ c_List_Olist__ex(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8738]),
    [final] ).

cnf(i_0_14927,hypothesis,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
    inference(split_conjunct,[status(thm)],[conj_2]),
    [final] ).

cnf(i_0_14928,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_8739]),
    [final] ).

cnf(i_0_14929,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_8740]),
    [final] ).

cnf(i_0_14930,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_8317]),
    [final] ).

cnf(i_0_14931,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_8321]),
    [final] ).

cnf(i_0_14932,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_8320]),
    [final] ).

cnf(i_0_14933,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_8318]),
    [final] ).

cnf(i_0_14934,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_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_8319]),
    [final] ).

cnf(i_0_14935,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk572_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_7690]),
    [final] ).

cnf(i_0_14936,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),esk568_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_7680]),
    [final] ).

cnf(i_0_14937,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk415_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_8741]),
    [final] ).

cnf(i_0_14938,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_5333]),
    [final] ).

cnf(i_0_14939,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_8742]),
    [final] ).

cnf(i_0_14940,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_8743]),
    [final] ).

cnf(i_0_14941,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_8744]),
    [final] ).

cnf(i_0_14942,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_8745]),
    [final] ).

cnf(i_0_14943,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_8746]),
    [final] ).

cnf(i_0_14944,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_8747]),
    [final] ).

cnf(i_0_14945,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_8748,c_0_6139]),
    [final] ).

cnf(i_0_14946,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_8749]),
    [final] ).

cnf(i_0_14947,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_8750]),
    [final] ).

cnf(i_0_14948,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_8206]),
    [final] ).

cnf(i_0_14949,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_8751]),
    [final] ).

cnf(i_0_14950,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_8206]),
    [final] ).

cnf(i_0_14951,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_8752]),
    [final] ).

cnf(i_0_14952,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_8753]),
    [final] ).

cnf(i_0_14953,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_8754]),
    [final] ).

cnf(i_0_14954,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_8207]),
    [final] ).

cnf(i_0_14955,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_8755]),
    [final] ).

cnf(i_0_14956,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_8207]),
    [final] ).

cnf(i_0_14957,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_8756]),
    [final] ).

cnf(i_0_14958,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_8757]),
    [final] ).

cnf(i_0_14959,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk180_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_8758]),
    [final] ).

cnf(i_0_14960,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk84_3(X2,X3,X1)),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8759]),
    [final] ).

cnf(i_0_14961,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_8720]),
    [final] ).

cnf(i_0_14962,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_8720]),
    [final] ).

cnf(i_0_14963,plain,
    ( hAPP(c_Quotient_OBabs(X1,X4,X3,X5),X2) = hAPP(X5,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8760]),
    [final] ).

cnf(i_0_14964,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,esk27_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8761]),
    [final] ).

cnf(i_0_14965,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,esk26_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_14966,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)),X2)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8763]),
    [final] ).

cnf(i_0_14967,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_8764]),
    [final] ).

cnf(i_0_14968,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_8765]),
    [final] ).

cnf(i_0_14969,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk570_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_7690]),
    [final] ).

cnf(i_0_14970,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_3(X2,X1,X3)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_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_7680]),
    [final] ).

cnf(i_0_14971,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_8766]),
    [final] ).

cnf(i_0_14972,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_8157]),
    [final] ).

cnf(i_0_14973,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_8767]),
    [final] ).

cnf(i_0_14974,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_8768,c_0_8354]),c_0_8354]),
    [final] ).

cnf(i_0_14975,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_8769]),
    [final] ).

cnf(i_0_14976,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),esk570_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_7690]),
    [final] ).

cnf(i_0_14977,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),esk566_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_7680]),
    [final] ).

cnf(i_0_14978,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_8770]),
    [final] ).

cnf(i_0_14979,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_8771]),
    [final] ).

cnf(i_0_14980,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_8772]),
    [final] ).

cnf(i_0_14981,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_8772]),
    [final] ).

cnf(i_0_14982,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_8773]),
    [final] ).

cnf(i_0_14983,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_8348]),
    [final] ).

cnf(i_0_14984,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_8774]),
    [final] ).

cnf(i_0_14985,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_8775]),
    [final] ).

cnf(i_0_14986,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_8776]),
    [final] ).

cnf(i_0_14987,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_8777]),
    [final] ).

cnf(i_0_14988,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_8778]),
    [final] ).

cnf(i_0_14989,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_8779]),
    [final] ).

cnf(i_0_14990,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_8780]),
    [final] ).

cnf(i_0_14991,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_8781]),
    [final] ).

cnf(i_0_14992,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_8782]),
    [final] ).

cnf(i_0_14993,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_8783]),
    [final] ).

cnf(i_0_14994,plain,
    ( c_Divides_Odiv__class_Omod(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X3),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)) = c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8784]),
    [final] ).

cnf(i_0_14995,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_8785]),
    [final] ).

cnf(i_0_14996,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_8786]),
    [final] ).

cnf(i_0_14997,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_8787]),
    [final] ).

cnf(i_0_14998,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_5330]),
    [final] ).

cnf(i_0_14999,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_8788,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_15000,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_8789]),
    [final] ).

cnf(i_0_15001,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_8476]),
    [final] ).

cnf(i_0_15002,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_8790]),
    [final] ).

cnf(i_0_15003,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_8790]),
    [final] ).

cnf(i_0_15004,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_8791]),
    [final] ).

cnf(i_0_15005,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_8478]),
    [final] ).

cnf(i_0_15006,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_8792]),
    [final] ).

cnf(i_0_15007,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_8792]),
    [final] ).

cnf(i_0_15008,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_8244]),
    [final] ).

cnf(i_0_15009,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_8793]),
    [final] ).

cnf(i_0_15010,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_8794]),
    [final] ).

cnf(i_0_15011,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_8490]),
    [final] ).

cnf(i_0_15012,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_8795,c_0_6726]),
    [final] ).

cnf(i_0_15013,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_8796]),
    [final] ).

cnf(i_0_15014,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_8797]),
    [final] ).

cnf(i_0_15015,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_8720]),
    [final] ).

cnf(i_0_15016,plain,
    ( hBOOL(hAPP(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X3,X2)))
    | ~ hBOOL(hAPP(X1,esk73_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8191]),
    [final] ).

cnf(i_0_15017,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_8798]),
    [final] ).

cnf(i_0_15018,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),esk243_3(X3,X2,X1)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8733]),
    [final] ).

cnf(i_0_15019,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_8799]),
    [final] ).

cnf(i_0_15020,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_8800]),
    [final] ).

cnf(i_0_15021,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_8126]),
    [final] ).

cnf(i_0_15022,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk314_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_8801]),
    [final] ).

cnf(i_0_15023,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk434_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_OtakeWhile(X1,X3,X2) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8802]),
    [final] ).

cnf(i_0_15024,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_8803]),
    [final] ).

cnf(i_0_15025,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_8804]),
    [final] ).

cnf(i_0_15026,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk476_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X3)))
    | c_List_Olist__all(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8805]),
    [final] ).

cnf(i_0_15027,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk477_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__all(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8806]),
    [final] ).

cnf(i_0_15028,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk475_3(X2,X3,X1)),hAPP(c_List_Oset(X1),X2)))
    | c_List_Olist__all(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8807]),
    [final] ).

cnf(i_0_15029,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_8808]),
    [final] ).

cnf(i_0_15030,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_8809,c_0_6289]),
    [final] ).

cnf(i_0_15031,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_8810]),
    [final] ).

cnf(i_0_15032,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_8811]),
    [final] ).

cnf(i_0_15033,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_8812]),
    [final] ).

cnf(i_0_15034,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8555]),
    [final] ).

cnf(i_0_15035,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Divides_Odiv__class_Omod(X1,X3,X4)))
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8813]),
    [final] ).

cnf(i_0_15036,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_8814]),
    [final] ).

cnf(i_0_15037,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_8815]),
    [final] ).

cnf(i_0_15038,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_8816]),
    [final] ).

cnf(i_0_15039,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_8817]),
    [final] ).

cnf(i_0_15040,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_8818]),
    [final] ).

cnf(i_0_15041,plain,
    ( hBOOL(hAPP(hAPP(c_member(X2),X4),X3))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),hAPP(hAPP(c_Set_Oinsert(X2),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(X5,X4)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X2,X1),X5),X3))
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8819]),
    [final] ).

cnf(i_0_15042,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_8820]),
    [final] ).

cnf(i_0_15043,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),esk219_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_7023]),
    [final] ).

cnf(i_0_15044,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_8541]),
    [final] ).

cnf(i_0_15045,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_8821]),
    [final] ).

cnf(i_0_15046,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_8822]),
    [final] ).

cnf(i_0_15047,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_8823]),
    [final] ).

cnf(i_0_15048,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk149_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8824]),
    [final] ).

cnf(i_0_15049,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_8825]),
    [final] ).

cnf(i_0_15050,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_7087]),
    [final] ).

cnf(i_0_15051,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_8826]),
    [final] ).

cnf(i_0_15052,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_8827,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_15053,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk537_3(X2,X3,X1)),c_Quotient_ORespects(X1,X3)))
    | ~ hBOOL(hAPP(X2,X4))
    | ~ c_Equiv__Relations_Oequivp(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8828]),
    [final] ).

cnf(i_0_15054,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_8829]),
    [final] ).

cnf(i_0_15055,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_8829]),
    [final] ).

cnf(i_0_15056,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_8830]),
    [final] ).

cnf(i_0_15057,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk425_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_8831]),
    [final] ).

cnf(i_0_15058,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_8656]),
    [final] ).

cnf(i_0_15059,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8832]),
    [final] ).

cnf(i_0_15060,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4)))
    | ~ class_Rings_Ocomm__ring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8833]),
    [final] ).

cnf(i_0_15061,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_8834]),
    [final] ).

cnf(i_0_15062,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_8835]),
    [final] ).

cnf(i_0_15063,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__inf(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8836]),
    [final] ).

cnf(i_0_15064,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_8837]),
    [final] ).

cnf(i_0_15065,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_8838]),
    [final] ).

cnf(i_0_15066,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_8839]),
    [final] ).

cnf(i_0_15067,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_8840]),
    [final] ).

cnf(i_0_15068,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk144_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_8696]),
    [final] ).

cnf(i_0_15069,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_8841]),
    [final] ).

cnf(i_0_15070,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_8842]),
    [final] ).

cnf(i_0_15071,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk63_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8208]),
    [final] ).

cnf(i_0_15072,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk27_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8761]),
    [final] ).

cnf(i_0_15073,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)))
    | ~ hBOOL(hAPP(X1,esk26_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15074,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk424_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_8843]),
    [final] ).

cnf(i_0_15075,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),esk465_3(X2,X3,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8612]),
    [final] ).

cnf(i_0_15076,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),esk431_3(X3,X2,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8613]),
    [final] ).

cnf(i_0_15077,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),esk428_3(X3,X2,X1)))
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8614]),
    [final] ).

cnf(i_0_15078,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_8844]),
    [final] ).

cnf(i_0_15079,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_8845]),
    [final] ).

cnf(i_0_15080,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_8846,c_0_6726]),
    [final] ).

cnf(i_0_15081,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_8847]),
    [final] ).

cnf(i_0_15082,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_8848]),
    [final] ).

cnf(i_0_15083,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X4),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8849]),
    [final] ).

cnf(i_0_15084,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X4),X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8850]),
    [final] ).

cnf(i_0_15085,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_8849]),
    [final] ).

cnf(i_0_15086,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_8851]),
    [final] ).

cnf(i_0_15087,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_8852]),
    [final] ).

cnf(i_0_15088,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_8853]),
    [final] ).

cnf(i_0_15089,plain,
    ( c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
    | ~ c_Predicate_Osymp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8228]),
    [final] ).

cnf(i_0_15090,plain,
    ( c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X2)))
    | ~ c_Predicate_Otransp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8229]),
    [final] ).

cnf(i_0_15091,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_8854]),
    [final] ).

cnf(i_0_15092,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_8230]),
    [final] ).

cnf(i_0_15093,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_7762]),
    [final] ).

cnf(i_0_15094,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_8855]),
    [final] ).

cnf(i_0_15095,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_8856]),
    [final] ).

cnf(i_0_15096,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_8857]),
    [final] ).

cnf(i_0_15097,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_8858]),
    [final] ).

cnf(i_0_15098,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_8859]),
    [final] ).

cnf(i_0_15099,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_8860]),
    [final] ).

cnf(i_0_15100,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk146_2(X1,X2)),X2))
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8861]),
    [final] ).

cnf(i_0_15101,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8125]),
    [final] ).

cnf(i_0_15102,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_8862]),
    [final] ).

cnf(i_0_15103,plain,
    hAPP(c_Lazy__Sequence_Obind(X1,X2,X3),X4) = c_Lazy__Sequence_Oflat(X2,c_Lazy__Sequence_Omap(X1,tc_Lazy__Sequence_Olazy__sequence(X2),X4,X3)),
    inference(split_conjunct,[status(thm)],[i_0_8863]),
    [final] ).

cnf(i_0_15104,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_8864]),
    [final] ).

cnf(i_0_15105,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_8413]),
    [final] ).

cnf(i_0_15106,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_8414]),
    [final] ).

cnf(i_0_15107,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_8865]),
    [final] ).

cnf(i_0_15108,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_8416]),
    [final] ).

cnf(i_0_15109,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_8866,c_0_6103]),
    [final] ).

cnf(i_0_15110,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_8867,c_0_6103]),
    [final] ).

cnf(i_0_15111,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_8868]),
    [final] ).

cnf(i_0_15112,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_8869]),
    [final] ).

cnf(i_0_15113,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_8870]),
    [final] ).

cnf(i_0_15114,plain,
    ( 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))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8871]),
    [final] ).

cnf(i_0_15115,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8872]),
    [final] ).

cnf(i_0_15116,plain,
    ( hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8873]),
    [final] ).

cnf(i_0_15117,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X1)))),
    inference(split_conjunct,[status(thm)],[i_0_8874]),
    [final] ).

cnf(i_0_15118,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),c_List_Obutlast(X1,X3)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8875]),
    [final] ).

cnf(i_0_15119,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X4),hAPP(X5,X2)),hAPP(c_Set_Oimage(X1,X4,X5),X3)) = hAPP(c_Set_Oimage(X1,X4,X5),X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8876]),
    [final] ).

cnf(i_0_15120,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8877,c_0_6070]),c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_15121,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8878,c_0_6070]),c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_15122,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8879]),
    [final] ).

cnf(i_0_15123,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(X1,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8880]),
    [final] ).

cnf(i_0_15124,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X5),X4))
    | hAPP(X3,hAPP(hAPP(c_Set_Oinsert(X1),X5),X4)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,X2),X5),X4)
    | ~ c_Finite__Set_Ofolding__one(X1,X2,X3)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8881]),
    [final] ).

cnf(i_0_15125,plain,
    ( c_Wellfounded_Owf(X1,X3)
    | ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8882]),
    [final] ).

cnf(i_0_15126,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8883]),
    [final] ).

cnf(i_0_15127,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8884]),
    [final] ).

cnf(i_0_15128,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X3))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8885]),
    [final] ).

cnf(i_0_15129,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X2)),hAPP(c_Int_Oring__1__class_Oof__int(X1),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8886]),
    [final] ).

cnf(i_0_15130,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X3)))
    | ~ class_Rings_Olinordered__semidom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8887]),
    [final] ).

cnf(i_0_15131,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_8775]),
    [final] ).

cnf(i_0_15132,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),esk304_1(X1)),c_Int_OInteg)),
    inference(split_conjunct,[status(thm)],[i_0_8888]),
    [final] ).

cnf(i_0_15133,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)),X2))
    | 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)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8407]),
    [final] ).

cnf(i_0_15134,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),X2))
    | 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)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8408]),
    [final] ).

cnf(i_0_15135,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8889,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_15136,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X2)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),X1),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8890,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_15137,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Power_Opower__class_Opower(X1),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),X3),X2)),X4) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X1),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X3),X4)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X4))
    | ~ class_Fields_Ofield(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8891]),
    [final] ).

cnf(i_0_15138,plain,
    ( hBOOL(hAPP(X1,esk562_3(X2,X1,X3)))
    | ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X4)))
    | ~ class_Rings_Odvd(X3)
    | ~ class_Rings_Osemiring__0(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7715]),
    [final] ).

cnf(i_0_15139,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_8467]),
    [final] ).

cnf(i_0_15140,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint))),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8892]),
    [final] ).

cnf(i_0_15141,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Big__Operators_Olattice__class_OInf__fin(X1,X2)),c_Big__Operators_Olattice__class_OInf__fin(X1,X3))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8893]),
    [final] ).

cnf(i_0_15142,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Big__Operators_Olattice__class_OSup__fin(X1,X2)),c_Big__Operators_Olattice__class_OSup__fin(X1,X3))
    | ~ class_Lattices_Olattice(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8894]),
    [final] ).

cnf(i_0_15143,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_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_8895]),
    [final] ).

cnf(i_0_15144,plain,
    ( X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),c_Big__Operators_Olinorder__class_OMin(X1,X2)),c_Big__Operators_Olinorder__class_OMin(X1,X3))
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8896]),
    [final] ).

cnf(i_0_15145,plain,
    c_List_Osplice(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),hAPP(hAPP(c_List_Olist_OCons(X1),X4),X5)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),hAPP(hAPP(c_List_Olist_OCons(X1),X4),c_List_Osplice(X1,X3,X5))),
    inference(split_conjunct,[status(thm)],[i_0_8897]),
    [final] ).

cnf(i_0_15146,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8898]),
    [final] ).

cnf(i_0_15147,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8899]),
    [final] ).

cnf(i_0_15148,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8900]),
    [final] ).

cnf(i_0_15149,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8901]),
    [final] ).

cnf(i_0_15150,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8901]),
    [final] ).

cnf(i_0_15151,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,esk73_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8191]),
    [final] ).

cnf(i_0_15152,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_8857]),
    [final] ).

cnf(i_0_15153,plain,
    hAPP(X1,hAPP(hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X1),X4)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(X2,X2),X3),X1),hAPP(X1,X4)),
    inference(split_conjunct,[status(thm)],[i_0_8902]),
    [final] ).

cnf(i_0_15154,plain,
    ( hBOOL(hAPP(X1,esk143_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_8660]),
    [final] ).

cnf(i_0_15155,plain,
    ( hBOOL(hAPP(X2,X3))
    | hAPP(c_List_Ofilter(X4,X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X1,X5),X3),X6)) = hAPP(c_List_Ofilter(X4,X2),X6)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8903]),
    [final] ).

cnf(i_0_15156,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8904]),
    [final] ).

cnf(i_0_15157,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_8905]),
    [final] ).

cnf(i_0_15158,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_8906]),
    [final] ).

cnf(i_0_15159,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_8907]),
    [final] ).

cnf(i_0_15160,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_8908]),
    [final] ).

cnf(i_0_15161,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_8909]),
    [final] ).

cnf(i_0_15162,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_8910]),
    [final] ).

cnf(i_0_15163,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_8911]),
    [final] ).

cnf(i_0_15164,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_8912]),
    [final] ).

cnf(i_0_15165,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_8913]),
    [final] ).

cnf(i_0_15166,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_8914]),
    [final] ).

cnf(i_0_15167,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X3)),X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4))
    | ~ class_Rings_Ocomm__semiring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8915]),
    [final] ).

cnf(i_0_15168,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8916]),
    [final] ).

cnf(i_0_15169,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X4)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8917]),
    [final] ).

cnf(i_0_15170,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8918]),
    [final] ).

cnf(i_0_15171,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X3)),X4) = hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X2),X4)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X3),X4))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8919]),
    [final] ).

cnf(i_0_15172,plain,
    ( hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),X4),hAPP(c_List_Oset(X2),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8920]),
    [final] ).

cnf(i_0_15173,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8921]),
    [final] ).

cnf(i_0_15174,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_8688]),
    [final] ).

cnf(i_0_15175,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8922]),
    [final] ).

cnf(i_0_15176,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8923]),
    [final] ).

cnf(i_0_15177,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8924]),
    [final] ).

cnf(i_0_15178,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X5),X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | X4 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X5)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X5))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X4),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8925]),
    [final] ).

cnf(i_0_15179,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)
    | X5 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X4),X5)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X5),X4))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8925]),
    [final] ).

cnf(i_0_15180,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_8926]),
    [final] ).

cnf(i_0_15181,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omin(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8927]),
    [final] ).

cnf(i_0_15182,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8928]),
    [final] ).

cnf(i_0_15183,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),hAPP(c_Relation_Oconverse(X2,X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8929]),
    [final] ).

cnf(i_0_15184,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8930]),
    [final] ).

cnf(i_0_15185,plain,
    ( hAPP(c_List_Oset(X1),c_List_Oremove1(X1,X3,X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X2)),hAPP(hAPP(c_Set_Oinsert(X1),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8931]),
    [final] ).

cnf(i_0_15186,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8932]),
    [final] ).

cnf(i_0_15187,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),X3)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8933]),
    [final] ).

cnf(i_0_15188,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X2,X1,X3),X4),X5)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X5))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8934]),
    [final] ).

cnf(i_0_15189,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8935]),
    [final] ).

cnf(i_0_15190,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(rw,[status(thm)],[i_0_8936,c_0_6070]),
    [final] ).

cnf(i_0_15191,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_8775]),
    [final] ).

cnf(i_0_15192,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_8937]),
    [final] ).

cnf(i_0_15193,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_8261]),
    [final] ).

cnf(i_0_15194,plain,
    ( c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X1,X1,c_COMBI(X1)),X2),X3)) = X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8938]),
    [final] ).

cnf(i_0_15195,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk302_3(X2,X3,X1)),X2))
    | hBOOL(hAPP(c_Predicate_OPowp(X1,X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8939]),
    [final] ).

cnf(i_0_15196,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),c_Product__Type_Ocurry(X1,X2,X3,X4)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_8940]),
    [final] ).

cnf(i_0_15197,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk142_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_8660]),
    [final] ).

cnf(i_0_15198,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
    | ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8941]),
    [final] ).

cnf(i_0_15199,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X4) = X3
    | X1 != hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)
    | X4 != hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8942]),
    [final] ).

cnf(i_0_15200,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | hAPP(c_Finite__Set_Ofold1(X1,c_Groups_Otimes__class_Otimes(X1)),hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Groups_Otimes__class_Otimes(X1)),X3),X2)
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8943]),
    [final] ).

cnf(i_0_15201,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))
    | ~ class_Int_Onumber__ring(X1) ),
    inference(rw,[status(thm)],[i_0_8944,c_0_6070]),
    [final] ).

cnf(i_0_15202,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_8183]),
    [final] ).

cnf(i_0_15203,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_8309]),
    [final] ).

cnf(i_0_15204,plain,
    ( hBOOL(hAPP(X1,esk66_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_7654]),
    [final] ).

cnf(i_0_15205,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_8945]),
    [final] ).

cnf(i_0_15206,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X2)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_8946]),
    [final] ).

cnf(i_0_15207,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_7968]),
    [final] ).

cnf(i_0_15208,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_7967]),
    [final] ).

cnf(i_0_15209,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8947,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15210,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_8446]),
    [final] ).

cnf(i_0_15211,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_8446]),
    [final] ).

cnf(i_0_15212,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8510]),
    [final] ).

cnf(i_0_15213,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_7642]),
    [final] ).

cnf(i_0_15214,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_7747]),
    [final] ).

cnf(i_0_15215,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),X3) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),X3),
    inference(split_conjunct,[status(thm)],[i_0_8948]),
    [final] ).

cnf(i_0_15216,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_8724]),
    [final] ).

cnf(i_0_15217,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_7762]),
    [final] ).

cnf(i_0_15218,plain,
    ( hBOOL(hAPP(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X2,hAPP(c_Code__Numeral_Onat__of,esk526_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8949]),
    [final] ).

cnf(i_0_15219,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_6624]),
    [final] ).

cnf(i_0_15220,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,X1),hAPP(c_List_Onth(X1),X2)),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)))) = X2,
    inference(rw,[status(thm)],[i_0_8950,c_0_6187]),
    [final] ).

cnf(i_0_15221,plain,
    ( X2 = X3
    | hAPP(hAPP(c_List_Onth(X1),X2),esk382_3(X1,X3,X2)) != hAPP(hAPP(c_List_Onth(X1),X3),esk382_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_8636]),
    [final] ).

cnf(i_0_15222,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_8717]),
    [final] ).

cnf(i_0_15223,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_8710]),
    [final] ).

cnf(i_0_15224,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8935]),
    [final] ).

cnf(i_0_15225,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X3)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8951]),
    [final] ).

cnf(i_0_15226,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_7087]),
    [final] ).

cnf(i_0_15227,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_8834]),
    [final] ).

cnf(i_0_15228,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8834]),
    [final] ).

cnf(i_0_15229,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8952]),
    [final] ).

cnf(i_0_15230,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X3),X4)))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8837]),
    [final] ).

cnf(i_0_15231,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3)))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8952]),
    [final] ).

cnf(i_0_15232,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X4),X3)))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8837]),
    [final] ).

cnf(i_0_15233,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8953]),
    [final] ).

cnf(i_0_15234,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X3),X4)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8840]),
    [final] ).

cnf(i_0_15235,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8953]),
    [final] ).

cnf(i_0_15236,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X4),X3)))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8840]),
    [final] ).

cnf(i_0_15237,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,esk567_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_15238,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8954]),
    [final] ).

cnf(i_0_15239,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8955]),
    [final] ).

cnf(i_0_15240,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)),X3)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8956]),
    [final] ).

cnf(i_0_15241,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8957]),
    [final] ).

cnf(i_0_15242,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8958]),
    [final] ).

cnf(i_0_15243,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8959]),
    [final] ).

cnf(i_0_15244,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8960]),
    [final] ).

cnf(i_0_15245,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X3),X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8961]),
    [final] ).

cnf(i_0_15246,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_8764]),
    [final] ).

cnf(i_0_15247,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_8460]),
    [final] ).

cnf(i_0_15248,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)),X3) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X4),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8962]),
    [final] ).

cnf(i_0_15249,plain,
    hAPP(c_Set_OCollect(X1),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X1),c_fNot),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Set_OCollect(X1),X2)),
    inference(split_conjunct,[status(thm)],[i_0_8963]),
    [final] ).

cnf(i_0_15250,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_8362]),
    [final] ).

cnf(i_0_15251,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),X3),X2) = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8964]),
    [final] ).

cnf(i_0_15252,plain,
    ( hAPP(hAPP(c_List_Odrop(X1),X3),X2) = c_List_Olist_ONil(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8965]),
    [final] ).

cnf(i_0_15253,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8966]),
    [final] ).

cnf(i_0_15254,plain,
    ( X2 = X3
    | hBOOL(hAPP(hAPP(c_member(X1),X2),X4))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_8967]),
    [final] ).

cnf(i_0_15255,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,esk63_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8208]),
    [final] ).

cnf(i_0_15256,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk145_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_8696]),
    [final] ).

cnf(i_0_15257,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,esk565_3(X3,X1,X2)))
    | ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_15258,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(rw,[status(thm)],[i_0_8968,c_0_6070]),
    [final] ).

cnf(i_0_15259,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_8969,c_0_6070]),
    [final] ).

cnf(i_0_15260,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OMin)) ),
    inference(rw,[status(thm)],[i_0_8970,c_0_6070]),
    [final] ).

cnf(i_0_15261,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Int_OPls)) ),
    inference(rw,[status(thm)],[i_0_8971,c_0_6070]),
    [final] ).

cnf(i_0_15262,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(rw,[status(thm)],[i_0_8972,c_0_6070]),
    [final] ).

cnf(i_0_15263,plain,
    ( hAPP(hAPP(c_List_Otake(X1),X3),X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8973]),
    [final] ).

cnf(i_0_15264,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(c_Nat_OSuc,X2)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_8974,c_0_8975]),c_0_8975]),
    [final] ).

cnf(i_0_15265,plain,
    ( c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(rw,[status(thm)],[i_0_8976,c_0_6103]),
    [final] ).

cnf(i_0_15266,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(rw,[status(thm)],[i_0_8977,c_0_6103]),
    [final] ).

cnf(i_0_15267,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_8400]),
    [final] ).

cnf(i_0_15268,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,esk572_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_15269,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X4)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X2),X3)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(X1,X3),X4)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8978]),
    [final] ).

cnf(i_0_15270,plain,
    ( hBOOL(hAPP(hAPP(X1,esk92_3(X2,X1,X3)),X2))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8979]),
    [final] ).

cnf(i_0_15271,plain,
    ( hBOOL(hAPP(hAPP(X1,esk91_3(X2,X1,X3)),X2))
    | hBOOL(hAPP(c_Wellfounded_Oaccp(X3,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8980]),
    [final] ).

cnf(i_0_15272,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X2,X2),X3),c_Transitive__Closure_Ortrancl(X2,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)))) = X3,
    inference(rw,[status(thm)],[i_0_8981,c_0_6096]),
    [final] ).

cnf(i_0_15273,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_8561]),
    [final] ).

cnf(i_0_15274,plain,
    ( X3 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | X4 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(X1,X2),X3),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),X4)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8982]),
    [final] ).

cnf(i_0_15275,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OMin)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(rw,[status(thm)],[i_0_8983,c_0_6219]),
    [final] ).

cnf(i_0_15276,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = hAPP(c_SetInterval_Oord__class_OatLeast(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8984]),
    [final] ).

cnf(i_0_15277,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X3)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8985]),
    [final] ).

cnf(i_0_15278,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_OatLeast(X1),X3)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X1),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8986]),
    [final] ).

cnf(i_0_15279,plain,
    ( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_List_Oset(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8987]),
    [final] ).

cnf(i_0_15280,plain,
    ( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_List_Oset(X1),X2)) = hAPP(c_List_Ofoldl(X1,X1,c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X2)
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8988]),
    [final] ).

cnf(i_0_15281,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X2)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_8989]),
    [final] ).

cnf(i_0_15282,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X1,X3,X4),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8990]),
    [final] ).

cnf(i_0_15283,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk341_3(X2,X3,X1)),X3))
    | c_Relation_Ototal__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_15284,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk340_3(X2,X3,X1)),X3))
    | c_Relation_Ototal__on(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_15285,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)
    | esk420_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_8991,c_0_6139]),
    [final] ).

cnf(i_0_15286,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)
    | esk421_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(rw,[status(thm)],[i_0_8992,c_0_6139]),
    [final] ).

cnf(i_0_15287,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8993]),
    [final] ).

cnf(i_0_15288,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8994]),
    [final] ).

cnf(i_0_15289,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_8995]),
    [final] ).

cnf(i_0_15290,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_8996]),
    [final] ).

cnf(i_0_15291,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,esk570_3(X3,X1,X2)))
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_15292,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)),X2)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8997]),
    [final] ).

cnf(i_0_15293,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_8998]),
    [final] ).

cnf(i_0_15294,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_8999]),
    [final] ).

cnf(i_0_15295,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_9000]),
    [final] ).

cnf(i_0_15296,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_9001]),
    [final] ).

cnf(i_0_15297,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_9002]),
    [final] ).

cnf(i_0_15298,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X4),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X4),X3))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8613]),
    [final] ).

cnf(i_0_15299,plain,
    ( 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_8614]),
    [final] ).

cnf(i_0_15300,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_9003]),
    [final] ).

cnf(i_0_15301,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_15302,plain,
    hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),c_Transitive__Closure_Ortrancl(X1,X2)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9004]),
    [final] ).

cnf(i_0_15303,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_9005,c_0_6103]),
    [final] ).

cnf(i_0_15304,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_9006]),
    [final] ).

cnf(i_0_15305,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_9007,c_0_6103]),
    [final] ).

cnf(i_0_15306,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),esk246_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_8535]),
    [final] ).

cnf(i_0_15307,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_9008]),
    [final] ).

cnf(i_0_15308,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_9009]),
    [final] ).

cnf(i_0_15309,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(X2)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),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_9010]),
    [final] ).

cnf(i_0_15310,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_9010]),
    [final] ).

cnf(i_0_15311,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_8244]),
    [final] ).

cnf(i_0_15312,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8872]),
    [final] ).

cnf(i_0_15313,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_9011]),
    [final] ).

cnf(i_0_15314,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_9012]),
    [final] ).

cnf(i_0_15315,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_9013]),
    [final] ).

cnf(i_0_15316,plain,
    ( c_Relation_Otrans(tc_prod(X1,X3),c_Wellfounded_Olex__prod(X1,X3,X2,X4))
    | ~ c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Otrans(X3,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9014]),
    [final] ).

cnf(i_0_15317,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_9015]),
    [final] ).

cnf(i_0_15318,plain,
    ( hBOOL(hAPP(X1,esk66_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_7654]),
    [final] ).

cnf(i_0_15319,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_9016,c_0_6139]),
    [final] ).

cnf(i_0_15320,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9017]),
    [final] ).

cnf(i_0_15321,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) != c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9018]),
    [final] ).

cnf(i_0_15322,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_9019]),
    [final] ).

cnf(i_0_15323,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_9020]),
    [final] ).

cnf(i_0_15324,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_9021]),
    [final] ).

cnf(i_0_15325,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_9022]),
    [final] ).

cnf(i_0_15326,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X3),X2)) = hAPP(hAPP(c_Finite__Set_Ofold(X1,X1,c_Orderings_Oord__class_Omax(X1)),X3),X2)
    | ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9023]),
    [final] ).

cnf(i_0_15327,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_9024]),
    [final] ).

cnf(i_0_15328,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_8765]),
    [final] ).

cnf(i_0_15329,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_9025]),
    [final] ).

cnf(i_0_15330,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_9026]),
    [final] ).

cnf(i_0_15331,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_9027]),
    [final] ).

cnf(i_0_15332,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_8469]),
    [final] ).

cnf(i_0_15333,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_9028]),
    [final] ).

cnf(i_0_15334,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_9029]),
    [final] ).

cnf(i_0_15335,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_9030]),
    [final] ).

cnf(i_0_15336,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_9031]),
    [final] ).

cnf(i_0_15337,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_9032]),
    [final] ).

cnf(i_0_15338,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk146_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8861]),
    [final] ).

cnf(i_0_15339,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_9033]),
    [final] ).

cnf(i_0_15340,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9034]),
    [final] ).

cnf(i_0_15341,plain,
    c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2))),
    inference(rw,[status(thm)],[i_0_9035,c_0_6103]),
    [final] ).

cnf(i_0_15342,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_9036]),
    [final] ).

cnf(i_0_15343,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_9037]),
    [final] ).

cnf(i_0_15344,plain,
    ( hBOOL(hAPP(hAPP(X3,esk288_2(X4,X3)),X4))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9038]),
    [final] ).

cnf(i_0_15345,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9039]),
    [final] ).

cnf(i_0_15346,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(split_conjunct,[status(thm)],[i_0_9040]),
    [final] ).

cnf(i_0_15347,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X1,X2)),c_Nitpick_Opair__box_OPairBox(X1,X2,X3,X4)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_9041]),
    [final] ).

cnf(i_0_15348,plain,
    ( X1 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | c_List_Obutlast(X2,hAPP(hAPP(c_List_Olist__update(X2,X3),X1),X4)) = hAPP(hAPP(c_List_Olist__update(X2,c_List_Obutlast(X2,X3)),X1),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_9042]),
    [final] ).

cnf(i_0_15349,plain,
    hAPP(c_Set_Oimage(X1,X2,X3),hAPP(hAPP(c_Set_Oinsert(X1),X4),X5)) = hAPP(hAPP(c_Set_Oinsert(X2),hAPP(X3,X4)),hAPP(c_Set_Oimage(X1,X2,X3),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9043]),
    [final] ).

cnf(i_0_15350,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(rw,[status(thm)],[i_0_9044,c_0_6187]),
    [final] ).

cnf(i_0_15351,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9045]),
    [final] ).

cnf(i_0_15352,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9046]),
    [final] ).

cnf(i_0_15353,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X3),X4),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X3,tc_HOL_Obool)),X1),X5)) = hAPP(hAPP(c_Set_Oinsert(X3),X4),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_7668]),
    [final] ).

cnf(i_0_15354,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9047]),
    [final] ).

cnf(i_0_15355,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Groups_Oordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9048]),
    [final] ).

cnf(i_0_15356,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk17_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_7244]),
    [final] ).

cnf(i_0_15357,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),c_List_Olinorder__class_Osort__key(X2,X1,X3,X4)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9049]),
    [final] ).

cnf(i_0_15358,plain,
    ( hBOOL(hAPP(X4,esk536_3(X4,X3,X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Quotient_ORespects(X1,X3)))
    | ~ hBOOL(hAPP(X4,X2))
    | ~ c_Equiv__Relations_Oequivp(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8828]),
    [final] ).

cnf(i_0_15359,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk148_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8824]),
    [final] ).

cnf(i_0_15360,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2)))
    | c_Divides_Odiv__class_Omod(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X2),hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ class_Int_Onumber(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8784]),
    [final] ).

cnf(i_0_15361,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_9050]),
    [final] ).

cnf(i_0_15362,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_9051]),
    [final] ).

cnf(i_0_15363,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_8417]),
    [final] ).

cnf(i_0_15364,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X1,X2,X3)),hAPP(c_SetInterval_Oord__class_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_9052]),
    [final] ).

cnf(i_0_15365,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_9053]),
    [final] ).

cnf(i_0_15366,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_9054]),
    [final] ).

cnf(i_0_15367,plain,
    hAPP(hAPP(hAPP(c_COMBC(X1,X2,X3),X4),X5),X6) = hAPP(hAPP(X4,X6),X5),
    inference(split_conjunct,[status(thm)],[i_0_9055]),
    [final] ).

cnf(i_0_15368,plain,
    hAPP(hAPP(hAPP(c_COMBB(X1,X2,X3),X4),X5),X6) = hAPP(X4,hAPP(X5,X6)),
    inference(split_conjunct,[status(thm)],[i_0_9056]),
    [final] ).

cnf(i_0_15369,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_9057]),
    [final] ).

cnf(i_0_15370,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8921]),
    [final] ).

cnf(i_0_15371,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8921]),
    [final] ).

cnf(i_0_15372,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_9058]),
    [final] ).

cnf(i_0_15373,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_9059]),
    [final] ).

cnf(i_0_15374,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_7426]),
    [final] ).

cnf(i_0_15375,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_7427]),
    [final] ).

cnf(i_0_15376,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_7428]),
    [final] ).

cnf(i_0_15377,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_9060]),
    [final] ).

cnf(i_0_15378,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_9061]),
    [final] ).

cnf(i_0_15379,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_9062]),
    [final] ).

cnf(i_0_15380,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_9063]),
    [final] ).

cnf(i_0_15381,plain,
    ( hAPP(c_Random_Oiterate(X2,X3,X1,X4),X5) = hAPP(c_Product__Type_OPair(X2,X3),X5)
    | X1 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_7324]),
    [final] ).

cnf(i_0_15382,plain,
    ( hBOOL(hAPP(X1,esk17_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_7244]),
    [final] ).

cnf(i_0_15383,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(X1,X2))),hAPP(hAPP(c_List_Ozip(X1,X2),X3),X4)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X4)),
    inference(split_conjunct,[status(thm)],[i_0_9064]),
    [final] ).

cnf(i_0_15384,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3),
    inference(split_conjunct,[status(thm)],[i_0_9065]),
    [final] ).

cnf(i_0_15385,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_Oimage(X2,tc_fun(X1,tc_HOL_Obool),X3),X4)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X2,tc_fun(X1,tc_HOL_Obool)),X4),X3),
    inference(split_conjunct,[status(thm)],[i_0_9066]),
    [final] ).

cnf(i_0_15386,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OInf__class_OInf(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9067]),
    [final] ).

cnf(i_0_15387,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X1,tc_fun(X2,tc_HOL_Obool)),X3),X4) = c_Complete__Lattice_OSup__class_OSup(tc_fun(X2,tc_HOL_Obool),hAPP(c_Set_Oimage(X1,tc_fun(X2,tc_HOL_Obool),X4),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9068]),
    [final] ).

cnf(i_0_15388,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,hAPP(c_Nat_OSuc,X3),X4) = c_Nat_Osemiring__1__class_Oof__nat__aux(X1,X2,X3,hAPP(X2,X4))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9069]),
    [final] ).

cnf(i_0_15389,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9070]),
    [final] ).

cnf(i_0_15390,plain,
    ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,X1),hAPP(c_Int_Onat,X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9071]),
    [final] ).

cnf(i_0_15391,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9072]),
    [final] ).

cnf(i_0_15392,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X2)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_9073]),
    [final] ).

cnf(i_0_15393,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk572_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_15394,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3))
    | X3 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk567_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_15395,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X2)),X1)))
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_8438]),
    [final] ).

cnf(i_0_15396,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9074]),
    [final] ).

cnf(i_0_15397,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8803]),
    [final] ).

cnf(i_0_15398,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9075]),
    [final] ).

cnf(i_0_15399,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8804]),
    [final] ).

cnf(i_0_15400,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),X2),X3)))
    | ~ class_Rings_Olinordered__semidom(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Oone__class_Oone(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9076]),
    [final] ).

cnf(i_0_15401,plain,
    ( hAPP(c_Set_Oimage(X1,X4,hAPP(c_COMBK(X4,X1),X5)),X3) = hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9077]),
    [final] ).

cnf(i_0_15402,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8899]),
    [final] ).

cnf(i_0_15403,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8900]),
    [final] ).

cnf(i_0_15404,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9078]),
    [final] ).

cnf(i_0_15405,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_8901]),
    [final] ).

cnf(i_0_15406,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8901]),
    [final] ).

cnf(i_0_15407,plain,
    hAPP(hAPP(c_Product__Type_OSigma(X1,X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X1),c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),
    inference(split_conjunct,[status(thm)],[i_0_9079]),
    [final] ).

cnf(i_0_15408,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9080]),
    [final] ).

cnf(i_0_15409,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk92_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8979]),
    [final] ).

cnf(i_0_15410,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk91_3(X3,X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8980]),
    [final] ).

cnf(i_0_15411,plain,
    ( X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8438]),
    [final] ).

cnf(i_0_15412,plain,
    hAPP(c_Relation_Oconverse(X1,X1),c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))) = c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9081,c_0_6096]),c_0_6096]),
    [final] ).

cnf(i_0_15413,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9082]),
    [final] ).

cnf(i_0_15414,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9083]),
    [final] ).

cnf(i_0_15415,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),X2)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk249_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(X1,tc_HOL_Obool)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8544]),
    [final] ).

cnf(i_0_15416,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4)))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9084]),
    [final] ).

cnf(i_0_15417,plain,
    hAPP(hAPP(c_Nat_Ocompow(X1,X1),X2),hAPP(hAPP(c_Nat_Ocompow(X1,X1),X3),X4)) = hAPP(hAPP(c_Nat_Ocompow(X1,X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X3),X2)),X4),
    inference(split_conjunct,[status(thm)],[i_0_9085]),
    [final] ).

cnf(i_0_15418,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk147_2(X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8861]),
    [final] ).

cnf(i_0_15419,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9086]),
    [final] ).

cnf(i_0_15420,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8765]),
    [final] ).

cnf(i_0_15421,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9087]),
    [final] ).

cnf(i_0_15422,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9088]),
    [final] ).

cnf(i_0_15423,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9089]),
    [final] ).

cnf(i_0_15424,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9090]),
    [final] ).

cnf(i_0_15425,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9091]),
    [final] ).

cnf(i_0_15426,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9092]),
    [final] ).

cnf(i_0_15427,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9093]),
    [final] ).

cnf(i_0_15428,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9094]),
    [final] ).

cnf(i_0_15429,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X2))),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2))),X3)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9095]),
    [final] ).

cnf(i_0_15430,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)),X3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X2),c_Groups_Oone__class_Oone(X1))),X3)
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9096]),
    [final] ).

cnf(i_0_15431,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),X3) = X4
    | hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9097]),
    [final] ).

cnf(i_0_15432,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9098]),
    [final] ).

cnf(i_0_15433,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),X1))
    | ~ c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8536]),
    [final] ).

cnf(i_0_15434,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_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_9099]),
    [final] ).

cnf(i_0_15435,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
    | c_Big__Operators_Olattice_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_9100]),
    [final] ).

cnf(i_0_15436,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9101]),
    [final] ).

cnf(i_0_15437,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),X2))),
    inference(split_conjunct,[status(thm)],[i_0_9102]),
    [final] ).

cnf(i_0_15438,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred2_3(X2,X1,X3)
    | ~ hBOOL(hAPP(X2,esk570_3(X3,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_15439,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | X1 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | epred1_3(X2,X1,X3)
    | ~ hBOOL(hAPP(X2,esk565_3(X3,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_7680]),
    [final] ).

cnf(i_0_15440,plain,
    ( hBOOL(hAPP(X1,esk149_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8824]),
    [final] ).

cnf(i_0_15441,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X3),X2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X1),X3)),X2),
    inference(split_conjunct,[status(thm)],[i_0_9103]),
    [final] ).

cnf(i_0_15442,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_9104,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_15443,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9105]),
    [final] ).

cnf(i_0_15444,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9106]),
    [final] ).

cnf(i_0_15445,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9107]),
    [final] ).

cnf(i_0_15446,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)),X3) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),
    inference(split_conjunct,[status(thm)],[i_0_9108]),
    [final] ).

cnf(i_0_15447,plain,
    hAPP(hAPP(c_List_Onth(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X4) = c_Nat_Onat_Onat__case(X1,X2,hAPP(c_List_Onth(X1),X3),X4),
    inference(split_conjunct,[status(thm)],[i_0_9109]),
    [final] ).

cnf(i_0_15448,plain,
    ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8488]),
    [final] ).

cnf(i_0_15449,plain,
    ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | esk408_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_8185]),
    [final] ).

cnf(i_0_15450,plain,
    c_List_Oreplicate(X1,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3)),X2) = hAPP(c_List_Ofilter(X1,hAPP(c_fequal,X2)),X3),
    inference(split_conjunct,[status(thm)],[i_0_9110]),
    [final] ).

cnf(i_0_15451,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | c_Sum__Type_OPlus(X2,X3,X1,X4) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X3),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9111]),
    [final] ).

cnf(i_0_15452,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | c_Sum__Type_OPlus(X3,X2,X4,X1) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X3,X2),tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9111]),
    [final] ).

cnf(i_0_15453,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9112]),
    [final] ).

cnf(i_0_15454,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9113]),
    [final] ).

cnf(i_0_15455,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_9114]),
    [final] ).

cnf(i_0_15456,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_7353]),
    [final] ).

cnf(i_0_15457,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_7354]),
    [final] ).

cnf(i_0_15458,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_7355]),
    [final] ).

cnf(i_0_15459,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_7356]),
    [final] ).

cnf(i_0_15460,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_9115]),
    [final] ).

cnf(i_0_15461,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_7911]),
    [final] ).

cnf(i_0_15462,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_7087]),
    [final] ).

cnf(i_0_15463,plain,
    ( X1 = X2
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_9116]),
    [final] ).

cnf(i_0_15464,plain,
    ( X1 = X2
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3,X1) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(split_conjunct,[status(thm)],[i_0_9116]),
    [final] ).

cnf(i_0_15465,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_9039]),
    [final] ).

cnf(i_0_15466,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_9117]),
    [final] ).

cnf(i_0_15467,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_9118]),
    [final] ).

cnf(i_0_15468,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_9119]),
    [final] ).

cnf(i_0_15469,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_9120]),
    [final] ).

cnf(i_0_15470,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_8684]),
    [final] ).

cnf(i_0_15471,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_8685]),
    [final] ).

cnf(i_0_15472,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_9121]),
    [final] ).

cnf(i_0_15473,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_9122]),
    [final] ).

cnf(i_0_15474,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_9123]),
    [final] ).

cnf(i_0_15475,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_9124]),
    [final] ).

cnf(i_0_15476,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_9125]),
    [final] ).

cnf(i_0_15477,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_9126]),
    [final] ).

cnf(i_0_15478,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_9127]),
    [final] ).

cnf(i_0_15479,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_9128]),
    [final] ).

cnf(i_0_15480,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_9129]),
    [final] ).

cnf(i_0_15481,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_9130]),
    [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)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk566_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_7680]),
    [final] ).

cnf(i_0_15483,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[i_0_9084]),
    [final] ).

cnf(i_0_15484,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X1,X2),X3))
    | ~ hBOOL(hAPP(c_List_Olistsp(X1,X2),hAPP(hAPP(c_List_Oappend(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9084]),
    [final] ).

cnf(i_0_15485,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_9131]),
    [final] ).

cnf(i_0_15486,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_9132]),
    [final] ).

cnf(i_0_15487,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_9133]),
    [final] ).

cnf(i_0_15488,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_9134]),
    [final] ).

cnf(i_0_15489,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X2,X1)),hAPP(c_Relation_Oconverse(X1,X2),X3)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8929]),
    [final] ).

cnf(i_0_15490,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_9135]),
    [final] ).

cnf(i_0_15491,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_9136]),
    [final] ).

cnf(i_0_15492,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_9137]),
    [final] ).

cnf(i_0_15493,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_9138]),
    [final] ).

cnf(i_0_15494,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_9139]),
    [final] ).

cnf(i_0_15495,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_9140]),
    [final] ).

cnf(i_0_15496,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_8733]),
    [final] ).

cnf(i_0_15497,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_9141]),
    [final] ).

cnf(i_0_15498,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_9142]),
    [final] ).

cnf(i_0_15499,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_9143]),
    [final] ).

cnf(i_0_15500,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_9144]),
    [final] ).

cnf(i_0_15501,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_9145]),
    [final] ).

cnf(i_0_15502,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_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_7680]),
    [final] ).

cnf(i_0_15503,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4),X5) = hAPP(hAPP(X4,hAPP(c_Product__Type_Ofst(X1,X2),X5)),hAPP(c_Product__Type_Osnd(X1,X2),X5)),
    inference(split_conjunct,[status(thm)],[i_0_9146]),
    [final] ).

cnf(i_0_15504,plain,
    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_9147]),
    [final] ).

cnf(i_0_15505,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_9148]),
    [final] ).

cnf(i_0_15506,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_9149]),
    [final] ).

cnf(i_0_15507,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_9150]),
    [final] ).

cnf(i_0_15508,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_9150]),
    [final] ).

cnf(i_0_15509,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9151]),
    [final] ).

cnf(i_0_15510,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_9152]),
    [final] ).

cnf(i_0_15511,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_9153]),
    [final] ).

cnf(i_0_15512,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)),esk570_3(X2,X1,X3)))
    | epred2_3(X3,X1,X2)
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_7690]),
    [final] ).

cnf(i_0_15513,plain,
    ( hAPP(hAPP(c_Set_Oinsert(X5),X1),hAPP(hAPP(c_Set_Oinsert(X5),X3),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(X5),X4),hAPP(hAPP(c_Set_Oinsert(X5),X2),c_Orderings_Obot__class_Obot(tc_fun(X5,tc_HOL_Obool))))
    | X1 != X2
    | X3 != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8516]),
    [final] ).

cnf(i_0_15514,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_9154]),
    [final] ).

cnf(i_0_15515,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9155]),
    [final] ).

cnf(i_0_15516,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X2))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9156]),
    [final] ).

cnf(i_0_15517,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3)),X3))
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9157]),
    [final] ).

cnf(i_0_15518,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_9158]),
    [final] ).

cnf(i_0_15519,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_9159]),
    [final] ).

cnf(i_0_15520,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_9160]),
    [final] ).

cnf(i_0_15521,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_9161]),
    [final] ).

cnf(i_0_15522,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_8511]),
    [final] ).

cnf(i_0_15523,plain,
    ( hAPP(hAPP(c_List_Olist__update(X1,X2),X3),X4) = X2
    | hAPP(hAPP(c_List_Onth(X1),X2),X3) != X4
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9097]),
    [final] ).

cnf(i_0_15524,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_9162]),
    [final] ).

cnf(i_0_15525,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_9163]),
    [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_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_9164]),
    [final] ).

cnf(i_0_15527,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9165]),
    [final] ).

cnf(i_0_15528,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9166]),
    [final] ).

cnf(i_0_15529,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_8476]),
    [final] ).

cnf(i_0_15530,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_8478]),
    [final] ).

cnf(i_0_15531,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_9167]),
    [final] ).

cnf(i_0_15532,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_9168]),
    [final] ).

cnf(i_0_15533,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_9169]),
    [final] ).

cnf(i_0_15534,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_9170]),
    [final] ).

cnf(i_0_15535,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_9171]),
    [final] ).

cnf(i_0_15536,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_9172]),
    [final] ).

cnf(i_0_15537,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_9173]),
    [final] ).

cnf(i_0_15538,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_9174]),
    [final] ).

cnf(i_0_15539,plain,
    hAPP(c_Fun_Ocomp(X1,X1,X2,c_Fun_Oid(X1)),X3) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9175]),
    [final] ).

cnf(i_0_15540,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_9176]),
    [final] ).

cnf(i_0_15541,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_9177,c_0_8354]),
    [final] ).

cnf(i_0_15542,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_9178]),
    [final] ).

cnf(i_0_15543,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_9179]),
    [final] ).

cnf(i_0_15544,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_9180]),
    [final] ).

cnf(i_0_15545,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_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_7690]),
    [final] ).

cnf(i_0_15546,plain,
    ( hBOOL(hAPP(hAPP(X3,X4),esk295_2(X4,X3)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(X1,X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9181]),
    [final] ).

cnf(i_0_15547,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_9182]),
    [final] ).

cnf(i_0_15548,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_9183]),
    [final] ).

cnf(i_0_15549,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X3) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_8960]),
    [final] ).

cnf(i_0_15550,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_9184]),
    [final] ).

cnf(i_0_15551,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_7702]),
    [final] ).

cnf(i_0_15552,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_7696]),
    [final] ).

cnf(i_0_15553,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1))
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2,X1) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9185]),
    [final] ).

cnf(i_0_15554,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_8761]),
    [final] ).

cnf(i_0_15555,plain,
    ( hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15556,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_9186]),
    [final] ).

cnf(i_0_15557,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_9187]),
    [final] ).

cnf(i_0_15558,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_9188,c_0_6219]),
    [final] ).

cnf(i_0_15559,plain,
    ( hBOOL(hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),esk37_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_9189]),
    [final] ).

cnf(i_0_15560,plain,
    hAPP(c_List_Ofoldl(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_9190]),
    [final] ).

cnf(i_0_15561,plain,
    hAPP(c_List_Olist_Olist__case(X1,X2,X3,X4),c_List_Olist_ONil(X2)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9191]),
    [final] ).

cnf(i_0_15562,plain,
    hAPP(c_Fun_Ocomp(X1,X2,X1,X3),c_Fun_Oid(X1)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_9192]),
    [final] ).

cnf(i_0_15563,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_9193]),
    [final] ).

cnf(i_0_15564,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_9193]),
    [final] ).

cnf(i_0_15565,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_9194,c_0_6187]),
    [final] ).

cnf(i_0_15566,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_9195]),
    [final] ).

cnf(i_0_15567,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_9196]),
    [final] ).

cnf(i_0_15568,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_9197]),
    [final] ).

cnf(i_0_15569,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_8858]),
    [final] ).

cnf(i_0_15570,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_9198]),
    [final] ).

cnf(i_0_15571,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_8859]),
    [final] ).

cnf(i_0_15572,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_9199]),
    [final] ).

cnf(i_0_15573,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_8860]),
    [final] ).

cnf(i_0_15574,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_9200,c_0_6070]),
    [final] ).

cnf(i_0_15575,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_9201,c_0_6070]),
    [final] ).

cnf(i_0_15576,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_9202,c_0_6070]),
    [final] ).

cnf(i_0_15577,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_9203,c_0_6070]),
    [final] ).

cnf(i_0_15578,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_9204]),
    [final] ).

cnf(i_0_15579,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_9205]),
    [final] ).

cnf(i_0_15580,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_9206]),
    [final] ).

cnf(i_0_15581,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_8535]),
    [final] ).

cnf(i_0_15582,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_9207]),
    [final] ).

cnf(i_0_15583,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_9208]),
    [final] ).

cnf(i_0_15584,plain,
    ( c_FunDef_OTHE__default(X2,X1,X3) = c_HOL_OThe(X2,X3)
    | esk492_4(X1,X2,X3,X4) != X4
    | ~ hBOOL(hAPP(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_8076]),
    [final] ).

cnf(i_0_15585,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_9209]),
    [final] ).

cnf(i_0_15586,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),esk13_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_6759]),
    [final] ).

cnf(i_0_15587,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_9210]),
    [final] ).

cnf(i_0_15588,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_15589,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_9211]),
    [final] ).

cnf(i_0_15590,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_9212]),
    [final] ).

cnf(i_0_15591,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_9213]),
    [final] ).

cnf(i_0_15592,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_9214]),
    [final] ).

cnf(i_0_15593,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_9215]),
    [final] ).

cnf(i_0_15594,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_8712]),
    [final] ).

cnf(i_0_15595,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_8869]),
    [final] ).

cnf(i_0_15596,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_8870]),
    [final] ).

cnf(i_0_15597,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_9216]),
    [final] ).

cnf(i_0_15598,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_9217]),
    [final] ).

cnf(i_0_15599,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_9218]),
    [final] ).

cnf(i_0_15600,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_9219]),
    [final] ).

cnf(i_0_15601,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_9220]),
    [final] ).

cnf(i_0_15602,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_8786]),
    [final] ).

cnf(i_0_15603,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_9221]),
    [final] ).

cnf(i_0_15604,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_8250]),
    [final] ).

cnf(i_0_15605,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_8250]),
    [final] ).

cnf(i_0_15606,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_9222]),
    [final] ).

cnf(i_0_15607,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),hAPP(hAPP(c_Set_Oinsert(X1),X2),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_8634]),
    [final] ).

cnf(i_0_15608,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_9223]),
    [final] ).

cnf(i_0_15609,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_15610,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_9224]),
    [final] ).

cnf(i_0_15611,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_9225]),
    [final] ).

cnf(i_0_15612,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_9226]),
    [final] ).

cnf(i_0_15613,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_9227]),
    [final] ).

cnf(i_0_15614,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_9228]),
    [final] ).

cnf(i_0_15615,plain,
    ( hBOOL(hAPP(X1,esk13_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_6759]),
    [final] ).

cnf(i_0_15616,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_9229]),
    [final] ).

cnf(i_0_15617,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_9193]),
    [final] ).

cnf(i_0_15618,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_9230,c_0_6726]),
    [final] ).

cnf(i_0_15619,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_9231]),
    [final] ).

cnf(i_0_15620,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_9232,c_0_6726]),
    [final] ).

cnf(i_0_15621,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_9233]),
    [final] ).

cnf(i_0_15622,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_9234]),
    [final] ).

cnf(i_0_15623,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ class_Rings_Olinordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8883]),
    [final] ).

cnf(i_0_15624,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8884]),
    [final] ).

cnf(i_0_15625,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Oring__1__class_Oof__int(X3),X1)),hAPP(c_Int_Oring__1__class_Oof__int(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ class_Rings_Olinordered__idom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8886]),
    [final] ).

cnf(i_0_15626,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X3),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ class_Rings_Olinordered__semidom(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8887]),
    [final] ).

cnf(i_0_15627,plain,
    ( hBOOL(hAPP(X1,X4))
    | ~ c_List_Oall__interval__nat(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8700]),
    [final] ).

cnf(i_0_15628,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_9235]),
    [final] ).

cnf(i_0_15629,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_9236]),
    [final] ).

cnf(i_0_15630,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_9237]),
    [final] ).

cnf(i_0_15631,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_9238]),
    [final] ).

cnf(i_0_15632,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_9239]),
    [final] ).

cnf(i_0_15633,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_9240]),
    [final] ).

cnf(i_0_15634,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_9241]),
    [final] ).

cnf(i_0_15635,plain,
    c_Product__Type_Ocurry(X1,X2,X3,hAPP(c_Product__Type_Oprod_Oprod__case(X1,X2,X3),X4)) = X4,
    inference(split_conjunct,[status(thm)],[i_0_9242]),
    [final] ).

cnf(i_0_15636,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_9243]),
    [final] ).

cnf(i_0_15637,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_9244]),
    [final] ).

cnf(i_0_15638,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9112]),
    [final] ).

cnf(i_0_15639,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X1))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9113]),
    [final] ).

cnf(i_0_15640,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X3),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X3),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
    | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9245]),
    [final] ).

cnf(i_0_15641,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9246]),
    [final] ).

cnf(i_0_15642,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9247]),
    [final] ).

cnf(i_0_15643,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_9248]),
    [final] ).

cnf(i_0_15644,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_9249]),
    [final] ).

cnf(i_0_15645,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_8714]),
    [final] ).

cnf(i_0_15646,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_9250]),
    [final] ).

cnf(i_0_15647,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_8714]),
    [final] ).

cnf(i_0_15648,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_9251]),
    [final] ).

cnf(i_0_15649,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_9252]),
    [final] ).

cnf(i_0_15650,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_9253]),
    [final] ).

cnf(i_0_15651,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_9254]),
    [final] ).

cnf(i_0_15652,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_8715]),
    [final] ).

cnf(i_0_15653,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_9255]),
    [final] ).

cnf(i_0_15654,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_8715]),
    [final] ).

cnf(i_0_15655,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_9256,c_0_6070]),
    [final] ).

cnf(i_0_15656,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_9042]),
    [final] ).

cnf(i_0_15657,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_9257]),
    [final] ).

cnf(i_0_15658,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_9047]),
    [final] ).

cnf(i_0_15659,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_9048]),
    [final] ).

cnf(i_0_15660,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_9258]),
    [final] ).

cnf(i_0_15661,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_9259]),
    [final] ).

cnf(i_0_15662,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_9260]),
    [final] ).

cnf(i_0_15663,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_9261]),
    [final] ).

cnf(i_0_15664,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_9262]),
    [final] ).

cnf(i_0_15665,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_8777]),
    [final] ).

cnf(i_0_15666,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_9263]),
    [final] ).

cnf(i_0_15667,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_9131]),
    [final] ).

cnf(i_0_15668,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_9264]),
    [final] ).

cnf(i_0_15669,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)),esk570_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_7690]),
    [final] ).

cnf(i_0_15670,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)),esk566_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_7680]),
    [final] ).

cnf(i_0_15671,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_9265]),
    [final] ).

cnf(i_0_15672,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_9266]),
    [final] ).

cnf(i_0_15673,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_9267]),
    [final] ).

cnf(i_0_15674,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X4),X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8966]),
    [final] ).

cnf(i_0_15675,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_9268]),
    [final] ).

cnf(i_0_15676,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_9269]),
    [final] ).

cnf(i_0_15677,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_9270]),
    [final] ).

cnf(i_0_15678,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_9270]),
    [final] ).

cnf(i_0_15679,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_9271]),
    [final] ).

cnf(i_0_15680,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_9271]),
    [final] ).

cnf(i_0_15681,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_9272]),
    [final] ).

cnf(i_0_15682,plain,
    ( X2 = esk486_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_7283]),
    [final] ).

cnf(i_0_15683,plain,
    ( X2 = esk478_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_7284]),
    [final] ).

cnf(i_0_15684,plain,
    ( hBOOL(hAPP(X1,esk324_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_7437]),
    [final] ).

cnf(i_0_15685,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_9273]),
    [final] ).

cnf(i_0_15686,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_9274]),
    [final] ).

cnf(i_0_15687,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_9275]),
    [final] ).

cnf(i_0_15688,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_9276,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15689,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_9277,c_0_9278]),
    [final] ).

cnf(i_0_15690,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_9279]),
    [final] ).

cnf(i_0_15691,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_9280]),
    [final] ).

cnf(i_0_15692,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_8401]),
    [final] ).

cnf(i_0_15693,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_9281,c_0_6187]),
    [final] ).

cnf(i_0_15694,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_9282]),
    [final] ).

cnf(i_0_15695,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_9283]),
    [final] ).

cnf(i_0_15696,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk572_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_7690]),
    [final] ).

cnf(i_0_15697,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),esk568_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_7680]),
    [final] ).

cnf(i_0_15698,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_8657]),
    [final] ).

cnf(i_0_15699,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_9284]),
    [final] ).

cnf(i_0_15700,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9082]),
    [final] ).

cnf(i_0_15701,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),X2))
    | ~ class_Groups_Olinordered__ab__group__add(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9083]),
    [final] ).

cnf(i_0_15702,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_9285]),
    [final] ).

cnf(i_0_15703,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X2)),hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9078]),
    [final] ).

cnf(i_0_15704,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_9286]),
    [final] ).

cnf(i_0_15705,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_9286]),
    [final] ).

cnf(i_0_15706,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_9287]),
    [final] ).

cnf(i_0_15707,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_9288]),
    [final] ).

cnf(i_0_15708,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_9289]),
    [final] ).

cnf(i_0_15709,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_9290,c_0_6219]),
    [final] ).

cnf(i_0_15710,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_9291]),
    [final] ).

cnf(i_0_15711,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_9292]),
    [final] ).

cnf(i_0_15712,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_9293]),
    [final] ).

cnf(i_0_15713,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_9294]),
    [final] ).

cnf(i_0_15714,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_9295]),
    [final] ).

cnf(i_0_15715,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_9296]),
    [final] ).

cnf(i_0_15716,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_9297]),
    [final] ).

cnf(i_0_15717,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_9298]),
    [final] ).

cnf(i_0_15718,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_9299]),
    [final] ).

cnf(i_0_15719,plain,
    ( esk181_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_7303]),
    [final] ).

cnf(i_0_15720,plain,
    ( hBOOL(hAPP(c_List_Olistsp(X3,X1),X2))
    | ~ hBOOL(hAPP(X1,esk415_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8741]),
    [final] ).

cnf(i_0_15721,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(X3,X1),X2))
    | ~ hBOOL(hAPP(X1,esk302_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8939]),
    [final] ).

cnf(i_0_15722,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_7087]),
    [final] ).

cnf(i_0_15723,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_9300]),
    [final] ).

cnf(i_0_15724,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),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9301]),
    [final] ).

cnf(i_0_15725,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_9302]),
    [final] ).

cnf(i_0_15726,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_9303,c_0_6187]),c_0_6187]),
    [final] ).

cnf(i_0_15727,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_9304]),
    [final] ).

cnf(i_0_15728,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_9305]),
    [final] ).

cnf(i_0_15729,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_9131]),
    [final] ).

cnf(i_0_15730,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_9306]),
    [final] ).

cnf(i_0_15731,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8993]),
    [final] ).

cnf(i_0_15732,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8994]),
    [final] ).

cnf(i_0_15733,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_9307]),
    [final] ).

cnf(i_0_15734,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_9308]),
    [final] ).

cnf(i_0_15735,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_9309]),
    [final] ).

cnf(i_0_15736,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_9310]),
    [final] ).

cnf(i_0_15737,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_9311]),
    [final] ).

cnf(i_0_15738,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_9312]),
    [final] ).

cnf(i_0_15739,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_9313]),
    [final] ).

cnf(i_0_15740,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_9314]),
    [final] ).

cnf(i_0_15741,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_8793]),
    [final] ).

cnf(i_0_15742,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_9315]),
    [final] ).

cnf(i_0_15743,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_9316]),
    [final] ).

cnf(i_0_15744,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_9317]),
    [final] ).

cnf(i_0_15745,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk27_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_8761]),
    [final] ).

cnf(i_0_15746,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk26_3(X2,X1,X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15747,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_8644]),
    [final] ).

cnf(i_0_15748,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_9318]),
    [final] ).

cnf(i_0_15749,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),hAPP(c_Int_Onat,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9078]),
    [final] ).

cnf(i_0_15750,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_9319]),
    [final] ).

cnf(i_0_15751,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_9320]),
    [final] ).

cnf(i_0_15752,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_9321]),
    [final] ).

cnf(i_0_15753,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_9322]),
    [final] ).

cnf(i_0_15754,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_9323]),
    [final] ).

cnf(i_0_15755,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_9324]),
    [final] ).

cnf(i_0_15756,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk482_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_7924]),
    [final] ).

cnf(i_0_15757,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),esk219_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_7023]),
    [final] ).

cnf(i_0_15758,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_9325]),
    [final] ).

cnf(i_0_15759,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_9326]),
    [final] ).

cnf(i_0_15760,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_9327]),
    [final] ).

cnf(i_0_15761,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_9051]),
    [final] ).

cnf(i_0_15762,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_8808]),
    [final] ).

cnf(i_0_15763,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_8808]),
    [final] ).

cnf(i_0_15764,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_9328]),
    [final] ).

cnf(i_0_15765,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_9329]),
    [final] ).

cnf(i_0_15766,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_9330]),
    [final] ).

cnf(i_0_15767,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_9331]),
    [final] ).

cnf(i_0_15768,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_9332]),
    [final] ).

cnf(i_0_15769,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_9333]),
    [final] ).

cnf(i_0_15770,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_9334]),
    [final] ).

cnf(i_0_15771,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_9335]),
    [final] ).

cnf(i_0_15772,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_9336]),
    [final] ).

cnf(i_0_15773,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_9337]),
    [final] ).

cnf(i_0_15774,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_9338]),
    [final] ).

cnf(i_0_15775,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_9339]),
    [final] ).

cnf(i_0_15776,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_9340]),
    [final] ).

cnf(i_0_15777,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_9233]),
    [final] ).

cnf(i_0_15778,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_8998]),
    [final] ).

cnf(i_0_15779,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_8999]),
    [final] ).

cnf(i_0_15780,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_9000]),
    [final] ).

cnf(i_0_15781,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_9001]),
    [final] ).

cnf(i_0_15782,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X4))
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_9341]),
    [final] ).

cnf(i_0_15783,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_9342]),
    [final] ).

cnf(i_0_15784,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_9343]),
    [final] ).

cnf(i_0_15785,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_9344]),
    [final] ).

cnf(i_0_15786,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_9345]),
    [final] ).

cnf(i_0_15787,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_9346]),
    [final] ).

cnf(i_0_15788,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_9347]),
    [final] ).

cnf(i_0_15789,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_9348]),
    [final] ).

cnf(i_0_15790,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_9349]),
    [final] ).

cnf(i_0_15791,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_9350]),
    [final] ).

cnf(i_0_15792,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_9351]),
    [final] ).

cnf(i_0_15793,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),esk387_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_8309]),
    [final] ).

cnf(i_0_15794,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_8741]),
    [final] ).

cnf(i_0_15795,plain,
    ( esk183_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_7311]),
    [final] ).

cnf(i_0_15796,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_9352]),
    [final] ).

cnf(i_0_15797,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_9353]),
    [final] ).

cnf(i_0_15798,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_9353]),
    [final] ).

cnf(i_0_15799,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_9354]),
    [final] ).

cnf(i_0_15800,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_9354]),
    [final] ).

cnf(i_0_15801,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_9355]),
    [final] ).

cnf(i_0_15802,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_9356]),
    [final] ).

cnf(i_0_15803,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_9357,c_0_6096]),
    [final] ).

cnf(i_0_15804,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_9237]),
    [final] ).

cnf(i_0_15805,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_9358,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15806,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_9359]),
    [final] ).

cnf(i_0_15807,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_9360]),
    [final] ).

cnf(i_0_15808,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_9361,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15809,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_9362,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15810,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_9363]),
    [final] ).

cnf(i_0_15811,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_9364]),
    [final] ).

cnf(i_0_15812,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_9365]),
    [final] ).

cnf(i_0_15813,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_9366]),
    [final] ).

cnf(i_0_15814,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_9367]),
    [final] ).

cnf(i_0_15815,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_9368]),
    [final] ).

cnf(i_0_15816,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_9369]),
    [final] ).

cnf(i_0_15817,plain,
    ( c_List_OtakeWhile(X3,X1,X2) = X2
    | ~ hBOOL(hAPP(X1,esk434_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8802]),
    [final] ).

cnf(i_0_15818,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_9370]),
    [final] ).

cnf(i_0_15819,plain,
    ( c_List_Oall__interval__nat(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk560_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8700]),
    [final] ).

cnf(i_0_15820,plain,
    ( c_List_Oall__interval__int(X1,X3,X2)
    | ~ hBOOL(hAPP(X1,esk497_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_8561]),
    [final] ).

cnf(i_0_15821,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk477_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8806]),
    [final] ).

cnf(i_0_15822,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk476_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8805]),
    [final] ).

cnf(i_0_15823,plain,
    ( c_List_Olist__all(X3,X1,X2)
    | ~ hBOOL(hAPP(X1,esk475_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8807]),
    [final] ).

cnf(i_0_15824,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_8853]),
    [final] ).

cnf(i_0_15825,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_9122]),
    [final] ).

cnf(i_0_15826,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_9123]),
    [final] ).

cnf(i_0_15827,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_9371]),
    [final] ).

cnf(i_0_15828,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_9372]),
    [final] ).

cnf(i_0_15829,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_8761]),
    [final] ).

cnf(i_0_15830,plain,
    ( hBOOL(hAPP(X4,X3))
    | X1 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3)
    | ~ hBOOL(hAPP(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15831,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9087]),
    [final] ).

cnf(i_0_15832,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9088]),
    [final] ).

cnf(i_0_15833,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9086]),
    [final] ).

cnf(i_0_15834,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9090]),
    [final] ).

cnf(i_0_15835,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9091]),
    [final] ).

cnf(i_0_15836,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9089]),
    [final] ).

cnf(i_0_15837,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_8868]),
    [final] ).

cnf(i_0_15838,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9092]),
    [final] ).

cnf(i_0_15839,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9080]),
    [final] ).

cnf(i_0_15840,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9094]),
    [final] ).

cnf(i_0_15841,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9093]),
    [final] ).

cnf(i_0_15842,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9166]),
    [final] ).

cnf(i_0_15843,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9165]),
    [final] ).

cnf(i_0_15844,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_9373]),
    [final] ).

cnf(i_0_15845,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_9374]),
    [final] ).

cnf(i_0_15846,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_6612]),
    [final] ).

cnf(i_0_15847,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_6613]),
    [final] ).

cnf(i_0_15848,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3)),X2))
    | hAPP(hAPP(c_List_Odrop(X1),X2),X3) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8965]),
    [final] ).

cnf(i_0_15849,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X2) = X3
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9375]),
    [final] ).

cnf(i_0_15850,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_9376]),
    [final] ).

cnf(i_0_15851,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_9377,c_0_6070]),
    [final] ).

cnf(i_0_15852,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_9378]),
    [final] ).

cnf(i_0_15853,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_9379]),
    [final] ).

cnf(i_0_15854,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6612]),
    [final] ).

cnf(i_0_15855,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X2,X4) ),
    inference(split_conjunct,[status(thm)],[i_0_6613]),
    [final] ).

cnf(i_0_15856,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6612]),
    [final] ).

cnf(i_0_15857,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_6613]),
    [final] ).

cnf(i_0_15858,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_9380]),
    [final] ).

cnf(i_0_15859,plain,
    ( v_P(X2,X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9381]),
    [final] ).

cnf(i_0_15860,plain,
    ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X3))))
    | hAPP(c_Int_Onumber__class_Onumber__of(X1),X2) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X3)
    | ~ class_Int_Onumber__ring(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8941]),
    [final] ).

cnf(i_0_15861,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_8490]),
    [final] ).

cnf(i_0_15862,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_8490]),
    [final] ).

cnf(i_0_15863,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_8786]),
    [final] ).

cnf(i_0_15864,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_9382]),
    [final] ).

cnf(i_0_15865,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_9383,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_15866,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_8868]),
    [final] ).

cnf(i_0_15867,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_9384]),
    [final] ).

cnf(i_0_15868,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_9385]),
    [final] ).

cnf(i_0_15869,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_9386,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15870,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_9387,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15871,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_9388,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15872,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_9389,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15873,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_9390]),
    [final] ).

cnf(i_0_15874,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_9391]),
    [final] ).

cnf(i_0_15875,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_9392]),
    [final] ).

cnf(i_0_15876,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_9133]),
    [final] ).

cnf(i_0_15877,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_9134]),
    [final] ).

cnf(i_0_15878,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_9393]),
    [final] ).

cnf(i_0_15879,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_9394]),
    [final] ).

cnf(i_0_15880,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_9395]),
    [final] ).

cnf(i_0_15881,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_9396]),
    [final] ).

cnf(i_0_15882,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_9397]),
    [final] ).

cnf(i_0_15883,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_9398]),
    [final] ).

cnf(i_0_15884,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_9399]),
    [final] ).

cnf(i_0_15885,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_9400]),
    [final] ).

cnf(i_0_15886,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_9401]),
    [final] ).

cnf(i_0_15887,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_9402]),
    [final] ).

cnf(i_0_15888,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_9403]),
    [final] ).

cnf(i_0_15889,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_9404]),
    [final] ).

cnf(i_0_15890,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_9405]),
    [final] ).

cnf(i_0_15891,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_9406]),
    [final] ).

cnf(i_0_15892,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_8428]),
    [final] ).

cnf(i_0_15893,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_9407]),
    [final] ).

cnf(i_0_15894,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_8829]),
    [final] ).

cnf(i_0_15895,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_5750]),
    [final] ).

cnf(i_0_15896,plain,
    ( c_Wellfounded_Owf(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),esk290_2(X2,X1)),c_Wellfounded_Oacc(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9408]),
    [final] ).

cnf(i_0_15897,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_9409]),
    [final] ).

cnf(i_0_15898,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_9410]),
    [final] ).

cnf(i_0_15899,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_9411]),
    [final] ).

cnf(i_0_15900,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_9039]),
    [final] ).

cnf(i_0_15901,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_9412]),
    [final] ).

cnf(i_0_15902,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_9413]),
    [final] ).

cnf(i_0_15903,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)),X2) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
    | ~ class_Divides_Oring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9414]),
    [final] ).

cnf(i_0_15904,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_9415,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15905,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_9416,c_0_6069]),c_0_6070]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_15906,plain,
    ( X1 = hAPP(hAPP(c_Set_Oinsert(X2),esk35_3(X3,X1,X2)),esk36_3(X3,X1,X2))
    | hAPP(c_Finite__Set_Ocard(X2),X1) != hAPP(c_Nat_OSuc,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7995]),
    [final] ).

cnf(i_0_15907,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_9417]),
    [final] ).

cnf(i_0_15908,plain,
    ( hAPP(c_List_Ofilter(X3,X1),X2) = X2
    | ~ hBOOL(hAPP(X1,esk424_3(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8843]),
    [final] ).

cnf(i_0_15909,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_9418]),
    [final] ).

cnf(i_0_15910,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_9419]),
    [final] ).

cnf(i_0_15911,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_9204]),
    [final] ).

cnf(i_0_15912,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_9420]),
    [final] ).

cnf(i_0_15913,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_9421]),
    [final] ).

cnf(i_0_15914,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_9422]),
    [final] ).

cnf(i_0_15915,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_9423]),
    [final] ).

cnf(i_0_15916,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_9424]),
    [final] ).

cnf(i_0_15917,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_9425]),
    [final] ).

cnf(i_0_15918,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_9426,c_0_7117]),
    [final] ).

cnf(i_0_15919,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_9427]),
    [final] ).

cnf(i_0_15920,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X1)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9151]),
    [final] ).

cnf(i_0_15921,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_9428]),
    [final] ).

cnf(i_0_15922,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_9429]),
    [final] ).

cnf(i_0_15923,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_9430]),
    [final] ).

cnf(i_0_15924,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_9431]),
    [final] ).

cnf(i_0_15925,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_9432]),
    [final] ).

cnf(i_0_15926,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_9433]),
    [final] ).

cnf(i_0_15927,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_9434]),
    [final] ).

cnf(i_0_15928,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_9435]),
    [final] ).

cnf(i_0_15929,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),esk2_2(X1,X2)),v_U))
    | v_P(X1,hAPP(hAPP(c_Set_Oinsert(t_a),v_mgt(X2)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))))
    | ~ v_wt(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8221]),
    [final] ).

cnf(i_0_15930,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_9436]),
    [final] ).

cnf(i_0_15931,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_9437]),
    [final] ).

cnf(i_0_15932,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk24_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_9438]),
    [final] ).

cnf(i_0_15933,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk27_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_8761]),
    [final] ).

cnf(i_0_15934,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),esk26_3(X2,X1,X3))
    | hBOOL(hAPP(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X2)))
    | ~ hBOOL(hAPP(X3,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_8762]),
    [final] ).

cnf(i_0_15935,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_9439,c_0_8300]),
    [final] ).

cnf(i_0_15936,plain,
    ( hBOOL(hAPP(X3,esk503_1(X3)))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9440]),
    [final] ).

cnf(i_0_15937,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_9302]),
    [final] ).

cnf(i_0_15938,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_9441]),
    [final] ).

cnf(i_0_15939,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_9442,c_0_6187]),
    [final] ).

cnf(i_0_15940,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_9443]),
    [final] ).

cnf(i_0_15941,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_9444]),
    [final] ).

cnf(i_0_15942,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_9445]),
    [final] ).

cnf(i_0_15943,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_9446]),
    [final] ).

cnf(i_0_15944,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_9447]),
    [final] ).

cnf(i_0_15945,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_9448]),
    [final] ).

cnf(i_0_15946,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_9449]),
    [final] ).

cnf(i_0_15947,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_9450]),
    [final] ).

cnf(i_0_15948,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_9451]),
    [final] ).

cnf(i_0_15949,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_9452]),
    [final] ).

cnf(i_0_15950,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_9453]),
    [final] ).

cnf(i_0_15951,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_9454]),
    [final] ).

cnf(i_0_15952,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_9455]),
    [final] ).

cnf(i_0_15953,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_9456]),
    [final] ).

cnf(i_0_15954,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_9457]),
    [final] ).

cnf(i_0_15955,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_9458]),
    [final] ).

cnf(i_0_15956,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_9459]),
    [final] ).

cnf(i_0_15957,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_9460]),
    [final] ).

cnf(i_0_15958,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_9461]),
    [final] ).

cnf(i_0_15959,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_9462]),
    [final] ).

cnf(i_0_15960,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_9463]),
    [final] ).

cnf(i_0_15961,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_9464]),
    [final] ).

cnf(i_0_15962,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_9465]),
    [final] ).

cnf(i_0_15963,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_9466]),
    [final] ).

cnf(i_0_15964,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_9467]),
    [final] ).

cnf(i_0_15965,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_9468]),
    [final] ).

cnf(i_0_15966,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_9469]),
    [final] ).

cnf(i_0_15967,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_9470]),
    [final] ).

cnf(i_0_15968,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_9273]),
    [final] ).

cnf(i_0_15969,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_5334]),
    [final] ).

cnf(i_0_15970,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_9471]),
    [final] ).

cnf(i_0_15971,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_9472]),
    [final] ).

cnf(i_0_15972,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_9473]),
    [final] ).

cnf(i_0_15973,plain,
    ( c_Sum__Type_OPlus(X2,X4,X1,X3) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(X2,X4),tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | X3 != c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9111]),
    [final] ).

cnf(i_0_15974,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_9474]),
    [final] ).

cnf(i_0_15975,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_9475]),
    [final] ).

cnf(i_0_15976,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_9476]),
    [final] ).

cnf(i_0_15977,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_9477]),
    [final] ).

cnf(i_0_15978,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_9478]),
    [final] ).

cnf(i_0_15979,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_9479]),
    [final] ).

cnf(i_0_15980,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_9480]),
    [final] ).

cnf(i_0_15981,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_9481]),
    [final] ).

cnf(i_0_15982,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_9482]),
    [final] ).

cnf(i_0_15983,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_9483]),
    [final] ).

cnf(i_0_15984,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_9484]),
    [final] ).

cnf(i_0_15985,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_9485]),
    [final] ).

cnf(i_0_15986,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_9486]),
    [final] ).

cnf(i_0_15987,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_9487]),
    [final] ).

cnf(i_0_15988,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9488]),
    [final] ).

cnf(i_0_15989,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_8191]),
    [final] ).

cnf(i_0_15990,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_9489]),
    [final] ).

cnf(i_0_15991,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_9285]),
    [final] ).

cnf(i_0_15992,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_9490]),
    [final] ).

cnf(i_0_15993,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_9491]),
    [final] ).

cnf(i_0_15994,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_9492]),
    [final] ).

cnf(i_0_15995,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),esk426_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_9258]),
    [final] ).

cnf(i_0_15996,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_9493,c_0_6070]),
    [final] ).

cnf(i_0_15997,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_9494,c_0_6070]),
    [final] ).

cnf(i_0_15998,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_9495,c_0_6070]),
    [final] ).

cnf(i_0_15999,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_9496,c_0_6070]),
    [final] ).

cnf(i_0_16000,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_9497]),
    [final] ).

cnf(i_0_16001,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_9498]),
    [final] ).

cnf(i_0_16002,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_9499]),
    [final] ).

cnf(i_0_16003,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_9500]),
    [final] ).

cnf(i_0_16004,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_8802]),
    [final] ).

cnf(i_0_16005,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_8831]),
    [final] ).

cnf(i_0_16006,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_9501]),
    [final] ).

cnf(i_0_16007,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_9502]),
    [final] ).

cnf(i_0_16008,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_8806]),
    [final] ).

cnf(i_0_16009,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_8805]),
    [final] ).

cnf(i_0_16010,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ c_List_Olist__all(X1,X2,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_8807]),
    [final] ).

cnf(i_0_16011,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_9503,c_0_6096]),
    [final] ).

cnf(i_0_16012,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_9504,c_0_6096]),
    [final] ).

cnf(i_0_16013,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_9505]),
    [final] ).

cnf(i_0_16014,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_9506]),
    [final] ).

cnf(i_0_16015,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_9507]),
    [final] ).

cnf(i_0_16016,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_9508]),
    [final] ).

cnf(i_0_16017,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_9509]),
    [final] ).

cnf(i_0_16018,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_9510]),
    [final] ).

cnf(i_0_16019,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_9511]),
    [final] ).

cnf(i_0_16020,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_9512]),
    [final] ).

cnf(i_0_16021,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_9339]),
    [final] ).

cnf(i_0_16022,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_9340]),
    [final] ).

cnf(i_0_16023,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9513]),
    [final] ).

cnf(i_0_16024,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9514]),
    [final] ).

cnf(i_0_16025,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_9515]),
    [final] ).

cnf(i_0_16026,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_9516]),
    [final] ).

cnf(i_0_16027,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_9517]),
    [final] ).

cnf(i_0_16028,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_9518]),
    [final] ).

cnf(i_0_16029,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_9519]),
    [final] ).

cnf(i_0_16030,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_9520]),
    [final] ).

cnf(i_0_16031,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_9521]),
    [final] ).

cnf(i_0_16032,plain,
    ( c_List_Oall__interval__nat(X1,X2,X3)
    | ~ c_List_Olist__all(tc_Nat_Onat,X1,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3))) ),
    inference(rw,[status(thm)],[i_0_9522,c_0_6187]),
    [final] ).

cnf(i_0_16033,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_5333]),
    [final] ).

cnf(i_0_16034,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_9523]),
    [final] ).

cnf(i_0_16035,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_9524]),
    [final] ).

cnf(i_0_16036,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_9525]),
    [final] ).

cnf(i_0_16037,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_9526]),
    [final] ).

cnf(i_0_16038,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_9527,c_0_6103]),
    [final] ).

cnf(i_0_16039,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_9528]),
    [final] ).

cnf(i_0_16040,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_9413]),
    [final] ).

cnf(i_0_16041,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_9529]),
    [final] ).

cnf(i_0_16042,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_9530]),
    [final] ).

cnf(i_0_16043,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_9531]),
    [final] ).

cnf(i_0_16044,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_9378]),
    [final] ).

cnf(i_0_16045,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_9532,c_0_8354]),
    [final] ).

cnf(i_0_16046,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_9533,c_0_8354]),
    [final] ).

cnf(i_0_16047,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_9317]),
    [final] ).

cnf(i_0_16048,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_9534]),
    [final] ).

cnf(i_0_16049,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_9013]),
    [final] ).

cnf(i_0_16050,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_9012]),
    [final] ).

cnf(i_0_16051,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_9535]),
    [final] ).

cnf(i_0_16052,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_16053,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_9536]),
    [final] ).

cnf(i_0_16054,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_9537,c_0_6096]),
    [final] ).

cnf(i_0_16055,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9538]),
    [final] ).

cnf(i_0_16056,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_9539]),
    [final] ).

cnf(i_0_16057,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_9540]),
    [final] ).

cnf(i_0_16058,plain,
    ( c_Divides_Odiv__class_Omod(X1,c_Divides_Odiv__class_Omod(X1,X4,X3),X2) = c_Divides_Odiv__class_Omod(X1,X4,X2)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9541]),
    [final] ).

cnf(i_0_16059,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_8758]),
    [final] ).

cnf(i_0_16060,plain,
    ( hAPP(X2,X4) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(X1,tc_Nat_Onat),X2),X3) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8759]),
    [final] ).

cnf(i_0_16061,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_8736]),
    [final] ).

cnf(i_0_16062,plain,
    ( c_List_Olist__ex(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8737]),
    [final] ).

cnf(i_0_16063,plain,
    ( c_List_Olist__ex(X1,X4,X3)
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | ~ hBOOL(hAPP(X4,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8738]),
    [final] ).

cnf(i_0_16064,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_9272]),
    [final] ).

cnf(i_0_16065,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_9542]),
    [final] ).

cnf(i_0_16066,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_9543]),
    [final] ).

cnf(i_0_16067,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_9544]),
    [final] ).

cnf(i_0_16068,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_6147]),
    [final] ).

cnf(i_0_16069,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2))
    | ~ class_Divides_Oring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9545]),
    [final] ).

cnf(i_0_16070,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_9010]),
    [final] ).

cnf(i_0_16071,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_9546]),
    [final] ).

cnf(i_0_16072,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_9547]),
    [final] ).

cnf(i_0_16073,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_9548]),
    [final] ).

cnf(i_0_16074,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_9549]),
    [final] ).

cnf(i_0_16075,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_9550]),
    [final] ).

cnf(i_0_16076,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_9551]),
    [final] ).

cnf(i_0_16077,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_9552]),
    [final] ).

cnf(i_0_16078,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_9553]),
    [final] ).

cnf(i_0_16079,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_9554]),
    [final] ).

cnf(i_0_16080,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_9555]),
    [final] ).

cnf(i_0_16081,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk55_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_9556]),
    [final] ).

cnf(i_0_16082,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_9557]),
    [final] ).

cnf(i_0_16083,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_9558]),
    [final] ).

cnf(i_0_16084,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(X2,X3),X1),hAPP(c_COMBK(tc_fun(X3,tc_HOL_Obool),X2),X4)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X3),tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8982]),
    [final] ).

cnf(i_0_16085,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(X3,X2),X4),hAPP(c_COMBK(tc_fun(X2,tc_HOL_Obool),X3),X1)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X3,X2),tc_HOL_Obool))
    | X1 != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8982]),
    [final] ).

cnf(i_0_16086,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_9317]),
    [final] ).

cnf(i_0_16087,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_9559]),
    [final] ).

cnf(i_0_16088,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_9560]),
    [final] ).

cnf(i_0_16089,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_8843]),
    [final] ).

cnf(i_0_16090,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_9561]),
    [final] ).

cnf(i_0_16091,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_9366]),
    [final] ).

cnf(i_0_16092,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_9367]),
    [final] ).

cnf(i_0_16093,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_9368]),
    [final] ).

cnf(i_0_16094,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_9562]),
    [final] ).

cnf(i_0_16095,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_9418]),
    [final] ).

cnf(i_0_16096,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_9419]),
    [final] ).

cnf(i_0_16097,plain,
    ( hBOOL(hAPP(hAPP(X1,esk518_1(X1)),esk518_1(X1)))
    | hBOOL(hAPP(hAPP(X1,esk517_1(X1)),esk518_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_16098,plain,
    ( hBOOL(hAPP(hAPP(X1,esk517_1(X1)),esk517_1(X1)))
    | hBOOL(hAPP(hAPP(X1,esk517_1(X1)),esk518_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_16099,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_9563]),
    [final] ).

cnf(i_0_16100,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_9319]),
    [final] ).

cnf(i_0_16101,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_9318]),
    [final] ).

cnf(i_0_16102,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_9321]),
    [final] ).

cnf(i_0_16103,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_9564]),
    [final] ).

cnf(i_0_16104,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_9323]),
    [final] ).

cnf(i_0_16105,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_9322]),
    [final] ).

cnf(i_0_16106,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_9324]),
    [final] ).

cnf(i_0_16107,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_9565]),
    [final] ).

cnf(i_0_16108,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_9566]),
    [final] ).

cnf(i_0_16109,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_9567]),
    [final] ).

cnf(i_0_16110,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9568]),
    [final] ).

cnf(i_0_16111,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_9421]),
    [final] ).

cnf(i_0_16112,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_9569]),
    [final] ).

cnf(i_0_16113,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_9570]),
    [final] ).

cnf(i_0_16114,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_9571]),
    [final] ).

cnf(i_0_16115,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_9572]),
    [final] ).

cnf(i_0_16116,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_9573]),
    [final] ).

cnf(i_0_16117,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_9574]),
    [final] ).

cnf(i_0_16118,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_9463]),
    [final] ).

cnf(i_0_16119,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_9575]),
    [final] ).

cnf(i_0_16120,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_9576]),
    [final] ).

cnf(i_0_16121,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_9577]),
    [final] ).

cnf(i_0_16122,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_9578]),
    [final] ).

cnf(i_0_16123,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_9579]),
    [final] ).

cnf(i_0_16124,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_9580]),
    [final] ).

cnf(i_0_16125,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,esk57_2(X2,X1))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9581]),
    [final] ).

cnf(i_0_16126,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_9476]),
    [final] ).

cnf(i_0_16127,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_9477]),
    [final] ).

cnf(i_0_16128,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_9582,c_0_6187]),
    [final] ).

cnf(i_0_16129,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_9583]),
    [final] ).

cnf(i_0_16130,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_9584]),
    [final] ).

cnf(i_0_16131,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_9585]),
    [final] ).

cnf(i_0_16132,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_9586]),
    [final] ).

cnf(i_0_16133,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_7349]),
    [final] ).

cnf(i_0_16134,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_9587]),
    [final] ).

cnf(i_0_16135,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9181]),
    [final] ).

cnf(i_0_16136,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(X4,X5,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9588]),
    [final] ).

cnf(i_0_16137,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9038]),
    [final] ).

cnf(i_0_16138,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(X4,X5,X1),X3))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9589]),
    [final] ).

cnf(i_0_16139,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_8208]),
    [final] ).

cnf(i_0_16140,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_9590]),
    [final] ).

cnf(i_0_16141,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_9591]),
    [final] ).

cnf(i_0_16142,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_9592]),
    [final] ).

cnf(i_0_16143,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_9593]),
    [final] ).

cnf(i_0_16144,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_9594,c_0_8300]),
    [final] ).

cnf(i_0_16145,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_9595]),
    [final] ).

cnf(i_0_16146,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_9145]),
    [final] ).

cnf(i_0_16147,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9098]),
    [final] ).

cnf(i_0_16148,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_9596]),
    [final] ).

cnf(i_0_16149,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_9597]),
    [final] ).

cnf(i_0_16150,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_9598,c_0_6187]),
    [final] ).

cnf(i_0_16151,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_9599]),
    [final] ).

cnf(i_0_16152,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_9600]),
    [final] ).

cnf(i_0_16153,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_8032]),
    [final] ).

cnf(i_0_16154,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_9017]),
    [final] ).

cnf(i_0_16155,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9018]),
    [final] ).

cnf(i_0_16156,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_9601]),
    [final] ).

cnf(i_0_16157,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_9602]),
    [final] ).

cnf(i_0_16158,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk395_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_8346]),
    [final] ).

cnf(i_0_16159,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk394_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_8346]),
    [final] ).

cnf(i_0_16160,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_9603]),
    [final] ).

cnf(i_0_16161,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_9604]),
    [final] ).

cnf(i_0_16162,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_9605,c_0_6096]),
    [final] ).

cnf(i_0_16163,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_9606]),
    [final] ).

cnf(i_0_16164,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_9607]),
    [final] ).

cnf(i_0_16165,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_8590]),
    [final] ).

cnf(i_0_16166,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_9608]),
    [final] ).

cnf(i_0_16167,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_9609]),
    [final] ).

cnf(i_0_16168,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_9057]),
    [final] ).

cnf(i_0_16169,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X5))
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9610]),
    [final] ).

cnf(i_0_16170,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X5))
    | ~ c_Predicate_Otransp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[i_0_9611]),
    [final] ).

cnf(i_0_16171,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_9612]),
    [final] ).

cnf(i_0_16172,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_9613]),
    [final] ).

cnf(i_0_16173,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_9614]),
    [final] ).

cnf(i_0_16174,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_9317]),
    [final] ).

cnf(i_0_16175,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_9615]),
    [final] ).

cnf(i_0_16176,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_9616]),
    [final] ).

cnf(i_0_16177,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_9617]),
    [final] ).

cnf(i_0_16178,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_9618]),
    [final] ).

cnf(i_0_16179,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_9619]),
    [final] ).

cnf(i_0_16180,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_9620]),
    [final] ).

cnf(i_0_16181,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_8216]),
    [final] ).

cnf(i_0_16182,plain,
    ( hAPP(X1,esk181_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_7303]),
    [final] ).

cnf(i_0_16183,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),esk37_2(X2,X3)))
    | ~ hBOOL(hAPP(X3,X1))
    | ~ hBOOL(hAPP(X3,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9189]),
    [final] ).

cnf(i_0_16184,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_9621]),
    [final] ).

cnf(i_0_16185,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_9622]),
    [final] ).

cnf(i_0_16186,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_9623]),
    [final] ).

cnf(i_0_16187,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_9624]),
    [final] ).

cnf(i_0_16188,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_9625]),
    [final] ).

cnf(i_0_16189,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_9626]),
    [final] ).

cnf(i_0_16190,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_9627]),
    [final] ).

cnf(i_0_16191,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_9628]),
    [final] ).

cnf(i_0_16192,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_9629]),
    [final] ).

cnf(i_0_16193,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_9630]),
    [final] ).

cnf(i_0_16194,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_9631]),
    [final] ).

cnf(i_0_16195,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk504_2(X2,X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9440]),
    [final] ).

cnf(i_0_16196,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_9632]),
    [final] ).

cnf(i_0_16197,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_9633]),
    [final] ).

cnf(i_0_16198,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_9634]),
    [final] ).

cnf(i_0_16199,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_9635]),
    [final] ).

cnf(i_0_16200,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_9636]),
    [final] ).

cnf(i_0_16201,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_9397]),
    [final] ).

cnf(i_0_16202,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_9398]),
    [final] ).

cnf(i_0_16203,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_9637]),
    [final] ).

cnf(i_0_16204,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_9638]),
    [final] ).

cnf(i_0_16205,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_9639]),
    [final] ).

cnf(i_0_16206,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_9640]),
    [final] ).

cnf(i_0_16207,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Oabs__class_Oabs(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Olinordered__idom(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9514]),
    [final] ).

cnf(i_0_16208,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X3)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Ocomm__ring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9513]),
    [final] ).

cnf(i_0_16209,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_9517]),
    [final] ).

cnf(i_0_16210,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_9515]),
    [final] ).

cnf(i_0_16211,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_9516]),
    [final] ).

cnf(i_0_16212,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_9518]),
    [final] ).

cnf(i_0_16213,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_9327]),
    [final] ).

cnf(i_0_16214,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_9641]),
    [final] ).

cnf(i_0_16215,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_9642]),
    [final] ).

cnf(i_0_16216,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_9643]),
    [final] ).

cnf(i_0_16217,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_9607]),
    [final] ).

cnf(i_0_16218,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_9644,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_16219,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_9645,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_16220,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_List_Oset(X1),X3)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Oremove1(X1,X2,X3)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8954]),
    [final] ).

cnf(i_0_16221,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_9646]),
    [final] ).

cnf(i_0_16222,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_9647]),
    [final] ).

cnf(i_0_16223,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_9648]),
    [final] ).

cnf(i_0_16224,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_9649,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_16225,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_9650,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_16226,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_9651]),
    [final] ).

cnf(i_0_16227,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_9652]),
    [final] ).

cnf(i_0_16228,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_9653]),
    [final] ).

cnf(i_0_16229,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_9654]),
    [final] ).

cnf(i_0_16230,plain,
    c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_9655,c_0_6096]),
    [final] ).

cnf(i_0_16231,plain,
    c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_9656,c_0_6096]),
    [final] ).

cnf(i_0_16232,plain,
    c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)))),
    inference(rw,[status(thm)],[i_0_9657,c_0_6096]),
    [final] ).

cnf(i_0_16233,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_9658,c_0_8354]),
    [final] ).

cnf(i_0_16234,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_9659,c_0_8354]),
    [final] ).

cnf(i_0_16235,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_9660]),
    [final] ).

cnf(i_0_16236,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,esk180_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_8758]),
    [final] ).

cnf(i_0_16237,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,esk84_3(X1,X2,X3)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8759]),
    [final] ).

cnf(i_0_16238,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_9661]),
    [final] ).

cnf(i_0_16239,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_9662]),
    [final] ).

cnf(i_0_16240,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_9663]),
    [final] ).

cnf(i_0_16241,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk32_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9664]),
    [final] ).

cnf(i_0_16242,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk34_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9665]),
    [final] ).

cnf(i_0_16243,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_9666]),
    [final] ).

cnf(i_0_16244,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X3),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | X1 != X2
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_9116]),
    [final] ).

cnf(i_0_16245,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_9667]),
    [final] ).

cnf(i_0_16246,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_9492]),
    [final] ).

cnf(i_0_16247,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_9668]),
    [final] ).

cnf(i_0_16248,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_9574]),
    [final] ).

cnf(i_0_16249,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_9669]),
    [final] ).

cnf(i_0_16250,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_9670]),
    [final] ).

cnf(i_0_16251,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_9671]),
    [final] ).

cnf(i_0_16252,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_9672]),
    [final] ).

cnf(i_0_16253,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_9673]),
    [final] ).

cnf(i_0_16254,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_9674]),
    [final] ).

cnf(i_0_16255,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_9675]),
    [final] ).

cnf(i_0_16256,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_9676]),
    [final] ).

cnf(i_0_16257,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_9677]),
    [final] ).

cnf(i_0_16258,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_9678]),
    [final] ).

cnf(i_0_16259,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_9679]),
    [final] ).

cnf(i_0_16260,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_9680]),
    [final] ).

cnf(i_0_16261,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_9681]),
    [final] ).

cnf(i_0_16262,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk438_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_7673]),
    [final] ).

cnf(i_0_16263,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk432_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_7674]),
    [final] ).

cnf(i_0_16264,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_9682]),
    [final] ).

cnf(i_0_16265,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9683]),
    [final] ).

cnf(i_0_16266,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_9684]),
    [final] ).

cnf(i_0_16267,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_9685]),
    [final] ).

cnf(i_0_16268,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_9686]),
    [final] ).

cnf(i_0_16269,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_9687]),
    [final] ).

cnf(i_0_16270,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_9688]),
    [final] ).

cnf(i_0_16271,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_9689]),
    [final] ).

cnf(i_0_16272,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_9690]),
    [final] ).

cnf(i_0_16273,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_9691]),
    [final] ).

cnf(i_0_16274,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_9692]),
    [final] ).

cnf(i_0_16275,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_9693]),
    [final] ).

cnf(i_0_16276,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_9694]),
    [final] ).

cnf(i_0_16277,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_9695]),
    [final] ).

cnf(i_0_16278,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_9543]),
    [final] ).

cnf(i_0_16279,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_9696]),
    [final] ).

cnf(i_0_16280,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_9697]),
    [final] ).

cnf(i_0_16281,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_9698]),
    [final] ).

cnf(i_0_16282,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_9699]),
    [final] ).

cnf(i_0_16283,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8979]),
    [final] ).

cnf(i_0_16284,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X4))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(X2,X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8980]),
    [final] ).

cnf(i_0_16285,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_9700]),
    [final] ).

cnf(i_0_16286,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_9701]),
    [final] ).

cnf(i_0_16287,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_9702]),
    [final] ).

cnf(i_0_16288,plain,
    c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_9703]),
    [final] ).

cnf(i_0_16289,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_9704]),
    [final] ).

cnf(i_0_16290,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_9705]),
    [final] ).

cnf(i_0_16291,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_9706]),
    [final] ).

cnf(i_0_16292,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_9707]),
    [final] ).

cnf(i_0_16293,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_9585]),
    [final] ).

cnf(i_0_16294,plain,
    ( hBOOL(hAPP(X1,esk439_3(X2,X1,X3)))
    | c_List_OtakeWhile(X3,X1,X2) = hAPP(c_List_Ofilter(X3,X1),X2) ),
    inference(split_conjunct,[status(thm)],[i_0_5447]),
    [final] ).

cnf(i_0_16295,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_9708]),
    [final] ).

cnf(i_0_16296,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_9709]),
    [final] ).

cnf(i_0_16297,plain,
    ( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk52_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_9710]),
    [final] ).

cnf(i_0_16298,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_9711]),
    [final] ).

cnf(i_0_16299,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_9548]),
    [final] ).

cnf(i_0_16300,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_9549]),
    [final] ).

cnf(i_0_16301,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_9712]),
    [final] ).

cnf(i_0_16302,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_9713]),
    [final] ).

cnf(i_0_16303,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_9714]),
    [final] ).

cnf(i_0_16304,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_9715]),
    [final] ).

cnf(i_0_16305,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_9716]),
    [final] ).

cnf(i_0_16306,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_9717,c_0_6187]),
    [final] ).

cnf(i_0_16307,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_6574]),
    [final] ).

cnf(i_0_16308,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_9718]),
    [final] ).

cnf(i_0_16309,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_9719]),
    [final] ).

cnf(i_0_16310,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_9720]),
    [final] ).

cnf(i_0_16311,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_9721]),
    [final] ).

cnf(i_0_16312,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_9722]),
    [final] ).

cnf(i_0_16313,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_9723]),
    [final] ).

cnf(i_0_16314,plain,
    ( hBOOL(hAPP(hAPP(X3,X2),X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Quotient_ORespects(X1,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_9724]),
    [final] ).

cnf(i_0_16315,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_9725]),
    [final] ).

cnf(i_0_16316,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_9726]),
    [final] ).

cnf(i_0_16317,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)) = X3
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9727]),
    [final] ).

cnf(i_0_16318,plain,
    ( hBOOL(hAPP(X2,esk59_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_9728]),
    [final] ).

cnf(i_0_16319,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_9720]),
    [final] ).

cnf(i_0_16320,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_9729]),
    [final] ).

cnf(i_0_16321,plain,
    ( hBOOL(hAPP(X1,esk507_3(X2,X1,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8736]),
    [final] ).

cnf(i_0_16322,plain,
    ( hBOOL(hAPP(X1,esk506_3(X1,X2,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8737]),
    [final] ).

cnf(i_0_16323,plain,
    ( hBOOL(hAPP(X1,esk486_3(X2,X1,X3)))
    | ~ c_List_Olist__ex1(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7283]),
    [final] ).

cnf(i_0_16324,plain,
    ( hBOOL(hAPP(X1,esk478_3(X2,X1,X3)))
    | ~ c_List_Olist__ex1(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7284]),
    [final] ).

cnf(i_0_16325,plain,
    ( hBOOL(hAPP(X1,esk469_3(X2,X1,X3)))
    | ~ c_List_Olist__ex(X3,X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8738]),
    [final] ).

cnf(i_0_16326,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_9730,c_0_6070]),
    [final] ).

cnf(i_0_16327,plain,
    ( hAPP(X1,esk183_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_7311]),
    [final] ).

cnf(i_0_16328,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_9731]),
    [final] ).

cnf(i_0_16329,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_9732]),
    [final] ).

cnf(i_0_16330,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_9733]),
    [final] ).

cnf(i_0_16331,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_9734]),
    [final] ).

cnf(i_0_16332,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_9735]),
    [final] ).

cnf(i_0_16333,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_9736]),
    [final] ).

cnf(i_0_16334,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_9737]),
    [final] ).

cnf(i_0_16335,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_9738]),
    [final] ).

cnf(i_0_16336,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_9739]),
    [final] ).

cnf(i_0_16337,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_9740,c_0_6187]),
    [final] ).

cnf(i_0_16338,plain,
    ( hBOOL(hAPP(X2,X4))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(X1,X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8939]),
    [final] ).

cnf(i_0_16339,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Power_Opower__class_Opower(X2),X1),X3)))
    | X1 != c_Groups_Oone__class_Oone(X2)
    | ~ class_Rings_Ocomm__semiring__1(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9245]),
    [final] ).

cnf(i_0_16340,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_9741]),
    [final] ).

cnf(i_0_16341,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_9742]),
    [final] ).

cnf(i_0_16342,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_9743]),
    [final] ).

cnf(i_0_16343,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_9744]),
    [final] ).

cnf(i_0_16344,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_9602]),
    [final] ).

cnf(i_0_16345,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_9399]),
    [final] ).

cnf(i_0_16346,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_9745]),
    [final] ).

cnf(i_0_16347,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_9746]),
    [final] ).

cnf(i_0_16348,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_9747]),
    [final] ).

cnf(i_0_16349,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_9748]),
    [final] ).

cnf(i_0_16350,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_9749]),
    [final] ).

cnf(i_0_16351,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_9750]),
    [final] ).

cnf(i_0_16352,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_9751]),
    [final] ).

cnf(i_0_16353,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_9752]),
    [final] ).

cnf(i_0_16354,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_9753]),
    [final] ).

cnf(i_0_16355,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_9754]),
    [final] ).

cnf(i_0_16356,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_9003]),
    [final] ).

cnf(i_0_16357,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_9670]),
    [final] ).

cnf(i_0_16358,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk528_2(X1,X2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | hBOOL(hAPP(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9755]),
    [final] ).

cnf(i_0_16359,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_9756]),
    [final] ).

cnf(i_0_16360,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_7680]),
    [final] ).

cnf(i_0_16361,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9757]),
    [final] ).

cnf(i_0_16362,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9758]),
    [final] ).

cnf(i_0_16363,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_9759]),
    [final] ).

cnf(i_0_16364,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_9760]),
    [final] ).

cnf(i_0_16365,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_9761]),
    [final] ).

cnf(i_0_16366,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_9762]),
    [final] ).

cnf(i_0_16367,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_9763]),
    [final] ).

cnf(i_0_16368,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_9764]),
    [final] ).

cnf(i_0_16369,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_9765]),
    [final] ).

cnf(i_0_16370,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_9766]),
    [final] ).

cnf(i_0_16371,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_9767]),
    [final] ).

cnf(i_0_16372,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_9768]),
    [final] ).

cnf(i_0_16373,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_9769,c_0_6726]),
    [final] ).

cnf(i_0_16374,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_9770]),
    [final] ).

cnf(i_0_16375,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),X1),X4) = X3
    | X4 = c_Groups_Ozero__class_Ozero(X2)
    | X1 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X3),X4)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X4),X1))
    | ~ class_Divides_Osemiring__div(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9771]),
    [final] ).

cnf(i_0_16376,plain,
    ( X2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X4),X3)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X3) != X4
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9771]),
    [final] ).

cnf(i_0_16377,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_9772]),
    [final] ).

cnf(i_0_16378,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_9773]),
    [final] ).

cnf(i_0_16379,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_9774]),
    [final] ).

cnf(i_0_16380,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_9775]),
    [final] ).

cnf(i_0_16381,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_9776,c_0_7117]),
    [final] ).

cnf(i_0_16382,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_9777,c_0_8300]),
    [final] ).

cnf(i_0_16383,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_9778,c_0_6187]),
    [final] ).

cnf(i_0_16384,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_9779]),
    [final] ).

cnf(i_0_16385,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_9780]),
    [final] ).

cnf(i_0_16386,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_9781]),
    [final] ).

cnf(i_0_16387,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_9782]),
    [final] ).

cnf(i_0_16388,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_9783]),
    [final] ).

cnf(i_0_16389,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_9784]),
    [final] ).

cnf(i_0_16390,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_9785]),
    [final] ).

cnf(i_0_16391,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_9786]),
    [final] ).

cnf(i_0_16392,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_9787]),
    [final] ).

cnf(i_0_16393,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_9788]),
    [final] ).

cnf(i_0_16394,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_9789]),
    [final] ).

cnf(i_0_16395,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_9790]),
    [final] ).

cnf(i_0_16396,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_9791]),
    [final] ).

cnf(i_0_16397,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_9792]),
    [final] ).

cnf(i_0_16398,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_9793]),
    [final] ).

cnf(i_0_16399,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_9794]),
    [final] ).

cnf(i_0_16400,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_9795]),
    [final] ).

cnf(i_0_16401,plain,
    ( hBOOL(hAPP(X1,esk537_3(X1,X2,X3)))
    | ~ hBOOL(hAPP(X1,X4))
    | ~ c_Equiv__Relations_Oequivp(X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8828]),
    [final] ).

cnf(i_0_16402,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(hAPP(c_Set_Oinsert(X3),X2),X4)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8966]),
    [final] ).

cnf(i_0_16403,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_9269]),
    [final] ).

cnf(i_0_16404,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_9796]),
    [final] ).

cnf(i_0_16405,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_9797]),
    [final] ).

cnf(i_0_16406,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_9798]),
    [final] ).

cnf(i_0_16407,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_9382]),
    [final] ).

cnf(i_0_16408,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_9799]),
    [final] ).

cnf(i_0_16409,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_9800]),
    [final] ).

cnf(i_0_16410,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_9801]),
    [final] ).

cnf(i_0_16411,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_9802]),
    [final] ).

cnf(i_0_16412,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_9803]),
    [final] ).

cnf(i_0_16413,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_9804]),
    [final] ).

cnf(i_0_16414,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,esk528_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9755]),
    [final] ).

cnf(i_0_16415,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,esk301_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_8662]),
    [final] ).

cnf(i_0_16416,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_9805]),
    [final] ).

cnf(i_0_16417,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_9806]),
    [final] ).

cnf(i_0_16418,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),esk31_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_9664]),
    [final] ).

cnf(i_0_16419,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),esk33_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_9665]),
    [final] ).

cnf(i_0_16420,plain,
    ( X1 = hAPP(c_Code__Numeral_Onat__of,esk527_1(X1))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9807]),
    [final] ).

cnf(i_0_16421,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_5237]),
    [final] ).

cnf(i_0_16422,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,esk60_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_9808]),
    [final] ).

cnf(i_0_16423,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(split_conjunct,[status(thm)],[i_0_9809]),
    [final] ).

cnf(i_0_16424,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_9438]),
    [final] ).

cnf(i_0_16425,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_16426,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_7690]),
    [final] ).

cnf(i_0_16427,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_9641]),
    [final] ).

cnf(i_0_16428,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_9810]),
    [final] ).

cnf(i_0_16429,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_9811]),
    [final] ).

cnf(i_0_16430,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_9039]),
    [final] ).

cnf(i_0_16431,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_9812,c_0_6071]),
    [final] ).

cnf(i_0_16432,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_9813,c_0_6219]),
    [final] ).

cnf(i_0_16433,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_9814]),
    [final] ).

cnf(i_0_16434,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_8856]),
    [final] ).

cnf(i_0_16435,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk147_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8861]),
    [final] ).

cnf(i_0_16436,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,esk145_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8696]),
    [final] ).

cnf(i_0_16437,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_9815]),
    [final] ).

cnf(i_0_16438,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_9816]),
    [final] ).

cnf(i_0_16439,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_9817]),
    [final] ).

cnf(i_0_16440,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,esk65_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9796]),
    [final] ).

cnf(i_0_16441,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_9379]),
    [final] ).

cnf(i_0_16442,plain,
    ( c_List_Olist__all(tc_Nat_Onat,X1,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X2),X3)))
    | ~ c_List_Oall__interval__nat(X1,X2,X3) ),
    inference(rw,[status(thm)],[i_0_9818,c_0_6187]),
    [final] ).

cnf(i_0_16443,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_9819]),
    [final] ).

cnf(i_0_16444,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_9820]),
    [final] ).

cnf(i_0_16445,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_9821,c_0_6219]),
    [final] ).

cnf(i_0_16446,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_9822]),
    [final] ).

cnf(i_0_16447,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_9823]),
    [final] ).

cnf(i_0_16448,plain,
    ( X2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk19_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9824]),
    [final] ).

cnf(i_0_16449,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_9825]),
    [final] ).

cnf(i_0_16450,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_9826]),
    [final] ).

cnf(i_0_16451,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X2),c_Transitive__Closure_Ortrancl(X1,X2)) = X2
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(rw,[status(thm)],[i_0_9827,c_0_6103]),
    [final] ).

cnf(i_0_16452,plain,
    ( hAPP(X1,esk517_1(X1)) = hAPP(X1,esk518_1(X1))
    | hBOOL(hAPP(hAPP(X1,esk517_1(X1)),esk518_1(X1)))
    | c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_16453,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_9828]),
    [final] ).

cnf(i_0_16454,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_9829]),
    [final] ).

cnf(i_0_16455,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_9830]),
    [final] ).

cnf(i_0_16456,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_9831]),
    [final] ).

cnf(i_0_16457,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_9378]),
    [final] ).

cnf(i_0_16458,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_6456]),
    [final] ).

cnf(i_0_16459,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_9317]),
    [final] ).

cnf(i_0_16460,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_9832]),
    [final] ).

cnf(i_0_16461,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_8661]),
    [final] ).

cnf(i_0_16462,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_9731]),
    [final] ).

cnf(i_0_16463,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_9731]),
    [final] ).

cnf(i_0_16464,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_9833]),
    [final] ).

cnf(i_0_16465,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_9834]),
    [final] ).

cnf(i_0_16466,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_6178]),
    [final] ).

cnf(i_0_16467,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_7995]),
    [final] ).

cnf(i_0_16468,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_9039]),
    [final] ).

cnf(i_0_16469,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk43_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_9835]),
    [final] ).

cnf(i_0_16470,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_9836]),
    [final] ).

cnf(i_0_16471,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_9837]),
    [final] ).

cnf(i_0_16472,plain,
    ( hBOOL(hAPP(X1,esk493_3(X2,X3,X1)))
    | c_FunDef_OTHE__default(X3,X2,X1) = X2 ),
    inference(split_conjunct,[status(thm)],[i_0_8076]),
    [final] ).

cnf(i_0_16473,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_9838]),
    [final] ).

cnf(i_0_16474,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9839]),
    [final] ).

cnf(i_0_16475,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9840]),
    [final] ).

cnf(i_0_16476,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9841]),
    [final] ).

cnf(i_0_16477,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9842]),
    [final] ).

cnf(i_0_16478,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9843]),
    [final] ).

cnf(i_0_16479,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9844]),
    [final] ).

cnf(i_0_16480,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9845]),
    [final] ).

cnf(i_0_16481,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9846]),
    [final] ).

cnf(i_0_16482,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9847]),
    [final] ).

cnf(i_0_16483,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_9848]),
    [final] ).

cnf(i_0_16484,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_9849]),
    [final] ).

cnf(i_0_16485,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_9850,c_0_6187]),
    [final] ).

cnf(i_0_16486,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_9851]),
    [final] ).

cnf(i_0_16487,plain,
    ( c_Quotient_OBabs(X1,X3,c_Quotient_ORespects(X1,X2),X4) = X4
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9852]),
    [final] ).

cnf(i_0_16488,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_9853]),
    [final] ).

cnf(i_0_16489,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_9854]),
    [final] ).

cnf(i_0_16490,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_9855]),
    [final] ).

cnf(i_0_16491,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_9856]),
    [final] ).

cnf(i_0_16492,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_9554]),
    [final] ).

cnf(i_0_16493,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_9857]),
    [final] ).

cnf(i_0_16494,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_9857]),
    [final] ).

cnf(i_0_16495,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_9858]),
    [final] ).

cnf(i_0_16496,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_9859]),
    [final] ).

cnf(i_0_16497,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_9860]),
    [final] ).

cnf(i_0_16498,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_9861]),
    [final] ).

cnf(i_0_16499,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_9862]),
    [final] ).

cnf(i_0_16500,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_9863]),
    [final] ).

cnf(i_0_16501,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_9864]),
    [final] ).

cnf(i_0_16502,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_9865]),
    [final] ).

cnf(i_0_16503,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_9866]),
    [final] ).

cnf(i_0_16504,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_9735]),
    [final] ).

cnf(i_0_16505,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_9736]),
    [final] ).

cnf(i_0_16506,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_9867,c_0_7117]),
    [final] ).

cnf(i_0_16507,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_9868,c_0_7117]),
    [final] ).

cnf(i_0_16508,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_9869]),
    [final] ).

cnf(i_0_16509,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_16510,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_8364]),
    [final] ).

cnf(i_0_16511,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_8364]),
    [final] ).

cnf(i_0_16512,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_9870]),
    [final] ).

cnf(i_0_16513,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_9870]),
    [final] ).

cnf(i_0_16514,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_8645]),
    [final] ).

cnf(i_0_16515,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_9871]),
    [final] ).

cnf(i_0_16516,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_9872]),
    [final] ).

cnf(i_0_16517,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_9051]),
    [final] ).

cnf(i_0_16518,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_9593]),
    [final] ).

cnf(i_0_16519,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_9873]),
    [final] ).

cnf(i_0_16520,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_9874]),
    [final] ).

cnf(i_0_16521,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_9875]),
    [final] ).

cnf(i_0_16522,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_8191]),
    [final] ).

cnf(i_0_16523,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_9833]),
    [final] ).

cnf(i_0_16524,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_9581]),
    [final] ).

cnf(i_0_16525,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_9876]),
    [final] ).

cnf(i_0_16526,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_9877]),
    [final] ).

cnf(i_0_16527,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_9878]),
    [final] ).

cnf(i_0_16528,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_9877]),
    [final] ).

cnf(i_0_16529,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_9878]),
    [final] ).

cnf(i_0_16530,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_9879]),
    [final] ).

cnf(i_0_16531,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_9880]),
    [final] ).

cnf(i_0_16532,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_9881]),
    [final] ).

cnf(i_0_16533,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9080]),
    [final] ).

cnf(i_0_16534,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_9882]),
    [final] ).

cnf(i_0_16535,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_9685]),
    [final] ).

cnf(i_0_16536,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_9883]),
    [final] ).

cnf(i_0_16537,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_9884]),
    [final] ).

cnf(i_0_16538,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_9885]),
    [final] ).

cnf(i_0_16539,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_9886]),
    [final] ).

cnf(i_0_16540,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_9887]),
    [final] ).

cnf(i_0_16541,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_9775]),
    [final] ).

cnf(i_0_16542,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_9888]),
    [final] ).

cnf(i_0_16543,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_9794]),
    [final] ).

cnf(i_0_16544,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_9889]),
    [final] ).

cnf(i_0_16545,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_9738]),
    [final] ).

cnf(i_0_16546,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_9701]),
    [final] ).

cnf(i_0_16547,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_9144]),
    [final] ).

cnf(i_0_16548,plain,
    ( hBOOL(hAPP(X1,esk425_3(X2,X1,X3)))
    | hAPP(c_List_Ofilter(X3,X1),X2) = c_List_Olist_ONil(X3) ),
    inference(split_conjunct,[status(thm)],[i_0_8831]),
    [final] ).

cnf(i_0_16549,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_9890]),
    [final] ).

cnf(i_0_16550,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_9891]),
    [final] ).

cnf(i_0_16551,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),c_Quotient_ORespects(X3,X1)))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9724]),
    [final] ).

cnf(i_0_16552,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_9607]),
    [final] ).

cnf(i_0_16553,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_9892]),
    [final] ).

cnf(i_0_16554,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_9893]),
    [final] ).

cnf(i_0_16555,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_9894]),
    [final] ).

cnf(i_0_16556,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_9369]),
    [final] ).

cnf(i_0_16557,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),esk140_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_9895]),
    [final] ).

cnf(i_0_16558,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_9896]),
    [final] ).

cnf(i_0_16559,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_9896]),
    [final] ).

cnf(i_0_16560,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_9897]),
    [final] ).

cnf(i_0_16561,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_9898]),
    [final] ).

cnf(i_0_16562,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_9899]),
    [final] ).

cnf(i_0_16563,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_9900]),
    [final] ).

cnf(i_0_16564,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_9901]),
    [final] ).

cnf(i_0_16565,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_9902]),
    [final] ).

cnf(i_0_16566,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_9903]),
    [final] ).

cnf(i_0_16567,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_9904]),
    [final] ).

cnf(i_0_16568,plain,
    c_Nat_Onat_Onat__case(X1,X2,X3,hAPP(c_Nat_OSuc,X4)) = hAPP(X3,X4),
    inference(split_conjunct,[status(thm)],[i_0_9905]),
    [final] ).

cnf(i_0_16569,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_9906]),
    [final] ).

cnf(i_0_16570,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_9907]),
    [final] ).

cnf(i_0_16571,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_9908]),
    [final] ).

cnf(i_0_16572,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_9909]),
    [final] ).

cnf(i_0_16573,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_9910]),
    [final] ).

cnf(i_0_16574,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_9911]),
    [final] ).

cnf(i_0_16575,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_9912]),
    [final] ).

cnf(i_0_16576,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_9671]),
    [final] ).

cnf(i_0_16577,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_9913]),
    [final] ).

cnf(i_0_16578,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_9914]),
    [final] ).

cnf(i_0_16579,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_9915]),
    [final] ).

cnf(i_0_16580,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_9916]),
    [final] ).

cnf(i_0_16581,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_9917]),
    [final] ).

cnf(i_0_16582,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_9918]),
    [final] ).

cnf(i_0_16583,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_9919]),
    [final] ).

cnf(i_0_16584,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_9920]),
    [final] ).

cnf(i_0_16585,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_9921]),
    [final] ).

cnf(i_0_16586,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_9922]),
    [final] ).

cnf(i_0_16587,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_9923]),
    [final] ).

cnf(i_0_16588,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_9924]),
    [final] ).

cnf(i_0_16589,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_16590,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_16591,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_16592,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_16593,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_9925]),
    [final] ).

cnf(i_0_16594,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_9926]),
    [final] ).

cnf(i_0_16595,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_9927]),
    [final] ).

cnf(i_0_16596,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_9928]),
    [final] ).

cnf(i_0_16597,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk37_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_9189]),
    [final] ).

cnf(i_0_16598,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X4),X1),X2))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9512]),
    [final] ).

cnf(i_0_16599,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_9929]),
    [final] ).

cnf(i_0_16600,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_9607]),
    [final] ).

cnf(i_0_16601,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_9911]),
    [final] ).

cnf(i_0_16602,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_9912]),
    [final] ).

cnf(i_0_16603,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_9930]),
    [final] ).

cnf(i_0_16604,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_9543]),
    [final] ).

cnf(i_0_16605,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_9931]),
    [final] ).

cnf(i_0_16606,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_9932]),
    [final] ).

cnf(i_0_16607,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_16608,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_9933]),
    [final] ).

cnf(i_0_16609,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_9364]),
    [final] ).

cnf(i_0_16610,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_9934]),
    [final] ).

cnf(i_0_16611,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_9935]),
    [final] ).

cnf(i_0_16612,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_9936,c_0_6071]),
    [final] ).

cnf(i_0_16613,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_9529]),
    [final] ).

cnf(i_0_16614,plain,
    ( esk199_3(X1,X2,X3) = esk200_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_8724]),
    [final] ).

cnf(i_0_16615,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_9937]),
    [final] ).

cnf(i_0_16616,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_9938]),
    [final] ).

cnf(i_0_16617,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk56_2(X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9939]),
    [final] ).

cnf(i_0_16618,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_9940]),
    [final] ).

cnf(i_0_16619,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_9941]),
    [final] ).

cnf(i_0_16620,plain,
    ( hBOOL(hAPP(X1,esk148_2(X1,X2)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X2))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_8824]),
    [final] ).

cnf(i_0_16621,plain,
    ( hBOOL(hAPP(X1,esk142_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_8660]),
    [final] ).

cnf(i_0_16622,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_9942]),
    [final] ).

cnf(i_0_16623,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_9942]),
    [final] ).

cnf(i_0_16624,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,esk123_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_9943]),
    [final] ).

cnf(i_0_16625,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_9944]),
    [final] ).

cnf(i_0_16626,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_9945]),
    [final] ).

cnf(i_0_16627,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_9946]),
    [final] ).

cnf(i_0_16628,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_9947]),
    [final] ).

cnf(i_0_16629,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_9720]),
    [final] ).

cnf(i_0_16630,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_9948]),
    [final] ).

cnf(i_0_16631,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_9949]),
    [final] ).

cnf(i_0_16632,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_9587]),
    [final] ).

cnf(i_0_16633,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_9950]),
    [final] ).

cnf(i_0_16634,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_9833]),
    [final] ).

cnf(i_0_16635,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_9951]),
    [final] ).

cnf(i_0_16636,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk361_2(X2,X1)),esk360_2(X2,X1)))
    | c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7070]),
    [final] ).

cnf(i_0_16637,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_9952]),
    [final] ).

cnf(i_0_16638,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_9953]),
    [final] ).

cnf(i_0_16639,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X2))
    | X2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X2) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(split_conjunct,[status(thm)],[i_0_8945]),
    [final] ).

cnf(i_0_16640,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_9954]),
    [final] ).

cnf(i_0_16641,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_9607]),
    [final] ).

cnf(i_0_16642,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_9955]),
    [final] ).

cnf(i_0_16643,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_9956]),
    [final] ).

cnf(i_0_16644,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_9957]),
    [final] ).

cnf(i_0_16645,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_9957]),
    [final] ).

cnf(i_0_16646,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_9958]),
    [final] ).

cnf(i_0_16647,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_9959]),
    [final] ).

cnf(i_0_16648,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_9960]),
    [final] ).

cnf(i_0_16649,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_9961]),
    [final] ).

cnf(i_0_16650,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_9962]),
    [final] ).

cnf(i_0_16651,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_9963]),
    [final] ).

cnf(i_0_16652,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_9964]),
    [final] ).

cnf(i_0_16653,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_9965]),
    [final] ).

cnf(i_0_16654,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_9966]),
    [final] ).

cnf(i_0_16655,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_9966]),
    [final] ).

cnf(i_0_16656,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_9965]),
    [final] ).

cnf(i_0_16657,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_7654]),
    [final] ).

cnf(i_0_16658,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_8208]),
    [final] ).

cnf(i_0_16659,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_6574]),
    [final] ).

cnf(i_0_16660,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_9967]),
    [final] ).

cnf(i_0_16661,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_9968]),
    [final] ).

cnf(i_0_16662,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_9536]),
    [final] ).

cnf(i_0_16663,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_6628]),
    [final] ).

cnf(i_0_16664,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_9969]),
    [final] ).

cnf(i_0_16665,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_9970]),
    [final] ).

cnf(i_0_16666,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_6865]),
    [final] ).

cnf(i_0_16667,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_6628]),
    [final] ).

cnf(i_0_16668,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_6866]),
    [final] ).

cnf(i_0_16669,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_9971]),
    [final] ).

cnf(i_0_16670,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_9972]),
    [final] ).

cnf(i_0_16671,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_9973]),
    [final] ).

cnf(i_0_16672,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_9974]),
    [final] ).

cnf(i_0_16673,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_9942]),
    [final] ).

cnf(i_0_16674,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk437_2(X1,X2)),esk438_2(X1,X2)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7673]),
    [final] ).

cnf(i_0_16675,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),esk433_2(X1,X2)),esk432_2(X1,X2)))
    | c_List_Olinorder__class_Osorted(X2,X1)
    | ~ class_Orderings_Olinorder(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7674]),
    [final] ).

cnf(i_0_16676,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_9975]),
    [final] ).

cnf(i_0_16677,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_9976]),
    [final] ).

cnf(i_0_16678,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_9977]),
    [final] ).

cnf(i_0_16679,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_9978]),
    [final] ).

cnf(i_0_16680,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_9979]),
    [final] ).

cnf(i_0_16681,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_9980]),
    [final] ).

cnf(i_0_16682,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_9980]),
    [final] ).

cnf(i_0_16683,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_9981]),
    [final] ).

cnf(i_0_16684,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_9607]),
    [final] ).

cnf(i_0_16685,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_9982]),
    [final] ).

cnf(i_0_16686,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk53_1(X1)))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9710]),
    [final] ).

cnf(i_0_16687,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_9983]),
    [final] ).

cnf(i_0_16688,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_9984]),
    [final] ).

cnf(i_0_16689,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_9985]),
    [final] ).

cnf(i_0_16690,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_9984]),
    [final] ).

cnf(i_0_16691,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_7690]),
    [final] ).

cnf(i_0_16692,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_7680]),
    [final] ).

cnf(i_0_16693,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_9986]),
    [final] ).

cnf(i_0_16694,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_9987]),
    [final] ).

cnf(i_0_16695,plain,
    ( c_Equiv__Relations_Oequivp(X2,X1)
    | ~ hBOOL(hAPP(hAPP(X1,esk239_1(X1)),esk240_1(X1)))
    | hAPP(X1,esk239_1(X1)) != hAPP(X1,esk240_1(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9988]),
    [final] ).

cnf(i_0_16696,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_9989]),
    [final] ).

cnf(i_0_16697,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_9990]),
    [final] ).

cnf(i_0_16698,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_9991]),
    [final] ).

cnf(i_0_16699,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_9992]),
    [final] ).

cnf(i_0_16700,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_9993]),
    [final] ).

cnf(i_0_16701,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk24_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_9438]),
    [final] ).

cnf(i_0_16702,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_9491]),
    [final] ).

cnf(i_0_16703,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9098]),
    [final] ).

cnf(i_0_16704,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_9994]),
    [final] ).

cnf(i_0_16705,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_9995]),
    [final] ).

cnf(i_0_16706,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_9736]),
    [final] ).

cnf(i_0_16707,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_9735]),
    [final] ).

cnf(i_0_16708,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X2)))
    | ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(X1,esk65_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9796]),
    [final] ).

cnf(i_0_16709,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_9810]),
    [final] ).

cnf(i_0_16710,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_9996]),
    [final] ).

cnf(i_0_16711,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_9997]),
    [final] ).

cnf(i_0_16712,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_9998]),
    [final] ).

cnf(i_0_16713,plain,
    ( X1 = hAPP(hAPP(c_List_Odrop(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X3)),X4)
    | hAPP(hAPP(c_List_Oappend(X2),X3),X1) != X4 ),
    inference(split_conjunct,[status(thm)],[i_0_8942]),
    [final] ).

cnf(i_0_16714,plain,
    ( X1 = hAPP(hAPP(c_List_Otake(X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1)),X3)
    | hAPP(hAPP(c_List_Oappend(X2),X1),X4) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_8942]),
    [final] ).

cnf(i_0_16715,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_9999]),
    [final] ).

cnf(i_0_16716,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_10000]),
    [final] ).

cnf(i_0_16717,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_10001]),
    [final] ).

cnf(i_0_16718,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_10002]),
    [final] ).

cnf(i_0_16719,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_7995]),
    [final] ).

cnf(i_0_16720,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_10003]),
    [final] ).

cnf(i_0_16721,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_10004]),
    [final] ).

cnf(i_0_16722,plain,
    ( hBOOL(hAPP(hAPP(X1,esk519_2(X1,X2)),esk519_2(X1,X2)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10005]),
    [final] ).

cnf(i_0_16723,plain,
    ( hBOOL(hAPP(hAPP(X1,esk515_2(X1,X2)),esk515_2(X1,X2)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10006]),
    [final] ).

cnf(i_0_16724,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_10007]),
    [final] ).

cnf(i_0_16725,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_10008]),
    [final] ).

cnf(i_0_16726,plain,
    c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10009]),
    [final] ).

cnf(i_0_16727,plain,
    c_List_Olistrelp(X1,X2,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10010]),
    [final] ).

cnf(i_0_16728,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_5944]),
    [final] ).

cnf(i_0_16729,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_5945]),
    [final] ).

cnf(i_0_16730,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_9857]),
    [final] ).

cnf(i_0_16731,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_10011]),
    [final] ).

cnf(i_0_16732,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_9891]),
    [final] ).

cnf(i_0_16733,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_10012]),
    [final] ).

cnf(i_0_16734,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_10013]),
    [final] ).

cnf(i_0_16735,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_10013]),
    [final] ).

cnf(i_0_16736,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_10014]),
    [final] ).

cnf(i_0_16737,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_10015]),
    [final] ).

cnf(i_0_16738,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_9965]),
    [final] ).

cnf(i_0_16739,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_9966]),
    [final] ).

cnf(i_0_16740,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_5335]),
    [final] ).

cnf(i_0_16741,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_10016]),
    [final] ).

cnf(i_0_16742,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_10017]),
    [final] ).

cnf(i_0_16743,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_10018]),
    [final] ).

cnf(i_0_16744,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_10019]),
    [final] ).

cnf(i_0_16745,plain,
    c_Lazy__Sequence_Omap(X1,X2,X3,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2),
    inference(split_conjunct,[status(thm)],[i_0_10020]),
    [final] ).

cnf(i_0_16746,plain,
    c_List_Omaps(X1,X2,X3,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(split_conjunct,[status(thm)],[i_0_10021]),
    [final] ).

cnf(i_0_16747,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_9824]),
    [final] ).

cnf(i_0_16748,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_10022,c_0_8300]),c_0_8300]),
    [final] ).

cnf(i_0_16749,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_10023]),
    [final] ).

cnf(i_0_16750,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_10024]),
    [final] ).

cnf(i_0_16751,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_10025]),
    [final] ).

cnf(i_0_16752,plain,
    ( X1 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(split_conjunct,[status(thm)],[i_0_10026]),
    [final] ).

cnf(i_0_16753,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_10027]),
    [final] ).

cnf(i_0_16754,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_10028]),
    [final] ).

cnf(i_0_16755,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_10029]),
    [final] ).

cnf(i_0_16756,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_10030]),
    [final] ).

cnf(i_0_16757,plain,
    c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10031]),
    [final] ).

cnf(i_0_16758,plain,
    c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10032]),
    [final] ).

cnf(i_0_16759,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_7917]),
    [final] ).

cnf(i_0_16760,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_10033]),
    [final] ).

cnf(i_0_16761,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_10034]),
    [final] ).

cnf(i_0_16762,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_10035]),
    [final] ).

cnf(i_0_16763,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_10036,c_0_6103]),
    [final] ).

cnf(i_0_16764,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_10037]),
    [final] ).

cnf(i_0_16765,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_10038,c_0_8300]),
    [final] ).

cnf(i_0_16766,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_10039]),
    [final] ).

cnf(i_0_16767,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_10040]),
    [final] ).

cnf(i_0_16768,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_10041]),
    [final] ).

cnf(i_0_16769,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_6820]),
    [final] ).

cnf(i_0_16770,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_10042]),
    [final] ).

cnf(i_0_16771,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_10043]),
    [final] ).

cnf(i_0_16772,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_10044]),
    [final] ).

cnf(i_0_16773,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_10045]),
    [final] ).

cnf(i_0_16774,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_10046]),
    [final] ).

cnf(i_0_16775,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_10047]),
    [final] ).

cnf(i_0_16776,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_10048]),
    [final] ).

cnf(i_0_16777,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_10049,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_16778,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_10050]),
    [final] ).

cnf(i_0_16779,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_10051]),
    [final] ).

cnf(i_0_16780,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_10052]),
    [final] ).

cnf(i_0_16781,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_10053]),
    [final] ).

cnf(i_0_16782,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_10054]),
    [final] ).

cnf(i_0_16783,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_10055]),
    [final] ).

cnf(i_0_16784,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_5335]),
    [final] ).

cnf(i_0_16785,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_10056]),
    [final] ).

cnf(i_0_16786,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_10056]),
    [final] ).

cnf(i_0_16787,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[i_0_10057,c_0_6069]),c_0_6070]),c_0_6071]),c_0_6071]),
    [final] ).

cnf(i_0_16788,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_10058]),
    [final] ).

cnf(i_0_16789,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_10059]),
    [final] ).

cnf(i_0_16790,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_10060]),
    [final] ).

cnf(i_0_16791,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_10061]),
    [final] ).

cnf(i_0_16792,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_10062]),
    [final] ).

cnf(i_0_16793,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_10063]),
    [final] ).

cnf(i_0_16794,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_10064]),
    [final] ).

cnf(i_0_16795,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_10065]),
    [final] ).

cnf(i_0_16796,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_10066]),
    [final] ).

cnf(i_0_16797,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_10067,c_0_7992]),c_0_7993]),
    [final] ).

cnf(i_0_16798,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_10068]),
    [final] ).

cnf(i_0_16799,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_10069]),
    [final] ).

cnf(i_0_16800,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_10070]),
    [final] ).

cnf(i_0_16801,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_10071]),
    [final] ).

cnf(i_0_16802,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_10072]),
    [final] ).

cnf(i_0_16803,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_10073]),
    [final] ).

cnf(i_0_16804,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_10074]),
    [final] ).

cnf(i_0_16805,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_10075]),
    [final] ).

cnf(i_0_16806,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_10076]),
    [final] ).

cnf(i_0_16807,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_10077]),
    [final] ).

cnf(i_0_16808,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_10078]),
    [final] ).

cnf(i_0_16809,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_9642]),
    [final] ).

cnf(i_0_16810,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_9642]),
    [final] ).

cnf(i_0_16811,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_9718]),
    [final] ).

cnf(i_0_16812,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_10079]),
    [final] ).

cnf(i_0_16813,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_10063]),
    [final] ).

cnf(i_0_16814,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_10080]),
    [final] ).

cnf(i_0_16815,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_10081]),
    [final] ).

cnf(i_0_16816,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_10082]),
    [final] ).

cnf(i_0_16817,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_10065]),
    [final] ).

cnf(i_0_16818,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_10066]),
    [final] ).

cnf(i_0_16819,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_10083]),
    [final] ).

cnf(i_0_16820,plain,
    ( X2 = X3
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X3))) ),
    inference(split_conjunct,[status(thm)],[i_0_10084]),
    [final] ).

cnf(i_0_16821,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_16822,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_10085]),
    [final] ).

cnf(i_0_16823,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_10086,c_0_6071]),
    [final] ).

cnf(i_0_16824,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_9039]),
    [final] ).

cnf(i_0_16825,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_10087]),
    [final] ).

cnf(i_0_16826,plain,
    ( X1 = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(X2),esk3_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10088]),
    [final] ).

cnf(i_0_16827,plain,
    ( hBOOL(hAPP(hAPP(c_member(X1),esk4_2(X2,X1)),X2))
    | X2 = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_10089]),
    [final] ).

cnf(i_0_16828,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_10090]),
    [final] ).

cnf(i_0_16829,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_10091,c_0_6187]),
    [final] ).

cnf(i_0_16830,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_9774]),
    [final] ).

cnf(i_0_16831,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X1),X4),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9512]),
    [final] ).

cnf(i_0_16832,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_10092]),
    [final] ).

cnf(i_0_16833,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_10093]),
    [final] ).

cnf(i_0_16834,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_10094]),
    [final] ).

cnf(i_0_16835,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_10095]),
    [final] ).

cnf(i_0_16836,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_9591]),
    [final] ).

cnf(i_0_16837,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_10096]),
    [final] ).

cnf(i_0_16838,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_10097]),
    [final] ).

cnf(i_0_16839,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_10098]),
    [final] ).

cnf(i_0_16840,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_10099]),
    [final] ).

cnf(i_0_16841,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_10100]),
    [final] ).

cnf(i_0_16842,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_10101]),
    [final] ).

cnf(i_0_16843,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_10102]),
    [final] ).

cnf(i_0_16844,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_10103]),
    [final] ).

cnf(i_0_16845,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_10104]),
    [final] ).

cnf(i_0_16846,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_10105]),
    [final] ).

cnf(i_0_16847,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_10106,c_0_6187]),
    [final] ).

cnf(i_0_16848,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_10107,c_0_6187]),
    [final] ).

cnf(i_0_16849,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_10108,c_0_6187]),
    [final] ).

cnf(i_0_16850,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_10109]),
    [final] ).

cnf(i_0_16851,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_9597]),
    [final] ).

cnf(i_0_16852,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_10110]),
    [final] ).

cnf(i_0_16853,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_10111]),
    [final] ).

cnf(i_0_16854,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk34_2(X1,X2)),X1))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9665]),
    [final] ).

cnf(i_0_16855,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk32_2(X1,X2)),X1))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_9664]),
    [final] ).

cnf(i_0_16856,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_9619]),
    [final] ).

cnf(i_0_16857,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_9620]),
    [final] ).

cnf(i_0_16858,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_10112]),
    [final] ).

cnf(i_0_16859,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_10113]),
    [final] ).

cnf(i_0_16860,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_10114]),
    [final] ).

cnf(i_0_16861,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_10115]),
    [final] ).

cnf(i_0_16862,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_10116]),
    [final] ).

cnf(i_0_16863,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_10117]),
    [final] ).

cnf(i_0_16864,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_10118]),
    [final] ).

cnf(i_0_16865,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Equiv__Relations_Opart__equivp(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_16866,plain,
    ( hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X3),X2))
    | ~ c_Equiv__Relations_Opart__equivp(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_16867,plain,
    ( hBOOL(hAPP(hAPP(X2,X4),X3))
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_10119]),
    [final] ).

cnf(i_0_16868,plain,
    ( hBOOL(hAPP(hAPP(X2,X4),X3))
    | ~ c_Predicate_Osymp(X1,X2)
    | ~ hBOOL(hAPP(hAPP(X2,X3),X4)) ),
    inference(split_conjunct,[status(thm)],[i_0_10120]),
    [final] ).

cnf(i_0_16869,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_10121]),
    [final] ).

cnf(i_0_16870,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_9666]),
    [final] ).

cnf(i_0_16871,plain,
    ( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10122]),
    [final] ).

cnf(i_0_16872,plain,
    ( c_Divides_Odiv__class_Omod(X1,X3,X2) = c_Groups_Ozero__class_Ozero(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10123]),
    [final] ).

cnf(i_0_16873,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_10124]),
    [final] ).

cnf(i_0_16874,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_10125]),
    [final] ).

cnf(i_0_16875,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_10126]),
    [final] ).

cnf(i_0_16876,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_10127]),
    [final] ).

cnf(i_0_16877,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_10128]),
    [final] ).

cnf(i_0_16878,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_10129]),
    [final] ).

cnf(i_0_16879,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_10130]),
    [final] ).

cnf(i_0_16880,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_10131]),
    [final] ).

cnf(i_0_16881,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_10132]),
    [final] ).

cnf(i_0_16882,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_10133]),
    [final] ).

cnf(i_0_16883,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_9765]),
    [final] ).

cnf(i_0_16884,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_10134]),
    [final] ).

cnf(i_0_16885,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_5967]),
    [final] ).

cnf(i_0_16886,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_10135]),
    [final] ).

cnf(i_0_16887,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_10136]),
    [final] ).

cnf(i_0_16888,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_10137]),
    [final] ).

cnf(i_0_16889,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_10138]),
    [final] ).

cnf(i_0_16890,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_10056]),
    [final] ).

cnf(i_0_16891,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_10139]),
    [final] ).

cnf(i_0_16892,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_10140]),
    [final] ).

cnf(i_0_16893,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_10141]),
    [final] ).

cnf(i_0_16894,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_10142]),
    [final] ).

cnf(i_0_16895,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_10143]),
    [final] ).

cnf(i_0_16896,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_10144]),
    [final] ).

cnf(i_0_16897,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_10145]),
    [final] ).

cnf(i_0_16898,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_10146]),
    [final] ).

cnf(i_0_16899,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_10147]),
    [final] ).

cnf(i_0_16900,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_10148]),
    [final] ).

cnf(i_0_16901,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_10149]),
    [final] ).

cnf(i_0_16902,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_10150]),
    [final] ).

cnf(i_0_16903,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_10151]),
    [final] ).

cnf(i_0_16904,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_10152]),
    [final] ).

cnf(i_0_16905,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_10153]),
    [final] ).

cnf(i_0_16906,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_10154]),
    [final] ).

cnf(i_0_16907,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_10155]),
    [final] ).

cnf(i_0_16908,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_10156]),
    [final] ).

cnf(i_0_16909,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_9874]),
    [final] ).

cnf(i_0_16910,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_10157]),
    [final] ).

cnf(i_0_16911,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_10158,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_16912,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_10159,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_16913,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_10160,c_0_6187]),
    [final] ).

cnf(i_0_16914,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_10161]),
    [final] ).

cnf(i_0_16915,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_10162]),
    [final] ).

cnf(i_0_16916,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_10163]),
    [final] ).

cnf(i_0_16917,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_10164]),
    [final] ).

cnf(i_0_16918,plain,
    ( c_Relation_Ototal__on(X3,X2,X1)
    | esk340_3(X1,X2,X3) != esk341_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_6814]),
    [final] ).

cnf(i_0_16919,plain,
    ( c_Relation_Osingle__valued(X3,X2,X1)
    | esk336_3(X1,X2,X3) != esk337_3(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_7013]),
    [final] ).

cnf(i_0_16920,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_10165]),
    [final] ).

cnf(i_0_16921,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_10166]),
    [final] ).

cnf(i_0_16922,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_10167]),
    [final] ).

cnf(i_0_16923,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_10168]),
    [final] ).

cnf(i_0_16924,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_9238]),
    [final] ).

cnf(i_0_16925,plain,
    ( c_Wellfounded_OwfP(X1,X2)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),esk298_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10169]),
    [final] ).

cnf(i_0_16926,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_10170]),
    [final] ).

cnf(i_0_16927,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_10171,c_0_6187]),
    [final] ).

cnf(i_0_16928,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_9586]),
    [final] ).

cnf(i_0_16929,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_10172]),
    [final] ).

cnf(i_0_16930,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_10173]),
    [final] ).

cnf(i_0_16931,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_9913]),
    [final] ).

cnf(i_0_16932,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_10174]),
    [final] ).

cnf(i_0_16933,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_10175]),
    [final] ).

cnf(i_0_16934,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_10176]),
    [final] ).

cnf(i_0_16935,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_10177]),
    [final] ).

cnf(i_0_16936,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_10178]),
    [final] ).

cnf(i_0_16937,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_10179]),
    [final] ).

cnf(i_0_16938,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_10180]),
    [final] ).

cnf(i_0_16939,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X3))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X3),X2))
    | X2 = X3
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9688]),
    [final] ).

cnf(i_0_16940,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_10181]),
    [final] ).

cnf(i_0_16941,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_10182]),
    [final] ).

cnf(i_0_16942,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_10183]),
    [final] ).

cnf(i_0_16943,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_10184]),
    [final] ).

cnf(i_0_16944,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_10185]),
    [final] ).

cnf(i_0_16945,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_10186]),
    [final] ).

cnf(i_0_16946,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_10187]),
    [final] ).

cnf(i_0_16947,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_10188]),
    [final] ).

cnf(i_0_16948,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_10189,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_16949,plain,
    ( X2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),esk18_2(X2,X1))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10190]),
    [final] ).

cnf(i_0_16950,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_10191]),
    [final] ).

cnf(i_0_16951,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),esk65_2(X1,X2))
    | hBOOL(hAPP(X2,hAPP(c_Int_Onat,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9796]),
    [final] ).

cnf(i_0_16952,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_10192]),
    [final] ).

cnf(i_0_16953,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_9942]),
    [final] ).

cnf(i_0_16954,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_10193]),
    [final] ).

cnf(i_0_16955,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_10194]),
    [final] ).

cnf(i_0_16956,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_9691]),
    [final] ).

cnf(i_0_16957,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_10195]),
    [final] ).

cnf(i_0_16958,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_9690]),
    [final] ).

cnf(i_0_16959,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_10196]),
    [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__eq(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10197]),
    [final] ).

cnf(i_0_16961,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_10198,c_0_6187]),
    [final] ).

cnf(i_0_16962,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_10199,c_0_6187]),
    [final] ).

cnf(i_0_16963,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_9699]),
    [final] ).

cnf(i_0_16964,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_10200]),
    [final] ).

cnf(i_0_16965,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_10201]),
    [final] ).

cnf(i_0_16966,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_10202]),
    [final] ).

cnf(i_0_16967,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_10203]),
    [final] ).

cnf(i_0_16968,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_10204,c_0_6071]),c_0_6219]),
    [final] ).

cnf(i_0_16969,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_9939]),
    [final] ).

cnf(i_0_16970,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_9994]),
    [final] ).

cnf(i_0_16971,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_9995]),
    [final] ).

cnf(i_0_16972,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_10205]),
    [final] ).

cnf(i_0_16973,plain,
    ( c_Relation_Osym(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10206]),
    [final] ).

cnf(i_0_16974,plain,
    ( c_Relation_Otrans(X3,hAPP(hAPP(c_Relation_Oinv__image(X1,X3),X2),X4))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10207]),
    [final] ).

cnf(i_0_16975,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_10208]),
    [final] ).

cnf(i_0_16976,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_10209]),
    [final] ).

cnf(i_0_16977,plain,
    ( X2 = c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10210]),
    [final] ).

cnf(i_0_16978,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_10211]),
    [final] ).

cnf(i_0_16979,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_10212]),
    [final] ).

cnf(i_0_16980,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_10213]),
    [final] ).

cnf(i_0_16981,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_10214]),
    [final] ).

cnf(i_0_16982,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_10215]),
    [final] ).

cnf(i_0_16983,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_10216]),
    [final] ).

cnf(i_0_16984,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_10217]),
    [final] ).

cnf(i_0_16985,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_10218]),
    [final] ).

cnf(i_0_16986,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_10219]),
    [final] ).

cnf(i_0_16987,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_10220]),
    [final] ).

cnf(i_0_16988,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_10221]),
    [final] ).

cnf(i_0_16989,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_10222]),
    [final] ).

cnf(i_0_16990,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_10223,c_0_6071]),
    [final] ).

cnf(i_0_16991,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_8260]),
    [final] ).

cnf(i_0_16992,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_10224]),
    [final] ).

cnf(i_0_16993,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_10225]),
    [final] ).

cnf(i_0_16994,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_10226]),
    [final] ).

cnf(i_0_16995,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_10227]),
    [final] ).

cnf(i_0_16996,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_10228]),
    [final] ).

cnf(i_0_16997,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_10229]),
    [final] ).

cnf(i_0_16998,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_10230]),
    [final] ).

cnf(i_0_16999,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_10231]),
    [final] ).

cnf(i_0_17000,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_10232]),
    [final] ).

cnf(i_0_17001,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_10233]),
    [final] ).

cnf(i_0_17002,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_10234]),
    [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_10235]),
    [final] ).

cnf(i_0_17004,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_10236]),
    [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_10237]),
    [final] ).

cnf(i_0_17006,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_10238]),
    [final] ).

cnf(i_0_17007,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk54_1(X1)))
    | hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9556]),
    [final] ).

cnf(i_0_17008,plain,
    c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X1),X2,X3)) = c_Lazy__Sequence_Oappend(X1,X2,c_Lazy__Sequence_Oflat(X1,X3)),
    inference(split_conjunct,[status(thm)],[i_0_10239]),
    [final] ).

cnf(i_0_17009,plain,
    ( X2 = esk453_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_10240]),
    [final] ).

cnf(i_0_17010,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_9756]),
    [final] ).

cnf(i_0_17011,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_10241]),
    [final] ).

cnf(i_0_17012,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_10242]),
    [final] ).

cnf(i_0_17013,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_10243]),
    [final] ).

cnf(i_0_17014,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_10244]),
    [final] ).

cnf(i_0_17015,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_9510]),
    [final] ).

cnf(i_0_17016,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_10089]),
    [final] ).

cnf(i_0_17017,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_10245]),
    [final] ).

cnf(i_0_17018,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_10088]),
    [final] ).

cnf(i_0_17019,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_10246]),
    [final] ).

cnf(i_0_17020,plain,
    ( hBOOL(hAPP(c_Quotient_ORespects(X3,X1),X2))
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10247]),
    [final] ).

cnf(i_0_17021,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ hBOOL(hAPP(c_Quotient_ORespects(X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10247]),
    [final] ).

cnf(i_0_17022,plain,
    ( hBOOL(hAPP(X1,esk315_2(X2,X1)))
    | ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_10248]),
    [final] ).

cnf(i_0_17023,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_10249]),
    [final] ).

cnf(i_0_17024,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_10250]),
    [final] ).

cnf(i_0_17025,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk529_1(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(split_conjunct,[status(thm)],[i_0_10251]),
    [final] ).

cnf(i_0_17026,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10252]),
    [final] ).

cnf(i_0_17027,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_10253]),
    [final] ).

cnf(i_0_17028,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_10254]),
    [final] ).

cnf(i_0_17029,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_10255]),
    [final] ).

cnf(i_0_17030,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_10256]),
    [final] ).

cnf(i_0_17031,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_6820]),
    [final] ).

cnf(i_0_17032,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_6820]),
    [final] ).

cnf(i_0_17033,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_10257]),
    [final] ).

cnf(i_0_17034,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_10258]),
    [final] ).

cnf(i_0_17035,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_10259]),
    [final] ).

cnf(i_0_17036,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_10260]),
    [final] ).

cnf(i_0_17037,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_10261]),
    [final] ).

cnf(i_0_17038,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_10262]),
    [final] ).

cnf(i_0_17039,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_10263]),
    [final] ).

cnf(i_0_17040,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_10264]),
    [final] ).

cnf(i_0_17041,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_10265]),
    [final] ).

cnf(i_0_17042,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_10255]),
    [final] ).

cnf(i_0_17043,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_10256]),
    [final] ).

cnf(i_0_17044,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_10266]),
    [final] ).

cnf(i_0_17045,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_10267]),
    [final] ).

cnf(i_0_17046,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_10268]),
    [final] ).

cnf(i_0_17047,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_10269]),
    [final] ).

cnf(i_0_17048,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_10270]),
    [final] ).

cnf(i_0_17049,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_10271]),
    [final] ).

cnf(i_0_17050,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_10272]),
    [final] ).

cnf(i_0_17051,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_10273,c_0_6187]),
    [final] ).

cnf(i_0_17052,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_10274]),
    [final] ).

cnf(i_0_17053,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_10275,c_0_6069]),c_0_6070]),c_0_6071]),
    [final] ).

cnf(i_0_17054,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | c_Divides_Odiv__class_Omod(X1,X2,X3) != c_Groups_Ozero__class_Ozero(X1)
    | ~ class_Divides_Osemiring__div(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10123]),
    [final] ).

cnf(i_0_17055,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_10276]),
    [final] ).

cnf(i_0_17056,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_10277]),
    [final] ).

cnf(i_0_17057,plain,
    ~ hBOOL(hAPP(hAPP(c_List_Oset(X1),c_List_Olist_ONil(X1)),X2)),
    inference(rw,[status(thm)],[i_0_10278,c_0_8354]),
    [final] ).

cnf(i_0_17058,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_10279]),
    [final] ).

cnf(i_0_17059,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_10109]),
    [final] ).

cnf(i_0_17060,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_10280]),
    [final] ).

cnf(i_0_17061,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_7878]),
    [final] ).

cnf(i_0_17062,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_7878]),
    [final] ).

cnf(i_0_17063,plain,
    ( c_List_Olinorder__class_Osorted(X1,X2)
    | ~ c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8613]),
    [final] ).

cnf(i_0_17064,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_8614]),
    [final] ).

cnf(i_0_17065,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_9718]),
    [final] ).

cnf(i_0_17066,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_10281,c_0_7117]),
    [final] ).

cnf(i_0_17067,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_17068,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_10282]),
    [final] ).

cnf(i_0_17069,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_10283]),
    [final] ).

cnf(i_0_17070,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),esk390_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_9906]),
    [final] ).

cnf(i_0_17071,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_10284]),
    [final] ).

cnf(i_0_17072,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_10285]),
    [final] ).

cnf(i_0_17073,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_9881]),
    [final] ).

cnf(i_0_17074,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_10286]),
    [final] ).

cnf(i_0_17075,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_10287]),
    [final] ).

cnf(i_0_17076,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_9965]),
    [final] ).

cnf(i_0_17077,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_9966]),
    [final] ).

cnf(i_0_17078,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_10288]),
    [final] ).

cnf(i_0_17079,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_10289]),
    [final] ).

cnf(i_0_17080,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_10290]),
    [final] ).

cnf(i_0_17081,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_10291]),
    [final] ).

cnf(i_0_17082,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_10292]),
    [final] ).

cnf(i_0_17083,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_10293]),
    [final] ).

cnf(i_0_17084,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_10294]),
    [final] ).

cnf(i_0_17085,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_10295]),
    [final] ).

cnf(i_0_17086,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_10296]),
    [final] ).

cnf(i_0_17087,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_10297]),
    [final] ).

cnf(i_0_17088,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_10298]),
    [final] ).

cnf(i_0_17089,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_10299]),
    [final] ).

cnf(i_0_17090,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_10300]),
    [final] ).

cnf(i_0_17091,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_10301]),
    [final] ).

cnf(i_0_17092,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_10302]),
    [final] ).

cnf(i_0_17093,plain,
    ( hAPP(hAPP(c_List_Onth(X1),X2),esk394_2(X2,X1)) = hAPP(hAPP(c_List_Onth(X1),X2),esk395_2(X2,X1))
    | hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8346]),
    [final] ).

cnf(i_0_17094,plain,
    ( hBOOL(hAPP(X3,X2))
    | ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_10303]),
    [final] ).

cnf(i_0_17095,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X3))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X3) != X2
    | ~ class_Lattices_Osemilattice__inf(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10140]),
    [final] ).

cnf(i_0_17096,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_10142]),
    [final] ).

cnf(i_0_17097,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_10145]),
    [final] ).

cnf(i_0_17098,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_10149]),
    [final] ).

cnf(i_0_17099,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X2))
    | ~ class_Rings_Odvd(X1)
    | X2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X4) ),
    inference(split_conjunct,[status(thm)],[i_0_10304]),
    [final] ).

cnf(i_0_17100,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_10305,c_0_7117]),
    [final] ).

cnf(i_0_17101,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_10306]),
    [final] ).

cnf(i_0_17102,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_10307]),
    [final] ).

cnf(i_0_17103,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_10308]),
    [final] ).

cnf(i_0_17104,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_6865]),
    [final] ).

cnf(i_0_17105,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_6866]),
    [final] ).

cnf(i_0_17106,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_10309]),
    [final] ).

cnf(i_0_17107,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_10310]),
    [final] ).

cnf(i_0_17108,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_10311]),
    [final] ).

cnf(i_0_17109,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_10312]),
    [final] ).

cnf(i_0_17110,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_10313]),
    [final] ).

cnf(i_0_17111,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_10314]),
    [final] ).

cnf(i_0_17112,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_9828]),
    [final] ).

cnf(i_0_17113,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_9829]),
    [final] ).

cnf(i_0_17114,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_9830]),
    [final] ).

cnf(i_0_17115,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_9831]),
    [final] ).

cnf(i_0_17116,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_9396]),
    [final] ).

cnf(i_0_17117,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_10315]),
    [final] ).

cnf(i_0_17118,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_10316]),
    [final] ).

cnf(i_0_17119,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_10317]),
    [final] ).

cnf(i_0_17120,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_10318]),
    [final] ).

cnf(i_0_17121,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_10319]),
    [final] ).

cnf(i_0_17122,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_10320]),
    [final] ).

cnf(i_0_17123,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_10321]),
    [final] ).

cnf(i_0_17124,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_10322]),
    [final] ).

cnf(i_0_17125,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_10323]),
    [final] ).

cnf(i_0_17126,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_10324]),
    [final] ).

cnf(i_0_17127,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_10007]),
    [final] ).

cnf(i_0_17128,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_10008]),
    [final] ).

cnf(i_0_17129,plain,
    ( X1 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk140_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_9895]),
    [final] ).

cnf(i_0_17130,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)),esk74_1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9998]),
    [final] ).

cnf(i_0_17131,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_10325]),
    [final] ).

cnf(i_0_17132,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_10326]),
    [final] ).

cnf(i_0_17133,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_10327]),
    [final] ).

cnf(i_0_17134,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_9618]),
    [final] ).

cnf(i_0_17135,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_10328]),
    [final] ).

cnf(i_0_17136,plain,
    ( hBOOL(hAPP(X1,esk53_1(X1)))
    | ~ hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
    inference(split_conjunct,[status(thm)],[i_0_9710]),
    [final] ).

cnf(i_0_17137,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_5974]),
    [final] ).

cnf(i_0_17138,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_17139,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_10329,c_0_7117]),
    [final] ).

cnf(i_0_17140,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_10330]),
    [final] ).

cnf(i_0_17141,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_10331]),
    [final] ).

cnf(i_0_17142,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_10118]),
    [final] ).

cnf(i_0_17143,plain,
    ( c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Predicate_Osymp(X3,X1)
    | ~ c_Predicate_Otransp(X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10332]),
    [final] ).

cnf(i_0_17144,plain,
    ( c_Equiv__Relations_Opart__equivp(X3,X1)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X2))
    | ~ c_Predicate_Osymp(X3,X1)
    | ~ c_Predicate_Otransp(X3,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10006]),
    [final] ).

cnf(i_0_17145,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_10333]),
    [final] ).

cnf(i_0_17146,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_10334]),
    [final] ).

cnf(i_0_17147,plain,
    ( hBOOL(hAPP(X1,X2))
    | ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk61_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[i_0_9808]),
    [final] ).

cnf(i_0_17148,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_10335]),
    [final] ).

cnf(i_0_17149,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_10336]),
    [final] ).

cnf(i_0_17150,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_10337]),
    [final] ).

cnf(i_0_17151,plain,
    ( X1 = hAPP(c_Nat_OSuc,esk25_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_10338]),
    [final] ).

cnf(i_0_17152,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_10339]),
    [final] ).

cnf(i_0_17153,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_10340]),
    [final] ).

cnf(i_0_17154,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_10341]),
    [final] ).

cnf(i_0_17155,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_10342]),
    [final] ).

cnf(i_0_17156,plain,
    ( c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Osym(X1,X3)
    | ~ c_Relation_Otrans(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10343]),
    [final] ).

cnf(i_0_17157,plain,
    ( c_Equiv__Relations_Oequiv(X1,X2,X3)
    | ~ c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Relation_Osym(X1,X3)
    | ~ c_Relation_Otrans(X1,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10344]),
    [final] ).

cnf(i_0_17158,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_10135]),
    [final] ).

cnf(i_0_17159,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_10345]),
    [final] ).

cnf(i_0_17160,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_10136]),
    [final] ).

cnf(i_0_17161,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_10346]),
    [final] ).

cnf(i_0_17162,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_10347]),
    [final] ).

cnf(i_0_17163,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_10321]),
    [final] ).

cnf(i_0_17164,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_10322]),
    [final] ).

cnf(i_0_17165,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_10348]),
    [final] ).

cnf(i_0_17166,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_10349]),
    [final] ).

cnf(i_0_17167,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_10096]),
    [final] ).

cnf(i_0_17168,plain,
    ( v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X1)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X1),v_U)) ),
    inference(split_conjunct,[status(thm)],[i_0_10350]),
    [final] ).

cnf(i_0_17169,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_10351]),
    [final] ).

cnf(i_0_17170,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_10352]),
    [final] ).

cnf(i_0_17171,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_10353]),
    [final] ).

cnf(i_0_17172,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_10354]),
    [final] ).

cnf(i_0_17173,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_10355,c_0_6187]),
    [final] ).

cnf(i_0_17174,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_10053]),
    [final] ).

cnf(i_0_17175,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_17176,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_10356]),
    [final] ).

cnf(i_0_17177,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_9408]),
    [final] ).

cnf(i_0_17178,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_10357]),
    [final] ).

cnf(i_0_17179,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_9934]),
    [final] ).

cnf(i_0_17180,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_9935]),
    [final] ).

cnf(i_0_17181,plain,
    ( hAPP(X1,X2) = hAPP(X1,X3)
    | ~ hBOOL(hAPP(hAPP(X1,X2),X3))
    | ~ c_Equiv__Relations_Opart__equivp(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_17182,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_9988]),
    [final] ).

cnf(i_0_17183,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_10358]),
    [final] ).

cnf(i_0_17184,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_10359]),
    [final] ).

cnf(i_0_17185,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_10360]),
    [final] ).

cnf(i_0_17186,plain,
    ( hAPP(c_Finite__Set_Ocard(X1),esk36_3(X2,X3,X1)) = X2
    | hAPP(c_Finite__Set_Ocard(X1),X3) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7995]),
    [final] ).

cnf(i_0_17187,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_10361]),
    [final] ).

cnf(i_0_17188,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))
    | ~ hBOOL(hAPP(X1,esk463_2(X1,X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10362]),
    [final] ).

cnf(i_0_17189,plain,
    ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X2),X1))
    | ~ hBOOL(hAPP(X1,esk462_2(X1,X2)))
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10363]),
    [final] ).

cnf(i_0_17190,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_10293]),
    [final] ).

cnf(i_0_17191,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_10294]),
    [final] ).

cnf(i_0_17192,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_10364]),
    [final] ).

cnf(i_0_17193,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_10365,c_0_6187]),
    [final] ).

cnf(i_0_17194,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_9796]),
    [final] ).

cnf(i_0_17195,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | X1 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(split_conjunct,[status(thm)],[i_0_10026]),
    [final] ).

cnf(i_0_17196,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_9912]),
    [final] ).

cnf(i_0_17197,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_9688]),
    [final] ).

cnf(i_0_17198,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_10366]),
    [final] ).

cnf(i_0_17199,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_10367]),
    [final] ).

cnf(i_0_17200,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_10368]),
    [final] ).

cnf(i_0_17201,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_10175]),
    [final] ).

cnf(i_0_17202,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_10175]),
    [final] ).

cnf(i_0_17203,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_9743]),
    [final] ).

cnf(i_0_17204,plain,
    ( X2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),esk65_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_9796]),
    [final] ).

cnf(i_0_17205,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_17206,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_10369,c_0_7317]),
    [final] ).

cnf(i_0_17207,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ class_Rings_Olinordered__idom(X1)
    | hAPP(c_Groups_Oabs__class_Oabs(X1),X2) != hAPP(c_Groups_Oabs__class_Oabs(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10370]),
    [final] ).

cnf(i_0_17208,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_10371]),
    [final] ).

cnf(i_0_17209,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_10372]),
    [final] ).

cnf(i_0_17210,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_10372]),
    [final] ).

cnf(i_0_17211,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_10373]),
    [final] ).

cnf(i_0_17212,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_6166]),
    [final] ).

cnf(i_0_17213,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_6167]),
    [final] ).

cnf(i_0_17214,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_9879]),
    [final] ).

cnf(i_0_17215,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_10374]),
    [final] ).

cnf(i_0_17216,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_9534]),
    [final] ).

cnf(i_0_17217,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_10375]),
    [final] ).

cnf(i_0_17218,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10376]),
    [final] ).

cnf(i_0_17219,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_9299]),
    [final] ).

cnf(i_0_17220,plain,
    ( hBOOL(hAPP(hAPP(X1,esk239_1(X1)),esk240_1(X1)))
    | hAPP(X1,esk239_1(X1)) = hAPP(X1,esk240_1(X1))
    | c_Equiv__Relations_Oequivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9988]),
    [final] ).

cnf(i_0_17221,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_10377]),
    [final] ).

cnf(i_0_17222,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_10378]),
    [final] ).

cnf(i_0_17223,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_10379]),
    [final] ).

cnf(i_0_17224,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_10380]),
    [final] ).

cnf(i_0_17225,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_10381]),
    [final] ).

cnf(i_0_17226,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_10382]),
    [final] ).

cnf(i_0_17227,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_10383]),
    [final] ).

cnf(i_0_17228,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_10384]),
    [final] ).

cnf(i_0_17229,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_10384]),
    [final] ).

cnf(i_0_17230,plain,
    ( X1 = X2
    | c_List_Oreplicate(X3,X1,X4) != c_List_Oreplicate(X3,X2,X5) ),
    inference(split_conjunct,[status(thm)],[i_0_10371]),
    [final] ).

cnf(i_0_17231,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_10385]),
    [final] ).

cnf(i_0_17232,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_10386]),
    [final] ).

cnf(i_0_17233,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_10013]),
    [final] ).

cnf(i_0_17234,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_10387]),
    [final] ).

cnf(i_0_17235,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_9983]),
    [final] ).

cnf(i_0_17236,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_7087]),
    [final] ).

cnf(i_0_17237,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_10351]),
    [final] ).

cnf(i_0_17238,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_10352]),
    [final] ).

cnf(i_0_17239,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_10388]),
    [final] ).

cnf(i_0_17240,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_10308]),
    [final] ).

cnf(i_0_17241,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_10268]),
    [final] ).

cnf(i_0_17242,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_9465]),
    [final] ).

cnf(i_0_17243,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_10389]),
    [final] ).

cnf(i_0_17244,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_10390]),
    [final] ).

cnf(i_0_17245,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_10391]),
    [final] ).

cnf(i_0_17246,hypothesis,
    hBOOL(hAPP(hAPP(c_member(t_a),hAPP(v_mgt__call,v_pn)),v_G)),
    inference(split_conjunct,[status(thm)],[conj_6]),
    [final] ).

cnf(i_0_17247,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_10392]),
    [final] ).

cnf(i_0_17248,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_6463]),
    [final] ).

cnf(i_0_17249,plain,
    c_Relation_Oantisym(X1,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X1,X1),tc_HOL_Obool))),
    inference(split_conjunct,[status(thm)],[i_0_10393]),
    [final] ).

cnf(i_0_17250,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_10394]),
    [final] ).

cnf(i_0_17251,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_10395]),
    [final] ).

cnf(i_0_17252,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_10172]),
    [final] ).

cnf(i_0_17253,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_10173]),
    [final] ).

cnf(i_0_17254,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),esk453_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10240]),
    [final] ).

cnf(i_0_17255,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_10396]),
    [final] ).

cnf(i_0_17256,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_10190]),
    [final] ).

cnf(i_0_17257,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_10397]),
    [final] ).

cnf(i_0_17258,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_10398]),
    [final] ).

cnf(i_0_17259,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_10130]),
    [final] ).

cnf(i_0_17260,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_10399]),
    [final] ).

cnf(i_0_17261,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_10400]),
    [final] ).

cnf(i_0_17262,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk58_1(X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9728]),
    [final] ).

cnf(i_0_17263,plain,
    ( X1 = hAPP(hAPP(c_List_Olist_OCons(X2),esk443_2(X1,X2)),esk442_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_7362]),
    [final] ).

cnf(i_0_17264,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_10401]),
    [final] ).

cnf(i_0_17265,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_10401]),
    [final] ).

cnf(i_0_17266,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_10402]),
    [final] ).

cnf(i_0_17267,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_10403]),
    [final] ).

cnf(i_0_17268,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_10404]),
    [final] ).

cnf(i_0_17269,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_10361]),
    [final] ).

cnf(i_0_17270,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_9481]),
    [final] ).

cnf(i_0_17271,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_10405]),
    [final] ).

cnf(i_0_17272,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_9299]),
    [final] ).

cnf(i_0_17273,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_10406]),
    [final] ).

cnf(i_0_17274,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_17275,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_8734]),
    [final] ).

cnf(i_0_17276,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_10407]),
    [final] ).

cnf(i_0_17277,plain,
    ( c_Quickcheck_Obeyond(X1,X2) = X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10408]),
    [final] ).

cnf(i_0_17278,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_10409]),
    [final] ).

cnf(i_0_17279,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_10410]),
    [final] ).

cnf(i_0_17280,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_10411]),
    [final] ).

cnf(i_0_17281,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_10412,c_0_6726]),
    [final] ).

cnf(i_0_17282,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_10413]),
    [final] ).

cnf(i_0_17283,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_10414]),
    [final] ).

cnf(i_0_17284,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_10415]),
    [final] ).

cnf(i_0_17285,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_10416]),
    [final] ).

cnf(i_0_17286,plain,
    c_Predicate_Oconversep(X1,X2,c_Predicate_Oconversep(X2,X1,X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10417]),
    [final] ).

cnf(i_0_17287,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_10418]),
    [final] ).

cnf(i_0_17288,plain,
    ( X1 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(split_conjunct,[status(thm)],[i_0_10419]),
    [final] ).

cnf(i_0_17289,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_9738]),
    [final] ).

cnf(i_0_17290,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
    | ~ hBOOL(hAPP(X1,esk54_1(X1))) ),
    inference(split_conjunct,[status(thm)],[i_0_9556]),
    [final] ).

cnf(i_0_17291,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_10420]),
    [final] ).

cnf(i_0_17292,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_9770]),
    [final] ).

cnf(i_0_17293,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_9735]),
    [final] ).

cnf(i_0_17294,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_9736]),
    [final] ).

cnf(i_0_17295,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_10421]),
    [final] ).

cnf(i_0_17296,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_10422]),
    [final] ).

cnf(i_0_17297,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_10423]),
    [final] ).

cnf(i_0_17298,plain,
    ( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),esk62_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_10424]),
    [final] ).

cnf(i_0_17299,plain,
    ( X1 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk71_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_10425]),
    [final] ).

cnf(i_0_17300,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_10426]),
    [final] ).

cnf(i_0_17301,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_10110]),
    [final] ).

cnf(i_0_17302,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10427]),
    [final] ).

cnf(i_0_17303,plain,
    ( c_Relation_Oantisym(X1,X2)
    | ~ c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10428]),
    [final] ).

cnf(i_0_17304,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10429]),
    [final] ).

cnf(i_0_17305,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10430]),
    [final] ).

cnf(i_0_17306,plain,
    ( X2 = esk493_3(X3,X4,X1)
    | c_FunDef_OTHE__default(X4,X3,X1) = X3
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_8076]),
    [final] ).

cnf(i_0_17307,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_10078]),
    [final] ).

cnf(i_0_17308,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_10431]),
    [final] ).

cnf(i_0_17309,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_10432]),
    [final] ).

cnf(i_0_17310,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_10433]),
    [final] ).

cnf(i_0_17311,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_10434]),
    [final] ).

cnf(i_0_17312,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_10435]),
    [final] ).

cnf(i_0_17313,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_10314]),
    [final] ).

cnf(i_0_17314,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_10436]),
    [final] ).

cnf(i_0_17315,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_10437]),
    [final] ).

cnf(i_0_17316,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_10438]),
    [final] ).

cnf(i_0_17317,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_10439]),
    [final] ).

cnf(i_0_17318,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_10440]),
    [final] ).

cnf(i_0_17319,plain,
    ( hBOOL(hAPP(X2,esk450_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10441]),
    [final] ).

cnf(i_0_17320,plain,
    ( hBOOL(hAPP(X2,esk449_2(X2,X1)))
    | ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X2))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10442]),
    [final] ).

cnf(i_0_17321,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_10443]),
    [final] ).

cnf(i_0_17322,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_10444]),
    [final] ).

cnf(i_0_17323,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_10445]),
    [final] ).

cnf(i_0_17324,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X1),hAPP(c_fequal,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10084]),
    [final] ).

cnf(i_0_17325,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_10446]),
    [final] ).

cnf(i_0_17326,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_10447]),
    [final] ).

cnf(i_0_17327,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_10448]),
    [final] ).

cnf(i_0_17328,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_10449]),
    [final] ).

cnf(i_0_17329,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_10450]),
    [final] ).

cnf(i_0_17330,plain,
    ( hBOOL(hAPP(hAPP(c_member(X3),X2),X1))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10303]),
    [final] ).

cnf(i_0_17331,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_10451]),
    [final] ).

cnf(i_0_17332,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_10452]),
    [final] ).

cnf(i_0_17333,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_10453]),
    [final] ).

cnf(i_0_17334,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_10454]),
    [final] ).

cnf(i_0_17335,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_10455]),
    [final] ).

cnf(i_0_17336,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_9965]),
    [final] ).

cnf(i_0_17337,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_9966]),
    [final] ).

cnf(i_0_17338,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_10456]),
    [final] ).

cnf(i_0_17339,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10063]),
    [final] ).

cnf(i_0_17340,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10066]),
    [final] ).

cnf(i_0_17341,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10457]),
    [final] ).

cnf(i_0_17342,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10458]),
    [final] ).

cnf(i_0_17343,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10327]),
    [final] ).

cnf(i_0_17344,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_10327]),
    [final] ).

cnf(i_0_17345,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_10459,c_0_7117]),
    [final] ).

cnf(i_0_17346,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_10460]),
    [final] ).

cnf(i_0_17347,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_10461,c_0_7117]),
    [final] ).

cnf(i_0_17348,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_10462]),
    [final] ).

cnf(i_0_17349,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_10463]),
    [final] ).

cnf(i_0_17350,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_10464]),
    [final] ).

cnf(i_0_17351,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_10465]),
    [final] ).

cnf(i_0_17352,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_10466]),
    [final] ).

cnf(i_0_17353,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_10467]),
    [final] ).

cnf(i_0_17354,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_10468]),
    [final] ).

cnf(i_0_17355,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_10469]),
    [final] ).

cnf(i_0_17356,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_10470]),
    [final] ).

cnf(i_0_17357,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_10471]),
    [final] ).

cnf(i_0_17358,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_10472]),
    [final] ).

cnf(i_0_17359,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_10473]),
    [final] ).

cnf(i_0_17360,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_10474]),
    [final] ).

cnf(i_0_17361,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_10453]),
    [final] ).

cnf(i_0_17362,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_10454]),
    [final] ).

cnf(i_0_17363,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_10475]),
    [final] ).

cnf(i_0_17364,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_10476]),
    [final] ).

cnf(i_0_17365,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_10477]),
    [final] ).

cnf(i_0_17366,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_10454]),
    [final] ).

cnf(i_0_17367,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_10453]),
    [final] ).

cnf(i_0_17368,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_10478]),
    [final] ).

cnf(i_0_17369,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_10477]),
    [final] ).

cnf(i_0_17370,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_10476]),
    [final] ).

cnf(i_0_17371,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_10479]),
    [final] ).

cnf(i_0_17372,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_10480]),
    [final] ).

cnf(i_0_17373,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_10481]),
    [final] ).

cnf(i_0_17374,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_10482]),
    [final] ).

cnf(i_0_17375,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_10483]),
    [final] ).

cnf(i_0_17376,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_10484]),
    [final] ).

cnf(i_0_17377,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_9988]),
    [final] ).

cnf(i_0_17378,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_10260]),
    [final] ).

cnf(i_0_17379,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),esk61_1(X1)))
    | hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9808]),
    [final] ).

cnf(i_0_17380,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_10485]),
    [final] ).

cnf(i_0_17381,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10486]),
    [final] ).

cnf(i_0_17382,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10487]),
    [final] ).

cnf(i_0_17383,plain,
    ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,esk58_1(X1))))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_9728]),
    [final] ).

cnf(i_0_17384,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_10467]),
    [final] ).

cnf(i_0_17385,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_10488]),
    [final] ).

cnf(i_0_17386,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_10114]),
    [final] ).

cnf(i_0_17387,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_10489,c_0_6070]),c_0_6070]),
    [final] ).

cnf(i_0_17388,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_10490]),
    [final] ).

cnf(i_0_17389,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_10491]),
    [final] ).

cnf(i_0_17390,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_10492]),
    [final] ).

cnf(i_0_17391,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_10493]),
    [final] ).

cnf(i_0_17392,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_10494]),
    [final] ).

cnf(i_0_17393,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_10495]),
    [final] ).

cnf(i_0_17394,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_10496]),
    [final] ).

cnf(i_0_17395,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_9438]),
    [final] ).

cnf(i_0_17396,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_10497]),
    [final] ).

cnf(i_0_17397,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_8649]),
    [final] ).

cnf(i_0_17398,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_10498]),
    [final] ).

cnf(i_0_17399,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_10499]),
    [final] ).

cnf(i_0_17400,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_8651]),
    [final] ).

cnf(i_0_17401,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_10500]),
    [final] ).

cnf(i_0_17402,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_10501]),
    [final] ).

cnf(i_0_17403,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_10316]),
    [final] ).

cnf(i_0_17404,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_10502]),
    [final] ).

cnf(i_0_17405,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_10503]),
    [final] ).

cnf(i_0_17406,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_10504]),
    [final] ).

cnf(i_0_17407,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_10505]),
    [final] ).

cnf(i_0_17408,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_10506]),
    [final] ).

cnf(i_0_17409,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_10507]),
    [final] ).

cnf(i_0_17410,plain,
    ( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10508]),
    [final] ).

cnf(i_0_17411,plain,
    ( c_Wellfounded_Owf(X1,c_Wellfounded_Omlex__prod(X1,X3,X2))
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10509]),
    [final] ).

cnf(i_0_17412,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_9775]),
    [final] ).

cnf(i_0_17413,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_10510]),
    [final] ).

cnf(i_0_17414,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_10347]),
    [final] ).

cnf(i_0_17415,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_10342]),
    [final] ).

cnf(i_0_17416,plain,
    ( hBOOL(hAPP(hAPP(X1,esk516_1(X1)),esk516_1(X1)))
    | ~ c_Equiv__Relations_Opart__equivp(X2,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_8595]),
    [final] ).

cnf(i_0_17417,plain,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10343]),
    [final] ).

cnf(i_0_17418,plain,
    ( c_Relation_Orefl__on(X1,X2,X3)
    | ~ c_Equiv__Relations_Oequiv(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10511]),
    [final] ).

cnf(i_0_17419,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_10512]),
    [final] ).

cnf(i_0_17420,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_10513]),
    [final] ).

cnf(i_0_17421,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_10514]),
    [final] ).

cnf(i_0_17422,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_10515]),
    [final] ).

cnf(i_0_17423,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_10516]),
    [final] ).

cnf(i_0_17424,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_10517]),
    [final] ).

cnf(i_0_17425,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_10518]),
    [final] ).

cnf(i_0_17426,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_10519]),
    [final] ).

cnf(i_0_17427,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_10520]),
    [final] ).

cnf(i_0_17428,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_10521]),
    [final] ).

cnf(i_0_17429,plain,
    ( esk36_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_7995]),
    [final] ).

cnf(i_0_17430,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_10522]),
    [final] ).

cnf(i_0_17431,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_10523]),
    [final] ).

cnf(i_0_17432,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_10295]),
    [final] ).

cnf(i_0_17433,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_10524]),
    [final] ).

cnf(i_0_17434,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_10525]),
    [final] ).

cnf(i_0_17435,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X2))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10526]),
    [final] ).

cnf(i_0_17436,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_10527]),
    [final] ).

cnf(i_0_17437,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_10528]),
    [final] ).

cnf(i_0_17438,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_10529]),
    [final] ).

cnf(i_0_17439,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_10530]),
    [final] ).

cnf(i_0_17440,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_10531]),
    [final] ).

cnf(i_0_17441,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_10523]),
    [final] ).

cnf(i_0_17442,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_10532]),
    [final] ).

cnf(i_0_17443,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_10533]),
    [final] ).

cnf(i_0_17444,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_10534]),
    [final] ).

cnf(i_0_17445,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_10535]),
    [final] ).

cnf(i_0_17446,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_10265]),
    [final] ).

cnf(i_0_17447,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_10536]),
    [final] ).

cnf(i_0_17448,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_10537]),
    [final] ).

cnf(i_0_17449,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_10538]),
    [final] ).

cnf(i_0_17450,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_10539]),
    [final] ).

cnf(i_0_17451,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_10540]),
    [final] ).

cnf(i_0_17452,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_10541]),
    [final] ).

cnf(i_0_17453,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_10250]),
    [final] ).

cnf(i_0_17454,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_10542]),
    [final] ).

cnf(i_0_17455,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
    inference(split_conjunct,[status(thm)],[i_0_10543]),
    [final] ).

cnf(i_0_17456,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10544]),
    [final] ).

cnf(i_0_17457,plain,
    hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10545]),
    [final] ).

cnf(i_0_17458,plain,
    hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10546]),
    [final] ).

cnf(i_0_17459,plain,
    hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10547]),
    [final] ).

cnf(i_0_17460,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_9735]),
    [final] ).

cnf(i_0_17461,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_9736]),
    [final] ).

cnf(i_0_17462,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_10548]),
    [final] ).

cnf(i_0_17463,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_10255]),
    [final] ).

cnf(i_0_17464,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_10256]),
    [final] ).

cnf(i_0_17465,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_10549]),
    [final] ).

cnf(i_0_17466,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_10550,c_0_8300]),
    [final] ).

cnf(i_0_17467,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_10551,c_0_8300]),
    [final] ).

cnf(i_0_17468,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10552]),
    [final] ).

cnf(i_0_17469,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_10553]),
    [final] ).

cnf(i_0_17470,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_10554]),
    [final] ).

cnf(i_0_17471,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_10555]),
    [final] ).

cnf(i_0_17472,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_10556]),
    [final] ).

cnf(i_0_17473,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_10557]),
    [final] ).

cnf(i_0_17474,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_10558]),
    [final] ).

cnf(i_0_17475,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_10559]),
    [final] ).

cnf(i_0_17476,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_10560]),
    [final] ).

cnf(i_0_17477,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_10561]),
    [final] ).

cnf(i_0_17478,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_10562]),
    [final] ).

cnf(i_0_17479,plain,
    ( hBOOL(hAPP(X1,esk504_2(X1,X2)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(split_conjunct,[status(thm)],[i_0_9440]),
    [final] ).

cnf(i_0_17480,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10563]),
    [final] ).

cnf(i_0_17481,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10564]),
    [final] ).

cnf(i_0_17482,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10565]),
    [final] ).

cnf(i_0_17483,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X3,X1)))
    | ~ hBOOL(hAPP(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10248]),
    [final] ).

cnf(i_0_17484,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_10424]),
    [final] ).

cnf(i_0_17485,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_10425]),
    [final] ).

cnf(i_0_17486,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10566]),
    [final] ).

cnf(i_0_17487,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_7680]),
    [final] ).

cnf(i_0_17488,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_10296]),
    [final] ).

cnf(i_0_17489,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_10567]),
    [final] ).

cnf(i_0_17490,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_10568]),
    [final] ).

cnf(i_0_17491,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_10338]),
    [final] ).

cnf(i_0_17492,plain,
    ( X1 = X2
    | hAPP(X1,esk1_2(X2,X1)) != hAPP(X2,esk1_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_10569]),
    [final] ).

cnf(i_0_17493,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_10570]),
    [final] ).

cnf(i_0_17494,plain,
    ( hAPP(hAPP(X2,X4),X4) = X4
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X2,X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10571]),
    [final] ).

cnf(i_0_17495,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_10572]),
    [final] ).

cnf(i_0_17496,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_10255]),
    [final] ).

cnf(i_0_17497,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_10256]),
    [final] ).

cnf(i_0_17498,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),c_Groups_Ozero__class_Ozero(X1)))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10573]),
    [final] ).

cnf(i_0_17499,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_10574]),
    [final] ).

cnf(i_0_17500,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_10575]),
    [final] ).

cnf(i_0_17501,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_10533]),
    [final] ).

cnf(i_0_17502,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_10576]),
    [final] ).

cnf(i_0_17503,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_10577]),
    [final] ).

cnf(i_0_17504,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_10578]),
    [final] ).

cnf(i_0_17505,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_10579]),
    [final] ).

cnf(i_0_17506,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_10385]),
    [final] ).

cnf(i_0_17507,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10580]),
    [final] ).

cnf(i_0_17508,plain,
    ( hBOOL(X2)
    | ~ hBOOL(hAPP(hAPP(c_fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10581]),
    [final] ).

cnf(i_0_17509,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_10582]),
    [final] ).

cnf(i_0_17510,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_10583]),
    [final] ).

cnf(i_0_17511,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_10584]),
    [final] ).

cnf(i_0_17512,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_10320]),
    [final] ).

cnf(i_0_17513,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),esk74_1(X1)),X1))
    | c_Nat__Transfer_Onat__set(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_9998]),
    [final] ).

cnf(i_0_17514,plain,
    hAPP(c_List_Otl(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10585]),
    [final] ).

cnf(i_0_17515,plain,
    hAPP(c_List_Ohd(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10586]),
    [final] ).

cnf(i_0_17516,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_10587]),
    [final] ).

cnf(i_0_17517,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_10587]),
    [final] ).

cnf(i_0_17518,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_7690]),
    [final] ).

cnf(i_0_17519,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_10588]),
    [final] ).

cnf(i_0_17520,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_10409]),
    [final] ).

cnf(i_0_17521,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_10411]),
    [final] ).

cnf(i_0_17522,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_10589]),
    [final] ).

cnf(i_0_17523,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_10590]),
    [final] ).

cnf(i_0_17524,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(hAPP(c_fequal,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10591]),
    [final] ).

cnf(i_0_17525,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_10592]),
    [final] ).

cnf(i_0_17526,plain,
    ( hAPP(c_List_Oset(X1),esk453_2(X2,X1)) = X2
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10240]),
    [final] ).

cnf(i_0_17527,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_10396]),
    [final] ).

cnf(i_0_17528,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_10593]),
    [final] ).

cnf(i_0_17529,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_10594]),
    [final] ).

cnf(i_0_17530,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_10595]),
    [final] ).

cnf(i_0_17531,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_10596]),
    [final] ).

cnf(i_0_17532,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_10323]),
    [final] ).

cnf(i_0_17533,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_10597]),
    [final] ).

cnf(i_0_17534,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X2))),
    inference(split_conjunct,[status(thm)],[i_0_10598]),
    [final] ).

cnf(i_0_17535,plain,
    hAPP(c_Relation_Oconverse(X1,X2),hAPP(c_Relation_Oconverse(X2,X1),X3)) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10599]),
    [final] ).

cnf(i_0_17536,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_10371]),
    [final] ).

cnf(i_0_17537,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_17538,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_10600]),
    [final] ).

cnf(i_0_17539,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_10601]),
    [final] ).

cnf(i_0_17540,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_10602]),
    [final] ).

cnf(i_0_17541,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_10603]),
    [final] ).

cnf(i_0_17542,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_10604]),
    [final] ).

cnf(i_0_17543,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_10561]),
    [final] ).

cnf(i_0_17544,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_10561]),
    [final] ).

cnf(i_0_17545,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_10605]),
    [final] ).

cnf(i_0_17546,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_10562]),
    [final] ).

cnf(i_0_17547,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_10562]),
    [final] ).

cnf(i_0_17548,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_9681]),
    [final] ).

cnf(i_0_17549,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_9681]),
    [final] ).

cnf(i_0_17550,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_10606]),
    [final] ).

cnf(i_0_17551,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_9911]),
    [final] ).

cnf(i_0_17552,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_10607]),
    [final] ).

cnf(i_0_17553,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_10608]),
    [final] ).

cnf(i_0_17554,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_10609]),
    [final] ).

cnf(i_0_17555,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_10610]),
    [final] ).

cnf(i_0_17556,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_10611]),
    [final] ).

cnf(i_0_17557,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_10612]),
    [final] ).

cnf(i_0_17558,plain,
    ( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10427]),
    [final] ).

cnf(i_0_17559,plain,
    ( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Oantisym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10428]),
    [final] ).

cnf(i_0_17560,plain,
    ( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10429]),
    [final] ).

cnf(i_0_17561,plain,
    ( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10430]),
    [final] ).

cnf(i_0_17562,plain,
    ( c_List_Olinorder__class_Osorted(X1,esk453_2(X2,X1))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10240]),
    [final] ).

cnf(i_0_17563,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_10396]),
    [final] ).

cnf(i_0_17564,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_10613]),
    [final] ).

cnf(i_0_17565,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_10614]),
    [final] ).

cnf(i_0_17566,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_10615]),
    [final] ).

cnf(i_0_17567,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_10387]),
    [final] ).

cnf(i_0_17568,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2))
    | ~ class_Rings_Ocomm__semiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10616]),
    [final] ).

cnf(i_0_17569,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10617]),
    [final] ).

cnf(i_0_17570,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_10614]),
    [final] ).

cnf(i_0_17571,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_10614]),
    [final] ).

cnf(i_0_17572,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_10618]),
    [final] ).

cnf(i_0_17573,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_17574,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_17575,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_17576,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_10619]),
    [final] ).

cnf(i_0_17577,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_10620]),
    [final] ).

cnf(i_0_17578,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_10621]),
    [final] ).

cnf(i_0_17579,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_10622]),
    [final] ).

cnf(i_0_17580,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_10623]),
    [final] ).

cnf(i_0_17581,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_10624]),
    [final] ).

cnf(i_0_17582,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_10625]),
    [final] ).

cnf(i_0_17583,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_10626]),
    [final] ).

cnf(i_0_17584,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_10627]),
    [final] ).

cnf(i_0_17585,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_10628]),
    [final] ).

cnf(i_0_17586,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_10629]),
    [final] ).

cnf(i_0_17587,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_10630]),
    [final] ).

cnf(i_0_17588,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_10631]),
    [final] ).

cnf(i_0_17589,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_10632]),
    [final] ).

cnf(i_0_17590,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_10633]),
    [final] ).

cnf(i_0_17591,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X2))
    | c_Quickcheck_Obeyond(X1,X2) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(split_conjunct,[status(thm)],[i_0_10408]),
    [final] ).

cnf(i_0_17592,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_9407]),
    [final] ).

cnf(i_0_17593,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_10263]),
    [final] ).

cnf(i_0_17594,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_10634]),
    [final] ).

cnf(i_0_17595,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_10635]),
    [final] ).

cnf(i_0_17596,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_10377]),
    [final] ).

cnf(i_0_17597,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_5228]),
    [final] ).

cnf(i_0_17598,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_5226]),
    [final] ).

cnf(i_0_17599,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_10636]),
    [final] ).

cnf(i_0_17600,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_10637]),
    [final] ).

cnf(i_0_17601,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_10638]),
    [final] ).

cnf(i_0_17602,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_5228]),
    [final] ).

cnf(i_0_17603,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_5226]),
    [final] ).

cnf(i_0_17604,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_10639]),
    [final] ).

cnf(i_0_17605,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_10639]),
    [final] ).

cnf(i_0_17606,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_10640,c_0_8975]),
    [final] ).

cnf(i_0_17607,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_10568]),
    [final] ).

cnf(i_0_17608,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10641]),
    [final] ).

cnf(i_0_17609,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_10642]),
    [final] ).

cnf(i_0_17610,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_10643]),
    [final] ).

cnf(i_0_17611,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | X1 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10419]),
    [final] ).

cnf(i_0_17612,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_10418]),
    [final] ).

cnf(i_0_17613,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_10644]),
    [final] ).

cnf(i_0_17614,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_10645]),
    [final] ).

cnf(i_0_17615,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_10646]),
    [final] ).

cnf(i_0_17616,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_10647]),
    [final] ).

cnf(i_0_17617,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_10648]),
    [final] ).

cnf(i_0_17618,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_10649]),
    [final] ).

cnf(i_0_17619,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_10650]),
    [final] ).

cnf(i_0_17620,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_10651]),
    [final] ).

cnf(i_0_17621,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_10652]),
    [final] ).

cnf(i_0_17622,plain,
    hAPP(hAPP(c_List_Omap(X1,X1),c_COMBI(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10653]),
    [final] ).

cnf(i_0_17623,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10654]),
    [final] ).

cnf(i_0_17624,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X2),X3))
    | ~ c_Wellfounded_OwfP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10169]),
    [final] ).

cnf(i_0_17625,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ c_Predicate_Oreflp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10655]),
    [final] ).

cnf(i_0_17626,plain,
    ( hBOOL(hAPP(hAPP(X2,X3),X3))
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10656]),
    [final] ).

cnf(i_0_17627,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_10453]),
    [final] ).

cnf(i_0_17628,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_10454]),
    [final] ).

cnf(i_0_17629,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_10362]),
    [final] ).

cnf(i_0_17630,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_10363]),
    [final] ).

cnf(i_0_17631,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_10561]),
    [final] ).

cnf(i_0_17632,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_10562]),
    [final] ).

cnf(i_0_17633,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_10444]),
    [final] ).

cnf(i_0_17634,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_10443]),
    [final] ).

cnf(i_0_17635,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_10445]),
    [final] ).

cnf(i_0_17636,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_10657]),
    [final] ).

cnf(i_0_17637,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_10658]),
    [final] ).

cnf(i_0_17638,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_10659]),
    [final] ).

cnf(i_0_17639,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_10660]),
    [final] ).

cnf(i_0_17640,plain,
    ( hBOOL(hAPP(X1,X3))
    | ~ hBOOL(hAPP(X1,X2))
    | X3 != c_Hilbert__Choice_OEps(X4,X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10661]),
    [final] ).

cnf(i_0_17641,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_10662]),
    [final] ).

cnf(i_0_17642,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_10663]),
    [final] ).

cnf(i_0_17643,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_10664]),
    [final] ).

cnf(i_0_17644,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_10665]),
    [final] ).

cnf(i_0_17645,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_10666]),
    [final] ).

cnf(i_0_17646,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_10667]),
    [final] ).

cnf(i_0_17647,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_10668]),
    [final] ).

cnf(i_0_17648,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_10669]),
    [final] ).

cnf(i_0_17649,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_10669]),
    [final] ).

cnf(i_0_17650,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_10670]),
    [final] ).

cnf(i_0_17651,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_10670]),
    [final] ).

cnf(i_0_17652,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_10671]),
    [final] ).

cnf(i_0_17653,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_10672]),
    [final] ).

cnf(i_0_17654,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_10673]),
    [final] ).

cnf(i_0_17655,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10343]),
    [final] ).

cnf(i_0_17656,plain,
    ( c_Relation_Osym(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10511]),
    [final] ).

cnf(i_0_17657,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10343]),
    [final] ).

cnf(i_0_17658,plain,
    ( c_Relation_Otrans(X1,X2)
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10511]),
    [final] ).

cnf(i_0_17659,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_10674]),
    [final] ).

cnf(i_0_17660,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_10675]),
    [final] ).

cnf(i_0_17661,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_9586]),
    [final] ).

cnf(i_0_17662,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_10676,c_0_8975]),
    [final] ).

cnf(i_0_17663,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_9835]),
    [final] ).

cnf(i_0_17664,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_10677]),
    [final] ).

cnf(i_0_17665,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_10465]),
    [final] ).

cnf(i_0_17666,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_10466]),
    [final] ).

cnf(i_0_17667,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_10464]),
    [final] ).

cnf(i_0_17668,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_10678]),
    [final] ).

cnf(i_0_17669,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_10679]),
    [final] ).

cnf(i_0_17670,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10680]),
    [final] ).

cnf(i_0_17671,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9846]),
    [final] ).

cnf(i_0_17672,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_9847]),
    [final] ).

cnf(i_0_17673,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[i_0_9847]),
    [final] ).

cnf(i_0_17674,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10081]),
    [final] ).

cnf(i_0_17675,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10065]),
    [final] ).

cnf(i_0_17676,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10681]),
    [final] ).

cnf(i_0_17677,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_10441]),
    [final] ).

cnf(i_0_17678,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_10442]),
    [final] ).

cnf(i_0_17679,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_10682]),
    [final] ).

cnf(i_0_17680,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_10587]),
    [final] ).

cnf(i_0_17681,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_10683]),
    [final] ).

cnf(i_0_17682,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_10668]),
    [final] ).

cnf(i_0_17683,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_10668]),
    [final] ).

cnf(i_0_17684,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_10668]),
    [final] ).

cnf(i_0_17685,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_10668]),
    [final] ).

cnf(i_0_17686,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_10608]),
    [final] ).

cnf(i_0_17687,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_10684]),
    [final] ).

cnf(i_0_17688,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_10685]),
    [final] ).

cnf(i_0_17689,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_10686]),
    [final] ).

cnf(i_0_17690,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_10529]),
    [final] ).

cnf(i_0_17691,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_10687]),
    [final] ).

cnf(i_0_17692,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_10688]),
    [final] ).

cnf(i_0_17693,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_10689]),
    [final] ).

cnf(i_0_17694,plain,
    ~ c_List_Olist__ex1(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10690]),
    [final] ).

cnf(i_0_17695,plain,
    ~ c_List_Olist__ex(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10691]),
    [final] ).

cnf(i_0_17696,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_10692]),
    [final] ).

cnf(i_0_17697,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_17698,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10693]),
    [final] ).

cnf(i_0_17699,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10694]),
    [final] ).

cnf(i_0_17700,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
    inference(split_conjunct,[status(thm)],[i_0_10695]),
    [final] ).

cnf(i_0_17701,plain,
    hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10696]),
    [final] ).

cnf(i_0_17702,plain,
    hBOOL(hAPP(c_List_Olistsp(X1,X2),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10697]),
    [final] ).

cnf(i_0_17703,plain,
    hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10698]),
    [final] ).

cnf(i_0_17704,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_10561]),
    [final] ).

cnf(i_0_17705,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_10561]),
    [final] ).

cnf(i_0_17706,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_10562]),
    [final] ).

cnf(i_0_17707,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_10562]),
    [final] ).

cnf(i_0_17708,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_10699]),
    [final] ).

cnf(i_0_17709,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_10699]),
    [final] ).

cnf(i_0_17710,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_10700]),
    [final] ).

cnf(i_0_17711,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_10700]),
    [final] ).

cnf(i_0_17712,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_10701,c_0_6219]),
    [final] ).

cnf(i_0_17713,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_10702,c_0_6071]),
    [final] ).

cnf(i_0_17714,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_10703,c_0_6187]),
    [final] ).

cnf(i_0_17715,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_10704]),
    [final] ).

cnf(i_0_17716,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_10705]),
    [final] ).

cnf(i_0_17717,plain,
    hAPP(hAPP(c_COMBK(X1,X2),X3),X4) = X3,
    inference(split_conjunct,[status(thm)],[i_0_10706]),
    [final] ).

cnf(i_0_17718,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_10707,c_0_6187]),
    [final] ).

cnf(i_0_17719,plain,
    c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3) != c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),
    inference(split_conjunct,[status(thm)],[i_0_10708]),
    [final] ).

cnf(i_0_17720,plain,
    c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) != c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[i_0_10709]),
    [final] ).

cnf(i_0_17721,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_10710]),
    [final] ).

cnf(i_0_17722,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_10711]),
    [final] ).

cnf(i_0_17723,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_10712]),
    [final] ).

cnf(i_0_17724,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_10713]),
    [final] ).

cnf(i_0_17725,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_10714]),
    [final] ).

cnf(i_0_17726,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_10715]),
    [final] ).

cnf(i_0_17727,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_10716]),
    [final] ).

cnf(i_0_17728,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,X1),X2))
    | ~ hBOOL(X1)
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10717]),
    [final] ).

cnf(i_0_17729,plain,
    ( hBOOL(hAPP(X1,esk279_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_10589]),
    [final] ).

cnf(i_0_17730,plain,
    ( hBOOL(hAPP(X1,esk278_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_10590]),
    [final] ).

cnf(i_0_17731,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10718]),
    [final] ).

cnf(i_0_17732,plain,
    ( X3 = c_List_Olist_ONil(X1)
    | hAPP(hAPP(c_List_Oappend(X1),X2),X3) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10719]),
    [final] ).

cnf(i_0_17733,plain,
    ( X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10720]),
    [final] ).

cnf(i_0_17734,plain,
    ( X3 = c_List_Olist_ONil(X2)
    | X1 != hAPP(hAPP(c_List_Oappend(X2),X3),X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10721]),
    [final] ).

cnf(i_0_17735,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_10722]),
    [final] ).

cnf(i_0_17736,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10723]),
    [final] ).

cnf(i_0_17737,plain,
    c_List_Olist_ONil(X1) != hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),
    inference(split_conjunct,[status(thm)],[i_0_10724]),
    [final] ).

cnf(i_0_17738,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X2))),
    inference(split_conjunct,[status(thm)],[i_0_10725]),
    [final] ).

cnf(i_0_17739,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_10605]),
    [final] ).

cnf(i_0_17740,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_10726,c_0_6219]),
    [final] ).

cnf(i_0_17741,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X2),X1))
    | esk394_2(X1,X2) != esk395_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_8346]),
    [final] ).

cnf(i_0_17742,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_10722]),
    [final] ).

cnf(i_0_17743,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_10727]),
    [final] ).

cnf(i_0_17744,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_10728]),
    [final] ).

cnf(i_0_17745,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_10729]),
    [final] ).

cnf(i_0_17746,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_10730]),
    [final] ).

cnf(i_0_17747,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_10731]),
    [final] ).

cnf(i_0_17748,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_10732]),
    [final] ).

cnf(i_0_17749,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_10733]),
    [final] ).

cnf(i_0_17750,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_17751,hypothesis,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_pn),v_U)),
    inference(split_conjunct,[status(thm)],[conj_5]),
    [final] ).

cnf(i_0_17752,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_17753,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_17754,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_17755,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_17756,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_10734]),
    [final] ).

cnf(i_0_17757,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_10735]),
    [final] ).

cnf(i_0_17758,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_10736]),
    [final] ).

cnf(i_0_17759,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_10737]),
    [final] ).

cnf(i_0_17760,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_10738]),
    [final] ).

cnf(i_0_17761,plain,
    hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3) != X3,
    inference(split_conjunct,[status(thm)],[i_0_10739]),
    [final] ).

cnf(i_0_17762,plain,
    X1 != hAPP(hAPP(c_List_Olist_OCons(X2),X3),X1),
    inference(split_conjunct,[status(thm)],[i_0_10740]),
    [final] ).

cnf(i_0_17763,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_10741]),
    [final] ).

cnf(i_0_17764,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10742]),
    [final] ).

cnf(i_0_17765,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10743]),
    [final] ).

cnf(i_0_17766,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,X2),X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10744]),
    [final] ).

cnf(i_0_17767,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_10745]),
    [final] ).

cnf(i_0_17768,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_10746]),
    [final] ).

cnf(i_0_17769,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_10747]),
    [final] ).

cnf(i_0_17770,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_10748]),
    [final] ).

cnf(i_0_17771,plain,
    ( c_Equiv__Relations_Oequivp(X1,X2)
    | ~ c_Predicate_Oreflp(X1,X2)
    | ~ c_Predicate_Osymp(X1,X2)
    | ~ c_Predicate_Otransp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10749]),
    [final] ).

cnf(i_0_17772,plain,
    ( c_Equiv__Relations_Oequivp(X1,X2)
    | ~ c_Predicate_Oreflp(X1,X2)
    | ~ c_Predicate_Osymp(X1,X2)
    | ~ c_Predicate_Otransp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10750]),
    [final] ).

cnf(i_0_17773,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_10751]),
    [final] ).

cnf(i_0_17774,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10752]),
    [final] ).

cnf(i_0_17775,plain,
    ( c_List_Oremdups(X1,X2) = X2
    | ~ hBOOL(hAPP(c_List_Odistinct(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10753]),
    [final] ).

cnf(i_0_17776,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_10754,c_0_7992]),
    [final] ).

cnf(i_0_17777,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_10755]),
    [final] ).

cnf(i_0_17778,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_10756]),
    [final] ).

cnf(i_0_17779,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(hAPP(c_fimplies,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[i_0_10757]),
    [final] ).

cnf(i_0_17780,plain,
    c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10758]),
    [final] ).

cnf(i_0_17781,plain,
    c_Relation_Orefl__on(X1,X2,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_10759]),
    [final] ).

cnf(i_0_17782,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_10760]),
    [final] ).

cnf(i_0_17783,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_10760]),
    [final] ).

cnf(i_0_17784,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_10761]),
    [final] ).

cnf(i_0_17785,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_10761]),
    [final] ).

cnf(i_0_17786,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_10762]),
    [final] ).

cnf(i_0_17787,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_10762]),
    [final] ).

cnf(i_0_17788,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_10669]),
    [final] ).

cnf(i_0_17789,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_10670]),
    [final] ).

cnf(i_0_17790,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_10763]),
    [final] ).

cnf(i_0_17791,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_10764]),
    [final] ).

cnf(i_0_17792,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10765]),
    [final] ).

cnf(i_0_17793,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_10766]),
    [final] ).

cnf(i_0_17794,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_10767]),
    [final] ).

cnf(i_0_17795,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_10768]),
    [final] ).

cnf(i_0_17796,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_10769]),
    [final] ).

cnf(i_0_17797,plain,
    ( c_Wellfounded_Owf(X2,X1)
    | esk316_2(X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) ),
    inference(split_conjunct,[status(thm)],[i_0_8235]),
    [final] ).

cnf(i_0_17798,plain,
    ( c_Relation_Osym(X1,X2)
    | hAPP(c_Relation_Oconverse(X1,X1),X2) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10770]),
    [final] ).

cnf(i_0_17799,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_10771]),
    [final] ).

cnf(i_0_17800,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_10772]),
    [final] ).

cnf(i_0_17801,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_10639]),
    [final] ).

cnf(i_0_17802,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_10773]),
    [final] ).

cnf(i_0_17803,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_10774]),
    [final] ).

cnf(i_0_17804,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_10775]),
    [final] ).

cnf(i_0_17805,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_10776]),
    [final] ).

cnf(i_0_17806,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_10453]),
    [final] ).

cnf(i_0_17807,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_10454]),
    [final] ).

cnf(i_0_17808,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_10777]),
    [final] ).

cnf(i_0_17809,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_10778]),
    [final] ).

cnf(i_0_17810,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_10779]),
    [final] ).

cnf(i_0_17811,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_10780]),
    [final] ).

cnf(i_0_17812,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_10781]),
    [final] ).

cnf(i_0_17813,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_10782]),
    [final] ).

cnf(i_0_17814,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_10783]),
    [final] ).

cnf(i_0_17815,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_10784]),
    [final] ).

cnf(i_0_17816,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X2) = c_Orderings_Otop__class_Otop(X1)
    | ~ class_Lattices_Obounded__lattice__top(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10785]),
    [final] ).

cnf(i_0_17817,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_10786]),
    [final] ).

cnf(i_0_17818,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_10787]),
    [final] ).

cnf(i_0_17819,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_10788]),
    [final] ).

cnf(i_0_17820,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_10789]),
    [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_10790]),
    [final] ).

cnf(i_0_17822,plain,
    ( c_List_Olinorder__class_Osorted(X1,esk442_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_7362]),
    [final] ).

cnf(i_0_17823,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_10791]),
    [final] ).

cnf(i_0_17824,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_10792]),
    [final] ).

cnf(i_0_17825,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_10378]),
    [final] ).

cnf(i_0_17826,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_10793]),
    [final] ).

cnf(i_0_17827,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_10794,c_0_6070]),
    [final] ).

cnf(i_0_17828,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_10795,c_0_6070]),
    [final] ).

cnf(i_0_17829,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_10796]),
    [final] ).

cnf(i_0_17830,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_10699]),
    [final] ).

cnf(i_0_17831,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_10700]),
    [final] ).

cnf(i_0_17832,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_10797]),
    [final] ).

cnf(i_0_17833,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1) != c_Int_OMin,
    inference(rw,[status(thm)],[i_0_10798,c_0_6070]),
    [final] ).

cnf(i_0_17834,plain,
    c_Int_OMin != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X1),
    inference(rw,[status(thm)],[i_0_10799,c_0_6070]),
    [final] ).

cnf(i_0_17835,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_10800]),
    [final] ).

cnf(i_0_17836,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_10801]),
    [final] ).

cnf(i_0_17837,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_10802]),
    [final] ).

cnf(i_0_17838,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_10803]),
    [final] ).

cnf(i_0_17839,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_10804]),
    [final] ).

cnf(i_0_17840,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_10805]),
    [final] ).

cnf(i_0_17841,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_10806]),
    [final] ).

cnf(i_0_17842,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_10807]),
    [final] ).

cnf(i_0_17843,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_10808]),
    [final] ).

cnf(i_0_17844,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_10809]),
    [final] ).

cnf(i_0_17845,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_10810]),
    [final] ).

cnf(i_0_17846,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_10811]),
    [final] ).

cnf(i_0_17847,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_10812]),
    [final] ).

cnf(i_0_17848,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_10813]),
    [final] ).

cnf(i_0_17849,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_10814]),
    [final] ).

cnf(i_0_17850,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_10815]),
    [final] ).

cnf(i_0_17851,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_10658]),
    [final] ).

cnf(i_0_17852,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_10816]),
    [final] ).

cnf(i_0_17853,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_10568]),
    [final] ).

cnf(i_0_17854,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_10644]),
    [final] ).

cnf(i_0_17855,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_10644]),
    [final] ).

cnf(i_0_17856,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_10672]),
    [final] ).

cnf(i_0_17857,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_10673]),
    [final] ).

cnf(i_0_17858,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_10817]),
    [final] ).

cnf(i_0_17859,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_10818]),
    [final] ).

cnf(i_0_17860,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_10819]),
    [final] ).

cnf(i_0_17861,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_10820]),
    [final] ).

cnf(i_0_17862,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_10821]),
    [final] ).

cnf(i_0_17863,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_10822]),
    [final] ).

cnf(i_0_17864,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_10823]),
    [final] ).

cnf(i_0_17865,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_10824]),
    [final] ).

cnf(i_0_17866,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_10825]),
    [final] ).

cnf(i_0_17867,plain,
    ( c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10826]),
    [final] ).

cnf(i_0_17868,plain,
    ( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10827]),
    [final] ).

cnf(i_0_17869,plain,
    ( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X2))
    | ~ c_Relation_Otrans(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10828]),
    [final] ).

cnf(i_0_17870,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_10829]),
    [final] ).

cnf(i_0_17871,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_10830]),
    [final] ).

cnf(i_0_17872,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X3),c_List_Olist_ONil(X3)),X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10831]),
    [final] ).

cnf(i_0_17873,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_10684]),
    [final] ).

cnf(i_0_17874,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_10816]),
    [final] ).

cnf(i_0_17875,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_10832]),
    [final] ).

cnf(i_0_17876,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_10833]),
    [final] ).

cnf(i_0_17877,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_10834]),
    [final] ).

cnf(i_0_17878,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_10835]),
    [final] ).

cnf(i_0_17879,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_10836]),
    [final] ).

cnf(i_0_17880,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_10837]),
    [final] ).

cnf(i_0_17881,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_10838]),
    [final] ).

cnf(i_0_17882,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_10839]),
    [final] ).

cnf(i_0_17883,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_10840]),
    [final] ).

cnf(i_0_17884,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_10841]),
    [final] ).

cnf(i_0_17885,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_10605]),
    [final] ).

cnf(i_0_17886,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_10678]),
    [final] ).

cnf(i_0_17887,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_10679]),
    [final] ).

cnf(i_0_17888,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_10557]),
    [final] ).

cnf(i_0_17889,plain,
    hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10842]),
    [final] ).

cnf(i_0_17890,plain,
    hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10843]),
    [final] ).

cnf(i_0_17891,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_10844]),
    [final] ).

cnf(i_0_17892,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_10845]),
    [final] ).

cnf(i_0_17893,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_10846]),
    [final] ).

cnf(i_0_17894,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_10847]),
    [final] ).

cnf(i_0_17895,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_10848]),
    [final] ).

cnf(i_0_17896,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_10849]),
    [final] ).

cnf(i_0_17897,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_10850]),
    [final] ).

cnf(i_0_17898,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_10851]),
    [final] ).

cnf(i_0_17899,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_10852]),
    [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_10853]),
    [final] ).

cnf(i_0_17901,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_10854]),
    [final] ).

cnf(i_0_17902,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_10855]),
    [final] ).

cnf(i_0_17903,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_10856]),
    [final] ).

cnf(i_0_17904,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_10857]),
    [final] ).

cnf(i_0_17905,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_10858]),
    [final] ).

cnf(i_0_17906,plain,
    ( hBOOL(hAPP(c_List_Odistinct(X1),X2))
    | c_List_Oremdups(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[i_0_10752]),
    [final] ).

cnf(i_0_17907,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_10859]),
    [final] ).

cnf(i_0_17908,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_10860]),
    [final] ).

cnf(i_0_17909,plain,
    hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X2)) = hAPP(c_List_Oset(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10861]),
    [final] ).

cnf(i_0_17910,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_10862]),
    [final] ).

cnf(i_0_17911,plain,
    ( X2 = X3
    | hAPP(c_List_Orev(X1),X2) != hAPP(c_List_Orev(X1),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10863]),
    [final] ).

cnf(i_0_17912,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_8304]),
    [final] ).

cnf(i_0_17913,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_10557]),
    [final] ).

cnf(i_0_17914,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_10864]),
    [final] ).

cnf(i_0_17915,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_10865]),
    [final] ).

cnf(i_0_17916,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_17917,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10866]),
    [final] ).

cnf(i_0_17918,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_10682]),
    [final] ).

cnf(i_0_17919,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_10867]),
    [final] ).

cnf(i_0_17920,plain,
    c_List_Osublist(X1,c_List_Olist_ONil(X1),X2) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10868]),
    [final] ).

cnf(i_0_17921,plain,
    c_List_OtakeWhile(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10869]),
    [final] ).

cnf(i_0_17922,plain,
    c_List_Oremove1(X1,X2,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10870]),
    [final] ).

cnf(i_0_17923,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_10685]),
    [final] ).

cnf(i_0_17924,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_10686]),
    [final] ).

cnf(i_0_17925,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_10871]),
    [final] ).

cnf(i_0_17926,plain,
    ( hAPP(c_Relation_Oconverse(X1,X1),X2) = X2
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10770]),
    [final] ).

cnf(i_0_17927,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_10872]),
    [final] ).

cnf(i_0_17928,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_10873]),
    [final] ).

cnf(i_0_17929,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_10874]),
    [final] ).

cnf(i_0_17930,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_10875]),
    [final] ).

cnf(i_0_17931,plain,
    ( c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X2))
    | ~ c_Relation_Osym(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10876]),
    [final] ).

cnf(i_0_17932,plain,
    ( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X2))
    | ~ c_Wellfounded_Oacyclic(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10877]),
    [final] ).

cnf(i_0_17933,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_10878]),
    [final] ).

cnf(i_0_17934,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_10879]),
    [final] ).

cnf(i_0_17935,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_10880]),
    [final] ).

cnf(i_0_17936,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_10682]),
    [final] ).

cnf(i_0_17937,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_10881]),
    [final] ).

cnf(i_0_17938,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_10881]),
    [final] ).

cnf(i_0_17939,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_10882]),
    [final] ).

cnf(i_0_17940,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_10882]),
    [final] ).

cnf(i_0_17941,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_10883]),
    [final] ).

cnf(i_0_17942,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X1),X3) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10718]),
    [final] ).

cnf(i_0_17943,plain,
    ( hAPP(hAPP(c_List_Oappend(X2),X3),X1) = X3
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10719]),
    [final] ).

cnf(i_0_17944,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),X1),X3)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10721]),
    [final] ).

cnf(i_0_17945,plain,
    ( X3 = hAPP(hAPP(c_List_Oappend(X2),X3),X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10720]),
    [final] ).

cnf(i_0_17946,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_10884]),
    [final] ).

cnf(i_0_17947,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_10885]),
    [final] ).

cnf(i_0_17948,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_10886]),
    [final] ).

cnf(i_0_17949,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_10887]),
    [final] ).

cnf(i_0_17950,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_10888]),
    [final] ).

cnf(i_0_17951,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_10889]),
    [final] ).

cnf(i_0_17952,plain,
    c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10890]),
    [final] ).

cnf(i_0_17953,plain,
    c_List_Osplice(X1,c_List_Olist_ONil(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10891]),
    [final] ).

cnf(i_0_17954,plain,
    c_List_Osplice(X1,X2,c_List_Olist_ONil(X1)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10892]),
    [final] ).

cnf(i_0_17955,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_10893]),
    [final] ).

cnf(i_0_17956,plain,
    c_List_Olist__all(X1,X2,c_List_Olist_ONil(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10894]),
    [final] ).

cnf(i_0_17957,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_10668]),
    [final] ).

cnf(i_0_17958,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_10761]),
    [final] ).

cnf(i_0_17959,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_10760]),
    [final] ).

cnf(i_0_17960,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_10762]),
    [final] ).

cnf(i_0_17961,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_10895]),
    [final] ).

cnf(i_0_17962,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_10896]),
    [final] ).

cnf(i_0_17963,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X2) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10897]),
    [final] ).

cnf(i_0_17964,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X2) = X2
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10898]),
    [final] ).

cnf(i_0_17965,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_10899]),
    [final] ).

cnf(i_0_17966,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_10900]),
    [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_10901]),
    [final] ).

cnf(i_0_17968,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10902]),
    [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_10903]),
    [final] ).

cnf(i_0_17970,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X2),X2) = X2
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10904]),
    [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_10905]),
    [final] ).

cnf(i_0_17972,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_10906]),
    [final] ).

cnf(i_0_17973,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_10907]),
    [final] ).

cnf(i_0_17974,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_10908]),
    [final] ).

cnf(i_0_17975,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_10909]),
    [final] ).

cnf(i_0_17976,plain,
    hAPP(c_New__DSequence_Opos__single(X1,X2),X3) = hAPP(c_Lazy__Sequence_Osingle(X1),X2),
    inference(split_conjunct,[status(thm)],[i_0_10910]),
    [final] ).

cnf(i_0_17977,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_6227]),
    [final] ).

cnf(i_0_17978,plain,
    hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10911]),
    [final] ).

cnf(i_0_17979,plain,
    hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10912]),
    [final] ).

cnf(i_0_17980,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_10913]),
    [final] ).

cnf(i_0_17981,plain,
    ( c_Relation_Oantisym(X2,X1)
    | esk511_2(X1,X2) != esk512_2(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_7082]),
    [final] ).

cnf(i_0_17982,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_10914]),
    [final] ).

cnf(i_0_17983,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_10915]),
    [final] ).

cnf(i_0_17984,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_10916]),
    [final] ).

cnf(i_0_17985,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_17986,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_10917]),
    [final] ).

cnf(i_0_17987,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_10918]),
    [final] ).

cnf(i_0_17988,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_10919]),
    [final] ).

cnf(i_0_17989,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_10920]),
    [final] ).

cnf(i_0_17990,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_10921]),
    [final] ).

cnf(i_0_17991,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_10922]),
    [final] ).

cnf(i_0_17992,plain,
    hAPP(c_List_Omap(X1,X1),c_COMBI(X1)) = c_Fun_Oid(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10923]),
    [final] ).

cnf(i_0_17993,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_10924]),
    [final] ).

cnf(i_0_17994,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_10925]),
    [final] ).

cnf(i_0_17995,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_10768]),
    [final] ).

cnf(i_0_17996,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_10769]),
    [final] ).

cnf(i_0_17997,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_10926]),
    [final] ).

cnf(i_0_17998,plain,
    ( hAPP(c_List_Orev(X2),X1) = X3
    | X1 != hAPP(c_List_Orev(X2),X3) ),
    inference(split_conjunct,[status(thm)],[i_0_10927]),
    [final] ).

cnf(i_0_17999,plain,
    ( X2 = hAPP(c_List_Orev(X1),X3)
    | hAPP(c_List_Orev(X1),X2) != X3 ),
    inference(split_conjunct,[status(thm)],[i_0_10927]),
    [final] ).

cnf(i_0_18000,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_10928]),
    [final] ).

cnf(i_0_18001,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_10929]),
    [final] ).

cnf(i_0_18002,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_10930]),
    [final] ).

cnf(i_0_18003,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_10931]),
    [final] ).

cnf(i_0_18004,plain,
    hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olist_ONil(X1))),
    inference(split_conjunct,[status(thm)],[i_0_10932]),
    [final] ).

cnf(i_0_18005,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_9607]),
    [final] ).

cnf(i_0_18006,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_9571]),
    [final] ).

cnf(i_0_18007,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_9036]),
    [final] ).

cnf(i_0_18008,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_10738]),
    [final] ).

cnf(i_0_18009,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_10738]),
    [final] ).

cnf(i_0_18010,plain,
    hAPP(c_New__DSequence_Oneg__single(X1,X2),X3) = c_Lazy__Sequence_Ohb__single(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10933]),
    [final] ).

cnf(i_0_18011,plain,
    c_List_Oremdups(X1,c_List_Oremdups(X1,X2)) = c_List_Oremdups(X1,X2),
    inference(split_conjunct,[status(thm)],[i_0_10934]),
    [final] ).

cnf(i_0_18012,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_10935]),
    [final] ).

cnf(i_0_18013,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_10936]),
    [final] ).

cnf(i_0_18014,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_10937]),
    [final] ).

cnf(i_0_18015,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_10938]),
    [final] ).

cnf(i_0_18016,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_10939]),
    [final] ).

cnf(i_0_18017,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_10940]),
    [final] ).

cnf(i_0_18018,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_10941]),
    [final] ).

cnf(i_0_18019,plain,
    c_Predicate_Oconversep(X1,X1,c_fequal) = c_fequal,
    inference(split_conjunct,[status(thm)],[i_0_10942]),
    [final] ).

cnf(i_0_18020,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_9120]),
    [final] ).

cnf(i_0_18021,plain,
    ( c_List_Otranspose(X2,X1) = c_List_Olist_ONil(tc_List_Olist(X2))
    | esk426_2(X1,X2) != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9258]),
    [final] ).

cnf(i_0_18022,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10943]),
    [final] ).

cnf(i_0_18023,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(split_conjunct,[status(thm)],[i_0_10944]),
    [final] ).

cnf(i_0_18024,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_10945]),
    [final] ).

cnf(i_0_18025,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_10946]),
    [final] ).

cnf(i_0_18026,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_10947]),
    [final] ).

cnf(i_0_18027,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_10948]),
    [final] ).

cnf(i_0_18028,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_10920]),
    [final] ).

cnf(i_0_18029,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_10949]),
    [final] ).

cnf(i_0_18030,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_10950]),
    [final] ).

cnf(i_0_18031,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_10951]),
    [final] ).

cnf(i_0_18032,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_10952]),
    [final] ).

cnf(i_0_18033,plain,
    ( ~ hBOOL(hAPP(c_fNot,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10953]),
    [final] ).

cnf(i_0_18034,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_10954]),
    [final] ).

cnf(i_0_18035,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_10955]),
    [final] ).

cnf(i_0_18036,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_10956]),
    [final] ).

cnf(i_0_18037,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_10957]),
    [final] ).

cnf(i_0_18038,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_10958]),
    [final] ).

cnf(i_0_18039,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_10959]),
    [final] ).

cnf(i_0_18040,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_10960]),
    [final] ).

cnf(i_0_18041,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_10961]),
    [final] ).

cnf(i_0_18042,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_18043,plain,
    hAPP(c_List_Ofilter(X1,X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_10962]),
    [final] ).

cnf(i_0_18044,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10963]),
    [final] ).

cnf(i_0_18045,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_10964]),
    [final] ).

cnf(i_0_18046,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_10965]),
    [final] ).

cnf(i_0_18047,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_10966]),
    [final] ).

cnf(i_0_18048,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_18049,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_10967,c_0_6070]),
    [final] ).

cnf(i_0_18050,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_10968,c_0_6070]),
    [final] ).

cnf(i_0_18051,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_18052,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_10969]),
    [final] ).

cnf(i_0_18053,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_10970]),
    [final] ).

cnf(i_0_18054,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_10255]),
    [final] ).

cnf(i_0_18055,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_10256]),
    [final] ).

cnf(i_0_18056,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_10971]),
    [final] ).

cnf(i_0_18057,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_10972]),
    [final] ).

cnf(i_0_18058,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_10973]),
    [final] ).

cnf(i_0_18059,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10974]),
    [final] ).

cnf(i_0_18060,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OPls) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10975]),
    [final] ).

cnf(i_0_18061,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_10976]),
    [final] ).

cnf(i_0_18062,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_10977]),
    [final] ).

cnf(i_0_18063,plain,
    ( class_Enum_Oenum(tc_prod(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10978]),
    [final] ).

cnf(i_0_18064,plain,
    ( class_Enum_Oenum(tc_sum(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10979]),
    [final] ).

cnf(i_0_18065,plain,
    ( class_Enum_Oenum(tc_fun(X1,X2))
    | ~ class_Enum_Oenum(X1)
    | ~ class_Enum_Oenum(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10980]),
    [final] ).

cnf(i_0_18066,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_10981]),
    [final] ).

cnf(i_0_18067,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_10982]),
    [final] ).

cnf(i_0_18068,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_10983]),
    [final] ).

cnf(i_0_18069,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_10984]),
    [final] ).

cnf(i_0_18070,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_18071,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_18072,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_10985]),
    [final] ).

cnf(i_0_18073,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_10883]),
    [final] ).

cnf(i_0_18074,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_10986]),
    [final] ).

cnf(i_0_18075,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_10987]),
    [final] ).

cnf(i_0_18076,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_10988]),
    [final] ).

cnf(i_0_18077,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_10907]),
    [final] ).

cnf(i_0_18078,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_10989]),
    [final] ).

cnf(i_0_18079,plain,
    c_Relation_Otrans(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10990]),
    [final] ).

cnf(i_0_18080,plain,
    c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10991]),
    [final] ).

cnf(i_0_18081,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_10992]),
    [final] ).

cnf(i_0_18082,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_10265]),
    [final] ).

cnf(i_0_18083,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_9983]),
    [final] ).

cnf(i_0_18084,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_10993,c_0_6219]),
    [final] ).

cnf(i_0_18085,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_10994,c_0_6070]),
    [final] ).

cnf(i_0_18086,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_10995,c_0_6071]),
    [final] ).

cnf(i_0_18087,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10996]),
    [final] ).

cnf(i_0_18088,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Onat__of,X1) != hAPP(c_Code__Numeral_Onat__of,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10997]),
    [final] ).

cnf(i_0_18089,plain,
    ( X1 = X2
    | hAPP(c_Code__Numeral_Oof__nat,X1) != hAPP(c_Code__Numeral_Oof__nat,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10998]),
    [final] ).

cnf(i_0_18090,plain,
    ( X1 = X2
    | hAPP(c_Int_ORep__Integ,X1) != hAPP(c_Int_ORep__Integ,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10999]),
    [final] ).

cnf(i_0_18091,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11000]),
    [final] ).

cnf(i_0_18092,plain,
    ( X1 = X2
    | hAPP(c_Nat_OSuc,X1) != hAPP(c_Nat_OSuc,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11001]),
    [final] ).

cnf(i_0_18093,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_11002]),
    [final] ).

cnf(i_0_18094,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_11003]),
    [final] ).

cnf(i_0_18095,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_11004]),
    [final] ).

cnf(i_0_18096,plain,
    c_Relation_Osym(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11005]),
    [final] ).

cnf(i_0_18097,plain,
    c_Relation_Oantisym(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11006]),
    [final] ).

cnf(i_0_18098,plain,
    c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11007]),
    [final] ).

cnf(i_0_18099,plain,
    c_Relation_Otrans(X1,c_Relation_OId__on(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11008]),
    [final] ).

cnf(i_0_18100,plain,
    c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11009]),
    [final] ).

cnf(i_0_18101,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_10951]),
    [final] ).

cnf(i_0_18102,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_10952]),
    [final] ).

cnf(i_0_18103,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_10950]),
    [final] ).

cnf(i_0_18104,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | ~ c_Int_Oiszero(X1,c_Groups_Oone__class_Oone(X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11010]),
    [final] ).

cnf(i_0_18105,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11011]),
    [final] ).

cnf(i_0_18106,plain,
    c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11012]),
    [final] ).

cnf(i_0_18107,plain,
    c_HOL_OThe(X1,hAPP(c_fequal,X2)) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11013]),
    [final] ).

cnf(i_0_18108,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_11014]),
    [final] ).

cnf(i_0_18109,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_11015]),
    [final] ).

cnf(i_0_18110,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_11016]),
    [final] ).

cnf(i_0_18111,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_11017]),
    [final] ).

cnf(i_0_18112,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_11018]),
    [final] ).

cnf(i_0_18113,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_11019]),
    [final] ).

cnf(i_0_18114,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11020]),
    [final] ).

cnf(i_0_18115,plain,
    ( class_Orderings_Otop(tc_fun(X2,X1))
    | ~ class_Orderings_Otop(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11021]),
    [final] ).

cnf(i_0_18116,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11022]),
    [final] ).

cnf(i_0_18117,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11023]),
    [final] ).

cnf(i_0_18118,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(X2,X1))
    | ~ class_Lattices_Odistrib__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11024]),
    [final] ).

cnf(i_0_18119,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X2,X1))
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11025]),
    [final] ).

cnf(i_0_18120,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(X2,X1))
    | ~ class_Lattices_Obounded__lattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11026]),
    [final] ).

cnf(i_0_18121,plain,
    ( class_Lattices_Olattice(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11027]),
    [final] ).

cnf(i_0_18122,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(X2,X1))
    | ~ class_Lattices_Olattice(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11028]),
    [final] ).

cnf(i_0_18123,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(X2,X1))
    | ~ class_Lattices_Oboolean__algebra(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11029]),
    [final] ).

cnf(i_0_18124,plain,
    ( class_Groups_Ouminus(tc_fun(X2,X1))
    | ~ class_Groups_Ouminus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11030]),
    [final] ).

cnf(i_0_18125,plain,
    ( class_Groups_Ominus(tc_fun(X2,X1))
    | ~ class_Groups_Ominus(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11031]),
    [final] ).

cnf(i_0_18126,plain,
    ( class_Orderings_Oord(tc_fun(X2,X1))
    | ~ class_Orderings_Oord(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11032]),
    [final] ).

cnf(i_0_18127,plain,
    ( class_Orderings_Oorder(tc_fun(X2,X1))
    | ~ class_Orderings_Oorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11033]),
    [final] ).

cnf(i_0_18128,plain,
    ( class_Orderings_Obot(tc_fun(X2,X1))
    | ~ class_Orderings_Obot(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11034]),
    [final] ).

cnf(i_0_18129,plain,
    ( class_Orderings_Opreorder(tc_fun(X2,X1))
    | ~ class_Orderings_Opreorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11035]),
    [final] ).

cnf(i_0_18130,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_10965]),
    [final] ).

cnf(i_0_18131,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_5237]),
    [final] ).

cnf(i_0_18132,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_10966]),
    [final] ).

cnf(i_0_18133,plain,
    ( c_Equiv__Relations_Opart__equivp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11036]),
    [final] ).

cnf(i_0_18134,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10005]),
    [final] ).

cnf(i_0_18135,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10006]),
    [final] ).

cnf(i_0_18136,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11037]),
    [final] ).

cnf(i_0_18137,plain,
    ( c_Predicate_Osymp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10750]),
    [final] ).

cnf(i_0_18138,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10005]),
    [final] ).

cnf(i_0_18139,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Opart__equivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10006]),
    [final] ).

cnf(i_0_18140,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11037]),
    [final] ).

cnf(i_0_18141,plain,
    ( c_Predicate_Otransp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10750]),
    [final] ).

cnf(i_0_18142,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Nitpick_Owf_H(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_9983]),
    [final] ).

cnf(i_0_18143,plain,
    ( c_Wellfounded_Oacyclic(X1,X2)
    | ~ c_Wellfounded_Owf(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11038]),
    [final] ).

cnf(i_0_18144,plain,
    ( c_Predicate_Oreflp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11037]),
    [final] ).

cnf(i_0_18145,plain,
    ( c_Predicate_Oreflp(X1,X2)
    | ~ c_Equiv__Relations_Oequivp(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_10750]),
    [final] ).

cnf(i_0_18146,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_10972]),
    [final] ).

cnf(i_0_18147,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_10973]),
    [final] ).

cnf(i_0_18148,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_11039]),
    [final] ).

cnf(i_0_18149,plain,
    c_Lazy__Sequence_Oflat(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X1))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),
    inference(split_conjunct,[status(thm)],[i_0_11040]),
    [final] ).

cnf(i_0_18150,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11041]),
    [final] ).

cnf(i_0_18151,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11042]),
    [final] ).

cnf(i_0_18152,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11043]),
    [final] ).

cnf(i_0_18153,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X1)) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11044]),
    [final] ).

cnf(i_0_18154,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_11045]),
    [final] ).

cnf(i_0_18155,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_11046]),
    [final] ).

cnf(i_0_18156,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_11047]),
    [final] ).

cnf(i_0_18157,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_11048]),
    [final] ).

cnf(i_0_18158,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_11049]),
    [final] ).

cnf(i_0_18159,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_11050]),
    [final] ).

cnf(i_0_18160,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_11051]),
    [final] ).

cnf(i_0_18161,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Oremdups(X1,X2) != c_List_Olist_ONil(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11052]),
    [final] ).

cnf(i_0_18162,plain,
    ( X2 = c_List_Olist_ONil(X1)
    | c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11053]),
    [final] ).

cnf(i_0_18163,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_10096]),
    [final] ).

cnf(i_0_18164,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_11002]),
    [final] ).

cnf(i_0_18165,hypothesis,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)),
    inference(split_conjunct,[status(thm)],[conj_0]),
    [final] ).

cnf(i_0_18166,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_10986]),
    [final] ).

cnf(i_0_18167,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_10987]),
    [final] ).

cnf(i_0_18168,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_10988]),
    [final] ).

cnf(i_0_18169,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_18170,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_18171,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_18172,plain,
    ( hBOOL(X1)
    | hBOOL(hAPP(c_fNot,X1)) ),
    inference(split_conjunct,[status(thm)],[i_0_11054]),
    [final] ).

cnf(i_0_18173,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_11055]),
    [final] ).

cnf(i_0_18174,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_11056]),
    [final] ).

cnf(i_0_18175,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_11057]),
    [final] ).

cnf(i_0_18176,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_18177,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X1) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | esk390_1(X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_9906]),
    [final] ).

cnf(i_0_18178,plain,
    hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11058]),
    [final] ).

cnf(i_0_18179,plain,
    hAPP(c_List_Otl(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11059]),
    [final] ).

cnf(i_0_18180,plain,
    hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_9886]),
    [final] ).

cnf(i_0_18181,plain,
    class_Nat_Osize(tc_prod(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11060]),
    [final] ).

cnf(i_0_18182,plain,
    class_Nat_Osize(tc_Nitpick_Opair__box(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11061]),
    [final] ).

cnf(i_0_18183,plain,
    class_Nat_Osize(tc_sum(X1,X2)),
    inference(split_conjunct,[status(thm)],[i_0_11062]),
    [final] ).

cnf(i_0_18184,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_7362]),
    [final] ).

cnf(i_0_18185,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_11045]),
    [final] ).

cnf(i_0_18186,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_11063]),
    [final] ).

cnf(i_0_18187,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_11064]),
    [final] ).

cnf(i_0_18188,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11065]),
    [final] ).

cnf(i_0_18189,plain,
    ( c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1))
    | ~ class_Orderings_Olinorder(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11066]),
    [final] ).

cnf(i_0_18190,plain,
    ( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
    | ~ class_Rings_Osemiring__1(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11067]),
    [final] ).

cnf(i_0_18191,plain,
    ( c_List_Oremdups(X2,X1) = c_List_Olist_ONil(X2)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11052]),
    [final] ).

cnf(i_0_18192,plain,
    ( c_List_Olist_ONil(X2) = c_List_Oremdups(X2,X1)
    | X1 != c_List_Olist_ONil(X2) ),
    inference(split_conjunct,[status(thm)],[i_0_11053]),
    [final] ).

cnf(i_0_18193,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_11046]),
    [final] ).

cnf(i_0_18194,plain,
    hAPP(c_New__DSequence_Opos__empty(X1),X2) = c_Lazy__Sequence_Oempty(X1),
    inference(split_conjunct,[status(thm)],[i_0_11068]),
    [final] ).

cnf(i_0_18195,plain,
    c_List_Oremdups(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11069]),
    [final] ).

cnf(i_0_18196,plain,
    c_List_Obutlast(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(split_conjunct,[status(thm)],[i_0_11070]),
    [final] ).

cnf(i_0_18197,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11071]),
    [final] ).

cnf(i_0_18198,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11072]),
    [final] ).

cnf(i_0_18199,plain,
    hAPP(c_Nat_OSuc,X1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[i_0_11073]),
    [final] ).

cnf(i_0_18200,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11074]),
    [final] ).

cnf(i_0_18201,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11075]),
    [final] ).

cnf(i_0_18202,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11076]),
    [final] ).

cnf(i_0_18203,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_18204,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_18205,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_18206,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_18207,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_18208,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_18209,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_18210,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_11077]),
    [final] ).

cnf(i_0_18211,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_11078]),
    [final] ).

cnf(i_0_18212,plain,
    hAPP(c_Nat_OSuc,X1) != X1,
    inference(split_conjunct,[status(thm)],[i_0_11079]),
    [final] ).

cnf(i_0_18213,plain,
    X1 != hAPP(c_Nat_OSuc,X1),
    inference(split_conjunct,[status(thm)],[i_0_11080]),
    [final] ).

cnf(i_0_18214,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11081]),
    [final] ).

cnf(i_0_18215,plain,
    hAPP(c_Fun_Oid(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11082]),
    [final] ).

cnf(i_0_18216,plain,
    hAPP(c_Set_OCollect(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11083]),
    [final] ).

cnf(i_0_18217,plain,
    hAPP(c_COMBI(X1),X2) = X2,
    inference(split_conjunct,[status(thm)],[i_0_11084]),
    [final] ).

cnf(i_0_18218,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_10342]),
    [final] ).

cnf(i_0_18219,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_5265]),
    [final] ).

cnf(i_0_18220,plain,
    ( c_Nitpick_Onat__gcd(X2,X1) = X2
    | X1 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(split_conjunct,[status(thm)],[i_0_10534]),
    [final] ).

cnf(i_0_18221,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_18222,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_11085]),
    [final] ).

cnf(i_0_18223,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_11086]),
    [final] ).

cnf(i_0_18224,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_10865]),
    [final] ).

cnf(i_0_18225,plain,
    c_Quickcheck_Obeyond(X1,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[i_0_11087]),
    [final] ).

cnf(i_0_18226,plain,
    X1 = hAPP(c_Code__Numeral_Oof__nat,esk529_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_10251]),
    [final] ).

cnf(i_0_18227,plain,
    X1 = hAPP(c_Int_OAbs__Integ,esk304_1(X1)),
    inference(split_conjunct,[status(thm)],[i_0_8888]),
    [final] ).

cnf(i_0_18228,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11088]),
    [final] ).

cnf(i_0_18229,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11089]),
    [final] ).

cnf(i_0_18230,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_18231,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_18232,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_18233,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_18234,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_18235,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_18236,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_18237,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_18238,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_18239,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_18240,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_18241,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_18242,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11090]),
    [final] ).

cnf(i_0_18243,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) = X1,
    inference(split_conjunct,[status(thm)],[i_0_11091]),
    [final] ).

cnf(i_0_18244,plain,
    ( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X1))
    | ~ class_Lazy__Sequence_Osmall__lazy(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11092]),
    [final] ).

cnf(i_0_18245,plain,
    ( class_Enum_Oenum(tc_Option_Ooption(X1))
    | ~ class_Enum_Oenum(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11093]),
    [final] ).

cnf(i_0_18246,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(X1))
    | ~ class_Finite__Set_Ofinite(X1) ),
    inference(split_conjunct,[status(thm)],[i_0_11094]),
    [final] ).

cnf(i_0_18247,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_18248,plain,
    c_Equiv__Relations_Oequivp(X1,c_fequal),
    inference(split_conjunct,[status(thm)],[i_0_11095]),
    [final] ).

cnf(i_0_18249,plain,
    c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[fact_trans__less__than]),
    [final] ).

cnf(i_0_18250,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(split_conjunct,[status(thm)],[fact_wf__pred__nat]),
    [final] ).

cnf(i_0_18251,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(split_conjunct,[status(thm)],[fact_wf__less__than]),
    [final] ).

cnf(i_0_18252,plain,
    class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11096]),
    [final] ).

cnf(i_0_18253,plain,
    class_Nat_Osize(tc_List_Olist(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11097]),
    [final] ).

cnf(i_0_18254,plain,
    class_Nat_Osize(tc_Option_Ooption(X1)),
    inference(split_conjunct,[status(thm)],[i_0_11098]),
    [final] ).

cnf(i_0_18255,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_18256,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_18257,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_18258,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_18259,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_18260,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_18261,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_18262,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_18263,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_18264,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_18265,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_18266,plain,
    ~ hBOOL(c_fFalse),
    inference(split_conjunct,[status(thm)],[i_0_11099]),
    [final] ).

cnf(i_0_18267,plain,
    class_Lattices_Obounded__lattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Obounded__lattice]),
    [final] ).

cnf(i_0_18268,plain,
    class_Rings_Ocomm__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]),
    [final] ).

cnf(i_0_18269,plain,
    class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Odvd]),
    [final] ).

cnf(i_0_18270,plain,
    class_Rings_Odvd(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Odvd]),
    [final] ).

cnf(i_0_18271,plain,
    class_Rings_Odvd(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Odvd]),
    [final] ).

cnf(i_0_18272,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_18273,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_18274,plain,
    class_Nat_Osize(tc_Code__Evaluation_Oterm),
    inference(split_conjunct,[status(thm)],[arity_Code____Evaluation__Oterm__Nat_Osize]),
    [final] ).

cnf(i_0_18275,plain,
    class_Nat_Osize(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Nat_Osize]),
    [final] ).

cnf(i_0_18276,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_18277,plain,
    class_Nat_Osize(tc_Com_Ocom),
    inference(split_conjunct,[status(thm)],[arity_Com__Ocom__Nat_Osize]),
    [final] ).

cnf(i_0_18278,plain,
    class_Nat_Osize(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Nat_Osize]),
    [final] ).

cnf(i_0_18279,plain,
    class_Nat_Osize(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Nat_Osize]),
    [final] ).

cnf(i_0_18280,plain,
    class_Enum_Oenum(tc_Product__Type_Ounit),
    inference(split_conjunct,[status(thm)],[arity_Product____Type__Ounit__Enum_Oenum]),
    [final] ).

cnf(i_0_18281,plain,
    class_Enum_Oenum(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Enum_Oenum]),
    [final] ).

cnf(i_0_18282,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_18283,plain,
    class_Groups_Osemigroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18284,plain,
    class_Groups_Osemigroup__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Osemigroup__add]),
    [final] ).

cnf(i_0_18285,plain,
    class_Orderings_Owellorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Owellorder]),
    [final] ).

cnf(i_0_18286,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_18287,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_18288,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_18289,plain,
    class_Orderings_Otop(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Otop]),
    [final] ).

cnf(i_0_18290,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_18291,plain,
    class_Groups_Oabs__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]),
    [final] ).

cnf(i_0_18292,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_18293,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_18294,plain,
    class_Groups_Osgn__if(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]),
    [final] ).

cnf(i_0_18295,plain,
    class_Lattices_Osemilattice__inf(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18296,plain,
    class_Lattices_Osemilattice__inf(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18297,plain,
    class_Lattices_Osemilattice__inf(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__inf]),
    [final] ).

cnf(i_0_18298,plain,
    class_Lattices_Odistrib__lattice(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18299,plain,
    class_Lattices_Odistrib__lattice(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18300,plain,
    class_Lattices_Odistrib__lattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Odistrib__lattice]),
    [final] ).

cnf(i_0_18301,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_18302,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_18303,plain,
    class_Lattices_Olattice(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Olattice]),
    [final] ).

cnf(i_0_18304,plain,
    class_Lattices_Olattice(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Olattice]),
    [final] ).

cnf(i_0_18305,plain,
    class_Lattices_Olattice(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Olattice]),
    [final] ).

cnf(i_0_18306,plain,
    class_Lattices_Osemilattice__sup(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18307,plain,
    class_Lattices_Osemilattice__sup(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18308,plain,
    class_Lattices_Osemilattice__sup(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Osemilattice__sup]),
    [final] ).

cnf(i_0_18309,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_18310,plain,
    class_Rings_Oidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oidom]),
    [final] ).

cnf(i_0_18311,plain,
    class_Lattices_Oboolean__algebra(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]),
    [final] ).

cnf(i_0_18312,plain,
    class_Groups_Ouminus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ouminus]),
    [final] ).

cnf(i_0_18313,plain,
    class_Groups_Ouminus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]),
    [final] ).

cnf(i_0_18314,plain,
    class_Divides_Oring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Oring__div]),
    [final] ).

cnf(i_0_18315,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_18316,plain,
    class_Divides_Osemiring__div(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18317,plain,
    class_Divides_Osemiring__div(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Divides_Osemiring__div]),
    [final] ).

cnf(i_0_18318,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_18319,plain,
    class_Rings_Osemiring__0(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18320,plain,
    class_Rings_Osemiring__0(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]),
    [final] ).

cnf(i_0_18321,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_18322,plain,
    class_Power_Opower(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Power_Opower]),
    [final] ).

cnf(i_0_18323,plain,
    class_Power_Opower(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Power_Opower]),
    [final] ).

cnf(i_0_18324,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_18325,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_18326,plain,
    class_Rings_Osemiring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18327,plain,
    class_Rings_Osemiring__1(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]),
    [final] ).

cnf(i_0_18328,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_18329,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_18330,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_18331,plain,
    class_Int_Onumber__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]),
    [final] ).

cnf(i_0_18332,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_18333,plain,
    class_Int_Onumber(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Int_Onumber]),
    [final] ).

cnf(i_0_18334,plain,
    class_Int_Onumber(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Int_Onumber]),
    [final] ).

cnf(i_0_18335,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_18336,plain,
    class_Rings_Oring__1(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring__1]),
    [final] ).

cnf(i_0_18337,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_18338,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_18339,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_18340,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_18341,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_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__semiring__1__strict(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]),
    [final] ).

cnf(i_0_18346,plain,
    class_Rings_Oring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oring]),
    [final] ).

cnf(i_0_18347,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_18348,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_18349,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_18350,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_18351,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_18352,plain,
    class_Groups_Omonoid__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18353,plain,
    class_Groups_Omonoid__add(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]),
    [final] ).

cnf(i_0_18354,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_18355,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_18356,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_18357,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_18358,plain,
    class_Groups_Omonoid__mult(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18359,plain,
    class_Groups_Omonoid__mult(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]),
    [final] ).

cnf(i_0_18360,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_18361,plain,
    class_Rings_Olinordered__idom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]),
    [final] ).

cnf(i_0_18362,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_18363,plain,
    class_Rings_Olinordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_18364,plain,
    class_Rings_Olinordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]),
    [final] ).

cnf(i_0_18365,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_18366,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_18367,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_18368,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_18369,plain,
    class_Rings_Ocomm__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]),
    [final] ).

cnf(i_0_18370,plain,
    class_Rings_Ocomm__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]),
    [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_Omult__zero(tc_Code__Numeral_Ocode__numeral),
    inference(split_conjunct,[status(thm)],[arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero]),
    [final] ).

cnf(i_0_18375,plain,
    class_Rings_Omult__zero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]),
    [final] ).

cnf(i_0_18376,plain,
    class_Rings_Omult__zero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]),
    [final] ).

cnf(i_0_18377,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_18378,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_18379,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_18380,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_18381,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_18382,plain,
    class_Groups_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ozero]),
    [final] ).

cnf(i_0_18383,plain,
    class_Groups_Ozero(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ozero]),
    [final] ).

cnf(i_0_18384,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_18385,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_18386,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_18387,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_18388,plain,
    class_Rings_Oordered__semiring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18389,plain,
    class_Rings_Oordered__semiring(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]),
    [final] ).

cnf(i_0_18390,plain,
    class_Rings_Oordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]),
    [final] ).

cnf(i_0_18391,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_18392,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_18393,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_18394,plain,
    class_Rings_Olinordered__ring(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]),
    [final] ).

cnf(i_0_18395,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_18396,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_18397,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_18398,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_18399,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_18400,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_18401,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_18402,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_18403,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_18404,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_18405,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_18406,plain,
    class_Rings_Olinordered__semidom(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18407,plain,
    class_Rings_Olinordered__semidom(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]),
    [final] ).

cnf(i_0_18408,plain,
    class_Groups_Ogroup__add(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]),
    [final] ).

cnf(i_0_18409,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_18410,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_18411,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_18412,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_18413,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_18414,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_18415,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_18416,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_18417,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_18418,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_18419,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_18420,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_18421,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_18422,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_18423,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_18424,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_18425,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_18426,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_18427,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_18428,plain,
    class_Groups_Oone(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Oone]),
    [final] ).

cnf(i_0_18429,plain,
    class_Groups_Oone(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Oone]),
    [final] ).

cnf(i_0_18430,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_18431,plain,
    class_Groups_Ominus(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Groups_Ominus]),
    [final] ).

cnf(i_0_18432,plain,
    class_Groups_Ominus(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Groups_Ominus]),
    [final] ).

cnf(i_0_18433,plain,
    class_Groups_Ominus(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Groups_Ominus]),
    [final] ).

cnf(i_0_18434,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_18435,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_18436,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_18437,plain,
    class_Orderings_Oord(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oord]),
    [final] ).

cnf(i_0_18438,plain,
    class_Orderings_Oord(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oord]),
    [final] ).

cnf(i_0_18439,plain,
    class_Orderings_Oord(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oord]),
    [final] ).

cnf(i_0_18440,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_18441,plain,
    class_Orderings_Oorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Oorder]),
    [final] ).

cnf(i_0_18442,plain,
    class_Orderings_Oorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]),
    [final] ).

cnf(i_0_18443,plain,
    class_Orderings_Oorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]),
    [final] ).

cnf(i_0_18444,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_18445,plain,
    class_Orderings_Olinorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]),
    [final] ).

cnf(i_0_18446,plain,
    class_Orderings_Olinorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]),
    [final] ).

cnf(i_0_18447,plain,
    class_Orderings_Obot(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Obot]),
    [final] ).

cnf(i_0_18448,plain,
    class_Orderings_Obot(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Obot]),
    [final] ).

cnf(i_0_18449,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_18450,plain,
    class_Orderings_Opreorder(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18451,plain,
    class_Orderings_Opreorder(tc_Nat_Onat),
    inference(split_conjunct,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18452,plain,
    class_Orderings_Opreorder(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]),
    [final] ).

cnf(i_0_18453,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_18454,plain,
    class_Finite__Set_Ofinite(tc_HOL_Obool),
    inference(split_conjunct,[status(thm)],[arity_HOL__Obool__Finite__Set_Ofinite]),
    [final] ).

cnf(i_0_18455,plain,
    hBOOL(c_fTrue),
    inference(split_conjunct,[status(thm)],[help_c__fTrue__1]),
    [final] ).

cnf(i_0_18456,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_18457,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_18458,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(split_conjunct,[status(thm)],[fact_Pls__def]),
    [final] ).

cnf(i_0_18459,plain,
    c_Int_OMin != c_Int_OPls,
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I40_J]),
    [final] ).

cnf(i_0_18460,plain,
    c_Int_OPls != c_Int_OMin,
    inference(split_conjunct,[status(thm)],[fact_rel__simps_I37_J]),
    [final] ).

cnf(i_0_18461,axiom,
    X1 = X1 ).

cnf(i_0_18462,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_18463,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_18464,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_18465,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_18466,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_18467,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_18468,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_18469,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_18470,axiom,
    ( X1 != X2
    | c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).

cnf(i_0_18471,axiom,
    ( X1 != X2
    | c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).

cnf(i_0_18472,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X1,X3,X4,X5,X6) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18473,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X1,X4,X5,X6) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18474,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X1,X5,X6) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18475,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X1,X6) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18476,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X6,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18477,axiom,
    ( X1 != X2
    | c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).

cnf(i_0_18478,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).

cnf(i_0_18479,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).

cnf(i_0_18480,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).

cnf(i_0_18481,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).

cnf(i_0_18482,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).

cnf(i_0_18483,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).

cnf(i_0_18484,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).

cnf(i_0_18485,axiom,
    ( X1 != X2
    | c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).

cnf(i_0_18486,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).

cnf(i_0_18487,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).

cnf(i_0_18488,axiom,
    ( X1 != X2
    | c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).

cnf(i_0_18489,axiom,
    ( X1 != X2
    | c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).

cnf(i_0_18490,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_18491,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X1,X3,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18492,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X1,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18493,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X1,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18494,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X1,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18495,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X1,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18496,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X1) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18497,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_18498,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_18499,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_18500,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_18501,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_18502,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_18503,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).

cnf(i_0_18504,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).

cnf(i_0_18505,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).

cnf(i_0_18506,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).

cnf(i_0_18507,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).

cnf(i_0_18508,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).

cnf(i_0_18509,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).

cnf(i_0_18510,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).

cnf(i_0_18511,axiom,
    ( X1 != X2
    | c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).

cnf(i_0_18512,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).

cnf(i_0_18513,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).

cnf(i_0_18514,axiom,
    ( X1 != X2
    | esk524_6(X1,X3,X4,X5,X6,X7) = esk524_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18515,axiom,
    ( X1 != X2
    | esk524_6(X3,X1,X4,X5,X6,X7) = esk524_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18516,axiom,
    ( X1 != X2
    | esk524_6(X3,X4,X1,X5,X6,X7) = esk524_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18517,axiom,
    ( X1 != X2
    | esk524_6(X3,X4,X5,X1,X6,X7) = esk524_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18518,axiom,
    ( X1 != X2
    | esk524_6(X3,X4,X5,X6,X1,X7) = esk524_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18519,axiom,
    ( X1 != X2
    | esk524_6(X3,X4,X5,X6,X7,X1) = esk524_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18520,axiom,
    ( X1 != X2
    | esk525_6(X1,X3,X4,X5,X6,X7) = esk525_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18521,axiom,
    ( X1 != X2
    | esk525_6(X3,X1,X4,X5,X6,X7) = esk525_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18522,axiom,
    ( X1 != X2
    | esk525_6(X3,X4,X1,X5,X6,X7) = esk525_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18523,axiom,
    ( X1 != X2
    | esk525_6(X3,X4,X5,X1,X6,X7) = esk525_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18524,axiom,
    ( X1 != X2
    | esk525_6(X3,X4,X5,X6,X1,X7) = esk525_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18525,axiom,
    ( X1 != X2
    | esk525_6(X3,X4,X5,X6,X7,X1) = esk525_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18526,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_18527,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_18528,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).

cnf(i_0_18529,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).

cnf(i_0_18530,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).

cnf(i_0_18531,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).

cnf(i_0_18532,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).

cnf(i_0_18533,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).

cnf(i_0_18534,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).

cnf(i_0_18535,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_18536,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_18537,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_18538,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).

cnf(i_0_18539,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).

cnf(i_0_18540,axiom,
    ( X1 != X2
    | c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).

cnf(i_0_18541,axiom,
    ( X1 != X2
    | c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).

cnf(i_0_18542,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).

cnf(i_0_18543,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).

cnf(i_0_18544,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_18545,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_18546,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_18547,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_18548,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_18549,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_18550,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_18551,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_18552,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_18553,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_18554,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_18555,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_18556,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_18557,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_18558,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_18559,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_18560,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_18561,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_18562,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_18563,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_18564,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_18565,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_18566,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_18567,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_18568,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X1,X3,X4) = c_Lazy__Sequence_Oappend(X2,X3,X4) ) ).

cnf(i_0_18569,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X1,X4) = c_Lazy__Sequence_Oappend(X3,X2,X4) ) ).

cnf(i_0_18570,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X4,X1) = c_Lazy__Sequence_Oappend(X3,X4,X2) ) ).

cnf(i_0_18571,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X1,X3,X4,X5) = c_Lazy__Sequence_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18572,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X1,X4,X5) = c_Lazy__Sequence_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18573,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X1,X5) = c_Lazy__Sequence_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18574,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X5,X1) = c_Lazy__Sequence_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18575,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).

cnf(i_0_18576,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_18577,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_18578,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_18579,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_18580,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18581,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18582,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18583,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18584,axiom,
    ( X1 != X2
    | esk349_5(X1,X3,X4,X5,X6) = esk349_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18585,axiom,
    ( X1 != X2
    | esk349_5(X3,X1,X4,X5,X6) = esk349_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18586,axiom,
    ( X1 != X2
    | esk349_5(X3,X4,X1,X5,X6) = esk349_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18587,axiom,
    ( X1 != X2
    | esk349_5(X3,X4,X5,X1,X6) = esk349_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18588,axiom,
    ( X1 != X2
    | esk349_5(X3,X4,X5,X6,X1) = esk349_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18589,axiom,
    ( X1 != X2
    | esk350_5(X1,X3,X4,X5,X6) = esk350_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18590,axiom,
    ( X1 != X2
    | esk350_5(X3,X1,X4,X5,X6) = esk350_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18591,axiom,
    ( X1 != X2
    | esk350_5(X3,X4,X1,X5,X6) = esk350_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18592,axiom,
    ( X1 != X2
    | esk350_5(X3,X4,X5,X1,X6) = esk350_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18593,axiom,
    ( X1 != X2
    | esk350_5(X3,X4,X5,X6,X1) = esk350_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18594,axiom,
    ( X1 != X2
    | esk348_5(X1,X3,X4,X5,X6) = esk348_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18595,axiom,
    ( X1 != X2
    | esk348_5(X3,X1,X4,X5,X6) = esk348_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18596,axiom,
    ( X1 != X2
    | esk348_5(X3,X4,X1,X5,X6) = esk348_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18597,axiom,
    ( X1 != X2
    | esk348_5(X3,X4,X5,X1,X6) = esk348_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18598,axiom,
    ( X1 != X2
    | esk348_5(X3,X4,X5,X6,X1) = esk348_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18599,axiom,
    ( X1 != X2
    | esk347_5(X1,X3,X4,X5,X6) = esk347_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18600,axiom,
    ( X1 != X2
    | esk347_5(X3,X1,X4,X5,X6) = esk347_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18601,axiom,
    ( X1 != X2
    | esk347_5(X3,X4,X1,X5,X6) = esk347_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18602,axiom,
    ( X1 != X2
    | esk347_5(X3,X4,X5,X1,X6) = esk347_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18603,axiom,
    ( X1 != X2
    | esk347_5(X3,X4,X5,X6,X1) = esk347_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18604,axiom,
    ( X1 != X2
    | c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).

cnf(i_0_18605,axiom,
    ( X1 != X2
    | c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).

cnf(i_0_18606,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_18607,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_18608,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_18609,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_18610,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18611,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18612,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18613,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18614,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18615,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18616,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18617,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18618,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18619,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18620,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18621,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18622,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18623,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18624,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).

cnf(i_0_18625,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).

cnf(i_0_18626,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).

cnf(i_0_18627,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).

cnf(i_0_18628,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).

cnf(i_0_18629,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).

cnf(i_0_18630,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).

cnf(i_0_18631,axiom,
    ( X1 != X2
    | esk196_6(X1,X3,X4,X5,X6,X7) = esk196_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18632,axiom,
    ( X1 != X2
    | esk196_6(X3,X1,X4,X5,X6,X7) = esk196_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18633,axiom,
    ( X1 != X2
    | esk196_6(X3,X4,X1,X5,X6,X7) = esk196_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18634,axiom,
    ( X1 != X2
    | esk196_6(X3,X4,X5,X1,X6,X7) = esk196_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18635,axiom,
    ( X1 != X2
    | esk196_6(X3,X4,X5,X6,X1,X7) = esk196_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18636,axiom,
    ( X1 != X2
    | esk196_6(X3,X4,X5,X6,X7,X1) = esk196_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18637,axiom,
    ( X1 != X2
    | esk195_6(X1,X3,X4,X5,X6,X7) = esk195_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18638,axiom,
    ( X1 != X2
    | esk195_6(X3,X1,X4,X5,X6,X7) = esk195_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18639,axiom,
    ( X1 != X2
    | esk195_6(X3,X4,X1,X5,X6,X7) = esk195_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18640,axiom,
    ( X1 != X2
    | esk195_6(X3,X4,X5,X1,X6,X7) = esk195_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18641,axiom,
    ( X1 != X2
    | esk195_6(X3,X4,X5,X6,X1,X7) = esk195_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18642,axiom,
    ( X1 != X2
    | esk195_6(X3,X4,X5,X6,X7,X1) = esk195_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18643,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_18644,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X1,X3,X4) = c_Enum_On__lists(X2,X3,X4) ) ).

cnf(i_0_18645,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X1,X4) = c_Enum_On__lists(X3,X2,X4) ) ).

cnf(i_0_18646,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X4,X1) = c_Enum_On__lists(X3,X4,X2) ) ).

cnf(i_0_18647,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).

cnf(i_0_18648,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).

cnf(i_0_18649,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).

cnf(i_0_18650,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).

cnf(i_0_18651,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).

cnf(i_0_18652,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).

cnf(i_0_18653,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).

cnf(i_0_18654,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).

cnf(i_0_18655,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).

cnf(i_0_18656,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_18657,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_18658,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_18659,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_18660,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X2,X3,X4,X5) ) ).

cnf(i_0_18661,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X1,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X2,X4,X5) ) ).

cnf(i_0_18662,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X1,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X2,X5) ) ).

cnf(i_0_18663,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X2) ) ).

cnf(i_0_18664,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).

cnf(i_0_18665,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).

cnf(i_0_18666,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).

cnf(i_0_18667,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).

cnf(i_0_18668,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).

cnf(i_0_18669,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).

cnf(i_0_18670,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).

cnf(i_0_18671,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).

cnf(i_0_18672,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).

cnf(i_0_18673,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).

cnf(i_0_18674,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).

cnf(i_0_18675,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).

cnf(i_0_18676,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).

cnf(i_0_18677,axiom,
    ( X1 != X2
    | esk375_4(X1,X3,X4,X5) = esk375_4(X2,X3,X4,X5) ) ).

cnf(i_0_18678,axiom,
    ( X1 != X2
    | esk375_4(X3,X1,X4,X5) = esk375_4(X3,X2,X4,X5) ) ).

cnf(i_0_18679,axiom,
    ( X1 != X2
    | esk375_4(X3,X4,X1,X5) = esk375_4(X3,X4,X2,X5) ) ).

cnf(i_0_18680,axiom,
    ( X1 != X2
    | esk375_4(X3,X4,X5,X1) = esk375_4(X3,X4,X5,X2) ) ).

cnf(i_0_18681,axiom,
    ( X1 != X2
    | esk374_4(X1,X3,X4,X5) = esk374_4(X2,X3,X4,X5) ) ).

cnf(i_0_18682,axiom,
    ( X1 != X2
    | esk374_4(X3,X1,X4,X5) = esk374_4(X3,X2,X4,X5) ) ).

cnf(i_0_18683,axiom,
    ( X1 != X2
    | esk374_4(X3,X4,X1,X5) = esk374_4(X3,X4,X2,X5) ) ).

cnf(i_0_18684,axiom,
    ( X1 != X2
    | esk374_4(X3,X4,X5,X1) = esk374_4(X3,X4,X5,X2) ) ).

cnf(i_0_18685,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_18686,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_18687,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_18688,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_18689,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_18690,axiom,
    ( X1 != X2
    | c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).

cnf(i_0_18691,axiom,
    ( X1 != X2
    | c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).

cnf(i_0_18692,axiom,
    ( X1 != X2
    | c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).

cnf(i_0_18693,axiom,
    ( X1 != X2
    | c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).

cnf(i_0_18694,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_18695,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).

cnf(i_0_18696,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).

cnf(i_0_18697,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).

cnf(i_0_18698,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).

cnf(i_0_18699,axiom,
    ( X1 != X2
    | c_List_Omeasures(X1,X3) = c_List_Omeasures(X2,X3) ) ).

cnf(i_0_18700,axiom,
    ( X1 != X2
    | c_List_Omeasures(X3,X1) = c_List_Omeasures(X3,X2) ) ).

cnf(i_0_18701,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18702,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18703,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18704,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18705,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).

cnf(i_0_18706,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).

cnf(i_0_18707,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).

cnf(i_0_18708,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).

cnf(i_0_18709,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_18710,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_18711,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_18712,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).

cnf(i_0_18713,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).

cnf(i_0_18714,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).

cnf(i_0_18715,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_18716,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X1,X3) = c_Enum_Osublists(X2,X3) ) ).

cnf(i_0_18717,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X3,X1) = c_Enum_Osublists(X3,X2) ) ).

cnf(i_0_18718,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).

cnf(i_0_18719,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).

cnf(i_0_18720,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).

cnf(i_0_18721,axiom,
    ( X1 != X2
    | c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).

cnf(i_0_18722,axiom,
    ( X1 != X2
    | c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).

cnf(i_0_18723,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18724,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18725,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18726,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18727,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18728,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).

cnf(i_0_18729,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).

cnf(i_0_18730,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).

cnf(i_0_18731,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).

cnf(i_0_18732,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).

cnf(i_0_18733,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).

cnf(i_0_18734,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).

cnf(i_0_18735,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).

cnf(i_0_18736,axiom,
    ( X1 != X2
    | c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).

cnf(i_0_18737,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).

cnf(i_0_18738,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).

cnf(i_0_18739,axiom,
    ( X1 != X2
    | esk490_4(X1,X3,X4,X5) = esk490_4(X2,X3,X4,X5) ) ).

cnf(i_0_18740,axiom,
    ( X1 != X2
    | esk490_4(X3,X1,X4,X5) = esk490_4(X3,X2,X4,X5) ) ).

cnf(i_0_18741,axiom,
    ( X1 != X2
    | esk490_4(X3,X4,X1,X5) = esk490_4(X3,X4,X2,X5) ) ).

cnf(i_0_18742,axiom,
    ( X1 != X2
    | esk490_4(X3,X4,X5,X1) = esk490_4(X3,X4,X5,X2) ) ).

cnf(i_0_18743,axiom,
    ( X1 != X2
    | esk489_4(X1,X3,X4,X5) = esk489_4(X2,X3,X4,X5) ) ).

cnf(i_0_18744,axiom,
    ( X1 != X2
    | esk489_4(X3,X1,X4,X5) = esk489_4(X3,X2,X4,X5) ) ).

cnf(i_0_18745,axiom,
    ( X1 != X2
    | esk489_4(X3,X4,X1,X5) = esk489_4(X3,X4,X2,X5) ) ).

cnf(i_0_18746,axiom,
    ( X1 != X2
    | esk489_4(X3,X4,X5,X1) = esk489_4(X3,X4,X5,X2) ) ).

cnf(i_0_18747,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).

cnf(i_0_18748,axiom,
    ( X1 != X2
    | esk341_3(X1,X3,X4) = esk341_3(X2,X3,X4) ) ).

cnf(i_0_18749,axiom,
    ( X1 != X2
    | esk341_3(X3,X1,X4) = esk341_3(X3,X2,X4) ) ).

cnf(i_0_18750,axiom,
    ( X1 != X2
    | esk341_3(X3,X4,X1) = esk341_3(X3,X4,X2) ) ).

cnf(i_0_18751,axiom,
    ( X1 != X2
    | esk340_3(X1,X3,X4) = esk340_3(X2,X3,X4) ) ).

cnf(i_0_18752,axiom,
    ( X1 != X2
    | esk340_3(X3,X1,X4) = esk340_3(X3,X2,X4) ) ).

cnf(i_0_18753,axiom,
    ( X1 != X2
    | esk340_3(X3,X4,X1) = esk340_3(X3,X4,X2) ) ).

cnf(i_0_18754,axiom,
    ( X1 != X2
    | c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).

cnf(i_0_18755,axiom,
    ( X1 != X2
    | c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).

cnf(i_0_18756,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).

cnf(i_0_18757,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).

cnf(i_0_18758,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).

cnf(i_0_18759,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).

cnf(i_0_18760,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_18761,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_18762,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_18763,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_18764,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_18765,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).

cnf(i_0_18766,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).

cnf(i_0_18767,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).

cnf(i_0_18768,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).

cnf(i_0_18769,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).

cnf(i_0_18770,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_18771,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_18772,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_18773,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_18774,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).

cnf(i_0_18775,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).

cnf(i_0_18776,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).

cnf(i_0_18777,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_18778,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_18779,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_18780,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_18781,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).

cnf(i_0_18782,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X3,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18783,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X1,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18784,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X1,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18785,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X1,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18786,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X6,X1) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18787,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X3,X4) ) ).

cnf(i_0_18788,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4) ) ).

cnf(i_0_18789,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X2) ) ).

cnf(i_0_18790,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).

cnf(i_0_18791,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).

cnf(i_0_18792,axiom,
    ( X1 != X2
    | esk225_5(X1,X3,X4,X5,X6) = esk225_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18793,axiom,
    ( X1 != X2
    | esk225_5(X3,X1,X4,X5,X6) = esk225_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18794,axiom,
    ( X1 != X2
    | esk225_5(X3,X4,X1,X5,X6) = esk225_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18795,axiom,
    ( X1 != X2
    | esk225_5(X3,X4,X5,X1,X6) = esk225_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18796,axiom,
    ( X1 != X2
    | esk225_5(X3,X4,X5,X6,X1) = esk225_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18797,axiom,
    ( X1 != X2
    | esk337_3(X1,X3,X4) = esk337_3(X2,X3,X4) ) ).

cnf(i_0_18798,axiom,
    ( X1 != X2
    | esk337_3(X3,X1,X4) = esk337_3(X3,X2,X4) ) ).

cnf(i_0_18799,axiom,
    ( X1 != X2
    | esk337_3(X3,X4,X1) = esk337_3(X3,X4,X2) ) ).

cnf(i_0_18800,axiom,
    ( X1 != X2
    | esk336_3(X1,X3,X4) = esk336_3(X2,X3,X4) ) ).

cnf(i_0_18801,axiom,
    ( X1 != X2
    | esk336_3(X3,X1,X4) = esk336_3(X3,X2,X4) ) ).

cnf(i_0_18802,axiom,
    ( X1 != X2
    | esk336_3(X3,X4,X1) = esk336_3(X3,X4,X2) ) ).

cnf(i_0_18803,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).

cnf(i_0_18804,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).

cnf(i_0_18805,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).

cnf(i_0_18806,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_18807,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_18808,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_18809,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_18810,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_18811,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).

cnf(i_0_18812,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).

cnf(i_0_18813,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).

cnf(i_0_18814,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).

cnf(i_0_18815,axiom,
    ( X1 != X2
    | esk446_2(X1,X3) = esk446_2(X2,X3) ) ).

cnf(i_0_18816,axiom,
    ( X1 != X2
    | esk446_2(X3,X1) = esk446_2(X3,X2) ) ).

cnf(i_0_18817,axiom,
    ( X1 != X2
    | esk447_2(X1,X3) = esk447_2(X2,X3) ) ).

cnf(i_0_18818,axiom,
    ( X1 != X2
    | esk447_2(X3,X1) = esk447_2(X3,X2) ) ).

cnf(i_0_18819,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).

cnf(i_0_18820,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).

cnf(i_0_18821,axiom,
    ( X1 != X2
    | c_List_Oremdups(X1,X3) = c_List_Oremdups(X2,X3) ) ).

cnf(i_0_18822,axiom,
    ( X1 != X2
    | c_List_Oremdups(X3,X1) = c_List_Oremdups(X3,X2) ) ).

cnf(i_0_18823,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).

cnf(i_0_18824,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).

cnf(i_0_18825,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).

cnf(i_0_18826,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_18827,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_18828,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_18829,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_18830,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_18831,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_18832,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_18833,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_18834,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_18835,axiom,
    ( X1 != X2
    | esk222_3(X1,X3,X4) = esk222_3(X2,X3,X4) ) ).

cnf(i_0_18836,axiom,
    ( X1 != X2
    | esk222_3(X3,X1,X4) = esk222_3(X3,X2,X4) ) ).

cnf(i_0_18837,axiom,
    ( X1 != X2
    | esk222_3(X3,X4,X1) = esk222_3(X3,X4,X2) ) ).

cnf(i_0_18838,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).

cnf(i_0_18839,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).

cnf(i_0_18840,axiom,
    ( X1 != X2
    | esk521_3(X1,X3,X4) = esk521_3(X2,X3,X4) ) ).

cnf(i_0_18841,axiom,
    ( X1 != X2
    | esk521_3(X3,X1,X4) = esk521_3(X3,X2,X4) ) ).

cnf(i_0_18842,axiom,
    ( X1 != X2
    | esk521_3(X3,X4,X1) = esk521_3(X3,X4,X2) ) ).

cnf(i_0_18843,axiom,
    ( X1 != X2
    | esk487_4(X1,X3,X4,X5) = esk487_4(X2,X3,X4,X5) ) ).

cnf(i_0_18844,axiom,
    ( X1 != X2
    | esk487_4(X3,X1,X4,X5) = esk487_4(X3,X2,X4,X5) ) ).

cnf(i_0_18845,axiom,
    ( X1 != X2
    | esk487_4(X3,X4,X1,X5) = esk487_4(X3,X4,X2,X5) ) ).

cnf(i_0_18846,axiom,
    ( X1 != X2
    | esk487_4(X3,X4,X5,X1) = esk487_4(X3,X4,X5,X2) ) ).

cnf(i_0_18847,axiom,
    ( X1 != X2
    | esk479_4(X1,X3,X4,X5) = esk479_4(X2,X3,X4,X5) ) ).

cnf(i_0_18848,axiom,
    ( X1 != X2
    | esk479_4(X3,X1,X4,X5) = esk479_4(X3,X2,X4,X5) ) ).

cnf(i_0_18849,axiom,
    ( X1 != X2
    | esk479_4(X3,X4,X1,X5) = esk479_4(X3,X4,X2,X5) ) ).

cnf(i_0_18850,axiom,
    ( X1 != X2
    | esk479_4(X3,X4,X5,X1) = esk479_4(X3,X4,X5,X2) ) ).

cnf(i_0_18851,axiom,
    ( X1 != X2
    | esk182_4(X1,X3,X4,X5) = esk182_4(X2,X3,X4,X5) ) ).

cnf(i_0_18852,axiom,
    ( X1 != X2
    | esk182_4(X3,X1,X4,X5) = esk182_4(X3,X2,X4,X5) ) ).

cnf(i_0_18853,axiom,
    ( X1 != X2
    | esk182_4(X3,X4,X1,X5) = esk182_4(X3,X4,X2,X5) ) ).

cnf(i_0_18854,axiom,
    ( X1 != X2
    | esk182_4(X3,X4,X5,X1) = esk182_4(X3,X4,X5,X2) ) ).

cnf(i_0_18855,axiom,
    ( X1 != X2
    | esk184_4(X1,X3,X4,X5) = esk184_4(X2,X3,X4,X5) ) ).

cnf(i_0_18856,axiom,
    ( X1 != X2
    | esk184_4(X3,X1,X4,X5) = esk184_4(X3,X2,X4,X5) ) ).

cnf(i_0_18857,axiom,
    ( X1 != X2
    | esk184_4(X3,X4,X1,X5) = esk184_4(X3,X4,X2,X5) ) ).

cnf(i_0_18858,axiom,
    ( X1 != X2
    | esk184_4(X3,X4,X5,X1) = esk184_4(X3,X4,X5,X2) ) ).

cnf(i_0_18859,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X1,X3,X4,X5) = c_Enum_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18860,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X1,X4,X5) = c_Enum_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18861,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X1,X5) = c_Enum_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18862,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X5,X1) = c_Enum_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18863,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_18864,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_18865,axiom,
    ( X1 != X2
    | esk23_4(X1,X3,X4,X5) = esk23_4(X2,X3,X4,X5) ) ).

cnf(i_0_18866,axiom,
    ( X1 != X2
    | esk23_4(X3,X1,X4,X5) = esk23_4(X3,X2,X4,X5) ) ).

cnf(i_0_18867,axiom,
    ( X1 != X2
    | esk23_4(X3,X4,X1,X5) = esk23_4(X3,X4,X2,X5) ) ).

cnf(i_0_18868,axiom,
    ( X1 != X2
    | esk23_4(X3,X4,X5,X1) = esk23_4(X3,X4,X5,X2) ) ).

cnf(i_0_18869,axiom,
    ( X1 != X2
    | esk22_4(X1,X3,X4,X5) = esk22_4(X2,X3,X4,X5) ) ).

cnf(i_0_18870,axiom,
    ( X1 != X2
    | esk22_4(X3,X1,X4,X5) = esk22_4(X3,X2,X4,X5) ) ).

cnf(i_0_18871,axiom,
    ( X1 != X2
    | esk22_4(X3,X4,X1,X5) = esk22_4(X3,X4,X2,X5) ) ).

cnf(i_0_18872,axiom,
    ( X1 != X2
    | esk22_4(X3,X4,X5,X1) = esk22_4(X3,X4,X5,X2) ) ).

cnf(i_0_18873,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_18874,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_18875,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_18876,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_18877,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_18878,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).

cnf(i_0_18879,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).

cnf(i_0_18880,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).

cnf(i_0_18881,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).

cnf(i_0_18882,axiom,
    ( X1 != X2
    | esk253_3(X1,X3,X4) = esk253_3(X2,X3,X4) ) ).

cnf(i_0_18883,axiom,
    ( X1 != X2
    | esk253_3(X3,X1,X4) = esk253_3(X3,X2,X4) ) ).

cnf(i_0_18884,axiom,
    ( X1 != X2
    | esk253_3(X3,X4,X1) = esk253_3(X3,X4,X2) ) ).

cnf(i_0_18885,axiom,
    ( X1 != X2
    | esk254_3(X1,X3,X4) = esk254_3(X2,X3,X4) ) ).

cnf(i_0_18886,axiom,
    ( X1 != X2
    | esk254_3(X3,X1,X4) = esk254_3(X3,X2,X4) ) ).

cnf(i_0_18887,axiom,
    ( X1 != X2
    | esk254_3(X3,X4,X1) = esk254_3(X3,X4,X2) ) ).

cnf(i_0_18888,axiom,
    ( X1 != X2
    | esk224_4(X1,X3,X4,X5) = esk224_4(X2,X3,X4,X5) ) ).

cnf(i_0_18889,axiom,
    ( X1 != X2
    | esk224_4(X3,X1,X4,X5) = esk224_4(X3,X2,X4,X5) ) ).

cnf(i_0_18890,axiom,
    ( X1 != X2
    | esk224_4(X3,X4,X1,X5) = esk224_4(X3,X4,X2,X5) ) ).

cnf(i_0_18891,axiom,
    ( X1 != X2
    | esk224_4(X3,X4,X5,X1) = esk224_4(X3,X4,X5,X2) ) ).

cnf(i_0_18892,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).

cnf(i_0_18893,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).

cnf(i_0_18894,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_18895,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_18896,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_18897,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_18898,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_18899,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_18900,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_18901,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_18902,axiom,
    ( X1 != X2
    | esk251_3(X1,X3,X4) = esk251_3(X2,X3,X4) ) ).

cnf(i_0_18903,axiom,
    ( X1 != X2
    | esk251_3(X3,X1,X4) = esk251_3(X3,X2,X4) ) ).

cnf(i_0_18904,axiom,
    ( X1 != X2
    | esk251_3(X3,X4,X1) = esk251_3(X3,X4,X2) ) ).

cnf(i_0_18905,axiom,
    ( X1 != X2
    | esk250_3(X1,X3,X4) = esk250_3(X2,X3,X4) ) ).

cnf(i_0_18906,axiom,
    ( X1 != X2
    | esk250_3(X3,X1,X4) = esk250_3(X3,X2,X4) ) ).

cnf(i_0_18907,axiom,
    ( X1 != X2
    | esk250_3(X3,X4,X1) = esk250_3(X3,X4,X2) ) ).

cnf(i_0_18908,axiom,
    ( X1 != X2
    | c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).

cnf(i_0_18909,axiom,
    ( X1 != X2
    | c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).

cnf(i_0_18910,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_18911,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_18912,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_18913,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_18914,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_18915,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_18916,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_18917,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_18918,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_18919,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_18920,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_18921,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_18922,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_18923,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_18924,axiom,
    ( X1 != X2
    | esk512_2(X1,X3) = esk512_2(X2,X3) ) ).

cnf(i_0_18925,axiom,
    ( X1 != X2
    | esk512_2(X3,X1) = esk512_2(X3,X2) ) ).

cnf(i_0_18926,axiom,
    ( X1 != X2
    | esk511_2(X1,X3) = esk511_2(X2,X3) ) ).

cnf(i_0_18927,axiom,
    ( X1 != X2
    | esk511_2(X3,X1) = esk511_2(X3,X2) ) ).

cnf(i_0_18928,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18929,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18930,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18931,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18932,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) ) ).

cnf(i_0_18933,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_18934,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_18935,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_18936,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_18937,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_18938,axiom,
    ( X1 != X2
    | c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).

cnf(i_0_18939,axiom,
    ( X1 != X2
    | c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).

cnf(i_0_18940,axiom,
    ( X1 != X2
    | esk36_3(X1,X3,X4) = esk36_3(X2,X3,X4) ) ).

cnf(i_0_18941,axiom,
    ( X1 != X2
    | esk36_3(X3,X1,X4) = esk36_3(X3,X2,X4) ) ).

cnf(i_0_18942,axiom,
    ( X1 != X2
    | esk36_3(X3,X4,X1) = esk36_3(X3,X4,X2) ) ).

cnf(i_0_18943,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X3) = c_Lazy__Sequence_Osmall__lazy_H(X2,X3) ) ).

cnf(i_0_18944,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X3,X1) = c_Lazy__Sequence_Osmall__lazy_H(X3,X2) ) ).

cnf(i_0_18945,axiom,
    ( X1 != X2
    | esk492_4(X1,X3,X4,X5) = esk492_4(X2,X3,X4,X5) ) ).

cnf(i_0_18946,axiom,
    ( X1 != X2
    | esk492_4(X3,X1,X4,X5) = esk492_4(X3,X2,X4,X5) ) ).

cnf(i_0_18947,axiom,
    ( X1 != X2
    | esk492_4(X3,X4,X1,X5) = esk492_4(X3,X4,X2,X5) ) ).

cnf(i_0_18948,axiom,
    ( X1 != X2
    | esk492_4(X3,X4,X5,X1) = esk492_4(X3,X4,X5,X2) ) ).

cnf(i_0_18949,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X1,X3,X4) = c_FunDef_OTHE__default(X2,X3,X4) ) ).

cnf(i_0_18950,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X1,X4) = c_FunDef_OTHE__default(X3,X2,X4) ) ).

cnf(i_0_18951,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X4,X1) = c_FunDef_OTHE__default(X3,X4,X2) ) ).

cnf(i_0_18952,axiom,
    ( X1 != X2
    | c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).

cnf(i_0_18953,axiom,
    ( X1 != X2
    | c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).

cnf(i_0_18954,axiom,
    ( X1 != X2
    | c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).

cnf(i_0_18955,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).

cnf(i_0_18956,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).

cnf(i_0_18957,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).

cnf(i_0_18958,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).

cnf(i_0_18959,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).

cnf(i_0_18960,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).

cnf(i_0_18961,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).

cnf(i_0_18962,axiom,
    ( X1 != X2
    | esk316_2(X1,X3) = esk316_2(X2,X3) ) ).

cnf(i_0_18963,axiom,
    ( X1 != X2
    | esk316_2(X3,X1) = esk316_2(X3,X2) ) ).

cnf(i_0_18964,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).

cnf(i_0_18965,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).

cnf(i_0_18966,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).

cnf(i_0_18967,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).

cnf(i_0_18968,axiom,
    ( X1 != X2
    | esk420_2(X1,X3) = esk420_2(X2,X3) ) ).

cnf(i_0_18969,axiom,
    ( X1 != X2
    | esk420_2(X3,X1) = esk420_2(X3,X2) ) ).

cnf(i_0_18970,axiom,
    ( X1 != X2
    | esk421_2(X1,X3) = esk421_2(X2,X3) ) ).

cnf(i_0_18971,axiom,
    ( X1 != X2
    | esk421_2(X3,X1) = esk421_2(X3,X2) ) ).

cnf(i_0_18972,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_18973,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_18974,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_18975,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_18976,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X1,X3,X4,X5) = c_Lazy__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18977,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X1,X4,X5) = c_Lazy__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18978,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X4,X1,X5) = c_Lazy__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18979,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X4,X5,X1) = c_Lazy__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18980,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_18981,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_18982,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_18983,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_18984,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_18985,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_18986,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_18987,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_18988,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_18989,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_18990,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).

cnf(i_0_18991,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).

cnf(i_0_18992,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).

cnf(i_0_18993,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).

cnf(i_0_18994,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).

cnf(i_0_18995,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).

cnf(i_0_18996,axiom,
    ( X1 != X2
    | esk408_2(X1,X3) = esk408_2(X2,X3) ) ).

cnf(i_0_18997,axiom,
    ( X1 != X2
    | esk408_2(X3,X1) = esk408_2(X3,X2) ) ).

cnf(i_0_18998,axiom,
    ( X1 != X2
    | esk181_3(X1,X3,X4) = esk181_3(X2,X3,X4) ) ).

cnf(i_0_18999,axiom,
    ( X1 != X2
    | esk181_3(X3,X1,X4) = esk181_3(X3,X2,X4) ) ).

cnf(i_0_19000,axiom,
    ( X1 != X2
    | esk181_3(X3,X4,X1) = esk181_3(X3,X4,X2) ) ).

cnf(i_0_19001,axiom,
    ( X1 != X2
    | esk183_3(X1,X3,X4) = esk183_3(X2,X3,X4) ) ).

cnf(i_0_19002,axiom,
    ( X1 != X2
    | esk183_3(X3,X1,X4) = esk183_3(X3,X2,X4) ) ).

cnf(i_0_19003,axiom,
    ( X1 != X2
    | esk183_3(X3,X4,X1) = esk183_3(X3,X4,X2) ) ).

cnf(i_0_19004,axiom,
    ( X1 != X2
    | esk200_3(X1,X3,X4) = esk200_3(X2,X3,X4) ) ).

cnf(i_0_19005,axiom,
    ( X1 != X2
    | esk200_3(X3,X1,X4) = esk200_3(X3,X2,X4) ) ).

cnf(i_0_19006,axiom,
    ( X1 != X2
    | esk200_3(X3,X4,X1) = esk200_3(X3,X4,X2) ) ).

cnf(i_0_19007,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).

cnf(i_0_19008,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).

cnf(i_0_19009,axiom,
    ( X1 != X2
    | esk199_3(X1,X3,X4) = esk199_3(X2,X3,X4) ) ).

cnf(i_0_19010,axiom,
    ( X1 != X2
    | esk199_3(X3,X1,X4) = esk199_3(X3,X2,X4) ) ).

cnf(i_0_19011,axiom,
    ( X1 != X2
    | esk199_3(X3,X4,X1) = esk199_3(X3,X4,X2) ) ).

cnf(i_0_19012,axiom,
    ( X1 != X2
    | esk486_3(X1,X3,X4) = esk486_3(X2,X3,X4) ) ).

cnf(i_0_19013,axiom,
    ( X1 != X2
    | esk486_3(X3,X1,X4) = esk486_3(X3,X2,X4) ) ).

cnf(i_0_19014,axiom,
    ( X1 != X2
    | esk486_3(X3,X4,X1) = esk486_3(X3,X4,X2) ) ).

cnf(i_0_19015,axiom,
    ( X1 != X2
    | esk478_3(X1,X3,X4) = esk478_3(X2,X3,X4) ) ).

cnf(i_0_19016,axiom,
    ( X1 != X2
    | esk478_3(X3,X1,X4) = esk478_3(X3,X2,X4) ) ).

cnf(i_0_19017,axiom,
    ( X1 != X2
    | esk478_3(X3,X4,X1) = esk478_3(X3,X4,X2) ) ).

cnf(i_0_19018,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X1,X3,X4,X5) = c_Quotient_OBabs(X2,X3,X4,X5) ) ).

cnf(i_0_19019,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X1,X4,X5) = c_Quotient_OBabs(X3,X2,X4,X5) ) ).

cnf(i_0_19020,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X4,X1,X5) = c_Quotient_OBabs(X3,X4,X2,X5) ) ).

cnf(i_0_19021,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X4,X5,X1) = c_Quotient_OBabs(X3,X4,X5,X2) ) ).

cnf(i_0_19022,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oflat(X1,X3) = c_Lazy__Sequence_Oflat(X2,X3) ) ).

cnf(i_0_19023,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oflat(X3,X1) = c_Lazy__Sequence_Oflat(X3,X2) ) ).

cnf(i_0_19024,axiom,
    ( X1 != X2
    | c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).

cnf(i_0_19025,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).

cnf(i_0_19026,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).

cnf(i_0_19027,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).

cnf(i_0_19028,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).

cnf(i_0_19029,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).

cnf(i_0_19030,axiom,
    ( X1 != X2
    | c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).

cnf(i_0_19031,axiom,
    ( X1 != X2
    | c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).

cnf(i_0_19032,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).

cnf(i_0_19033,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).

cnf(i_0_19034,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).

cnf(i_0_19035,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).

cnf(i_0_19036,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).

cnf(i_0_19037,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).

cnf(i_0_19038,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_19039,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_19040,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_19041,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_19042,axiom,
    ( X1 != X2
    | esk426_2(X1,X3) = esk426_2(X2,X3) ) ).

cnf(i_0_19043,axiom,
    ( X1 != X2
    | esk426_2(X3,X1) = esk426_2(X3,X2) ) ).

cnf(i_0_19044,axiom,
    ( X1 != X2
    | c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).

cnf(i_0_19045,axiom,
    ( X1 != X2
    | c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).

cnf(i_0_19046,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).

cnf(i_0_19047,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).

cnf(i_0_19048,axiom,
    ( X1 != X2
    | esk395_2(X1,X3) = esk395_2(X2,X3) ) ).

cnf(i_0_19049,axiom,
    ( X1 != X2
    | esk395_2(X3,X1) = esk395_2(X3,X2) ) ).

cnf(i_0_19050,axiom,
    ( X1 != X2
    | esk394_2(X1,X3) = esk394_2(X2,X3) ) ).

cnf(i_0_19051,axiom,
    ( X1 != X2
    | esk394_2(X3,X1) = esk394_2(X3,X2) ) ).

cnf(i_0_19052,axiom,
    ( X1 != X2
    | c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).

cnf(i_0_19053,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).

cnf(i_0_19054,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).

cnf(i_0_19055,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_19056,axiom,
    ( X1 != X2
    | esk493_3(X1,X3,X4) = esk493_3(X2,X3,X4) ) ).

cnf(i_0_19057,axiom,
    ( X1 != X2
    | esk493_3(X3,X1,X4) = esk493_3(X3,X2,X4) ) ).

cnf(i_0_19058,axiom,
    ( X1 != X2
    | esk493_3(X3,X4,X1) = esk493_3(X3,X4,X2) ) ).

cnf(i_0_19059,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).

cnf(i_0_19060,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).

cnf(i_0_19061,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).

cnf(i_0_19062,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).

cnf(i_0_19063,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X1,X3,X4,X5,X6) = c_Predicate_Opred__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19064,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X1,X4,X5,X6) = c_Predicate_Opred__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19065,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X1,X5,X6) = c_Predicate_Opred__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19066,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X1,X6) = c_Predicate_Opred__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19067,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X6,X1) = c_Predicate_Opred__comp(X3,X4,X5,X6,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_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).

cnf(i_0_19071,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(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_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).

cnf(i_0_19075,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).

cnf(i_0_19076,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).

cnf(i_0_19077,axiom,
    ( X1 != X2
    | esk453_2(X1,X3) = esk453_2(X2,X3) ) ).

cnf(i_0_19078,axiom,
    ( X1 != X2
    | esk453_2(X3,X1) = esk453_2(X3,X2) ) ).

cnf(i_0_19079,axiom,
    ( X1 != X2
    | esk390_1(X1) = esk390_1(X2) ) ).

cnf(i_0_19080,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).

cnf(i_0_19081,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).

cnf(i_0_19082,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_19083,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).

cnf(i_0_19084,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).

cnf(i_0_19085,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).

cnf(i_0_19086,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).

cnf(i_0_19087,axiom,
    ( X1 != X2
    | c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).

cnf(i_0_19088,axiom,
    ( X1 != X2
    | c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).

cnf(i_0_19089,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_19090,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_19091,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_19092,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).

cnf(i_0_19093,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).

cnf(i_0_19094,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_19095,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_19096,axiom,
    ( X1 != X2
    | ~ epred2_3(X1,X3,X4)
    | epred2_3(X2,X3,X4) ) ).

cnf(i_0_19097,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X1,X4)
    | epred2_3(X3,X2,X4) ) ).

cnf(i_0_19098,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X4,X1)
    | epred2_3(X3,X4,X2) ) ).

cnf(i_0_19099,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_19100,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_19101,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_19102,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_19103,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_19104,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_19105,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_19106,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_19107,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X1,X3)
    | c_Predicate_Oreflp(X2,X3) ) ).

cnf(i_0_19108,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X3,X1)
    | c_Predicate_Oreflp(X3,X2) ) ).

cnf(i_0_19109,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_19110,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_19111,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_19112,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X1,X3)
    | c_Predicate_Osymp(X2,X3) ) ).

cnf(i_0_19113,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X3,X1)
    | c_Predicate_Osymp(X3,X2) ) ).

cnf(i_0_19114,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X1,X3)
    | c_Predicate_Otransp(X2,X3) ) ).

cnf(i_0_19115,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X3,X1)
    | c_Predicate_Otransp(X3,X2) ) ).

cnf(i_0_19116,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_19117,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_19118,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_19119,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_19120,axiom,
    ( X1 != X2
    | ~ class_Orderings_Owellorder(X1)
    | class_Orderings_Owellorder(X2) ) ).

cnf(i_0_19121,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_19122,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_19123,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_19124,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_19125,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_19126,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_19127,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_19128,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_19129,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).

cnf(i_0_19130,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).

cnf(i_0_19131,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).

cnf(i_0_19132,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).

cnf(i_0_19133,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_19134,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X1,X3)
    | c_Nitpick_Owf_H(X2,X3) ) ).

cnf(i_0_19135,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X3,X1)
    | c_Nitpick_Owf_H(X3,X2) ) ).

cnf(i_0_19136,axiom,
    ( X1 != X2
    | ~ c_List_Onat__list(X1)
    | c_List_Onat__list(X2) ) ).

cnf(i_0_19137,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | class_Groups_Olinordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19138,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_19139,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_19140,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_19141,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_19142,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
    | c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).

cnf(i_0_19143,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
    | c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).

cnf(i_0_19144,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
    | c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).

cnf(i_0_19145,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_19146,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19147,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ounknown(X1)
    | c_Nitpick_Ounknown(X2) ) ).

cnf(i_0_19148,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_19149,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_19150,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_19151,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_19152,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_19153,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_19154,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_19155,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_19156,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_19157,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_19158,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_19159,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_19160,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__top(X1)
    | class_Lattices_Obounded__lattice__top(X2) ) ).

cnf(i_0_19161,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__bot(X1)
    | class_Lattices_Obounded__lattice__bot(X2) ) ).

cnf(i_0_19162,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_19163,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_19164,axiom,
    ( X1 != X2
    | ~ class_Nat_Osize(X1)
    | class_Nat_Osize(X2) ) ).

cnf(i_0_19165,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_19166,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_19167,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_19168,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_19169,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_19170,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_19171,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_19172,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_19173,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_19174,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_19175,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_19176,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_19177,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_19178,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_19179,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_19180,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_19181,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_19182,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_19183,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_19184,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_19185,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_19186,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_19187,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X1,X3)
    | c_Equiv__Relations_Opart__equivp(X2,X3) ) ).

cnf(i_0_19188,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X3,X1)
    | c_Equiv__Relations_Opart__equivp(X3,X2) ) ).

cnf(i_0_19189,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_19190,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_19191,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_19192,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
    | c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).

cnf(i_0_19193,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
    | c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).

cnf(i_0_19194,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
    | c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).

cnf(i_0_19195,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
    | c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).

cnf(i_0_19196,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X1,X3,X4,X5)
    | c_List_Olistrelp(X2,X3,X4,X5) ) ).

cnf(i_0_19197,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X1,X4,X5)
    | c_List_Olistrelp(X3,X2,X4,X5) ) ).

cnf(i_0_19198,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X1,X5)
    | c_List_Olistrelp(X3,X4,X2,X5) ) ).

cnf(i_0_19199,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X5,X1)
    | c_List_Olistrelp(X3,X4,X5,X2) ) ).

cnf(i_0_19200,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X1,X3)
    | c_Equiv__Relations_Oequivp(X2,X3) ) ).

cnf(i_0_19201,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X3,X1)
    | c_Equiv__Relations_Oequivp(X3,X2) ) ).

cnf(i_0_19202,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X1,X3)
    | c_Wellfounded_Owf(X2,X3) ) ).

cnf(i_0_19203,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X3,X1)
    | c_Wellfounded_Owf(X3,X2) ) ).

cnf(i_0_19204,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X1,X3)
    | c_Wellfounded_OwfP(X2,X3) ) ).

cnf(i_0_19205,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X3,X1)
    | c_Wellfounded_OwfP(X3,X2) ) ).

cnf(i_0_19206,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).

cnf(i_0_19207,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).

cnf(i_0_19208,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).

cnf(i_0_19209,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_19210,axiom,
    ( X1 != X2
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | class_Lazy__Sequence_Osmall__lazy(X2) ) ).

cnf(i_0_19211,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
    | c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).

cnf(i_0_19212,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
    | c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).

cnf(i_0_19213,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
    | c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).

cnf(i_0_19214,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_19215,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_19216,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder_Ostrict__mono(X1,X3,X4,X5)
    | c_Orderings_Oorder_Ostrict__mono(X2,X3,X4,X5) ) ).

cnf(i_0_19217,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder_Ostrict__mono(X3,X1,X4,X5)
    | c_Orderings_Oorder_Ostrict__mono(X3,X2,X4,X5) ) ).

cnf(i_0_19218,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X1,X5)
    | c_Orderings_Oorder_Ostrict__mono(X3,X4,X2,X5) ) ).

cnf(i_0_19219,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X1)
    | c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X2) ) ).

cnf(i_0_19220,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_19221,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_19222,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_19223,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19224,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X1,X3,X4,X5,X6)
    | c_List_Olist__all2(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19225,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X1,X4,X5,X6)
    | c_List_Olist__all2(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19226,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X1,X5,X6)
    | c_List_Olist__all2(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19227,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X1,X6)
    | c_List_Olist__all2(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19228,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X6,X1)
    | c_List_Olist__all2(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19229,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19230,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
    | c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).

cnf(i_0_19231,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
    | c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).

cnf(i_0_19232,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
    | c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).

cnf(i_0_19233,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_19234,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_19235,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_19236,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
    | c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).

cnf(i_0_19237,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
    | c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).

cnf(i_0_19238,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
    | c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).

cnf(i_0_19239,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_19240,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X1,X3)
    | c_FunDef_Oreduction__pair(X2,X3) ) ).

cnf(i_0_19241,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X3,X1)
    | c_FunDef_Oreduction__pair(X3,X2) ) ).

cnf(i_0_19242,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | c_List_Olinorder__class_Osorted(X2,X3) ) ).

cnf(i_0_19243,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X3,X1)
    | c_List_Olinorder__class_Osorted(X3,X2) ) ).

cnf(i_0_19244,axiom,
    ( X1 != X2
    | ~ class_Enum_Oenum(X1)
    | class_Enum_Oenum(X2) ) ).

cnf(i_0_19245,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | c_Nat__Transfer_Ois__nat(X2) ) ).

cnf(i_0_19246,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X1,X3,X4,X5,X6)
    | c_Fun_Obij__betw(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19247,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X1,X4,X5,X6)
    | c_Fun_Obij__betw(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19248,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X1,X5,X6)
    | c_Fun_Obij__betw(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19249,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X1,X6)
    | c_Fun_Obij__betw(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19250,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X6,X1)
    | c_Fun_Obij__betw(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19251,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
    | c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).

cnf(i_0_19252,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
    | c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).

cnf(i_0_19253,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
    | c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).

cnf(i_0_19254,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_19255,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_19256,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_19257,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_19258,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X1,X3,X4)
    | c_Nitpick_Oless__frac(X2,X3,X4) ) ).

cnf(i_0_19259,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X1,X4)
    | c_Nitpick_Oless__frac(X3,X2,X4) ) ).

cnf(i_0_19260,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X4,X1)
    | c_Nitpick_Oless__frac(X3,X4,X2) ) ).

cnf(i_0_19261,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_19262,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_19263,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_19264,axiom,
    ( X1 != X2
    | ~ class_Rings_Oinverse(X1)
    | class_Rings_Oinverse(X2) ) ).

cnf(i_0_19265,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_19266,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X1,X3,X4)
    | c_List_Olist__ex1(X2,X3,X4) ) ).

cnf(i_0_19267,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X1,X4)
    | c_List_Olist__ex1(X3,X2,X4) ) ).

cnf(i_0_19268,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X4,X1)
    | c_List_Olist__ex1(X3,X4,X2) ) ).

cnf(i_0_19269,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X1,X3,X4)
    | c_List_Olist__all(X2,X3,X4) ) ).

cnf(i_0_19270,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X1,X4)
    | c_List_Olist__all(X3,X2,X4) ) ).

cnf(i_0_19271,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X4,X1)
    | c_List_Olist__all(X3,X4,X2) ) ).

cnf(i_0_19272,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_19273,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_19274,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_19275,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_19276,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_19277,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_19278,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_19279,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_19280,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_19281,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Onat__set(X1)
    | c_Nat__Transfer_Onat__set(X2) ) ).

cnf(i_0_19282,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_19283,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(X2,X3) ) ).

cnf(i_0_19284,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X3,X1)
    | c_Relation_Otrans(X3,X2) ) ).

cnf(i_0_19285,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_19286,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_19287,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_19288,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__sup(X1)
    | class_Lattices_Osemilattice__sup(X2) ) ).

cnf(i_0_19289,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_19290,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_19291,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X1,X3,X4)
    | c_Relation_Ototal__on(X2,X3,X4) ) ).

cnf(i_0_19292,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X1,X4)
    | c_Relation_Ototal__on(X3,X2,X4) ) ).

cnf(i_0_19293,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X4,X1)
    | c_Relation_Ototal__on(X3,X4,X2) ) ).

cnf(i_0_19294,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_19295,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_19296,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_19297,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_19298,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_19299,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring(X1)
    | class_Rings_Ocomm__ring(X2) ) ).

cnf(i_0_19300,axiom,
    ( X1 != X2
    | ~ class_Rings_Odvd(X1)
    | class_Rings_Odvd(X2) ) ).

cnf(i_0_19301,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_19302,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_19303,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_19304,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_19305,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).

cnf(i_0_19306,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).

cnf(i_0_19307,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).

cnf(i_0_19308,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).

cnf(i_0_19309,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X1,X3)
    | c_Relation_Osym(X2,X3) ) ).

cnf(i_0_19310,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X3,X1)
    | c_Relation_Osym(X3,X2) ) ).

cnf(i_0_19311,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_19312,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_19313,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
    | c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).

cnf(i_0_19314,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
    | c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).

cnf(i_0_19315,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
    | c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).

cnf(i_0_19316,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
    | c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).

cnf(i_0_19317,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | class_Lattices_Osemilattice__inf(X2) ) ).

cnf(i_0_19318,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_19319,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_19320,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_19321,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X1,X3)
    | c_Relation_Oantisym(X2,X3) ) ).

cnf(i_0_19322,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X3,X1)
    | c_Relation_Oantisym(X3,X2) ) ).

cnf(i_0_19323,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_19324,axiom,
    ( X1 != X2
    | ~ v_P(X1,X3)
    | v_P(X2,X3) ) ).

cnf(i_0_19325,axiom,
    ( X1 != X2
    | ~ v_P(X3,X1)
    | v_P(X3,X2) ) ).

cnf(i_0_19326,axiom,
    ( X1 != X2
    | ~ v_wt(X1)
    | v_wt(X2) ) ).

cnf(i_0_19327,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X1,X3)
    | c_Nitpick_Orefl_H(X2,X3) ) ).

cnf(i_0_19328,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X3,X1)
    | c_Nitpick_Orefl_H(X3,X2) ) ).

cnf(i_0_19329,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).

cnf(i_0_19330,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).

cnf(i_0_19331,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).

cnf(i_0_19332,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).

cnf(i_0_19333,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_19334,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_19335,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_19336,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_19337,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_19338,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_19339,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_19340,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
    | c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19341,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
    | c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19342,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
    | c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19343,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
    | c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19344,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
    | c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19345,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_19346,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X1,X3,X4)
    | c_List_Olist__ex(X2,X3,X4) ) ).

cnf(i_0_19347,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X1,X4)
    | c_List_Olist__ex(X3,X2,X4) ) ).

cnf(i_0_19348,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X4,X1)
    | c_List_Olist__ex(X3,X4,X2) ) ).

cnf(i_0_19349,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X1,X3,X4)
    | c_List_Oall__interval__nat(X2,X3,X4) ) ).

cnf(i_0_19350,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X3,X1,X4)
    | c_List_Oall__interval__nat(X3,X2,X4) ) ).

cnf(i_0_19351,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X3,X4,X1)
    | c_List_Oall__interval__nat(X3,X4,X2) ) ).

cnf(i_0_19352,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_19353,axiom,
    ( X1 != X2
    | ~ class_Groups_Osemigroup__add(X1)
    | class_Groups_Osemigroup__add(X2) ) ).

cnf(i_0_19354,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X1,X3,X4)
    | c_List_Oall__interval__int(X2,X3,X4) ) ).

cnf(i_0_19355,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X1,X4)
    | c_List_Oall__interval__int(X3,X2,X4) ) ).

cnf(i_0_19356,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X4,X1)
    | c_List_Oall__interval__int(X3,X4,X2) ) ).

cnf(i_0_19357,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X1,X3)
    | c_Relation_Oirrefl(X2,X3) ) ).

cnf(i_0_19358,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X3,X1)
    | c_Relation_Oirrefl(X3,X2) ) ).

cnf(i_0_19359,axiom,
    ( X1 != X2
    | ~ epred1_3(X1,X3,X4)
    | epred1_3(X2,X3,X4) ) ).

cnf(i_0_19360,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X1,X4)
    | epred1_3(X3,X2,X4) ) ).

cnf(i_0_19361,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X4,X1)
    | epred1_3(X3,X4,X2) ) ).

cnf(i_0_18461_001,axiom,
    X1 = X1 ).

cnf(i_0_18462_002,axiom,
    ( X1 = X2
    | X2 != X1 ) ).

cnf(i_0_18463_003,axiom,
    ( X1 = X2
    | X1 != X3
    | X3 != X2 ) ).

cnf(i_0_18464_004,axiom,
    ( X1 != X2
    | hAPP(X1,X3) = hAPP(X2,X3) ) ).

cnf(i_0_18465_005,axiom,
    ( X1 != X2
    | hAPP(X3,X1) = hAPP(X3,X2) ) ).

cnf(i_0_18466_006,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X1,X3) = c_Big__Operators_Olinorder__class_OMax(X2,X3) ) ).

cnf(i_0_18467_007,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMax(X3,X1) = c_Big__Operators_Olinorder__class_OMax(X3,X2) ) ).

cnf(i_0_18468_008,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X1,X3) = c_Big__Operators_Olinorder__class_OMin(X2,X3) ) ).

cnf(i_0_18469_009,axiom,
    ( X1 != X2
    | c_Big__Operators_Olinorder__class_OMin(X3,X1) = c_Big__Operators_Olinorder__class_OMin(X3,X2) ) ).

cnf(i_0_18470_010,axiom,
    ( X1 != X2
    | c_List_Olistrel(X1,X3) = c_List_Olistrel(X2,X3) ) ).

cnf(i_0_18471_011,axiom,
    ( X1 != X2
    | c_List_Olistrel(X3,X1) = c_List_Olistrel(X3,X2) ) ).

cnf(i_0_18472_012,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X1,X3,X4,X5,X6) = c_Option_Ooption_Ooption__case(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18473_013,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X1,X4,X5,X6) = c_Option_Ooption_Ooption__case(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18474_014,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X1,X5,X6) = c_Option_Ooption_Ooption__case(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18475_015,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X1,X6) = c_Option_Ooption_Ooption__case(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18476_016,axiom,
    ( X1 != X2
    | c_Option_Ooption_Ooption__case(X3,X4,X5,X6,X1) = c_Option_Ooption_Ooption__case(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18477_017,axiom,
    ( X1 != X2
    | c_List_Opartition(X1,X3,X4) = c_List_Opartition(X2,X3,X4) ) ).

cnf(i_0_18478_018,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X1,X4) = c_List_Opartition(X3,X2,X4) ) ).

cnf(i_0_18479_019,axiom,
    ( X1 != X2
    | c_List_Opartition(X3,X4,X1) = c_List_Opartition(X3,X4,X2) ) ).

cnf(i_0_18480_020,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X1,X3,X4,X5) = c_Wellfounded_Olex__prod(X2,X3,X4,X5) ) ).

cnf(i_0_18481_021,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X1,X4,X5) = c_Wellfounded_Olex__prod(X3,X2,X4,X5) ) ).

cnf(i_0_18482_022,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X1,X5) = c_Wellfounded_Olex__prod(X3,X4,X2,X5) ) ).

cnf(i_0_18483_023,axiom,
    ( X1 != X2
    | c_Wellfounded_Olex__prod(X3,X4,X5,X1) = c_Wellfounded_Olex__prod(X3,X4,X5,X2) ) ).

cnf(i_0_18484_024,axiom,
    ( X1 != X2
    | c_Power_Opower__class_Opower(X1) = c_Power_Opower__class_Opower(X2) ) ).

cnf(i_0_18485_025,axiom,
    ( X1 != X2
    | c_List_Osublist(X1,X3,X4) = c_List_Osublist(X2,X3,X4) ) ).

cnf(i_0_18486_026,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X1,X4) = c_List_Osublist(X3,X2,X4) ) ).

cnf(i_0_18487_027,axiom,
    ( X1 != X2
    | c_List_Osublist(X3,X4,X1) = c_List_Osublist(X3,X4,X2) ) ).

cnf(i_0_18488_028,axiom,
    ( X1 != X2
    | c_List_Otranspose(X1,X3) = c_List_Otranspose(X2,X3) ) ).

cnf(i_0_18489_029,axiom,
    ( X1 != X2
    | c_List_Otranspose(X3,X1) = c_List_Otranspose(X3,X2) ) ).

cnf(i_0_18490_030,axiom,
    ( X1 != X2
    | c_List_Olist_ONil(X1) = c_List_Olist_ONil(X2) ) ).

cnf(i_0_18491_031,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X1,X3,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18492_032,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X1,X4,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18493_033,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X1,X5,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18494_034,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X1,X6,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18495_035,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X1,X7) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18496_036,axiom,
    ( X1 != X2
    | c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X1) = c_Partial__Function_Ofun__lub(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18497_037,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X1,X3) = c_Complete__Lattice_OSup__class_OSup(X2,X3) ) ).

cnf(i_0_18498_038,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OSup__class_OSup(X3,X1) = c_Complete__Lattice_OSup__class_OSup(X3,X2) ) ).

cnf(i_0_18499_039,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X1,X3) = c_Complete__Lattice_OInf__class_OInf(X2,X3) ) ).

cnf(i_0_18500_040,axiom,
    ( X1 != X2
    | c_Complete__Lattice_OInf__class_OInf(X3,X1) = c_Complete__Lattice_OInf__class_OInf(X3,X2) ) ).

cnf(i_0_18501_041,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X1,X3) = c_Transitive__Closure_Ortrancl(X2,X3) ) ).

cnf(i_0_18502_042,axiom,
    ( X1 != X2
    | c_Transitive__Closure_Ortrancl(X3,X1) = c_Transitive__Closure_Ortrancl(X3,X2) ) ).

cnf(i_0_18503_043,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X1,X3) = c_Divides_Odivmod__int__rel(X2,X3) ) ).

cnf(i_0_18504_044,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int__rel(X3,X1) = c_Divides_Odivmod__int__rel(X3,X2) ) ).

cnf(i_0_18505_045,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X1,X3) = c_Set_Othe__elem(X2,X3) ) ).

cnf(i_0_18506_046,axiom,
    ( X1 != X2
    | c_Set_Othe__elem(X3,X1) = c_Set_Othe__elem(X3,X2) ) ).

cnf(i_0_18507_047,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X1,X3,X4,X5) = c_Nitpick_Osetsum_H(X2,X3,X4,X5) ) ).

cnf(i_0_18508_048,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X1,X4,X5) = c_Nitpick_Osetsum_H(X3,X2,X4,X5) ) ).

cnf(i_0_18509_049,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X1,X5) = c_Nitpick_Osetsum_H(X3,X4,X2,X5) ) ).

cnf(i_0_18510_050,axiom,
    ( X1 != X2
    | c_Nitpick_Osetsum_H(X3,X4,X5,X1) = c_Nitpick_Osetsum_H(X3,X4,X5,X2) ) ).

cnf(i_0_18511_051,axiom,
    ( X1 != X2
    | c_List_Omonoid__add__class_Olistsum(X1) = c_List_Omonoid__add__class_Olistsum(X2) ) ).

cnf(i_0_18512_052,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X1,X3) = c_Hilbert__Choice_OEps(X2,X3) ) ).

cnf(i_0_18513_053,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_OEps(X3,X1) = c_Hilbert__Choice_OEps(X3,X2) ) ).

cnf(i_0_18514_054,axiom,
    ( X1 != X2
    | esk524_6(X1,X3,X4,X5,X6,X7) = esk524_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18515_055,axiom,
    ( X1 != X2
    | esk524_6(X3,X1,X4,X5,X6,X7) = esk524_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18516_056,axiom,
    ( X1 != X2
    | esk524_6(X3,X4,X1,X5,X6,X7) = esk524_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18517_057,axiom,
    ( X1 != X2
    | esk524_6(X3,X4,X5,X1,X6,X7) = esk524_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18518_058,axiom,
    ( X1 != X2
    | esk524_6(X3,X4,X5,X6,X1,X7) = esk524_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18519_059,axiom,
    ( X1 != X2
    | esk524_6(X3,X4,X5,X6,X7,X1) = esk524_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18520_060,axiom,
    ( X1 != X2
    | esk525_6(X1,X3,X4,X5,X6,X7) = esk525_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18521_061,axiom,
    ( X1 != X2
    | esk525_6(X3,X1,X4,X5,X6,X7) = esk525_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18522_062,axiom,
    ( X1 != X2
    | esk525_6(X3,X4,X1,X5,X6,X7) = esk525_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18523_063,axiom,
    ( X1 != X2
    | esk525_6(X3,X4,X5,X1,X6,X7) = esk525_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18524_064,axiom,
    ( X1 != X2
    | esk525_6(X3,X4,X5,X6,X1,X7) = esk525_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18525_065,axiom,
    ( X1 != X2
    | esk525_6(X3,X4,X5,X6,X7,X1) = esk525_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18526_066,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_18527_067,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_18528_068,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X1,X3,X4,X5) = c_Random__Sequence_ORandom(X2,X3,X4,X5) ) ).

cnf(i_0_18529_069,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X1,X4,X5) = c_Random__Sequence_ORandom(X3,X2,X4,X5) ) ).

cnf(i_0_18530_070,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X1,X5) = c_Random__Sequence_ORandom(X3,X4,X2,X5) ) ).

cnf(i_0_18531_071,axiom,
    ( X1 != X2
    | c_Random__Sequence_ORandom(X3,X4,X5,X1) = c_Random__Sequence_ORandom(X3,X4,X5,X2) ) ).

cnf(i_0_18532_072,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__not__seq(X1) = c_Lazy__Sequence_Ohb__not__seq(X2) ) ).

cnf(i_0_18533_073,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X1,X3) = c_Wellfounded_Omax__ext(X2,X3) ) ).

cnf(i_0_18534_074,axiom,
    ( X1 != X2
    | c_Wellfounded_Omax__ext(X3,X1) = c_Wellfounded_Omax__ext(X3,X2) ) ).

cnf(i_0_18535_075,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X1,X3,X4) = c_Divides_Odiv__class_Omod(X2,X3,X4) ) ).

cnf(i_0_18536_076,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X1,X4) = c_Divides_Odiv__class_Omod(X3,X2,X4) ) ).

cnf(i_0_18537_077,axiom,
    ( X1 != X2
    | c_Divides_Odiv__class_Omod(X3,X4,X1) = c_Divides_Odiv__class_Omod(X3,X4,X2) ) ).

cnf(i_0_18538_078,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X1,X3) = c_Wellfounded_Omin__ext(X2,X3) ) ).

cnf(i_0_18539_079,axiom,
    ( X1 != X2
    | c_Wellfounded_Omin__ext(X3,X1) = c_Wellfounded_Omin__ext(X3,X2) ) ).

cnf(i_0_18540_080,axiom,
    ( X1 != X2
    | c_Divides_Oadjust(X1) = c_Divides_Oadjust(X2) ) ).

cnf(i_0_18541_081,axiom,
    ( X1 != X2
    | c_Wellfounded_Ofinite__psubset(X1) = c_Wellfounded_Ofinite__psubset(X2) ) ).

cnf(i_0_18542_082,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X1,X3) = c_Nitpick_Ocard_H(X2,X3) ) ).

cnf(i_0_18543_083,axiom,
    ( X1 != X2
    | c_Nitpick_Ocard_H(X3,X1) = c_Nitpick_Ocard_H(X3,X2) ) ).

cnf(i_0_18544_084,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_18545_085,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_18546_086,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_18547_087,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_18548_088,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_18549_089,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_18550_090,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_18551_091,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_18552_092,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_18553_093,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_18554_094,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_18555_095,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_18556_096,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_18557_097,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_18558_098,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_18559_099,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_18560_100,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_18561_101,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_18562_102,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_18563_103,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_18564_104,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_18565_105,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_18566_106,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_18567_107,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_18568_108,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X1,X3,X4) = c_Lazy__Sequence_Oappend(X2,X3,X4) ) ).

cnf(i_0_18569_109,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X1,X4) = c_Lazy__Sequence_Oappend(X3,X2,X4) ) ).

cnf(i_0_18570_110,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oappend(X3,X4,X1) = c_Lazy__Sequence_Oappend(X3,X4,X2) ) ).

cnf(i_0_18571_111,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X1,X3,X4,X5) = c_Lazy__Sequence_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18572_112,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X1,X4,X5) = c_Lazy__Sequence_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18573_113,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X1,X5) = c_Lazy__Sequence_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18574_114,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oproduct(X3,X4,X5,X1) = c_Lazy__Sequence_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18575_115,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oempty(X1) = c_Lazy__Sequence_Oempty(X2) ) ).

cnf(i_0_18576_116,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_18577_117,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_18578_118,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_18579_119,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_18580_120,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X1,X3,X4,X5) = c_New__DSequence_Oneg__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18581_121,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X1,X4,X5) = c_New__DSequence_Oneg__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18582_122,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X1,X5) = c_New__DSequence_Oneg__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18583_123,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__bind(X3,X4,X5,X1) = c_New__DSequence_Oneg__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18584_124,axiom,
    ( X1 != X2
    | esk349_5(X1,X3,X4,X5,X6) = esk349_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18585_125,axiom,
    ( X1 != X2
    | esk349_5(X3,X1,X4,X5,X6) = esk349_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18586_126,axiom,
    ( X1 != X2
    | esk349_5(X3,X4,X1,X5,X6) = esk349_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18587_127,axiom,
    ( X1 != X2
    | esk349_5(X3,X4,X5,X1,X6) = esk349_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18588_128,axiom,
    ( X1 != X2
    | esk349_5(X3,X4,X5,X6,X1) = esk349_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18589_129,axiom,
    ( X1 != X2
    | esk350_5(X1,X3,X4,X5,X6) = esk350_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18590_130,axiom,
    ( X1 != X2
    | esk350_5(X3,X1,X4,X5,X6) = esk350_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18591_131,axiom,
    ( X1 != X2
    | esk350_5(X3,X4,X1,X5,X6) = esk350_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18592_132,axiom,
    ( X1 != X2
    | esk350_5(X3,X4,X5,X1,X6) = esk350_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18593_133,axiom,
    ( X1 != X2
    | esk350_5(X3,X4,X5,X6,X1) = esk350_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18594_134,axiom,
    ( X1 != X2
    | esk348_5(X1,X3,X4,X5,X6) = esk348_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18595_135,axiom,
    ( X1 != X2
    | esk348_5(X3,X1,X4,X5,X6) = esk348_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18596_136,axiom,
    ( X1 != X2
    | esk348_5(X3,X4,X1,X5,X6) = esk348_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18597_137,axiom,
    ( X1 != X2
    | esk348_5(X3,X4,X5,X1,X6) = esk348_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18598_138,axiom,
    ( X1 != X2
    | esk348_5(X3,X4,X5,X6,X1) = esk348_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18599_139,axiom,
    ( X1 != X2
    | esk347_5(X1,X3,X4,X5,X6) = esk347_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18600_140,axiom,
    ( X1 != X2
    | esk347_5(X3,X1,X4,X5,X6) = esk347_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18601_141,axiom,
    ( X1 != X2
    | esk347_5(X3,X4,X1,X5,X6) = esk347_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18602_142,axiom,
    ( X1 != X2
    | esk347_5(X3,X4,X5,X1,X6) = esk347_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18603_143,axiom,
    ( X1 != X2
    | esk347_5(X3,X4,X5,X6,X1) = esk347_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18604_144,axiom,
    ( X1 != X2
    | c_HOL_OThe(X1,X3) = c_HOL_OThe(X2,X3) ) ).

cnf(i_0_18605_145,axiom,
    ( X1 != X2
    | c_HOL_OThe(X3,X1) = c_HOL_OThe(X3,X2) ) ).

cnf(i_0_18606_146,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_18607_147,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_18608_148,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_18609_149,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_18610_150,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X1,X3,X4,X5) = c_New__DSequence_Opos__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18611_151,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X1,X4,X5) = c_New__DSequence_Opos__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18612_152,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X1,X5) = c_New__DSequence_Opos__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18613_153,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__bind(X3,X4,X5,X1) = c_New__DSequence_Opos__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18614_154,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18615_155,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18616_156,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18617_157,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18618_158,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OatLeastLessThan(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18619_159,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X1,X3,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18620_160,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X1,X4,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18621_161,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X1,X5,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18622_162,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X1,X6) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18623_163,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X1) = c_SetInterval_Oord_OgreaterThanAtMost(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18624_164,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X1,X3,X4,X5) = c_Nitpick_Oprod(X2,X3,X4,X5) ) ).

cnf(i_0_18625_165,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X1,X4,X5) = c_Nitpick_Oprod(X3,X2,X4,X5) ) ).

cnf(i_0_18626_166,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X1,X5) = c_Nitpick_Oprod(X3,X4,X2,X5) ) ).

cnf(i_0_18627_167,axiom,
    ( X1 != X2
    | c_Nitpick_Oprod(X3,X4,X5,X1) = c_Nitpick_Oprod(X3,X4,X5,X2) ) ).

cnf(i_0_18628_168,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X1,X3,X4) = c_List_OtakeWhile(X2,X3,X4) ) ).

cnf(i_0_18629_169,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X1,X4) = c_List_OtakeWhile(X3,X2,X4) ) ).

cnf(i_0_18630_170,axiom,
    ( X1 != X2
    | c_List_OtakeWhile(X3,X4,X1) = c_List_OtakeWhile(X3,X4,X2) ) ).

cnf(i_0_18631_171,axiom,
    ( X1 != X2
    | esk196_6(X1,X3,X4,X5,X6,X7) = esk196_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18632_172,axiom,
    ( X1 != X2
    | esk196_6(X3,X1,X4,X5,X6,X7) = esk196_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18633_173,axiom,
    ( X1 != X2
    | esk196_6(X3,X4,X1,X5,X6,X7) = esk196_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18634_174,axiom,
    ( X1 != X2
    | esk196_6(X3,X4,X5,X1,X6,X7) = esk196_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18635_175,axiom,
    ( X1 != X2
    | esk196_6(X3,X4,X5,X6,X1,X7) = esk196_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18636_176,axiom,
    ( X1 != X2
    | esk196_6(X3,X4,X5,X6,X7,X1) = esk196_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18637_177,axiom,
    ( X1 != X2
    | esk195_6(X1,X3,X4,X5,X6,X7) = esk195_6(X2,X3,X4,X5,X6,X7) ) ).

cnf(i_0_18638_178,axiom,
    ( X1 != X2
    | esk195_6(X3,X1,X4,X5,X6,X7) = esk195_6(X3,X2,X4,X5,X6,X7) ) ).

cnf(i_0_18639_179,axiom,
    ( X1 != X2
    | esk195_6(X3,X4,X1,X5,X6,X7) = esk195_6(X3,X4,X2,X5,X6,X7) ) ).

cnf(i_0_18640_180,axiom,
    ( X1 != X2
    | esk195_6(X3,X4,X5,X1,X6,X7) = esk195_6(X3,X4,X5,X2,X6,X7) ) ).

cnf(i_0_18641_181,axiom,
    ( X1 != X2
    | esk195_6(X3,X4,X5,X6,X1,X7) = esk195_6(X3,X4,X5,X6,X2,X7) ) ).

cnf(i_0_18642_182,axiom,
    ( X1 != X2
    | esk195_6(X3,X4,X5,X6,X7,X1) = esk195_6(X3,X4,X5,X6,X7,X2) ) ).

cnf(i_0_18643_183,axiom,
    ( X1 != X2
    | c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ozero__class_Ozero(X2) ) ).

cnf(i_0_18644_184,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X1,X3,X4) = c_Enum_On__lists(X2,X3,X4) ) ).

cnf(i_0_18645_185,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X1,X4) = c_Enum_On__lists(X3,X2,X4) ) ).

cnf(i_0_18646_186,axiom,
    ( X1 != X2
    | c_Enum_On__lists(X3,X4,X1) = c_Enum_On__lists(X3,X4,X2) ) ).

cnf(i_0_18647_187,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X1,X3,X4) = c_Nitpick_Otimes__frac(X2,X3,X4) ) ).

cnf(i_0_18648_188,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X1,X4) = c_Nitpick_Otimes__frac(X3,X2,X4) ) ).

cnf(i_0_18649_189,axiom,
    ( X1 != X2
    | c_Nitpick_Otimes__frac(X3,X4,X1) = c_Nitpick_Otimes__frac(X3,X4,X2) ) ).

cnf(i_0_18650_190,axiom,
    ( X1 != X2
    | c_Groups_Ominus__class_Ominus(X1) = c_Groups_Ominus__class_Ominus(X2) ) ).

cnf(i_0_18651_191,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X1,X3) = c_Divides_OnegDivAlg(X2,X3) ) ).

cnf(i_0_18652_192,axiom,
    ( X1 != X2
    | c_Divides_OnegDivAlg(X3,X1) = c_Divides_OnegDivAlg(X3,X2) ) ).

cnf(i_0_18653_193,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X1,X3) = c_Divides_OposDivAlg(X2,X3) ) ).

cnf(i_0_18654_194,axiom,
    ( X1 != X2
    | c_Divides_OposDivAlg(X3,X1) = c_Divides_OposDivAlg(X3,X2) ) ).

cnf(i_0_18655_195,axiom,
    ( X1 != X2
    | c_Nat_Osemiring__1__class_Oof__nat(X1) = c_Nat_Osemiring__1__class_Oof__nat(X2) ) ).

cnf(i_0_18656_196,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X1,X3,X4,X5) = c_Nat_Onat_Onat__case(X2,X3,X4,X5) ) ).

cnf(i_0_18657_197,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X1,X4,X5) = c_Nat_Onat_Onat__case(X3,X2,X4,X5) ) ).

cnf(i_0_18658_198,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X1,X5) = c_Nat_Onat_Onat__case(X3,X4,X2,X5) ) ).

cnf(i_0_18659_199,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__case(X3,X4,X5,X1) = c_Nat_Onat_Onat__case(X3,X4,X5,X2) ) ).

cnf(i_0_18660_200,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X1,X3,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X2,X3,X4,X5) ) ).

cnf(i_0_18661_201,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X1,X4,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X2,X4,X5) ) ).

cnf(i_0_18662_202,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X1,X5) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X2,X5) ) ).

cnf(i_0_18663_203,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X1) = c_SetInterval_Oord_OgreaterThanLessThan(X3,X4,X5,X2) ) ).

cnf(i_0_18664_204,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X1,X3) = c_Relation_OId__on(X2,X3) ) ).

cnf(i_0_18665_205,axiom,
    ( X1 != X2
    | c_Relation_OId__on(X3,X1) = c_Relation_OId__on(X3,X2) ) ).

cnf(i_0_18666_206,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than(X1) = c_Int_Oint__ge__less__than(X2) ) ).

cnf(i_0_18667_207,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X1,X3) = c_List_Olistrel1(X2,X3) ) ).

cnf(i_0_18668_208,axiom,
    ( X1 != X2
    | c_List_Olistrel1(X3,X1) = c_List_Olistrel1(X3,X2) ) ).

cnf(i_0_18669_209,axiom,
    ( X1 != X2
    | c_Int_Onumber__class_Onumber__of(X1) = c_Int_Onumber__class_Onumber__of(X2) ) ).

cnf(i_0_18670_210,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X1,X3,X4) = c_Finite__Set_Ofold(X2,X3,X4) ) ).

cnf(i_0_18671_211,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X1,X4) = c_Finite__Set_Ofold(X3,X2,X4) ) ).

cnf(i_0_18672_212,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold(X3,X4,X1) = c_Finite__Set_Ofold(X3,X4,X2) ) ).

cnf(i_0_18673_213,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X1,X3) = c_Nitpick_Ouminus__frac(X2,X3) ) ).

cnf(i_0_18674_214,axiom,
    ( X1 != X2
    | c_Nitpick_Ouminus__frac(X3,X1) = c_Nitpick_Ouminus__frac(X3,X2) ) ).

cnf(i_0_18675_215,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X1,X3) = c_Nitpick_OAbs__Frac(X2,X3) ) ).

cnf(i_0_18676_216,axiom,
    ( X1 != X2
    | c_Nitpick_OAbs__Frac(X3,X1) = c_Nitpick_OAbs__Frac(X3,X2) ) ).

cnf(i_0_18677_217,axiom,
    ( X1 != X2
    | esk375_4(X1,X3,X4,X5) = esk375_4(X2,X3,X4,X5) ) ).

cnf(i_0_18678_218,axiom,
    ( X1 != X2
    | esk375_4(X3,X1,X4,X5) = esk375_4(X3,X2,X4,X5) ) ).

cnf(i_0_18679_219,axiom,
    ( X1 != X2
    | esk375_4(X3,X4,X1,X5) = esk375_4(X3,X4,X2,X5) ) ).

cnf(i_0_18680_220,axiom,
    ( X1 != X2
    | esk375_4(X3,X4,X5,X1) = esk375_4(X3,X4,X5,X2) ) ).

cnf(i_0_18681_221,axiom,
    ( X1 != X2
    | esk374_4(X1,X3,X4,X5) = esk374_4(X2,X3,X4,X5) ) ).

cnf(i_0_18682_222,axiom,
    ( X1 != X2
    | esk374_4(X3,X1,X4,X5) = esk374_4(X3,X2,X4,X5) ) ).

cnf(i_0_18683_223,axiom,
    ( X1 != X2
    | esk374_4(X3,X4,X1,X5) = esk374_4(X3,X4,X2,X5) ) ).

cnf(i_0_18684_224,axiom,
    ( X1 != X2
    | esk374_4(X3,X4,X5,X1) = esk374_4(X3,X4,X5,X2) ) ).

cnf(i_0_18685_225,axiom,
    ( X1 != X2
    | c_Groups_Oone__class_Oone(X1) = c_Groups_Oone__class_Oone(X2) ) ).

cnf(i_0_18686_226,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X1,X3,X4,X5) = c_Hilbert__Choice_Oinv__into(X2,X3,X4,X5) ) ).

cnf(i_0_18687_227,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X1,X4,X5) = c_Hilbert__Choice_Oinv__into(X3,X2,X4,X5) ) ).

cnf(i_0_18688_228,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X1,X5) = c_Hilbert__Choice_Oinv__into(X3,X4,X2,X5) ) ).

cnf(i_0_18689_229,axiom,
    ( X1 != X2
    | c_Hilbert__Choice_Oinv__into(X3,X4,X5,X1) = c_Hilbert__Choice_Oinv__into(X3,X4,X5,X2) ) ).

cnf(i_0_18690_230,axiom,
    ( X1 != X2
    | c_List_Olistsp(X1,X3) = c_List_Olistsp(X2,X3) ) ).

cnf(i_0_18691_231,axiom,
    ( X1 != X2
    | c_List_Olistsp(X3,X1) = c_List_Olistsp(X3,X2) ) ).

cnf(i_0_18692_232,axiom,
    ( X1 != X2
    | c_List_Olists(X1,X3) = c_List_Olists(X2,X3) ) ).

cnf(i_0_18693_233,axiom,
    ( X1 != X2
    | c_List_Olists(X3,X1) = c_List_Olists(X3,X2) ) ).

cnf(i_0_18694_234,axiom,
    ( X1 != X2
    | c_Fun_Oid(X1) = c_Fun_Oid(X2) ) ).

cnf(i_0_18695_235,axiom,
    ( X1 != X2
    | c_Int_Oint__ge__less__than2(X1) = c_Int_Oint__ge__less__than2(X2) ) ).

cnf(i_0_18696_236,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X1,X3,X4) = c_Nitpick_Oof__frac(X2,X3,X4) ) ).

cnf(i_0_18697_237,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X1,X4) = c_Nitpick_Oof__frac(X3,X2,X4) ) ).

cnf(i_0_18698_238,axiom,
    ( X1 != X2
    | c_Nitpick_Oof__frac(X3,X4,X1) = c_Nitpick_Oof__frac(X3,X4,X2) ) ).

cnf(i_0_18699_239,axiom,
    ( X1 != X2
    | c_List_Omeasures(X1,X3) = c_List_Omeasures(X2,X3) ) ).

cnf(i_0_18700_240,axiom,
    ( X1 != X2
    | c_List_Omeasures(X3,X1) = c_List_Omeasures(X3,X2) ) ).

cnf(i_0_18701_241,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X1,X3,X4,X5) = c_Random__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18702_242,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X1,X4,X5) = c_Random__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18703_243,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X1,X5) = c_Random__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18704_244,axiom,
    ( X1 != X2
    | c_Random__Sequence_Omap(X3,X4,X5,X1) = c_Random__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18705_245,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X1,X3,X4,X5) = c_Random__Sequence_Obind(X2,X3,X4,X5) ) ).

cnf(i_0_18706_246,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X1,X4,X5) = c_Random__Sequence_Obind(X3,X2,X4,X5) ) ).

cnf(i_0_18707_247,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X1,X5) = c_Random__Sequence_Obind(X3,X4,X2,X5) ) ).

cnf(i_0_18708_248,axiom,
    ( X1 != X2
    | c_Random__Sequence_Obind(X3,X4,X5,X1) = c_Random__Sequence_Obind(X3,X4,X5,X2) ) ).

cnf(i_0_18709_249,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X2,X3,X4) ) ).

cnf(i_0_18710_250,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X4) ) ).

cnf(i_0_18711_251,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X4,X2) ) ).

cnf(i_0_18712_252,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X1,X3,X4) = c_List_Olist_Olist__size(X2,X3,X4) ) ).

cnf(i_0_18713_253,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X1,X4) = c_List_Olist_Olist__size(X3,X2,X4) ) ).

cnf(i_0_18714_254,axiom,
    ( X1 != X2
    | c_List_Olist_Olist__size(X3,X4,X1) = c_List_Olist_Olist__size(X3,X4,X2) ) ).

cnf(i_0_18715_255,axiom,
    ( X1 != X2
    | c_Orderings_Obot__class_Obot(X1) = c_Orderings_Obot__class_Obot(X2) ) ).

cnf(i_0_18716_256,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X1,X3) = c_Enum_Osublists(X2,X3) ) ).

cnf(i_0_18717_257,axiom,
    ( X1 != X2
    | c_Enum_Osublists(X3,X1) = c_Enum_Osublists(X3,X2) ) ).

cnf(i_0_18718_258,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omax(X1) = c_Orderings_Oord__class_Omax(X2) ) ).

cnf(i_0_18719_259,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X1,X3) = c_Random_Oselect__weight(X2,X3) ) ).

cnf(i_0_18720_260,axiom,
    ( X1 != X2
    | c_Random_Oselect__weight(X3,X1) = c_Random_Oselect__weight(X3,X2) ) ).

cnf(i_0_18721_261,axiom,
    ( X1 != X2
    | c_Random_Opick(X1,X3) = c_Random_Opick(X2,X3) ) ).

cnf(i_0_18722_262,axiom,
    ( X1 != X2
    | c_Random_Opick(X3,X1) = c_Random_Opick(X3,X2) ) ).

cnf(i_0_18723_263,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X1,X3,X4,X5,X6) = c_Fun_Ofun__upd(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18724_264,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X1,X4,X5,X6) = c_Fun_Ofun__upd(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18725_265,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X1,X5,X6) = c_Fun_Ofun__upd(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18726_266,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X1,X6) = c_Fun_Ofun__upd(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18727_267,axiom,
    ( X1 != X2
    | c_Fun_Ofun__upd(X3,X4,X5,X6,X1) = c_Fun_Ofun__upd(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18728_268,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X1,X3,X4) = c_Wellfounded_Omlex__prod(X2,X3,X4) ) ).

cnf(i_0_18729_269,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X1,X4) = c_Wellfounded_Omlex__prod(X3,X2,X4) ) ).

cnf(i_0_18730_270,axiom,
    ( X1 != X2
    | c_Wellfounded_Omlex__prod(X3,X4,X1) = c_Wellfounded_Omlex__prod(X3,X4,X2) ) ).

cnf(i_0_18731_271,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X1,X3,X4) = c_Big__Operators_Olattice_OInf__fin(X2,X3,X4) ) ).

cnf(i_0_18732_272,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X1,X4) = c_Big__Operators_Olattice_OInf__fin(X3,X2,X4) ) ).

cnf(i_0_18733_273,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OInf__fin(X3,X4,X1) = c_Big__Operators_Olattice_OInf__fin(X3,X4,X2) ) ).

cnf(i_0_18734_274,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X1,X3) = c_Nitpick_Onorm__frac(X2,X3) ) ).

cnf(i_0_18735_275,axiom,
    ( X1 != X2
    | c_Nitpick_Onorm__frac(X3,X1) = c_Nitpick_Onorm__frac(X3,X2) ) ).

cnf(i_0_18736_276,axiom,
    ( X1 != X2
    | c_List_Oremove1(X1,X3,X4) = c_List_Oremove1(X2,X3,X4) ) ).

cnf(i_0_18737_277,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X1,X4) = c_List_Oremove1(X3,X2,X4) ) ).

cnf(i_0_18738_278,axiom,
    ( X1 != X2
    | c_List_Oremove1(X3,X4,X1) = c_List_Oremove1(X3,X4,X2) ) ).

cnf(i_0_18739_279,axiom,
    ( X1 != X2
    | esk490_4(X1,X3,X4,X5) = esk490_4(X2,X3,X4,X5) ) ).

cnf(i_0_18740_280,axiom,
    ( X1 != X2
    | esk490_4(X3,X1,X4,X5) = esk490_4(X3,X2,X4,X5) ) ).

cnf(i_0_18741_281,axiom,
    ( X1 != X2
    | esk490_4(X3,X4,X1,X5) = esk490_4(X3,X4,X2,X5) ) ).

cnf(i_0_18742_282,axiom,
    ( X1 != X2
    | esk490_4(X3,X4,X5,X1) = esk490_4(X3,X4,X5,X2) ) ).

cnf(i_0_18743_283,axiom,
    ( X1 != X2
    | esk489_4(X1,X3,X4,X5) = esk489_4(X2,X3,X4,X5) ) ).

cnf(i_0_18744_284,axiom,
    ( X1 != X2
    | esk489_4(X3,X1,X4,X5) = esk489_4(X3,X2,X4,X5) ) ).

cnf(i_0_18745_285,axiom,
    ( X1 != X2
    | esk489_4(X3,X4,X1,X5) = esk489_4(X3,X4,X2,X5) ) ).

cnf(i_0_18746_286,axiom,
    ( X1 != X2
    | esk489_4(X3,X4,X5,X1) = esk489_4(X3,X4,X5,X2) ) ).

cnf(i_0_18747_287,axiom,
    ( X1 != X2
    | c_Orderings_Oord__class_Omin(X1) = c_Orderings_Oord__class_Omin(X2) ) ).

cnf(i_0_18748_288,axiom,
    ( X1 != X2
    | esk341_3(X1,X3,X4) = esk341_3(X2,X3,X4) ) ).

cnf(i_0_18749_289,axiom,
    ( X1 != X2
    | esk341_3(X3,X1,X4) = esk341_3(X3,X2,X4) ) ).

cnf(i_0_18750_290,axiom,
    ( X1 != X2
    | esk341_3(X3,X4,X1) = esk341_3(X3,X4,X2) ) ).

cnf(i_0_18751_291,axiom,
    ( X1 != X2
    | esk340_3(X1,X3,X4) = esk340_3(X2,X3,X4) ) ).

cnf(i_0_18752_292,axiom,
    ( X1 != X2
    | esk340_3(X3,X1,X4) = esk340_3(X3,X2,X4) ) ).

cnf(i_0_18753_293,axiom,
    ( X1 != X2
    | esk340_3(X3,X4,X1) = esk340_3(X3,X4,X2) ) ).

cnf(i_0_18754_294,axiom,
    ( X1 != X2
    | c_Random_Oselect(X1,X3) = c_Random_Oselect(X2,X3) ) ).

cnf(i_0_18755_295,axiom,
    ( X1 != X2
    | c_Random_Oselect(X3,X1) = c_Random_Oselect(X3,X2) ) ).

cnf(i_0_18756_296,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X1,X3,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X2,X3,X4,X5) ) ).

cnf(i_0_18757_297,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X1,X4,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X2,X4,X5) ) ).

cnf(i_0_18758_298,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X1,X5) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X2,X5) ) ).

cnf(i_0_18759_299,axiom,
    ( X1 != X2
    | c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X1) = c_SetInterval_Oord_OatLeastAtMost(X3,X4,X5,X2) ) ).

cnf(i_0_18760_300,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_18761_301,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_18762_302,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_18763_303,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_18764_304,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_18765_305,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X1,X3,X4) = c_Big__Operators_Olattice_OSup__fin(X2,X3,X4) ) ).

cnf(i_0_18766_306,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X1,X4) = c_Big__Operators_Olattice_OSup__fin(X3,X2,X4) ) ).

cnf(i_0_18767_307,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice_OSup__fin(X3,X4,X1) = c_Big__Operators_Olattice_OSup__fin(X3,X4,X2) ) ).

cnf(i_0_18768_308,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X1,X3) = c_Finite__Set_Ofold1(X2,X3) ) ).

cnf(i_0_18769_309,axiom,
    ( X1 != X2
    | c_Finite__Set_Ofold1(X3,X1) = c_Finite__Set_Ofold1(X3,X2) ) ).

cnf(i_0_18770_310,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_18771_311,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_18772_312,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_18773_313,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_18774_314,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__inf__class_Oinf(X1) = c_Lattices_Osemilattice__inf__class_Oinf(X2) ) ).

cnf(i_0_18775_315,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X1,X3) = c_Big__Operators_Olattice__class_OSup__fin(X2,X3) ) ).

cnf(i_0_18776_316,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OSup__fin(X3,X1) = c_Big__Operators_Olattice__class_OSup__fin(X3,X2) ) ).

cnf(i_0_18777_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_18778_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_18779_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_18780_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_18781_321,axiom,
    ( X1 != X2
    | c_Lattices_Osemilattice__sup__class_Osup(X1) = c_Lattices_Osemilattice__sup__class_Osup(X2) ) ).

cnf(i_0_18782_322,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X1,X3,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18783_323,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X1,X4,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18784_324,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X1,X5,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18785_325,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X1,X6) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18786_326,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X6,X1) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18787_327,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X1,X3,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X3,X4) ) ).

cnf(i_0_18788_328,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X1,X4) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X2,X4) ) ).

cnf(i_0_18789_329,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X1) = c_Lazy__Sequence_Olazy__sequence_OInsert(X3,X4,X2) ) ).

cnf(i_0_18790_330,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X1,X3) = c_Big__Operators_Olattice__class_OInf__fin(X2,X3) ) ).

cnf(i_0_18791_331,axiom,
    ( X1 != X2
    | c_Big__Operators_Olattice__class_OInf__fin(X3,X1) = c_Big__Operators_Olattice__class_OInf__fin(X3,X2) ) ).

cnf(i_0_18792_332,axiom,
    ( X1 != X2
    | esk225_5(X1,X3,X4,X5,X6) = esk225_5(X2,X3,X4,X5,X6) ) ).

cnf(i_0_18793_333,axiom,
    ( X1 != X2
    | esk225_5(X3,X1,X4,X5,X6) = esk225_5(X3,X2,X4,X5,X6) ) ).

cnf(i_0_18794_334,axiom,
    ( X1 != X2
    | esk225_5(X3,X4,X1,X5,X6) = esk225_5(X3,X4,X2,X5,X6) ) ).

cnf(i_0_18795_335,axiom,
    ( X1 != X2
    | esk225_5(X3,X4,X5,X1,X6) = esk225_5(X3,X4,X5,X2,X6) ) ).

cnf(i_0_18796_336,axiom,
    ( X1 != X2
    | esk225_5(X3,X4,X5,X6,X1) = esk225_5(X3,X4,X5,X6,X2) ) ).

cnf(i_0_18797_337,axiom,
    ( X1 != X2
    | esk337_3(X1,X3,X4) = esk337_3(X2,X3,X4) ) ).

cnf(i_0_18798_338,axiom,
    ( X1 != X2
    | esk337_3(X3,X1,X4) = esk337_3(X3,X2,X4) ) ).

cnf(i_0_18799_339,axiom,
    ( X1 != X2
    | esk337_3(X3,X4,X1) = esk337_3(X3,X4,X2) ) ).

cnf(i_0_18800_340,axiom,
    ( X1 != X2
    | esk336_3(X1,X3,X4) = esk336_3(X2,X3,X4) ) ).

cnf(i_0_18801_341,axiom,
    ( X1 != X2
    | esk336_3(X3,X1,X4) = esk336_3(X3,X2,X4) ) ).

cnf(i_0_18802_342,axiom,
    ( X1 != X2
    | esk336_3(X3,X4,X1) = esk336_3(X3,X4,X2) ) ).

cnf(i_0_18803_343,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X1,X3,X4) = c_List_Oset__Cons(X2,X3,X4) ) ).

cnf(i_0_18804_344,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X1,X4) = c_List_Oset__Cons(X3,X2,X4) ) ).

cnf(i_0_18805_345,axiom,
    ( X1 != X2
    | c_List_Oset__Cons(X3,X4,X1) = c_List_Oset__Cons(X3,X4,X2) ) ).

cnf(i_0_18806_346,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_18807_347,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_18808_348,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_18809_349,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_18810_350,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_18811_351,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X1,X3,X4,X5) = c_Product__Type_Ocurry(X2,X3,X4,X5) ) ).

cnf(i_0_18812_352,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X1,X4,X5) = c_Product__Type_Ocurry(X3,X2,X4,X5) ) ).

cnf(i_0_18813_353,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X1,X5) = c_Product__Type_Ocurry(X3,X4,X2,X5) ) ).

cnf(i_0_18814_354,axiom,
    ( X1 != X2
    | c_Product__Type_Ocurry(X3,X4,X5,X1) = c_Product__Type_Ocurry(X3,X4,X5,X2) ) ).

cnf(i_0_18815_355,axiom,
    ( X1 != X2
    | esk446_2(X1,X3) = esk446_2(X2,X3) ) ).

cnf(i_0_18816_356,axiom,
    ( X1 != X2
    | esk446_2(X3,X1) = esk446_2(X3,X2) ) ).

cnf(i_0_18817_357,axiom,
    ( X1 != X2
    | esk447_2(X1,X3) = esk447_2(X2,X3) ) ).

cnf(i_0_18818_358,axiom,
    ( X1 != X2
    | esk447_2(X3,X1) = esk447_2(X3,X2) ) ).

cnf(i_0_18819_359,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X1,X3) = c_Nitpick_Onat__gcd(X2,X3) ) ).

cnf(i_0_18820_360,axiom,
    ( X1 != X2
    | c_Nitpick_Onat__gcd(X3,X1) = c_Nitpick_Onat__gcd(X3,X2) ) ).

cnf(i_0_18821_361,axiom,
    ( X1 != X2
    | c_List_Oremdups(X1,X3) = c_List_Oremdups(X2,X3) ) ).

cnf(i_0_18822_362,axiom,
    ( X1 != X2
    | c_List_Oremdups(X3,X1) = c_List_Oremdups(X3,X2) ) ).

cnf(i_0_18823_363,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X1,X3,X4) = c_Partial__Function_Oflat__lub(X2,X3,X4) ) ).

cnf(i_0_18824_364,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X1,X4) = c_Partial__Function_Oflat__lub(X3,X2,X4) ) ).

cnf(i_0_18825_365,axiom,
    ( X1 != X2
    | c_Partial__Function_Oflat__lub(X3,X4,X1) = c_Partial__Function_Oflat__lub(X3,X4,X2) ) ).

cnf(i_0_18826_366,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_18827_367,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_18828_368,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_18829_369,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_18830_370,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_18831_371,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_18832_372,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X1,X3,X4) = c_List_Oreplicate(X2,X3,X4) ) ).

cnf(i_0_18833_373,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X1,X4) = c_List_Oreplicate(X3,X2,X4) ) ).

cnf(i_0_18834_374,axiom,
    ( X1 != X2
    | c_List_Oreplicate(X3,X4,X1) = c_List_Oreplicate(X3,X4,X2) ) ).

cnf(i_0_18835_375,axiom,
    ( X1 != X2
    | esk222_3(X1,X3,X4) = esk222_3(X2,X3,X4) ) ).

cnf(i_0_18836_376,axiom,
    ( X1 != X2
    | esk222_3(X3,X1,X4) = esk222_3(X3,X2,X4) ) ).

cnf(i_0_18837_377,axiom,
    ( X1 != X2
    | esk222_3(X3,X4,X1) = esk222_3(X3,X4,X2) ) ).

cnf(i_0_18838_378,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X1,X3) = c_Divides_Odivmod__int(X2,X3) ) ).

cnf(i_0_18839_379,axiom,
    ( X1 != X2
    | c_Divides_Odivmod__int(X3,X1) = c_Divides_Odivmod__int(X3,X2) ) ).

cnf(i_0_18840_380,axiom,
    ( X1 != X2
    | esk521_3(X1,X3,X4) = esk521_3(X2,X3,X4) ) ).

cnf(i_0_18841_381,axiom,
    ( X1 != X2
    | esk521_3(X3,X1,X4) = esk521_3(X3,X2,X4) ) ).

cnf(i_0_18842_382,axiom,
    ( X1 != X2
    | esk521_3(X3,X4,X1) = esk521_3(X3,X4,X2) ) ).

cnf(i_0_18843_383,axiom,
    ( X1 != X2
    | esk487_4(X1,X3,X4,X5) = esk487_4(X2,X3,X4,X5) ) ).

cnf(i_0_18844_384,axiom,
    ( X1 != X2
    | esk487_4(X3,X1,X4,X5) = esk487_4(X3,X2,X4,X5) ) ).

cnf(i_0_18845_385,axiom,
    ( X1 != X2
    | esk487_4(X3,X4,X1,X5) = esk487_4(X3,X4,X2,X5) ) ).

cnf(i_0_18846_386,axiom,
    ( X1 != X2
    | esk487_4(X3,X4,X5,X1) = esk487_4(X3,X4,X5,X2) ) ).

cnf(i_0_18847_387,axiom,
    ( X1 != X2
    | esk479_4(X1,X3,X4,X5) = esk479_4(X2,X3,X4,X5) ) ).

cnf(i_0_18848_388,axiom,
    ( X1 != X2
    | esk479_4(X3,X1,X4,X5) = esk479_4(X3,X2,X4,X5) ) ).

cnf(i_0_18849_389,axiom,
    ( X1 != X2
    | esk479_4(X3,X4,X1,X5) = esk479_4(X3,X4,X2,X5) ) ).

cnf(i_0_18850_390,axiom,
    ( X1 != X2
    | esk479_4(X3,X4,X5,X1) = esk479_4(X3,X4,X5,X2) ) ).

cnf(i_0_18851_391,axiom,
    ( X1 != X2
    | esk182_4(X1,X3,X4,X5) = esk182_4(X2,X3,X4,X5) ) ).

cnf(i_0_18852_392,axiom,
    ( X1 != X2
    | esk182_4(X3,X1,X4,X5) = esk182_4(X3,X2,X4,X5) ) ).

cnf(i_0_18853_393,axiom,
    ( X1 != X2
    | esk182_4(X3,X4,X1,X5) = esk182_4(X3,X4,X2,X5) ) ).

cnf(i_0_18854_394,axiom,
    ( X1 != X2
    | esk182_4(X3,X4,X5,X1) = esk182_4(X3,X4,X5,X2) ) ).

cnf(i_0_18855_395,axiom,
    ( X1 != X2
    | esk184_4(X1,X3,X4,X5) = esk184_4(X2,X3,X4,X5) ) ).

cnf(i_0_18856_396,axiom,
    ( X1 != X2
    | esk184_4(X3,X1,X4,X5) = esk184_4(X3,X2,X4,X5) ) ).

cnf(i_0_18857_397,axiom,
    ( X1 != X2
    | esk184_4(X3,X4,X1,X5) = esk184_4(X3,X4,X2,X5) ) ).

cnf(i_0_18858_398,axiom,
    ( X1 != X2
    | esk184_4(X3,X4,X5,X1) = esk184_4(X3,X4,X5,X2) ) ).

cnf(i_0_18859_399,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X1,X3,X4,X5) = c_Enum_Oproduct(X2,X3,X4,X5) ) ).

cnf(i_0_18860_400,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X1,X4,X5) = c_Enum_Oproduct(X3,X2,X4,X5) ) ).

cnf(i_0_18861_401,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X1,X5) = c_Enum_Oproduct(X3,X4,X2,X5) ) ).

cnf(i_0_18862_402,axiom,
    ( X1 != X2
    | c_Enum_Oproduct(X3,X4,X5,X1) = c_Enum_Oproduct(X3,X4,X5,X2) ) ).

cnf(i_0_18863_403,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X1,X3) = c_Groups_Osgn__class_Osgn(X2,X3) ) ).

cnf(i_0_18864_404,axiom,
    ( X1 != X2
    | c_Groups_Osgn__class_Osgn(X3,X1) = c_Groups_Osgn__class_Osgn(X3,X2) ) ).

cnf(i_0_18865_405,axiom,
    ( X1 != X2
    | esk23_4(X1,X3,X4,X5) = esk23_4(X2,X3,X4,X5) ) ).

cnf(i_0_18866_406,axiom,
    ( X1 != X2
    | esk23_4(X3,X1,X4,X5) = esk23_4(X3,X2,X4,X5) ) ).

cnf(i_0_18867_407,axiom,
    ( X1 != X2
    | esk23_4(X3,X4,X1,X5) = esk23_4(X3,X4,X2,X5) ) ).

cnf(i_0_18868_408,axiom,
    ( X1 != X2
    | esk23_4(X3,X4,X5,X1) = esk23_4(X3,X4,X5,X2) ) ).

cnf(i_0_18869_409,axiom,
    ( X1 != X2
    | esk22_4(X1,X3,X4,X5) = esk22_4(X2,X3,X4,X5) ) ).

cnf(i_0_18870_410,axiom,
    ( X1 != X2
    | esk22_4(X3,X1,X4,X5) = esk22_4(X3,X2,X4,X5) ) ).

cnf(i_0_18871_411,axiom,
    ( X1 != X2
    | esk22_4(X3,X4,X1,X5) = esk22_4(X3,X4,X2,X5) ) ).

cnf(i_0_18872_412,axiom,
    ( X1 != X2
    | esk22_4(X3,X4,X5,X1) = esk22_4(X3,X4,X5,X2) ) ).

cnf(i_0_18873_413,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_18874_414,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_18875_415,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_18876_416,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_18877_417,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_18878_418,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X1,X3,X4,X5) = c_Nitpick_Opair__box_OPairBox(X2,X3,X4,X5) ) ).

cnf(i_0_18879_419,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X1,X4,X5) = c_Nitpick_Opair__box_OPairBox(X3,X2,X4,X5) ) ).

cnf(i_0_18880_420,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X1,X5) = c_Nitpick_Opair__box_OPairBox(X3,X4,X2,X5) ) ).

cnf(i_0_18881_421,axiom,
    ( X1 != X2
    | c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X1) = c_Nitpick_Opair__box_OPairBox(X3,X4,X5,X2) ) ).

cnf(i_0_18882_422,axiom,
    ( X1 != X2
    | esk253_3(X1,X3,X4) = esk253_3(X2,X3,X4) ) ).

cnf(i_0_18883_423,axiom,
    ( X1 != X2
    | esk253_3(X3,X1,X4) = esk253_3(X3,X2,X4) ) ).

cnf(i_0_18884_424,axiom,
    ( X1 != X2
    | esk253_3(X3,X4,X1) = esk253_3(X3,X4,X2) ) ).

cnf(i_0_18885_425,axiom,
    ( X1 != X2
    | esk254_3(X1,X3,X4) = esk254_3(X2,X3,X4) ) ).

cnf(i_0_18886_426,axiom,
    ( X1 != X2
    | esk254_3(X3,X1,X4) = esk254_3(X3,X2,X4) ) ).

cnf(i_0_18887_427,axiom,
    ( X1 != X2
    | esk254_3(X3,X4,X1) = esk254_3(X3,X4,X2) ) ).

cnf(i_0_18888_428,axiom,
    ( X1 != X2
    | esk224_4(X1,X3,X4,X5) = esk224_4(X2,X3,X4,X5) ) ).

cnf(i_0_18889_429,axiom,
    ( X1 != X2
    | esk224_4(X3,X1,X4,X5) = esk224_4(X3,X2,X4,X5) ) ).

cnf(i_0_18890_430,axiom,
    ( X1 != X2
    | esk224_4(X3,X4,X1,X5) = esk224_4(X3,X4,X2,X5) ) ).

cnf(i_0_18891_431,axiom,
    ( X1 != X2
    | esk224_4(X3,X4,X5,X1) = esk224_4(X3,X4,X5,X2) ) ).

cnf(i_0_18892_432,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X1,X3) = c_Divides_Opdivmod(X2,X3) ) ).

cnf(i_0_18893_433,axiom,
    ( X1 != X2
    | c_Divides_Opdivmod(X3,X1) = c_Divides_Opdivmod(X3,X2) ) ).

cnf(i_0_18894_434,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_18895_435,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_18896_436,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_18897_437,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_18898_438,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X1,X3,X4,X5) = c_Sum__Type_OPlus(X2,X3,X4,X5) ) ).

cnf(i_0_18899_439,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X1,X4,X5) = c_Sum__Type_OPlus(X3,X2,X4,X5) ) ).

cnf(i_0_18900_440,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X1,X5) = c_Sum__Type_OPlus(X3,X4,X2,X5) ) ).

cnf(i_0_18901_441,axiom,
    ( X1 != X2
    | c_Sum__Type_OPlus(X3,X4,X5,X1) = c_Sum__Type_OPlus(X3,X4,X5,X2) ) ).

cnf(i_0_18902_442,axiom,
    ( X1 != X2
    | esk251_3(X1,X3,X4) = esk251_3(X2,X3,X4) ) ).

cnf(i_0_18903_443,axiom,
    ( X1 != X2
    | esk251_3(X3,X1,X4) = esk251_3(X3,X2,X4) ) ).

cnf(i_0_18904_444,axiom,
    ( X1 != X2
    | esk251_3(X3,X4,X1) = esk251_3(X3,X4,X2) ) ).

cnf(i_0_18905_445,axiom,
    ( X1 != X2
    | esk250_3(X1,X3,X4) = esk250_3(X2,X3,X4) ) ).

cnf(i_0_18906_446,axiom,
    ( X1 != X2
    | esk250_3(X3,X1,X4) = esk250_3(X3,X2,X4) ) ).

cnf(i_0_18907_447,axiom,
    ( X1 != X2
    | esk250_3(X3,X4,X1) = esk250_3(X3,X4,X2) ) ).

cnf(i_0_18908_448,axiom,
    ( X1 != X2
    | c_List_Oupto(X1,X3) = c_List_Oupto(X2,X3) ) ).

cnf(i_0_18909_449,axiom,
    ( X1 != X2
    | c_List_Oupto(X3,X1) = c_List_Oupto(X3,X2) ) ).

cnf(i_0_18910_450,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_18911_451,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_18912_452,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_18913_453,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_18914_454,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_18915_455,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_18916_456,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_18917_457,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_18918_458,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_18919_459,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_18920_460,axiom,
    ( X1 != X2
    | c_List_Olast(X1,X3) = c_List_Olast(X2,X3) ) ).

cnf(i_0_18921_461,axiom,
    ( X1 != X2
    | c_List_Olast(X3,X1) = c_List_Olast(X3,X2) ) ).

cnf(i_0_18922_462,axiom,
    ( X1 != X2
    | c_List_Obutlast(X1,X3) = c_List_Obutlast(X2,X3) ) ).

cnf(i_0_18923_463,axiom,
    ( X1 != X2
    | c_List_Obutlast(X3,X1) = c_List_Obutlast(X3,X2) ) ).

cnf(i_0_18924_464,axiom,
    ( X1 != X2
    | esk512_2(X1,X3) = esk512_2(X2,X3) ) ).

cnf(i_0_18925_465,axiom,
    ( X1 != X2
    | esk512_2(X3,X1) = esk512_2(X3,X2) ) ).

cnf(i_0_18926_466,axiom,
    ( X1 != X2
    | esk511_2(X1,X3) = esk511_2(X2,X3) ) ).

cnf(i_0_18927_467,axiom,
    ( X1 != X2
    | esk511_2(X3,X1) = esk511_2(X3,X2) ) ).

cnf(i_0_18928_468,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X1,X3,X4,X5) = c_Lazy__Sequence_Ohb__bind(X2,X3,X4,X5) ) ).

cnf(i_0_18929_469,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X1,X4,X5) = c_Lazy__Sequence_Ohb__bind(X3,X2,X4,X5) ) ).

cnf(i_0_18930_470,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X1,X5) = c_Lazy__Sequence_Ohb__bind(X3,X4,X2,X5) ) ).

cnf(i_0_18931_471,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X1) = c_Lazy__Sequence_Ohb__bind(X3,X4,X5,X2) ) ).

cnf(i_0_18932_472,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) ) ).

cnf(i_0_18933_473,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_18934_474,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_18935_475,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_18936_476,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_18937_477,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_18938_478,axiom,
    ( X1 != X2
    | c_List_Olenlex(X1,X3) = c_List_Olenlex(X2,X3) ) ).

cnf(i_0_18939_479,axiom,
    ( X1 != X2
    | c_List_Olenlex(X3,X1) = c_List_Olenlex(X3,X2) ) ).

cnf(i_0_18940_480,axiom,
    ( X1 != X2
    | esk36_3(X1,X3,X4) = esk36_3(X2,X3,X4) ) ).

cnf(i_0_18941_481,axiom,
    ( X1 != X2
    | esk36_3(X3,X1,X4) = esk36_3(X3,X2,X4) ) ).

cnf(i_0_18942_482,axiom,
    ( X1 != X2
    | esk36_3(X3,X4,X1) = esk36_3(X3,X4,X2) ) ).

cnf(i_0_18943_483,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X1,X3) = c_Lazy__Sequence_Osmall__lazy_H(X2,X3) ) ).

cnf(i_0_18944_484,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Osmall__lazy_H(X3,X1) = c_Lazy__Sequence_Osmall__lazy_H(X3,X2) ) ).

cnf(i_0_18945_485,axiom,
    ( X1 != X2
    | esk492_4(X1,X3,X4,X5) = esk492_4(X2,X3,X4,X5) ) ).

cnf(i_0_18946_486,axiom,
    ( X1 != X2
    | esk492_4(X3,X1,X4,X5) = esk492_4(X3,X2,X4,X5) ) ).

cnf(i_0_18947_487,axiom,
    ( X1 != X2
    | esk492_4(X3,X4,X1,X5) = esk492_4(X3,X4,X2,X5) ) ).

cnf(i_0_18948_488,axiom,
    ( X1 != X2
    | esk492_4(X3,X4,X5,X1) = esk492_4(X3,X4,X5,X2) ) ).

cnf(i_0_18949_489,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X1,X3,X4) = c_FunDef_OTHE__default(X2,X3,X4) ) ).

cnf(i_0_18950_490,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X1,X4) = c_FunDef_OTHE__default(X3,X2,X4) ) ).

cnf(i_0_18951_491,axiom,
    ( X1 != X2
    | c_FunDef_OTHE__default(X3,X4,X1) = c_FunDef_OTHE__default(X3,X4,X2) ) ).

cnf(i_0_18952_492,axiom,
    ( X1 != X2
    | c_List_Olex(X1,X3) = c_List_Olex(X2,X3) ) ).

cnf(i_0_18953_493,axiom,
    ( X1 != X2
    | c_List_Olex(X3,X1) = c_List_Olex(X3,X2) ) ).

cnf(i_0_18954_494,axiom,
    ( X1 != X2
    | c_List_Omaps(X1,X3,X4,X5) = c_List_Omaps(X2,X3,X4,X5) ) ).

cnf(i_0_18955_495,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X1,X4,X5) = c_List_Omaps(X3,X2,X4,X5) ) ).

cnf(i_0_18956_496,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X1,X5) = c_List_Omaps(X3,X4,X2,X5) ) ).

cnf(i_0_18957_497,axiom,
    ( X1 != X2
    | c_List_Omaps(X3,X4,X5,X1) = c_List_Omaps(X3,X4,X5,X2) ) ).

cnf(i_0_18958_498,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X1,X3,X4,X5) = c_List_Ofoldl(X2,X3,X4,X5) ) ).

cnf(i_0_18959_499,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X1,X4,X5) = c_List_Ofoldl(X3,X2,X4,X5) ) ).

cnf(i_0_18960_500,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X1,X5) = c_List_Ofoldl(X3,X4,X2,X5) ) ).

cnf(i_0_18961_501,axiom,
    ( X1 != X2
    | c_List_Ofoldl(X3,X4,X5,X1) = c_List_Ofoldl(X3,X4,X5,X2) ) ).

cnf(i_0_18962_502,axiom,
    ( X1 != X2
    | esk316_2(X1,X3) = esk316_2(X2,X3) ) ).

cnf(i_0_18963_503,axiom,
    ( X1 != X2
    | esk316_2(X3,X1) = esk316_2(X3,X2) ) ).

cnf(i_0_18964_504,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X1,X3,X4,X5) = c_Fun_Ocomp(X2,X3,X4,X5) ) ).

cnf(i_0_18965_505,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X1,X4,X5) = c_Fun_Ocomp(X3,X2,X4,X5) ) ).

cnf(i_0_18966_506,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X1,X5) = c_Fun_Ocomp(X3,X4,X2,X5) ) ).

cnf(i_0_18967_507,axiom,
    ( X1 != X2
    | c_Fun_Ocomp(X3,X4,X5,X1) = c_Fun_Ocomp(X3,X4,X5,X2) ) ).

cnf(i_0_18968_508,axiom,
    ( X1 != X2
    | esk420_2(X1,X3) = esk420_2(X2,X3) ) ).

cnf(i_0_18969_509,axiom,
    ( X1 != X2
    | esk420_2(X3,X1) = esk420_2(X3,X2) ) ).

cnf(i_0_18970_510,axiom,
    ( X1 != X2
    | esk421_2(X1,X3) = esk421_2(X2,X3) ) ).

cnf(i_0_18971_511,axiom,
    ( X1 != X2
    | esk421_2(X3,X1) = esk421_2(X3,X2) ) ).

cnf(i_0_18972_512,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_18973_513,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_18974_514,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_18975_515,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_18976_516,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X1,X3,X4,X5) = c_Lazy__Sequence_Omap(X2,X3,X4,X5) ) ).

cnf(i_0_18977_517,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X1,X4,X5) = c_Lazy__Sequence_Omap(X3,X2,X4,X5) ) ).

cnf(i_0_18978_518,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X4,X1,X5) = c_Lazy__Sequence_Omap(X3,X4,X2,X5) ) ).

cnf(i_0_18979_519,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Omap(X3,X4,X5,X1) = c_Lazy__Sequence_Omap(X3,X4,X5,X2) ) ).

cnf(i_0_18980_520,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X2,X3,X4) ) ).

cnf(i_0_18981_521,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X2,X4) ) ).

cnf(i_0_18982_522,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanAtMost(X3,X4,X2) ) ).

cnf(i_0_18983_523,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X1,X3,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X2,X3,X4) ) ).

cnf(i_0_18984_524,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X1,X4) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X2,X4) ) ).

cnf(i_0_18985_525,axiom,
    ( X1 != X2
    | c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X1) = c_SetInterval_Oord__class_OgreaterThanLessThan(X3,X4,X2) ) ).

cnf(i_0_18986_526,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_18987_527,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_18988_528,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_18989_529,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_18990_530,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X1,X3,X4) = c_Power_Opower_Opower(X2,X3,X4) ) ).

cnf(i_0_18991_531,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X1,X4) = c_Power_Opower_Opower(X3,X2,X4) ) ).

cnf(i_0_18992_532,axiom,
    ( X1 != X2
    | c_Power_Opower_Opower(X3,X4,X1) = c_Power_Opower_Opower(X3,X4,X2) ) ).

cnf(i_0_18993_533,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X1,X3,X4) = c_Nitpick_Oplus__frac(X2,X3,X4) ) ).

cnf(i_0_18994_534,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X1,X4) = c_Nitpick_Oplus__frac(X3,X2,X4) ) ).

cnf(i_0_18995_535,axiom,
    ( X1 != X2
    | c_Nitpick_Oplus__frac(X3,X4,X1) = c_Nitpick_Oplus__frac(X3,X4,X2) ) ).

cnf(i_0_18996_536,axiom,
    ( X1 != X2
    | esk408_2(X1,X3) = esk408_2(X2,X3) ) ).

cnf(i_0_18997_537,axiom,
    ( X1 != X2
    | esk408_2(X3,X1) = esk408_2(X3,X2) ) ).

cnf(i_0_18998_538,axiom,
    ( X1 != X2
    | esk181_3(X1,X3,X4) = esk181_3(X2,X3,X4) ) ).

cnf(i_0_18999_539,axiom,
    ( X1 != X2
    | esk181_3(X3,X1,X4) = esk181_3(X3,X2,X4) ) ).

cnf(i_0_19000_540,axiom,
    ( X1 != X2
    | esk181_3(X3,X4,X1) = esk181_3(X3,X4,X2) ) ).

cnf(i_0_19001_541,axiom,
    ( X1 != X2
    | esk183_3(X1,X3,X4) = esk183_3(X2,X3,X4) ) ).

cnf(i_0_19002_542,axiom,
    ( X1 != X2
    | esk183_3(X3,X1,X4) = esk183_3(X3,X2,X4) ) ).

cnf(i_0_19003_543,axiom,
    ( X1 != X2
    | esk183_3(X3,X4,X1) = esk183_3(X3,X4,X2) ) ).

cnf(i_0_19004_544,axiom,
    ( X1 != X2
    | esk200_3(X1,X3,X4) = esk200_3(X2,X3,X4) ) ).

cnf(i_0_19005_545,axiom,
    ( X1 != X2
    | esk200_3(X3,X1,X4) = esk200_3(X3,X2,X4) ) ).

cnf(i_0_19006_546,axiom,
    ( X1 != X2
    | esk200_3(X3,X4,X1) = esk200_3(X3,X4,X2) ) ).

cnf(i_0_19007_547,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X1,X3) = c_Nitpick_Oint__lcm(X2,X3) ) ).

cnf(i_0_19008_548,axiom,
    ( X1 != X2
    | c_Nitpick_Oint__lcm(X3,X1) = c_Nitpick_Oint__lcm(X3,X2) ) ).

cnf(i_0_19009_549,axiom,
    ( X1 != X2
    | esk199_3(X1,X3,X4) = esk199_3(X2,X3,X4) ) ).

cnf(i_0_19010_550,axiom,
    ( X1 != X2
    | esk199_3(X3,X1,X4) = esk199_3(X3,X2,X4) ) ).

cnf(i_0_19011_551,axiom,
    ( X1 != X2
    | esk199_3(X3,X4,X1) = esk199_3(X3,X4,X2) ) ).

cnf(i_0_19012_552,axiom,
    ( X1 != X2
    | esk486_3(X1,X3,X4) = esk486_3(X2,X3,X4) ) ).

cnf(i_0_19013_553,axiom,
    ( X1 != X2
    | esk486_3(X3,X1,X4) = esk486_3(X3,X2,X4) ) ).

cnf(i_0_19014_554,axiom,
    ( X1 != X2
    | esk486_3(X3,X4,X1) = esk486_3(X3,X4,X2) ) ).

cnf(i_0_19015_555,axiom,
    ( X1 != X2
    | esk478_3(X1,X3,X4) = esk478_3(X2,X3,X4) ) ).

cnf(i_0_19016_556,axiom,
    ( X1 != X2
    | esk478_3(X3,X1,X4) = esk478_3(X3,X2,X4) ) ).

cnf(i_0_19017_557,axiom,
    ( X1 != X2
    | esk478_3(X3,X4,X1) = esk478_3(X3,X4,X2) ) ).

cnf(i_0_19018_558,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X1,X3,X4,X5) = c_Quotient_OBabs(X2,X3,X4,X5) ) ).

cnf(i_0_19019_559,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X1,X4,X5) = c_Quotient_OBabs(X3,X2,X4,X5) ) ).

cnf(i_0_19020_560,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X4,X1,X5) = c_Quotient_OBabs(X3,X4,X2,X5) ) ).

cnf(i_0_19021_561,axiom,
    ( X1 != X2
    | c_Quotient_OBabs(X3,X4,X5,X1) = c_Quotient_OBabs(X3,X4,X5,X2) ) ).

cnf(i_0_19022_562,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oflat(X1,X3) = c_Lazy__Sequence_Oflat(X2,X3) ) ).

cnf(i_0_19023_563,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Oflat(X3,X1) = c_Lazy__Sequence_Oflat(X3,X2) ) ).

cnf(i_0_19024_564,axiom,
    ( X1 != X2
    | c_List_Osplice(X1,X3,X4) = c_List_Osplice(X2,X3,X4) ) ).

cnf(i_0_19025_565,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X1,X4) = c_List_Osplice(X3,X2,X4) ) ).

cnf(i_0_19026_566,axiom,
    ( X1 != X2
    | c_List_Osplice(X3,X4,X1) = c_List_Osplice(X3,X4,X2) ) ).

cnf(i_0_19027_567,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohit__bound(X1) = c_Lazy__Sequence_Ohit__bound(X2) ) ).

cnf(i_0_19028_568,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X1,X3) = c_Nat__Transfer_Otsub(X2,X3) ) ).

cnf(i_0_19029_569,axiom,
    ( X1 != X2
    | c_Nat__Transfer_Otsub(X3,X1) = c_Nat__Transfer_Otsub(X3,X2) ) ).

cnf(i_0_19030_570,axiom,
    ( X1 != X2
    | c_Random_Olog(X1,X3) = c_Random_Olog(X2,X3) ) ).

cnf(i_0_19031_571,axiom,
    ( X1 != X2
    | c_Random_Olog(X3,X1) = c_Random_Olog(X3,X2) ) ).

cnf(i_0_19032_572,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X1,X3,X4) = c_Random_Ominus__shift(X2,X3,X4) ) ).

cnf(i_0_19033_573,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X1,X4) = c_Random_Ominus__shift(X3,X2,X4) ) ).

cnf(i_0_19034_574,axiom,
    ( X1 != X2
    | c_Random_Ominus__shift(X3,X4,X1) = c_Random_Ominus__shift(X3,X4,X2) ) ).

cnf(i_0_19035_575,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X1,X3,X4) = c_Random__Sequence_Oempty(X2,X3,X4) ) ).

cnf(i_0_19036_576,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X1,X4) = c_Random__Sequence_Oempty(X3,X2,X4) ) ).

cnf(i_0_19037_577,axiom,
    ( X1 != X2
    | c_Random__Sequence_Oempty(X3,X4,X1) = c_Random__Sequence_Oempty(X3,X4,X2) ) ).

cnf(i_0_19038_578,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_19039_579,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_19040_580,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_19041_581,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_19042_582,axiom,
    ( X1 != X2
    | esk426_2(X1,X3) = esk426_2(X2,X3) ) ).

cnf(i_0_19043_583,axiom,
    ( X1 != X2
    | esk426_2(X3,X1) = esk426_2(X3,X2) ) ).

cnf(i_0_19044_584,axiom,
    ( X1 != X2
    | c_List_Olistset(X1,X3) = c_List_Olistset(X2,X3) ) ).

cnf(i_0_19045_585,axiom,
    ( X1 != X2
    | c_List_Olistset(X3,X1) = c_List_Olistset(X3,X2) ) ).

cnf(i_0_19046_586,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X1,X3) = c_Code__Numeral_Odiv__mod__code__numeral(X2,X3) ) ).

cnf(i_0_19047_587,axiom,
    ( X1 != X2
    | c_Code__Numeral_Odiv__mod__code__numeral(X3,X1) = c_Code__Numeral_Odiv__mod__code__numeral(X3,X2) ) ).

cnf(i_0_19048_588,axiom,
    ( X1 != X2
    | esk395_2(X1,X3) = esk395_2(X2,X3) ) ).

cnf(i_0_19049_589,axiom,
    ( X1 != X2
    | esk395_2(X3,X1) = esk395_2(X3,X2) ) ).

cnf(i_0_19050_590,axiom,
    ( X1 != X2
    | esk394_2(X1,X3) = esk394_2(X2,X3) ) ).

cnf(i_0_19051_591,axiom,
    ( X1 != X2
    | esk394_2(X3,X1) = esk394_2(X3,X2) ) ).

cnf(i_0_19052_592,axiom,
    ( X1 != X2
    | c_List_Oinsert(X1,X3,X4) = c_List_Oinsert(X2,X3,X4) ) ).

cnf(i_0_19053_593,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X1,X4) = c_List_Oinsert(X3,X2,X4) ) ).

cnf(i_0_19054_594,axiom,
    ( X1 != X2
    | c_List_Oinsert(X3,X4,X1) = c_List_Oinsert(X3,X4,X2) ) ).

cnf(i_0_19055_595,axiom,
    ( X1 != X2
    | c_Orderings_Otop__class_Otop(X1) = c_Orderings_Otop__class_Otop(X2) ) ).

cnf(i_0_19056_596,axiom,
    ( X1 != X2
    | esk493_3(X1,X3,X4) = esk493_3(X2,X3,X4) ) ).

cnf(i_0_19057_597,axiom,
    ( X1 != X2
    | esk493_3(X3,X1,X4) = esk493_3(X3,X2,X4) ) ).

cnf(i_0_19058_598,axiom,
    ( X1 != X2
    | esk493_3(X3,X4,X1) = esk493_3(X3,X4,X2) ) ).

cnf(i_0_19059_599,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X1,X3) = c_SMT_Oz3div(X2,X3) ) ).

cnf(i_0_19060_600,axiom,
    ( X1 != X2
    | c_SMT_Oz3div(X3,X1) = c_SMT_Oz3div(X3,X2) ) ).

cnf(i_0_19061_601,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X1,X3) = c_Orderings_Oord_Omin(X2,X3) ) ).

cnf(i_0_19062_602,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omin(X3,X1) = c_Orderings_Oord_Omin(X3,X2) ) ).

cnf(i_0_19063_603,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X1,X3,X4,X5,X6) = c_Predicate_Opred__comp(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19064_604,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X1,X4,X5,X6) = c_Predicate_Opred__comp(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19065_605,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X1,X5,X6) = c_Predicate_Opred__comp(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19066_606,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X1,X6) = c_Predicate_Opred__comp(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19067_607,axiom,
    ( X1 != X2
    | c_Predicate_Opred__comp(X3,X4,X5,X6,X1) = c_Predicate_Opred__comp(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19068_608,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X1,X3) = c_Orderings_Oord_Omax(X2,X3) ) ).

cnf(i_0_19069_609,axiom,
    ( X1 != X2
    | c_Orderings_Oord_Omax(X3,X1) = c_Orderings_Oord_Omax(X3,X2) ) ).

cnf(i_0_19070_610,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X1,X3) = c_New__DSequence_Opos__single(X2,X3) ) ).

cnf(i_0_19071_611,axiom,
    ( X1 != X2
    | c_New__DSequence_Opos__single(X3,X1) = c_New__DSequence_Opos__single(X3,X2) ) ).

cnf(i_0_19072_612,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X1,X3) = c_New__DSequence_Oneg__single(X2,X3) ) ).

cnf(i_0_19073_613,axiom,
    ( X1 != X2
    | c_New__DSequence_Oneg__single(X3,X1) = c_New__DSequence_Oneg__single(X3,X2) ) ).

cnf(i_0_19074_614,axiom,
    ( X1 != X2
    | c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X1) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X2) ) ).

cnf(i_0_19075_615,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X1,X3) = c_SMT_Oz3mod(X2,X3) ) ).

cnf(i_0_19076_616,axiom,
    ( X1 != X2
    | c_SMT_Oz3mod(X3,X1) = c_SMT_Oz3mod(X3,X2) ) ).

cnf(i_0_19077_617,axiom,
    ( X1 != X2
    | esk453_2(X1,X3) = esk453_2(X2,X3) ) ).

cnf(i_0_19078_618,axiom,
    ( X1 != X2
    | esk453_2(X3,X1) = esk453_2(X3,X2) ) ).

cnf(i_0_19079_619,axiom,
    ( X1 != X2
    | esk390_1(X1) = esk390_1(X2) ) ).

cnf(i_0_19080_620,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X1,X3) = c_Quickcheck_Obeyond(X2,X3) ) ).

cnf(i_0_19081_621,axiom,
    ( X1 != X2
    | c_Quickcheck_Obeyond(X3,X1) = c_Quickcheck_Obeyond(X3,X2) ) ).

cnf(i_0_19082_622,axiom,
    ( X1 != X2
    | c_Nat_Onat_Onat__size(X1) = c_Nat_Onat_Onat__size(X2) ) ).

cnf(i_0_19083_623,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X1,X3) = c_Random_Oinc__shift(X2,X3) ) ).

cnf(i_0_19084_624,axiom,
    ( X1 != X2
    | c_Random_Oinc__shift(X3,X1) = c_Random_Oinc__shift(X3,X2) ) ).

cnf(i_0_19085_625,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X1,X3) = c_Lazy__Sequence_Ohb__single(X2,X3) ) ).

cnf(i_0_19086_626,axiom,
    ( X1 != X2
    | c_Lazy__Sequence_Ohb__single(X3,X1) = c_Lazy__Sequence_Ohb__single(X3,X2) ) ).

cnf(i_0_19087_627,axiom,
    ( X1 != X2
    | c_HOL_Obool_Obool__size(X1) = c_HOL_Obool_Obool__size(X2) ) ).

cnf(i_0_19088_628,axiom,
    ( X1 != X2
    | c_Int_Oring__1__class_Oof__int(X1) = c_Int_Oring__1__class_Oof__int(X2) ) ).

cnf(i_0_19089_629,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X1,X3,X4) = c_Predicate_Oconversep(X2,X3,X4) ) ).

cnf(i_0_19090_630,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X1,X4) = c_Predicate_Oconversep(X3,X2,X4) ) ).

cnf(i_0_19091_631,axiom,
    ( X1 != X2
    | c_Predicate_Oconversep(X3,X4,X1) = c_Predicate_Oconversep(X3,X4,X2) ) ).

cnf(i_0_19092_632,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X1,X3) = c_FunDef_Orp__inv__image(X2,X3) ) ).

cnf(i_0_19093_633,axiom,
    ( X1 != X2
    | c_FunDef_Orp__inv__image(X3,X1) = c_FunDef_Orp__inv__image(X3,X2) ) ).

cnf(i_0_19094_634,axiom,
    ( X1 != X2
    | ~ hBOOL(X1)
    | hBOOL(X2) ) ).

cnf(i_0_19095_635,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1(X1)
    | class_Rings_Oring__1(X2) ) ).

cnf(i_0_19096_636,axiom,
    ( X1 != X2
    | ~ epred2_3(X1,X3,X4)
    | epred2_3(X2,X3,X4) ) ).

cnf(i_0_19097_637,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X1,X4)
    | epred2_3(X3,X2,X4) ) ).

cnf(i_0_19098_638,axiom,
    ( X1 != X2
    | ~ epred2_3(X3,X4,X1)
    | epred2_3(X3,X4,X2) ) ).

cnf(i_0_19099_639,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__add(X1)
    | class_Groups_Oab__semigroup__add(X2) ) ).

cnf(i_0_19100_640,axiom,
    ( X1 != X2
    | ~ class_Int_Oring__char__0(X1)
    | class_Int_Oring__char__0(X2) ) ).

cnf(i_0_19101_641,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__strict(X1)
    | class_Rings_Olinordered__semiring__strict(X2) ) ).

cnf(i_0_19102_642,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__semiring(X1)
    | class_Rings_Oordered__semiring(X2) ) ).

cnf(i_0_19103_643,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring(X1)
    | class_Rings_Olinordered__semiring(X2) ) ).

cnf(i_0_19104_644,axiom,
    ( X1 != X2
    | ~ class_Rings_Oidom(X1)
    | class_Rings_Oidom(X2) ) ).

cnf(i_0_19105_645,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(X1)
    | class_Groups_Oordered__ab__semigroup__add__imp__le(X2) ) ).

cnf(i_0_19106_646,axiom,
    ( X1 != X2
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ).

cnf(i_0_19107_647,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X1,X3)
    | c_Predicate_Oreflp(X2,X3) ) ).

cnf(i_0_19108_648,axiom,
    ( X1 != X2
    | ~ c_Predicate_Oreflp(X3,X1)
    | c_Predicate_Oreflp(X3,X2) ) ).

cnf(i_0_19109_649,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__mult(X1)
    | class_Groups_Ocomm__monoid__mult(X2) ) ).

cnf(i_0_19110_650,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__comm__semiring__strict(X1)
    | class_Rings_Olinordered__comm__semiring__strict(X2) ) ).

cnf(i_0_19111_651,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__comm__semiring(X1)
    | class_Rings_Oordered__comm__semiring(X2) ) ).

cnf(i_0_19112_652,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X1,X3)
    | c_Predicate_Osymp(X2,X3) ) ).

cnf(i_0_19113_653,axiom,
    ( X1 != X2
    | ~ c_Predicate_Osymp(X3,X1)
    | c_Predicate_Osymp(X3,X2) ) ).

cnf(i_0_19114_654,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X1,X3)
    | c_Predicate_Otransp(X2,X3) ) ).

cnf(i_0_19115_655,axiom,
    ( X1 != X2
    | ~ c_Predicate_Otransp(X3,X1)
    | c_Predicate_Otransp(X3,X2) ) ).

cnf(i_0_19116_656,axiom,
    ( X1 != X2
    | ~ class_Divides_Oring__div(X1)
    | class_Divides_Oring__div(X2) ) ).

cnf(i_0_19117_657,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__group__add(X1)
    | class_Groups_Olinordered__ab__group__add(X2) ) ).

cnf(i_0_19118_658,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__cancel__semiring(X1)
    | class_Rings_Oordered__cancel__semiring(X2) ) ).

cnf(i_0_19119_659,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring__abs(X1)
    | class_Rings_Oordered__ring__abs(X2) ) ).

cnf(i_0_19120_660,axiom,
    ( X1 != X2
    | ~ class_Orderings_Owellorder(X1)
    | class_Orderings_Owellorder(X2) ) ).

cnf(i_0_19121_661,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring__1(X1)
    | class_Rings_Ocomm__ring__1(X2) ) ).

cnf(i_0_19122_662,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oord(X1)
    | class_Orderings_Oord(X2) ) ).

cnf(i_0_19123_663,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oboolean__algebra(X1)
    | class_Lattices_Oboolean__algebra(X2) ) ).

cnf(i_0_19124_664,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring(X1)
    | class_Rings_Odivision__ring(X2) ) ).

cnf(i_0_19125_665,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring(X1)
    | class_Rings_Ocomm__semiring(X2) ) ).

cnf(i_0_19126_666,axiom,
    ( X1 != X2
    | ~ class_Groups_Ominus(X1)
    | class_Groups_Ominus(X2) ) ).

cnf(i_0_19127_667,axiom,
    ( X1 != X2
    | ~ class_Orderings_Opreorder(X1)
    | class_Orderings_Opreorder(X2) ) ).

cnf(i_0_19128_668,axiom,
    ( X1 != X2
    | ~ class_Groups_Ogroup__add(X1)
    | class_Groups_Ogroup__add(X2) ) ).

cnf(i_0_19129_669,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X1,X3,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X2,X3,X4,X5) ) ).

cnf(i_0_19130_670,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X1,X4,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X2,X4,X5) ) ).

cnf(i_0_19131_671,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X1,X5)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X2,X5) ) ).

cnf(i_0_19132_672,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X1)
    | c_Nat__Transfer_Otransfer__morphism(X3,X4,X5,X2) ) ).

cnf(i_0_19133_673,axiom,
    ( X1 != X2
    | ~ class_Nat_Osemiring__char__0(X1)
    | class_Nat_Osemiring__char__0(X2) ) ).

cnf(i_0_19134_674,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X1,X3)
    | c_Nitpick_Owf_H(X2,X3) ) ).

cnf(i_0_19135_675,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Owf_H(X3,X1)
    | c_Nitpick_Owf_H(X3,X2) ) ).

cnf(i_0_19136_676,axiom,
    ( X1 != X2
    | ~ c_List_Onat__list(X1)
    | c_List_Onat__list(X2) ) ).

cnf(i_0_19137_677,axiom,
    ( X1 != X2
    | ~ class_Groups_Olinordered__ab__semigroup__add(X1)
    | class_Groups_Olinordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19138_678,axiom,
    ( X1 != X2
    | ~ class_Groups_Osgn__if(X1)
    | class_Groups_Osgn__if(X2) ) ).

cnf(i_0_19139_679,axiom,
    ( X1 != X2
    | ~ class_Power_Opower(X1)
    | class_Power_Opower(X2) ) ).

cnf(i_0_19140_680,axiom,
    ( X1 != X2
    | ~ class_Groups_Oabs__if(X1)
    | class_Groups_Oabs__if(X2) ) ).

cnf(i_0_19141_681,axiom,
    ( X1 != X2
    | ~ class_Groups_Ouminus(X1)
    | class_Groups_Ouminus(X2) ) ).

cnf(i_0_19142_682,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X1,X3,X4)
    | c_Big__Operators_Osemilattice__big(X2,X3,X4) ) ).

cnf(i_0_19143_683,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X1,X4)
    | c_Big__Operators_Osemilattice__big(X3,X2,X4) ) ).

cnf(i_0_19144_684,axiom,
    ( X1 != X2
    | ~ c_Big__Operators_Osemilattice__big(X3,X4,X1)
    | c_Big__Operators_Osemilattice__big(X3,X4,X2) ) ).

cnf(i_0_19145_685,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__semigroup__add(X1)
    | class_Groups_Ocancel__semigroup__add(X2) ) ).

cnf(i_0_19146_686,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocancel__ab__semigroup__add(X1)
    | class_Groups_Ocancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19147_687,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Ounknown(X1)
    | c_Nitpick_Ounknown(X2) ) ).

cnf(i_0_19148_688,axiom,
    ( X1 != X2
    | ~ class_Finite__Set_Ofinite(X1)
    | class_Finite__Set_Ofinite(X2) ) ).

cnf(i_0_19149_689,axiom,
    ( X1 != X2
    | ~ class_Orderings_Obot(X1)
    | class_Orderings_Obot(X2) ) ).

cnf(i_0_19150_690,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_19151_691,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_19152_692,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_19153_693,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_19154_694,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_19155_695,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_19156_696,axiom,
    ( X1 != X2
    | ~ class_Orderings_Otop(X1)
    | class_Orderings_Otop(X2) ) ).

cnf(i_0_19157_697,axiom,
    ( X1 != X2
    | ~ class_Rings_Omult__zero(X1)
    | class_Rings_Omult__zero(X2) ) ).

cnf(i_0_19158_698,axiom,
    ( X1 != X2
    | ~ class_Rings_Ozero__neq__one(X1)
    | class_Rings_Ozero__neq__one(X2) ) ).

cnf(i_0_19159_699,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__no__zero__divisors(X1)
    | class_Rings_Oring__no__zero__divisors(X2) ) ).

cnf(i_0_19160_700,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__top(X1)
    | class_Lattices_Obounded__lattice__top(X2) ) ).

cnf(i_0_19161_701,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice__bot(X1)
    | class_Lattices_Obounded__lattice__bot(X2) ) ).

cnf(i_0_19162_702,axiom,
    ( X1 != X2
    | ~ class_Rings_Odivision__ring__inverse__zero(X1)
    | class_Rings_Odivision__ring__inverse__zero(X2) ) ).

cnf(i_0_19163_703,axiom,
    ( X1 != X2
    | ~ class_Lattices_Obounded__lattice(X1)
    | class_Lattices_Obounded__lattice(X2) ) ).

cnf(i_0_19164_704,axiom,
    ( X1 != X2
    | ~ class_Nat_Osize(X1)
    | class_Nat_Osize(X2) ) ).

cnf(i_0_19165_705,axiom,
    ( X1 != X2
    | ~ class_Groups_Ozero(X1)
    | class_Groups_Ozero(X2) ) ).

cnf(i_0_19166_706,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__idom(X1)
    | class_Rings_Olinordered__idom(X2) ) ).

cnf(i_0_19167_707,axiom,
    ( X1 != X2
    | ~ class_Groups_Oone(X1)
    | class_Groups_Oone(X2) ) ).

cnf(i_0_19168_708,axiom,
    ( X1 != X2
    | ~ class_Complete__Lattice_Ocomplete__lattice(X1)
    | class_Complete__Lattice_Ocomplete__lattice(X2) ) ).

cnf(i_0_19169_709,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_19170_710,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_19171_711,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_19172_712,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_19173_713,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_19174_714,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_19175_715,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_19176_716,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_19177_717,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_19178_718,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_19179_719,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_19180_720,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber__ring(X1)
    | class_Int_Onumber__ring(X2) ) ).

cnf(i_0_19181_721,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_19182_722,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_19183_723,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_19184_724,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_19185_725,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_19186_726,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_19187_727,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X1,X3)
    | c_Equiv__Relations_Opart__equivp(X2,X3) ) ).

cnf(i_0_19188_728,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Opart__equivp(X3,X1)
    | c_Equiv__Relations_Opart__equivp(X3,X2) ) ).

cnf(i_0_19189_729,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X1,X3,X4)
    | c_Relation_Orefl__on(X2,X3,X4) ) ).

cnf(i_0_19190_730,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X1,X4)
    | c_Relation_Orefl__on(X3,X2,X4) ) ).

cnf(i_0_19191_731,axiom,
    ( X1 != X2
    | ~ c_Relation_Orefl__on(X3,X4,X1)
    | c_Relation_Orefl__on(X3,X4,X2) ) ).

cnf(i_0_19192_732,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X1,X3,X4,X5)
    | c_Wellfounded_Omax__extp(X2,X3,X4,X5) ) ).

cnf(i_0_19193_733,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X1,X4,X5)
    | c_Wellfounded_Omax__extp(X3,X2,X4,X5) ) ).

cnf(i_0_19194_734,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X1,X5)
    | c_Wellfounded_Omax__extp(X3,X4,X2,X5) ) ).

cnf(i_0_19195_735,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Omax__extp(X3,X4,X5,X1)
    | c_Wellfounded_Omax__extp(X3,X4,X5,X2) ) ).

cnf(i_0_19196_736,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X1,X3,X4,X5)
    | c_List_Olistrelp(X2,X3,X4,X5) ) ).

cnf(i_0_19197_737,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X1,X4,X5)
    | c_List_Olistrelp(X3,X2,X4,X5) ) ).

cnf(i_0_19198_738,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X1,X5)
    | c_List_Olistrelp(X3,X4,X2,X5) ) ).

cnf(i_0_19199_739,axiom,
    ( X1 != X2
    | ~ c_List_Olistrelp(X3,X4,X5,X1)
    | c_List_Olistrelp(X3,X4,X5,X2) ) ).

cnf(i_0_19200_740,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X1,X3)
    | c_Equiv__Relations_Oequivp(X2,X3) ) ).

cnf(i_0_19201_741,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequivp(X3,X1)
    | c_Equiv__Relations_Oequivp(X3,X2) ) ).

cnf(i_0_19202_742,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X1,X3)
    | c_Wellfounded_Owf(X2,X3) ) ).

cnf(i_0_19203_743,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Owf(X3,X1)
    | c_Wellfounded_Owf(X3,X2) ) ).

cnf(i_0_19204_744,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X1,X3)
    | c_Wellfounded_OwfP(X2,X3) ) ).

cnf(i_0_19205_745,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_OwfP(X3,X1)
    | c_Wellfounded_OwfP(X3,X2) ) ).

cnf(i_0_19206_746,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X1,X3,X4)
    | c_Finite__Set_Ofun__left__comm(X2,X3,X4) ) ).

cnf(i_0_19207_747,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X1,X4)
    | c_Finite__Set_Ofun__left__comm(X3,X2,X4) ) ).

cnf(i_0_19208_748,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofun__left__comm(X3,X4,X1)
    | c_Finite__Set_Ofun__left__comm(X3,X4,X2) ) ).

cnf(i_0_19209_749,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semidom(X1)
    | class_Rings_Olinordered__semidom(X2) ) ).

cnf(i_0_19210_750,axiom,
    ( X1 != X2
    | ~ class_Lazy__Sequence_Osmall__lazy(X1)
    | class_Lazy__Sequence_Osmall__lazy(X2) ) ).

cnf(i_0_19211_751,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X1,X3,X4)
    | c_Equiv__Relations_Oequiv(X2,X3,X4) ) ).

cnf(i_0_19212_752,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X1,X4)
    | c_Equiv__Relations_Oequiv(X3,X2,X4) ) ).

cnf(i_0_19213_753,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Oequiv(X3,X4,X1)
    | c_Equiv__Relations_Oequiv(X3,X4,X2) ) ).

cnf(i_0_19214_754,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add(X1)
    | class_Groups_Oordered__ab__group__add(X2) ) ).

cnf(i_0_19215_755,axiom,
    ( X1 != X2
    | ~ class_Orderings_Oorder(X1)
    | class_Orderings_Oorder(X2) ) ).

cnf(i_0_19216_756,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder_Ostrict__mono(X1,X3,X4,X5)
    | c_Orderings_Oorder_Ostrict__mono(X2,X3,X4,X5) ) ).

cnf(i_0_19217_757,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder_Ostrict__mono(X3,X1,X4,X5)
    | c_Orderings_Oorder_Ostrict__mono(X3,X2,X4,X5) ) ).

cnf(i_0_19218_758,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X1,X5)
    | c_Orderings_Oorder_Ostrict__mono(X3,X4,X2,X5) ) ).

cnf(i_0_19219_759,axiom,
    ( X1 != X2
    | ~ c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X1)
    | c_Orderings_Oorder_Ostrict__mono(X3,X4,X5,X2) ) ).

cnf(i_0_19220_760,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__mult(X1)
    | class_Groups_Omonoid__mult(X2) ) ).

cnf(i_0_19221_761,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__semigroup__mult(X1)
    | class_Groups_Oab__semigroup__mult(X2) ) ).

cnf(i_0_19222_762,axiom,
    ( X1 != X2
    | ~ class_Groups_Omonoid__add(X1)
    | class_Groups_Omonoid__add(X2) ) ).

cnf(i_0_19223_763,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__semigroup__add(X1)
    | class_Groups_Oordered__ab__semigroup__add(X2) ) ).

cnf(i_0_19224_764,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X1,X3,X4,X5,X6)
    | c_List_Olist__all2(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19225_765,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X1,X4,X5,X6)
    | c_List_Olist__all2(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19226_766,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X1,X5,X6)
    | c_List_Olist__all2(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19227_767,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X1,X6)
    | c_List_Olist__all2(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19228_768,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all2(X3,X4,X5,X6,X1)
    | c_List_Olist__all2(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19229_769,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(X1)
    | class_Groups_Oordered__cancel__ab__semigroup__add(X2) ) ).

cnf(i_0_19230_770,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X1,X3,X4)
    | c_Finite__Set_Ofolding__one__idem(X2,X3,X4) ) ).

cnf(i_0_19231_771,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X1,X4)
    | c_Finite__Set_Ofolding__one__idem(X3,X2,X4) ) ).

cnf(i_0_19232_772,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one__idem(X3,X4,X1)
    | c_Finite__Set_Ofolding__one__idem(X3,X4,X2) ) ).

cnf(i_0_19233_773,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__0(X1)
    | class_Rings_Osemiring__0(X2) ) ).

cnf(i_0_19234_774,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__semiring__1(X1)
    | class_Rings_Ocomm__semiring__1(X2) ) ).

cnf(i_0_19235_775,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring__1(X1)
    | class_Rings_Osemiring__1(X2) ) ).

cnf(i_0_19236_776,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X1,X3,X4)
    | c_Finite__Set_Ofolding__one(X2,X3,X4) ) ).

cnf(i_0_19237_777,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X1,X4)
    | c_Finite__Set_Ofolding__one(X3,X2,X4) ) ).

cnf(i_0_19238_778,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__one(X3,X4,X1)
    | c_Finite__Set_Ofolding__one(X3,X4,X2) ) ).

cnf(i_0_19239_779,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field__inverse__zero(X1)
    | class_Fields_Olinordered__field__inverse__zero(X2) ) ).

cnf(i_0_19240_780,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X1,X3)
    | c_FunDef_Oreduction__pair(X2,X3) ) ).

cnf(i_0_19241_781,axiom,
    ( X1 != X2
    | ~ c_FunDef_Oreduction__pair(X3,X1)
    | c_FunDef_Oreduction__pair(X3,X2) ) ).

cnf(i_0_19242_782,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X1,X3)
    | c_List_Olinorder__class_Osorted(X2,X3) ) ).

cnf(i_0_19243_783,axiom,
    ( X1 != X2
    | ~ c_List_Olinorder__class_Osorted(X3,X1)
    | c_List_Olinorder__class_Osorted(X3,X2) ) ).

cnf(i_0_19244_784,axiom,
    ( X1 != X2
    | ~ class_Enum_Oenum(X1)
    | class_Enum_Oenum(X2) ) ).

cnf(i_0_19245_785,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Ois__nat(X1)
    | c_Nat__Transfer_Ois__nat(X2) ) ).

cnf(i_0_19246_786,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X1,X3,X4,X5,X6)
    | c_Fun_Obij__betw(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19247_787,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X1,X4,X5,X6)
    | c_Fun_Obij__betw(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19248_788,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X1,X5,X6)
    | c_Fun_Obij__betw(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19249_789,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X1,X6)
    | c_Fun_Obij__betw(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19250_790,axiom,
    ( X1 != X2
    | ~ c_Fun_Obij__betw(X3,X4,X5,X6,X1)
    | c_Fun_Obij__betw(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19251_791,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X1,X3,X4)
    | c_Nitpick_Oless__eq__frac(X2,X3,X4) ) ).

cnf(i_0_19252_792,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X1,X4)
    | c_Nitpick_Oless__eq__frac(X3,X2,X4) ) ).

cnf(i_0_19253_793,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__eq__frac(X3,X4,X1)
    | c_Nitpick_Oless__eq__frac(X3,X4,X2) ) ).

cnf(i_0_19254_794,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X1,X3,X4,X5)
    | c_Fun_Oinj__on(X2,X3,X4,X5) ) ).

cnf(i_0_19255_795,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X1,X4,X5)
    | c_Fun_Oinj__on(X3,X2,X4,X5) ) ).

cnf(i_0_19256_796,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X1,X5)
    | c_Fun_Oinj__on(X3,X4,X2,X5) ) ).

cnf(i_0_19257_797,axiom,
    ( X1 != X2
    | ~ c_Fun_Oinj__on(X3,X4,X5,X1)
    | c_Fun_Oinj__on(X3,X4,X5,X2) ) ).

cnf(i_0_19258_798,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X1,X3,X4)
    | c_Nitpick_Oless__frac(X2,X3,X4) ) ).

cnf(i_0_19259_799,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X1,X4)
    | c_Nitpick_Oless__frac(X3,X2,X4) ) ).

cnf(i_0_19260_800,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Oless__frac(X3,X4,X1)
    | c_Nitpick_Oless__frac(X3,X4,X2) ) ).

cnf(i_0_19261_801,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__comm__monoid__add(X1)
    | class_Groups_Oordered__comm__monoid__add(X2) ) ).

cnf(i_0_19262_802,axiom,
    ( X1 != X2
    | ~ class_Rings_Oordered__ring(X1)
    | class_Rings_Oordered__ring(X2) ) ).

cnf(i_0_19263_803,axiom,
    ( X1 != X2
    | ~ class_Groups_Oab__group__add(X1)
    | class_Groups_Oab__group__add(X2) ) ).

cnf(i_0_19264_804,axiom,
    ( X1 != X2
    | ~ class_Rings_Oinverse(X1)
    | class_Rings_Oinverse(X2) ) ).

cnf(i_0_19265_805,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield(X1)
    | class_Fields_Ofield(X2) ) ).

cnf(i_0_19266_806,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X1,X3,X4)
    | c_List_Olist__ex1(X2,X3,X4) ) ).

cnf(i_0_19267_807,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X1,X4)
    | c_List_Olist__ex1(X3,X2,X4) ) ).

cnf(i_0_19268_808,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex1(X3,X4,X1)
    | c_List_Olist__ex1(X3,X4,X2) ) ).

cnf(i_0_19269_809,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X1,X3,X4)
    | c_List_Olist__all(X2,X3,X4) ) ).

cnf(i_0_19270_810,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X1,X4)
    | c_List_Olist__all(X3,X2,X4) ) ).

cnf(i_0_19271_811,axiom,
    ( X1 != X2
    | ~ c_List_Olist__all(X3,X4,X1)
    | c_List_Olist__all(X3,X4,X2) ) ).

cnf(i_0_19272_812,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_19273_813,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_19274_814,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_19275_815,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_19276_816,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_19277_817,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_19278_818,axiom,
    ( X1 != X2
    | ~ class_Groups_Oordered__ab__group__add__abs(X1)
    | class_Groups_Oordered__ab__group__add__abs(X2) ) ).

cnf(i_0_19279_819,axiom,
    ( X1 != X2
    | ~ class_Orderings_Olinorder(X1)
    | class_Orderings_Olinorder(X2) ) ).

cnf(i_0_19280_820,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring__1__no__zero__divisors(X1)
    | class_Rings_Oring__1__no__zero__divisors(X2) ) ).

cnf(i_0_19281_821,axiom,
    ( X1 != X2
    | ~ c_Nat__Transfer_Onat__set(X1)
    | c_Nat__Transfer_Onat__set(X2) ) ).

cnf(i_0_19282_822,axiom,
    ( X1 != X2
    | ~ class_Fields_Ofield__inverse__zero(X1)
    | class_Fields_Ofield__inverse__zero(X2) ) ).

cnf(i_0_19283_823,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X1,X3)
    | c_Relation_Otrans(X2,X3) ) ).

cnf(i_0_19284_824,axiom,
    ( X1 != X2
    | ~ c_Relation_Otrans(X3,X1)
    | c_Relation_Otrans(X3,X2) ) ).

cnf(i_0_19285_825,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_19286_826,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_19287_827,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_19288_828,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__sup(X1)
    | class_Lattices_Osemilattice__sup(X2) ) ).

cnf(i_0_19289_829,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X1,X3)
    | c_Int_Oiszero(X2,X3) ) ).

cnf(i_0_19290_830,axiom,
    ( X1 != X2
    | ~ c_Int_Oiszero(X3,X1)
    | c_Int_Oiszero(X3,X2) ) ).

cnf(i_0_19291_831,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X1,X3,X4)
    | c_Relation_Ototal__on(X2,X3,X4) ) ).

cnf(i_0_19292_832,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X1,X4)
    | c_Relation_Ototal__on(X3,X2,X4) ) ).

cnf(i_0_19293_833,axiom,
    ( X1 != X2
    | ~ c_Relation_Ototal__on(X3,X4,X1)
    | c_Relation_Ototal__on(X3,X4,X2) ) ).

cnf(i_0_19294_834,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X1,X3,X4)
    | c_Relation_Osingle__valued(X2,X3,X4) ) ).

cnf(i_0_19295_835,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X1,X4)
    | c_Relation_Osingle__valued(X3,X2,X4) ) ).

cnf(i_0_19296_836,axiom,
    ( X1 != X2
    | ~ c_Relation_Osingle__valued(X3,X4,X1)
    | c_Relation_Osingle__valued(X3,X4,X2) ) ).

cnf(i_0_19297_837,axiom,
    ( X1 != X2
    | ~ class_Int_Onumber(X1)
    | class_Int_Onumber(X2) ) ).

cnf(i_0_19298_838,axiom,
    ( X1 != X2
    | ~ class_Lattices_Odistrib__lattice(X1)
    | class_Lattices_Odistrib__lattice(X2) ) ).

cnf(i_0_19299_839,axiom,
    ( X1 != X2
    | ~ class_Rings_Ocomm__ring(X1)
    | class_Rings_Ocomm__ring(X2) ) ).

cnf(i_0_19300_840,axiom,
    ( X1 != X2
    | ~ class_Rings_Odvd(X1)
    | class_Rings_Odvd(X2) ) ).

cnf(i_0_19301_841,axiom,
    ( X1 != X2
    | ~ class_Divides_Osemiring__div(X1)
    | class_Divides_Osemiring__div(X2) ) ).

cnf(i_0_19302_842,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring__strict(X1)
    | class_Rings_Olinordered__ring__strict(X2) ) ).

cnf(i_0_19303_843,axiom,
    ( X1 != X2
    | ~ class_Lattices_Olattice(X1)
    | class_Lattices_Olattice(X2) ) ).

cnf(i_0_19304_844,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__ring(X1)
    | class_Rings_Olinordered__ring(X2) ) ).

cnf(i_0_19305_845,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding(X2,X3,X4,X5) ) ).

cnf(i_0_19306_846,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding(X3,X2,X4,X5) ) ).

cnf(i_0_19307_847,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding(X3,X4,X2,X5) ) ).

cnf(i_0_19308_848,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding(X3,X4,X5,X2) ) ).

cnf(i_0_19309_849,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X1,X3)
    | c_Relation_Osym(X2,X3) ) ).

cnf(i_0_19310_850,axiom,
    ( X1 != X2
    | ~ c_Relation_Osym(X3,X1)
    | c_Relation_Osym(X3,X2) ) ).

cnf(i_0_19311_851,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1__strict(X1)
    | class_Rings_Olinordered__semiring__1__strict(X2) ) ).

cnf(i_0_19312_852,axiom,
    ( X1 != X2
    | ~ class_Rings_Olinordered__semiring__1(X1)
    | class_Rings_Olinordered__semiring__1(X2) ) ).

cnf(i_0_19313_853,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X1,X3,X4,X5)
    | c_Equiv__Relations_Ocongruent(X2,X3,X4,X5) ) ).

cnf(i_0_19314_854,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X1,X4,X5)
    | c_Equiv__Relations_Ocongruent(X3,X2,X4,X5) ) ).

cnf(i_0_19315_855,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X1,X5)
    | c_Equiv__Relations_Ocongruent(X3,X4,X2,X5) ) ).

cnf(i_0_19316_856,axiom,
    ( X1 != X2
    | ~ c_Equiv__Relations_Ocongruent(X3,X4,X5,X1)
    | c_Equiv__Relations_Ocongruent(X3,X4,X5,X2) ) ).

cnf(i_0_19317_857,axiom,
    ( X1 != X2
    | ~ class_Lattices_Osemilattice__inf(X1)
    | class_Lattices_Osemilattice__inf(X2) ) ).

cnf(i_0_19318_858,axiom,
    ( X1 != X2
    | ~ class_Fields_Olinordered__field(X1)
    | class_Fields_Olinordered__field(X2) ) ).

cnf(i_0_19319_859,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X1,X3)
    | c_Wellfounded_Oacyclic(X2,X3) ) ).

cnf(i_0_19320_860,axiom,
    ( X1 != X2
    | ~ c_Wellfounded_Oacyclic(X3,X1)
    | c_Wellfounded_Oacyclic(X3,X2) ) ).

cnf(i_0_19321_861,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X1,X3)
    | c_Relation_Oantisym(X2,X3) ) ).

cnf(i_0_19322_862,axiom,
    ( X1 != X2
    | ~ c_Relation_Oantisym(X3,X1)
    | c_Relation_Oantisym(X3,X2) ) ).

cnf(i_0_19323_863,axiom,
    ( X1 != X2
    | ~ class_Lattices_Oab__semigroup__idem__mult(X1)
    | class_Lattices_Oab__semigroup__idem__mult(X2) ) ).

cnf(i_0_19324_864,axiom,
    ( X1 != X2
    | ~ v_P(X1,X3)
    | v_P(X2,X3) ) ).

cnf(i_0_19325_865,axiom,
    ( X1 != X2
    | ~ v_P(X3,X1)
    | v_P(X3,X2) ) ).

cnf(i_0_19326_866,axiom,
    ( X1 != X2
    | ~ v_wt(X1)
    | v_wt(X2) ) ).

cnf(i_0_19327_867,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X1,X3)
    | c_Nitpick_Orefl_H(X2,X3) ) ).

cnf(i_0_19328_868,axiom,
    ( X1 != X2
    | ~ c_Nitpick_Orefl_H(X3,X1)
    | c_Nitpick_Orefl_H(X3,X2) ) ).

cnf(i_0_19329_869,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X1,X3,X4,X5)
    | c_Finite__Set_Ofolding__idem(X2,X3,X4,X5) ) ).

cnf(i_0_19330_870,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X1,X4,X5)
    | c_Finite__Set_Ofolding__idem(X3,X2,X4,X5) ) ).

cnf(i_0_19331_871,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X1,X5)
    | c_Finite__Set_Ofolding__idem(X3,X4,X2,X5) ) ).

cnf(i_0_19332_872,axiom,
    ( X1 != X2
    | ~ c_Finite__Set_Ofolding__idem(X3,X4,X5,X1)
    | c_Finite__Set_Ofolding__idem(X3,X4,X5,X2) ) ).

cnf(i_0_19333_873,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_19334_874,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_19335_875,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_19336_876,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_19337_877,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_19338_878,axiom,
    ( X1 != X2
    | ~ class_Groups_Ocomm__monoid__add(X1)
    | class_Groups_Ocomm__monoid__add(X2) ) ).

cnf(i_0_19339_879,axiom,
    ( X1 != X2
    | ~ class_Rings_Ono__zero__divisors(X1)
    | class_Rings_Ono__zero__divisors(X2) ) ).

cnf(i_0_19340_880,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X1,X3,X4,X5,X6)
    | c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ) ).

cnf(i_0_19341_881,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X1,X4,X5,X6)
    | c_Typedef_Otype__definition(X3,X2,X4,X5,X6) ) ).

cnf(i_0_19342_882,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X1,X5,X6)
    | c_Typedef_Otype__definition(X3,X4,X2,X5,X6) ) ).

cnf(i_0_19343_883,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X1,X6)
    | c_Typedef_Otype__definition(X3,X4,X5,X2,X6) ) ).

cnf(i_0_19344_884,axiom,
    ( X1 != X2
    | ~ c_Typedef_Otype__definition(X3,X4,X5,X6,X1)
    | c_Typedef_Otype__definition(X3,X4,X5,X6,X2) ) ).

cnf(i_0_19345_885,axiom,
    ( X1 != X2
    | ~ class_Rings_Oring(X1)
    | class_Rings_Oring(X2) ) ).

cnf(i_0_19346_886,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X1,X3,X4)
    | c_List_Olist__ex(X2,X3,X4) ) ).

cnf(i_0_19347_887,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X1,X4)
    | c_List_Olist__ex(X3,X2,X4) ) ).

cnf(i_0_19348_888,axiom,
    ( X1 != X2
    | ~ c_List_Olist__ex(X3,X4,X1)
    | c_List_Olist__ex(X3,X4,X2) ) ).

cnf(i_0_19349_889,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X1,X3,X4)
    | c_List_Oall__interval__nat(X2,X3,X4) ) ).

cnf(i_0_19350_890,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X3,X1,X4)
    | c_List_Oall__interval__nat(X3,X2,X4) ) ).

cnf(i_0_19351_891,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__nat(X3,X4,X1)
    | c_List_Oall__interval__nat(X3,X4,X2) ) ).

cnf(i_0_19352_892,axiom,
    ( X1 != X2
    | ~ class_Rings_Osemiring(X1)
    | class_Rings_Osemiring(X2) ) ).

cnf(i_0_19353_893,axiom,
    ( X1 != X2
    | ~ class_Groups_Osemigroup__add(X1)
    | class_Groups_Osemigroup__add(X2) ) ).

cnf(i_0_19354_894,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X1,X3,X4)
    | c_List_Oall__interval__int(X2,X3,X4) ) ).

cnf(i_0_19355_895,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X1,X4)
    | c_List_Oall__interval__int(X3,X2,X4) ) ).

cnf(i_0_19356_896,axiom,
    ( X1 != X2
    | ~ c_List_Oall__interval__int(X3,X4,X1)
    | c_List_Oall__interval__int(X3,X4,X2) ) ).

cnf(i_0_19357_897,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X1,X3)
    | c_Relation_Oirrefl(X2,X3) ) ).

cnf(i_0_19358_898,axiom,
    ( X1 != X2
    | ~ c_Relation_Oirrefl(X3,X1)
    | c_Relation_Oirrefl(X3,X2) ) ).

cnf(i_0_19359_899,axiom,
    ( X1 != X2
    | ~ epred1_3(X1,X3,X4)
    | epred1_3(X2,X3,X4) ) ).

cnf(i_0_19360_900,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X1,X4)
    | epred1_3(X3,X2,X4) ) ).

cnf(i_0_19361_901,axiom,
    ( X1 != X2
    | ~ epred1_3(X3,X4,X1)
    | epred1_3(X3,X4,X2) ) ).

cnf(i_0_19362,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),esk190_7(X4,X4,X6,X5,X3,X2,X1)),esk191_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,[],[11134]) ).

cnf(i_0_19363,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),esk331_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
    inference(equality_inference,[],[11150]) ).

cnf(i_0_19364,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),esk125_8(X6,X7,hAPP(c_Set_Oimage(X1,X2,X3),X4),X4,X3,X2,X1,X5)),X4)) ),
    inference(equality_inference,[],[11151]) ).

cnf(i_0_19365,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)),esk388_4(X3,X2,X2,X1))) ),
    inference(equality_inference,[],[11172]) ).

cnf(i_0_19366,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),esk191_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,[],[11229]) ).

cnf(i_0_19367,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),esk190_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,[],[11230]) ).

cnf(i_0_19368,plain,
    ( ~ c_Finite__Set_Ofolding__image(X1,X2,X3,X4,X5)
    | hAPP(hAPP(X5,X6),X7) = hAPP(hAPP(X5,X6),X7)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X7)) ),
    inference(equality_inference,[],[11257]) ).

cnf(i_0_19369,plain,
    X1 = X1,
    inference(equality_inference,[],[11278]) ).

cnf(i_0_19370,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,esk190_7(X1,X1,X6,X5,X4,X3,X2)) = hAPP(X6,esk191_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,[],[11293]) ).

cnf(i_0_19371,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,esk209_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,[],[11351]) ).

cnf(i_0_19372,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),esk209_6(X5,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,X1),X4),X3),X4,X3,X2,X1)),X3)) ),
    inference(equality_inference,[],[11414]) ).

cnf(i_0_19373,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk452_5(X2,X3,X1,X3,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk452_5(X2,X3,X1,X3,X1)))) ),
    inference(equality_inference,[],[11416]) ).

cnf(i_0_19374,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | ~ hBOOL(hAPP(hAPP(X2,hAPP(hAPP(c_List_Onth(X1),X3),esk417_5(X3,X3,X2,X1,X1))),hAPP(hAPP(c_List_Onth(X1),X3),esk417_5(X3,X3,X2,X1,X1)))) ),
    inference(equality_inference,[],[11417]) ).

cnf(i_0_19375,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),esk427_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,[],[11425]) ).

cnf(i_0_19376,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),esk380_4(X3,X2,X2,X1))),hAPP(hAPP(c_List_Onth(X1),X2),esk380_4(X3,X2,X2,X1)))),X3)) ),
    inference(equality_inference,[],[11437]) ).

cnf(i_0_19377,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,[],[11480]) ).

cnf(i_0_19378,plain,
    hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Osnd(X2,X3),X4)),
    inference(equality_inference,[],[11488]) ).

cnf(i_0_19379,plain,
    hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)) = hAPP(X1,hAPP(c_Product__Type_Ofst(X2,X3),X4)),
    inference(equality_inference,[],[11489]) ).

cnf(i_0_19380,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,[],[11512]) ).

cnf(i_0_19381,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,[],[11561]) ).

cnf(i_0_19382,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,[],[11562]) ).

cnf(i_0_19383,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,[],[11582]) ).

cnf(i_0_19384,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,[],[11646]) ).

cnf(i_0_19385,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,[],[11649]) ).

cnf(i_0_19386,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,[],[11745]) ).

cnf(i_0_19387,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk418_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,[],[11746]) ).

cnf(i_0_19388,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),esk416_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,[],[11747]) ).

cnf(i_0_19389,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,[],[11763]) ).

cnf(i_0_19390,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk452_5(X2,X3,X1,X3,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[11768]) ).

cnf(i_0_19391,plain,
    ( c_List_Olist__all2(X1,X1,X2,X3,X3)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk417_5(X3,X3,X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X3))) ),
    inference(equality_inference,[],[11769]) ).

cnf(i_0_19392,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,[],[11812]) ).

cnf(i_0_19393,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),esk401_5(X2,X3,X2,X3,X1)),X2) = X2
    | X2 = hAPP(hAPP(c_List_Oappend(X1),esk402_5(X2,X3,X2,X3,X1)),X2) ),
    inference(equality_inference,[],[11853]) ).

cnf(i_0_19394,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),esk418_5(X2,X3,X3,X1,X1))) ),
    inference(equality_inference,[],[11859]) ).

cnf(i_0_19395,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),esk416_5(X3,X3,X2,X1,X1))) ),
    inference(equality_inference,[],[11860]) ).

cnf(i_0_19396,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,esk30_4(X4,X1,X2,hAPP(c_Set_Oimage(X1,X2,X3),X4))),hAPP(c_Set_Oimage(X1,X2,X3),X4))),X4)) ),
    inference(equality_inference,[],[11872]) ).

cnf(i_0_19397,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,[],[11900]) ).

cnf(i_0_19398,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,[],[11912]) ).

cnf(i_0_19399,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,[],[11913]) ).

cnf(i_0_19400,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,[],[11914]) ).

cnf(i_0_19401,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,[],[11915]) ).

cnf(i_0_19402,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),X4) = hAPP(hAPP(c_List_Omap(X1,X2),X3),X4),
    inference(equality_inference,[],[11950]) ).

cnf(i_0_19403,plain,
    ( hAPP(hAPP(c_List_Oappend(X1),X2),esk402_5(X3,X2,X3,X2,X1)) = X2
    | hAPP(hAPP(c_List_Oappend(X1),esk401_5(X3,X2,X3,X2,X1)),X3) = X3 ),
    inference(equality_inference,[],[11974]) ).

cnf(i_0_19404,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk401_5(X3,X1,X3,X1,X2))
    | X3 = hAPP(hAPP(c_List_Oappend(X2),esk402_5(X3,X1,X3,X1,X2)),X3) ),
    inference(equality_inference,[],[11975]) ).

cnf(i_0_19405,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,[],[12007]) ).

cnf(i_0_19406,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,[],[12012]) ).

cnf(i_0_19407,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,[],[12013]) ).

cnf(i_0_19408,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,[],[12014]) ).

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_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,[],[12015]) ).

cnf(i_0_19410,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),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,[],[12016]) ).

cnf(i_0_19411,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,[],[12037]) ).

cnf(i_0_19412,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,[],[12082]) ).

cnf(i_0_19413,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,[],[12089]) ).

cnf(i_0_19414,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,[],[12149]) ).

cnf(i_0_19415,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,[],[12161]) ).

cnf(i_0_19416,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,[],[12166]) ).

cnf(i_0_19417,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,[],[12167]) ).

cnf(i_0_19418,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,[],[12168]) ).

cnf(i_0_19419,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)),esk223_5(X4,X3,X1,X1,X2))) ),
    inference(equality_inference,[],[12182]) ).

cnf(i_0_19420,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)),esk220_5(X4,X3,X1,X1,X2))) ),
    inference(equality_inference,[],[12183]) ).

cnf(i_0_19421,plain,
    ( X1 = hAPP(hAPP(c_List_Oappend(X2),X1),esk401_5(X3,X1,X3,X1,X2))
    | hAPP(hAPP(c_List_Oappend(X2),X1),esk402_5(X3,X1,X3,X1,X2)) = X1 ),
    inference(equality_inference,[],[12186]) ).

cnf(i_0_19422,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)),esk388_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,[],[12189]) ).

cnf(i_0_19423,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,[],[12279]) ).

cnf(i_0_19424,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,[],[12282]) ).

cnf(i_0_19425,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,[],[12325]) ).

cnf(i_0_19426,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),esk380_4(X3,X2,X2,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2))) ),
    inference(equality_inference,[],[12330]) ).

cnf(i_0_19427,plain,
    ( c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4))
    | ~ c_Fun_Obij__betw(X1,X2,X3,X5,X6)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),X5)) ),
    inference(equality_inference,[],[12373]) ).

cnf(i_0_19428,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,[],[12419]) ).

cnf(i_0_19429,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,[],[12420]) ).

cnf(i_0_19430,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,[],[12436]) ).

cnf(i_0_19431,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,[],[12500]) ).

cnf(i_0_19432,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,[],[12515]) ).

cnf(i_0_19433,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,[],[12552]) ).

cnf(i_0_19434,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,[],[12553]) ).

cnf(i_0_19435,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,[],[12562]) ).

cnf(i_0_19436,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,[],[12585]) ).

cnf(i_0_19437,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),esk160_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,[],[12712]) ).

cnf(i_0_19438,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),esk158_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,[],[12713]) ).

cnf(i_0_19439,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,[],[12752]) ).

cnf(i_0_19440,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,[],[12755]) ).

cnf(i_0_19441,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,[],[12790]) ).

cnf(i_0_19442,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,[],[12803]) ).

cnf(i_0_19443,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),esk182_4(c_Nat_OSuc,X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X2)) ),
    inference(equality_inference,[],[12806]) ).

cnf(i_0_19444,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),esk161_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
    inference(equality_inference,[],[12808]) ).

cnf(i_0_19445,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),esk159_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),X3)) ),
    inference(equality_inference,[],[12809]) ).

cnf(i_0_19446,plain,
    hAPP(c_Fun_Ofun__upd(X1,X2,X3,X4,X5),X4) = X5,
    inference(equality_inference,[],[12825]) ).

cnf(i_0_19447,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,[],[12858]) ).

cnf(i_0_19448,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,[],[12870]) ).

cnf(i_0_19449,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),esk444_4(hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3),X1,X3,X2)),hAPP(c_List_Oset(X1),X3))) ),
    inference(equality_inference,[],[12893]) ).

cnf(i_0_19450,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,[],[12895]) ).

cnf(i_0_19451,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,[],[12897]) ).

cnf(i_0_19452,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,[],[12933]) ).

cnf(i_0_19453,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,[],[12934]) ).

cnf(i_0_19454,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,[],[12946]) ).

cnf(i_0_19455,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,[],[12997]) ).

cnf(i_0_19456,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,[],[12998]) ).

cnf(i_0_19457,plain,
    ( X1 = esk224_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,[],[13076]) ).

cnf(i_0_19458,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,[],[13112]) ).

cnf(i_0_19459,plain,
    ( X1 = X1
    | ~ c_Typedef_Otype__definition(X2,X3,X4,X5,X6) ),
    inference(equality_inference,[],[13119]) ).

cnf(i_0_19460,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,[],[13124]) ).

cnf(i_0_19461,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),esk161_4(X3,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X2),X2,X1)),esk160_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,[],[13129]) ).

cnf(i_0_19462,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),esk159_4(X3,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2),X2,X1)),esk158_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,[],[13130]) ).

cnf(i_0_19463,plain,
    ( c_Fun_Obij__betw(X1,X1,esk530_4(X2,X1,X2,X1),X2,X2)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
    inference(equality_inference,[],[13144]) ).

cnf(i_0_19464,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,[],[13152]) ).

cnf(i_0_19465,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,[],[13153]) ).

cnf(i_0_19466,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,[],[13162]) ).

cnf(i_0_19467,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),esk389_3(X2,X1,X1)),hAPP(c_List_Oset(tc_prod(X2,X2)),hAPP(hAPP(c_List_Ozip(X2,X2),X1),X1)))) ),
    inference(equality_inference,[],[13164]) ).

cnf(i_0_19468,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),esk444_4(hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2),X1,X2,X3))) ),
    inference(equality_inference,[],[13170]) ).

cnf(i_0_19469,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,[],[13207]) ).

cnf(i_0_19470,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,[],[13208]) ).

cnf(i_0_19471,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,[],[13226]) ).

cnf(i_0_19472,plain,
    ( ~ c_Fun_Oinj__on(X1,X2,X3,X4)
    | c_Fun_Obij__betw(X1,X2,X3,X4,hAPP(c_Set_Oimage(X1,X2,X3),X4)) ),
    inference(equality_inference,[],[13227]) ).

cnf(i_0_19473,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(X1,hAPP(X2,X3)),
    inference(equality_inference,[],[13309]) ).

cnf(i_0_19474,plain,
    hAPP(c_Fun_Oid(X1),hAPP(X2,X3)) = hAPP(X2,X3),
    inference(equality_inference,[],[13313]) ).

cnf(i_0_19475,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,[],[13319]) ).

cnf(i_0_19476,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,[],[13336]) ).

cnf(i_0_19477,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,[],[13337]) ).

cnf(i_0_19478,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,[],[13338]) ).

cnf(i_0_19479,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,[],[13463]) ).

cnf(i_0_19480,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,[],[13522]) ).

cnf(i_0_19481,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,[],[13544]) ).

cnf(i_0_19482,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,[],[13565]) ).

cnf(i_0_19483,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,[],[13587]) ).

cnf(i_0_19484,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,[],[13689]) ).

cnf(i_0_19485,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,[],[13717]) ).

cnf(i_0_19486,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,[],[13769]) ).

cnf(i_0_19487,plain,
    c_Fun_Ofun__upd(X1,X2,X3,X4,hAPP(X3,X4)) = X3,
    inference(equality_inference,[],[13784]) ).

cnf(i_0_19488,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,[],[13796]) ).

cnf(i_0_19489,plain,
    c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[13798]) ).

cnf(i_0_19490,plain,
    c_List_Olist__all2(X1,X2,X3,c_List_Olist_ONil(X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[13799]) ).

cnf(i_0_19491,plain,
    c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X2,X2),
    inference(equality_inference,[],[13810]) ).

cnf(i_0_19492,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),c_fequal),esk389_3(X2,X1,X1))) ),
    inference(equality_inference,[],[13814]) ).

cnf(i_0_19493,plain,
    c_List_Olist__all2(X1,X1,c_fequal,X2,X2),
    inference(equality_inference,[],[13820]) ).

cnf(i_0_19494,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,[],[13873]) ).

cnf(i_0_19495,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,[],[13876]) ).

cnf(i_0_19496,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,[],[13892]) ).

cnf(i_0_19497,plain,
    ( ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X1)
    | X2 = X3
    | X4 = X4 ),
    inference(equality_inference,[],[13915]) ).

cnf(i_0_19498,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,[],[13966]) ).

cnf(i_0_19499,plain,
    X1 = X1,
    inference(equality_inference,[],[13968]) ).

cnf(i_0_19500,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,[],[13992]) ).

cnf(i_0_19501,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,[],[14011]) ).

cnf(i_0_19502,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,[],[14013]) ).

cnf(i_0_19503,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,[],[14014]) ).

cnf(i_0_19504,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,[],[14039]) ).

cnf(i_0_19505,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,[],[14056]) ).

cnf(i_0_19506,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,[],[14111]) ).

cnf(i_0_19507,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,[],[14123]) ).

cnf(i_0_19508,plain,
    ( X1 = X1
    | ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4)) ),
    inference(equality_inference,[],[14170]) ).

cnf(i_0_19509,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,[],[14213]) ).

cnf(i_0_19510,plain,
    ( c_Fun_Oinj__on(X1,X2,esk30_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,[],[14224]) ).

cnf(i_0_19511,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,[],[14227]) ).

cnf(i_0_19512,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,[],[14228]) ).

cnf(i_0_19513,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,[],[14275]) ).

cnf(i_0_19514,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,[],[14276]) ).

cnf(i_0_19515,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,[],[14340]) ).

cnf(i_0_19516,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,[],[14352]) ).

cnf(i_0_19517,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,[],[14353]) ).

cnf(i_0_19518,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,[],[14367]) ).

cnf(i_0_19519,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,[],[14394]) ).

cnf(i_0_19520,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,[],[14420]) ).

cnf(i_0_19521,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,[],[14458]) ).

cnf(i_0_19522,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,[],[14480]) ).

cnf(i_0_19523,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[14509]) ).

cnf(i_0_19524,plain,
    hAPP(X1,hAPP(X2,X3)) = hAPP(hAPP(c_Fun_Ocomp(X4,X5,X6,X1),X2),X3),
    inference(equality_inference,[],[14510]) ).

cnf(i_0_19525,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,[],[14547]) ).

cnf(i_0_19526,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,[],[14553]) ).

cnf(i_0_19527,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,[],[14571]) ).

cnf(i_0_19528,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,[],[14572]) ).

cnf(i_0_19529,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,[],[14583]) ).

cnf(i_0_19530,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,[],[14585]) ).

cnf(i_0_19531,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,[],[14586]) ).

cnf(i_0_19532,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[14587]) ).

cnf(i_0_19533,plain,
    ( X1 = X2
    | X1 = X1 ),
    inference(equality_inference,[],[14588]) ).

cnf(i_0_19534,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[14589]) ).

cnf(i_0_19535,plain,
    ( X1 = X2
    | X2 = X2 ),
    inference(equality_inference,[],[14590]) ).

cnf(i_0_19536,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,[],[14594]) ).

cnf(i_0_19537,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,[],[14644]) ).

cnf(i_0_19538,plain,
    X1 = X1,
    inference(equality_inference,[],[14693]) ).

cnf(i_0_19539,plain,
    X1 = X1,
    inference(equality_inference,[],[14694]) ).

cnf(i_0_19540,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),esk408_2(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_List_Oset(tc_Nat_Onat),X1))) ),
    inference(equality_inference,[],[14697]) ).

cnf(i_0_19541,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,[],[14698]) ).

cnf(i_0_19542,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,[],[14701]) ).

cnf(i_0_19543,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,[],[14710]) ).

cnf(i_0_19544,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,[],[14717]) ).

cnf(i_0_19545,plain,
    ( X1 = X1
    | ~ c_Fun_Oinj__on(X2,X3,X4,c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool))) ),
    inference(equality_inference,[],[14727]) ).

cnf(i_0_19546,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,[],[14765]) ).

cnf(i_0_19547,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),esk382_3(X2,X1,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X2)),X1))) ),
    inference(equality_inference,[],[14773]) ).

cnf(i_0_19548,plain,
    ( ~ class_Rings_Oidom(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X3))) ),
    inference(equality_inference,[],[14825]) ).

cnf(i_0_19549,plain,
    ( ~ class_Rings_Oidom(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),c_Groups_Ozero__class_Ozero(X1))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),c_Groups_Ozero__class_Ozero(X1)))) ),
    inference(equality_inference,[],[14826]) ).

cnf(i_0_19550,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,[],[14847]) ).

cnf(i_0_19551,plain,
    X1 = X1,
    inference(equality_inference,[],[14899]) ).

cnf(i_0_19552,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,[],[14920]) ).

cnf(i_0_19553,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,[],[14995]) ).

cnf(i_0_19554,plain,
    ( X1 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),esk314_3(X1,X2,X1)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)) ),
    inference(equality_inference,[],[15022]) ).

cnf(i_0_19555,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,[],[15051]) ).

cnf(i_0_19556,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),
    inference(equality_inference,[],[15101]) ).

cnf(i_0_19557,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_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X1)),X1)) ),
    inference(equality_inference,[],[15133]) ).

cnf(i_0_19558,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_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)) ),
    inference(equality_inference,[],[15134]) ).

cnf(i_0_19559,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X3) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X2),X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X3),X3)) ),
    inference(equality_inference,[],[15178]) ).

cnf(i_0_19560,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(equality_inference,[],[15179]) ).

cnf(i_0_19561,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,[],[15193]) ).

cnf(i_0_19562,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,[],[15203]) ).

cnf(i_0_19563,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,[],[15214]) ).

cnf(i_0_19564,plain,
    ( hAPP(X1,X2) = hAPP(X1,X2)
    | ~ hBOOL(hAPP(hAPP(c_member(X3),X2),hAPP(c_List_Oset(X3),X4))) ),
    inference(equality_inference,[],[15219]) ).

cnf(i_0_19565,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,[],[15267]) ).

cnf(i_0_19566,plain,
    hAPP(hAPP(c_Set_Oinsert(X1),X2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(X3,tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X4)) = hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(equality_inference,[],[15353]) ).

cnf(i_0_19567,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,[],[15361]) ).

cnf(i_0_19568,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,[],[15374]) ).

cnf(i_0_19569,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,[],[15375]) ).

cnf(i_0_19570,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,[],[15376]) ).

cnf(i_0_19571,plain,
    hAPP(c_Random_Oiterate(X1,X2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),X3),X4) = hAPP(c_Product__Type_OPair(X1,X2),X4),
    inference(equality_inference,[],[15381]) ).

cnf(i_0_19572,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(equality_inference,[],[15395]) ).

cnf(i_0_19573,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,[],[15490]) ).

cnf(i_0_19574,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,[],[15491]) ).

cnf(i_0_19575,plain,
    X1 = X1,
    inference(equality_inference,[],[15507]) ).

cnf(i_0_19576,plain,
    X1 = X1,
    inference(equality_inference,[],[15508]) ).

cnf(i_0_19577,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,[],[15523]) ).

cnf(i_0_19578,plain,
    hBOOL(hAPP(hAPP(c_List_Oset(X1),hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)),X2)),
    inference(equality_inference,[],[15541]) ).

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,[],[15548]) ).

cnf(i_0_19580,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,[],[15551]) ).

cnf(i_0_19581,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,[],[15552]) ).

cnf(i_0_19582,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,[],[15656]) ).

cnf(i_0_19583,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,[],[15681]) ).

cnf(i_0_19584,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,[],[15706]) ).

cnf(i_0_19585,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,[],[15707]) ).

cnf(i_0_19586,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[15747]) ).

cnf(i_0_19587,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,[],[15760]) ).

cnf(i_0_19588,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,[],[15801]) ).

cnf(i_0_19589,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,[],[15830]) ).

cnf(i_0_19590,plain,
    ~ c_Wellfounded_Omax__extp(X1,X2,X3,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
    inference(equality_inference,[],[15847]) ).

cnf(i_0_19591,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,[],[15860]) ).

cnf(i_0_19592,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X3)),
    inference(equality_inference,[],[15887]) ).

cnf(i_0_19593,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,[],[15892]) ).

cnf(i_0_19594,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,[],[15900]) ).

cnf(i_0_19595,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,[],[15909]) ).

cnf(i_0_19596,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,[],[15910]) ).

cnf(i_0_19597,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,[],[15989]) ).

cnf(i_0_19598,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,[],[16017]) ).

cnf(i_0_19599,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,[],[16068]) ).

cnf(i_0_19600,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,[],[16084]) ).

cnf(i_0_19601,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,[],[16085]) ).

cnf(i_0_19602,plain,
    X1 = X1,
    inference(equality_inference,[],[16094]) ).

cnf(i_0_19603,plain,
    ( X1 = X1
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
    | hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ),
    inference(equality_inference,[],[16107]) ).

cnf(i_0_19604,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,[],[16108]) ).

cnf(i_0_19605,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,[],[16111]) ).

cnf(i_0_19606,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,[],[16124]) ).

cnf(i_0_19607,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,[],[16139]) ).

cnf(i_0_19608,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,[],[16141]) ).

cnf(i_0_19609,plain,
    ( ~ c_Nat__Transfer_Onat__set(X1)
    | ~ c_Nat__Transfer_Onat__set(X1)
    | X1 = X1 ),
    inference(equality_inference,[],[16152]) ).

cnf(i_0_19610,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,[],[16173]) ).

cnf(i_0_19611,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,[],[16223]) ).

cnf(i_0_19612,plain,
    X1 = hAPP(c_Product__Type_Ofst(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X1),X4)),
    inference(equality_inference,[],[16228]) ).

cnf(i_0_19613,plain,
    X1 = hAPP(c_Product__Type_Osnd(X2,X3),hAPP(hAPP(c_Product__Type_OPair(X2,X3),X4),X1)),
    inference(equality_inference,[],[16229]) ).

cnf(i_0_19614,plain,
    c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(equality_inference,[],[16265]) ).

cnf(i_0_19615,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,[],[16282]) ).

cnf(i_0_19616,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,[],[16310]) ).

cnf(i_0_19617,plain,
    X1 = X1,
    inference(equality_inference,[],[16330]) ).

cnf(i_0_19618,plain,
    ( ~ class_Rings_Ocomm__semiring__1(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X2))) ),
    inference(equality_inference,[],[16339]) ).

cnf(i_0_19619,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,[],[16344]) ).

cnf(i_0_19620,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,[],[16373]) ).

cnf(i_0_19621,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2)),X2) = X3
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X2))) ),
    inference(equality_inference,[],[16375]) ).

cnf(i_0_19622,plain,
    ( ~ class_Divides_Osemiring__div(X1)
    | X2 = c_Groups_Ozero__class_Ozero(X1)
    | X3 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X3),X2)),X2)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X3)) ),
    inference(equality_inference,[],[16376]) ).

cnf(i_0_19623,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,[],[16398]) ).

cnf(i_0_19624,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(hAPP(c_Set_Oinsert(X1),X2),X3))),
    inference(equality_inference,[],[16403]) ).

cnf(i_0_19625,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,[],[16424]) ).

cnf(i_0_19626,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,[],[16430]) ).

cnf(i_0_19627,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[16515]) ).

cnf(i_0_19628,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),X2)),
    inference(equality_inference,[],[16516]) ).

cnf(i_0_19629,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,[],[16517]) ).

cnf(i_0_19630,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,[],[16522]) ).

cnf(i_0_19631,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,[],[16524]) ).

cnf(i_0_19632,plain,
    X1 = X1,
    inference(equality_inference,[],[16525]) ).

cnf(i_0_19633,plain,
    X1 = X1,
    inference(equality_inference,[],[16527]) ).

cnf(i_0_19634,plain,
    X1 = X1,
    inference(equality_inference,[],[16529]) ).

cnf(i_0_19635,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,[],[16533]) ).

cnf(i_0_19636,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,[],[16556]) ).

cnf(i_0_19637,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,[],[16558]) ).

cnf(i_0_19638,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,[],[16559]) ).

cnf(i_0_19639,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,[],[16622]) ).

cnf(i_0_19640,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,[],[16623]) ).

cnf(i_0_19641,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,[],[16658]) ).

cnf(i_0_19642,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,[],[16681]) ).

cnf(i_0_19643,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,[],[16682]) ).

cnf(i_0_19644,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,[],[16702]) ).

cnf(i_0_19645,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,[],[16713]) ).

cnf(i_0_19646,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,[],[16714]) ).

cnf(i_0_19647,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,[],[16732]) ).

cnf(i_0_19648,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,[],[16747]) ).

cnf(i_0_19649,plain,
    X1 = X1,
    inference(equality_inference,[],[16748]) ).

cnf(i_0_19650,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,[],[16761]) ).

cnf(i_0_19651,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,[],[16798]) ).

cnf(i_0_19652,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,[],[16824]) ).

cnf(i_0_19653,plain,
    hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X1),X2),X3),X2)),
    inference(equality_inference,[],[16831]) ).

cnf(i_0_19654,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,[],[16856]) ).

cnf(i_0_19655,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,[],[16857]) ).

cnf(i_0_19656,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,[],[16911]) ).

cnf(i_0_19657,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,[],[16912]) ).

cnf(i_0_19658,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,[],[16931]) ).

cnf(i_0_19659,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,[],[16969]) ).

cnf(i_0_19660,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),c_List_Olists(X1,X2))),
    inference(equality_inference,[],[16991]) ).

cnf(i_0_19661,plain,
    ( ~ c_List_Olinorder__class_Osorted(X1,X2)
    | ~ class_Orderings_Olinorder(X1)
    | X2 = esk453_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,[],[17009]) ).

cnf(i_0_19662,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,[],[17015]) ).

cnf(i_0_19663,plain,
    ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
    inference(equality_inference,[],[17018]) ).

cnf(i_0_19664,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,[],[17029]) ).

cnf(i_0_19665,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,[],[17030]) ).

cnf(i_0_19666,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,[],[17031]) ).

cnf(i_0_19667,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,[],[17032]) ).

cnf(i_0_19668,plain,
    X1 = X1,
    inference(equality_inference,[],[17033]) ).

cnf(i_0_19669,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,[],[17041]) ).

cnf(i_0_19670,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,[],[17042]) ).

cnf(i_0_19671,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,[],[17043]) ).

cnf(i_0_19672,plain,
    ( ~ class_Rings_Odvd(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X2),X3))) ),
    inference(equality_inference,[],[17099]) ).

cnf(i_0_19673,plain,
    ( ~ class_Rings_Oidom(X1)
    | X2 = X2
    | X2 = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X2) ),
    inference(equality_inference,[],[17118]) ).

cnf(i_0_19674,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,[],[17122]) ).

cnf(i_0_19675,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,[],[17123]) ).

cnf(i_0_19676,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,[],[17124]) ).

cnf(i_0_19677,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,[],[17127]) ).

cnf(i_0_19678,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,[],[17128]) ).

cnf(i_0_19679,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,[],[17194]) ).

cnf(i_0_19680,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17198]) ).

cnf(i_0_19681,plain,
    ( ~ class_Orderings_Oorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17200]) ).

cnf(i_0_19682,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17201]) ).

cnf(i_0_19683,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X2),X2)) ),
    inference(equality_inference,[],[17202]) ).

cnf(i_0_19684,plain,
    ( ~ class_Rings_Olinordered__idom(X1)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X2),X2)) ),
    inference(equality_inference,[],[17207]) ).

cnf(i_0_19685,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17208]) ).

cnf(i_0_19686,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,[],[17222]) ).

cnf(i_0_19687,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[17224]) ).

cnf(i_0_19688,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__ab__semigroup__add(X2) ),
    inference(equality_inference,[],[17225]) ).

cnf(i_0_19689,plain,
    ( X1 = X1
    | ~ class_Groups_Ocancel__semigroup__add(X2) ),
    inference(equality_inference,[],[17227]) ).

cnf(i_0_19690,plain,
    X1 = X1,
    inference(equality_inference,[],[17228]) ).

cnf(i_0_19691,plain,
    X1 = X1,
    inference(equality_inference,[],[17229]) ).

cnf(i_0_19692,plain,
    X1 = X1,
    inference(equality_inference,[],[17230]) ).

cnf(i_0_19693,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,[],[17236]) ).

cnf(i_0_19694,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,[],[17237]) ).

cnf(i_0_19695,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,[],[17238]) ).

cnf(i_0_19696,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,[],[17251]) ).

cnf(i_0_19697,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,[],[17252]) ).

cnf(i_0_19698,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,[],[17253]) ).

cnf(i_0_19699,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,[],[17256]) ).

cnf(i_0_19700,plain,
    X1 = X1,
    inference(equality_inference,[],[17264]) ).

cnf(i_0_19701,plain,
    X1 = X1,
    inference(equality_inference,[],[17265]) ).

cnf(i_0_19702,plain,
    X1 = X1,
    inference(equality_inference,[],[17266]) ).

cnf(i_0_19703,plain,
    X1 = X1,
    inference(equality_inference,[],[17267]) ).

cnf(i_0_19704,plain,
    c_List_Oremove1(X1,X2,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X3)) = X3,
    inference(equality_inference,[],[17292]) ).

cnf(i_0_19705,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,[],[17301]) ).

cnf(i_0_19706,plain,
    hBOOL(hAPP(hAPP(c_member(X1),X2),hAPP(c_fequal,X2))),
    inference(equality_inference,[],[17324]) ).

cnf(i_0_19707,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(equality_inference,[],[17331]) ).

cnf(i_0_19708,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
    inference(equality_inference,[],[17339]) ).

cnf(i_0_19709,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17343]) ).

cnf(i_0_19710,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17344]) ).

cnf(i_0_19711,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,[],[17347]) ).

cnf(i_0_19712,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17350]) ).

cnf(i_0_19713,plain,
    ( X1 = X1
    | X2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(equality_inference,[],[17352]) ).

cnf(i_0_19714,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,[],[17353]) ).

cnf(i_0_19715,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,[],[17361]) ).

cnf(i_0_19716,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,[],[17362]) ).

cnf(i_0_19717,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,[],[17364]) ).

cnf(i_0_19718,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,[],[17365]) ).

cnf(i_0_19719,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,[],[17366]) ).

cnf(i_0_19720,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,[],[17367]) ).

cnf(i_0_19721,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,[],[17369]) ).

cnf(i_0_19722,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,[],[17370]) ).

cnf(i_0_19723,plain,
    ( ~ c_Equiv__Relations_Oequivp(X1,X2)
    | hBOOL(hAPP(hAPP(X2,X3),X3)) ),
    inference(equality_inference,[],[17377]) ).

cnf(i_0_19724,plain,
    X1 = X1,
    inference(equality_inference,[],[17387]) ).

cnf(i_0_19725,plain,
    X1 = X1,
    inference(equality_inference,[],[17388]) ).

cnf(i_0_19726,plain,
    X1 = X1,
    inference(equality_inference,[],[17389]) ).

cnf(i_0_19727,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,[],[17395]) ).

cnf(i_0_19728,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,[],[17403]) ).

cnf(i_0_19729,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X1))),
    inference(equality_inference,[],[17412]) ).

cnf(i_0_19730,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,[],[17431]) ).

cnf(i_0_19731,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,[],[17432]) ).

cnf(i_0_19732,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,[],[17438]) ).

cnf(i_0_19733,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,[],[17446]) ).

cnf(i_0_19734,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,[],[17463]) ).

cnf(i_0_19735,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,[],[17464]) ).

cnf(i_0_19736,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,[],[17484]) ).

cnf(i_0_19737,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,[],[17485]) ).

cnf(i_0_19738,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,[],[17487]) ).

cnf(i_0_19739,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,[],[17488]) ).

cnf(i_0_19740,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,[],[17491]) ).

cnf(i_0_19741,plain,
    X1 = X1,
    inference(equality_inference,[],[17492]) ).

cnf(i_0_19742,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,[],[17496]) ).

cnf(i_0_19743,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,[],[17497]) ).

cnf(i_0_19744,plain,
    c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Olist_ONil(X1))) = X2,
    inference(equality_inference,[],[17501]) ).

cnf(i_0_19745,plain,
    ( ~ epred2_3(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
    | hBOOL(hAPP(X1,X2)) ),
    inference(equality_inference,[],[17518]) ).

cnf(i_0_19746,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17549]) ).

cnf(i_0_19747,plain,
    ( ~ class_Orderings_Opreorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17550]) ).

cnf(i_0_19748,plain,
    ( ~ class_Orderings_Oorder(X1)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X2),X2)) ),
    inference(equality_inference,[],[17551]) ).

cnf(i_0_19749,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,[],[17598]) ).

cnf(i_0_19750,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,[],[17603]) ).

cnf(i_0_19751,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,[],[17607]) ).

cnf(i_0_19752,plain,
    hAPP(hAPP(c_List_Omap(X1,X2),X3),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X2),
    inference(equality_inference,[],[17633]) ).

cnf(i_0_19753,plain,
    hAPP(hAPP(c_List_Olist__update(X1,c_List_Olist_ONil(X1)),X2),X3) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17634]) ).

cnf(i_0_19754,plain,
    c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X3),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[17635]) ).

cnf(i_0_19755,plain,
    ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X2,X1)))
    | ~ hBOOL(hAPP(X1,X3)) ),
    inference(equality_inference,[],[17640]) ).

cnf(i_0_19756,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,[],[17662]) ).

cnf(i_0_19757,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,[],[17666]) ).

cnf(i_0_19758,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,[],[17667]) ).

cnf(i_0_19759,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17672]) ).

cnf(i_0_19760,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17673]) ).

cnf(i_0_19761,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
    inference(equality_inference,[],[17676]) ).

cnf(i_0_19762,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,[],[17680]) ).

cnf(i_0_19763,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,[],[17686]) ).

cnf(i_0_19764,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,[],[17718]) ).

cnf(i_0_19765,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,[],[17735]) ).

cnf(i_0_19766,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,[],[17739]) ).

cnf(i_0_19767,plain,
    ( ~ class_Int_Onumber__ring(X1)
    | ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17790]) ).

cnf(i_0_19768,plain,
    hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
    inference(equality_inference,[],[17792]) ).

cnf(i_0_19769,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17835]) ).

cnf(i_0_19770,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17836]) ).

cnf(i_0_19771,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17837]) ).

cnf(i_0_19772,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17838]) ).

cnf(i_0_19773,plain,
    ( ~ class_Int_Oring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17839]) ).

cnf(i_0_19774,plain,
    ( ~ class_Lattices_Oboolean__algebra(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17840]) ).

cnf(i_0_19775,plain,
    ( ~ class_Groups_Ogroup__add(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17841]) ).

cnf(i_0_19776,plain,
    ( ~ class_Nat_Osemiring__char__0(X1)
    | X2 = X2 ),
    inference(equality_inference,[],[17842]) ).

cnf(i_0_19777,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,[],[17851]) ).

cnf(i_0_19778,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,[],[17852]) ).

cnf(i_0_19779,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,[],[17853]) ).

cnf(i_0_19780,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,[],[17854]) ).

cnf(i_0_19781,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,[],[17855]) ).

cnf(i_0_19782,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,[],[17856]) ).

cnf(i_0_19783,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,[],[17857]) ).

cnf(i_0_19784,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
    inference(equality_inference,[],[17872]) ).

cnf(i_0_19785,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,[],[17873]) ).

cnf(i_0_19786,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,[],[17885]) ).

cnf(i_0_19787,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,[],[17886]) ).

cnf(i_0_19788,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,[],[17887]) ).

cnf(i_0_19789,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,[],[17888]) ).

cnf(i_0_19790,plain,
    X1 = X1,
    inference(equality_inference,[],[17911]) ).

cnf(i_0_19791,plain,
    hAPP(hAPP(c_List_Otake(X1),X2),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17918]) ).

cnf(i_0_19792,plain,
    c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17923]) ).

cnf(i_0_19793,plain,
    c_List_Olist_ONil(X1) = c_List_Oreplicate(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X2),
    inference(equality_inference,[],[17924]) ).

cnf(i_0_19794,plain,
    hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[17936]) ).

cnf(i_0_19795,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,[],[17938]) ).

cnf(i_0_19796,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,[],[17940]) ).

cnf(i_0_19797,plain,
    hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X2) = X2,
    inference(equality_inference,[],[17942]) ).

cnf(i_0_19798,plain,
    hAPP(hAPP(c_List_Oappend(X1),X2),c_List_Olist_ONil(X1)) = X2,
    inference(equality_inference,[],[17943]) ).

cnf(i_0_19799,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),c_List_Olist_ONil(X2)),X1),
    inference(equality_inference,[],[17944]) ).

cnf(i_0_19800,plain,
    X1 = hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Olist_ONil(X2)),
    inference(equality_inference,[],[17945]) ).

cnf(i_0_19801,plain,
    X1 = X1,
    inference(equality_inference,[],[17994]) ).

cnf(i_0_19802,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,[],[17995]) ).

cnf(i_0_19803,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,[],[17996]) ).

cnf(i_0_19804,plain,
    hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X2)) = X2,
    inference(equality_inference,[],[17998]) ).

cnf(i_0_19805,plain,
    X1 = hAPP(c_List_Orev(X2),hAPP(c_List_Orev(X2),X1)),
    inference(equality_inference,[],[17999]) ).

cnf(i_0_19806,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,[],[18005]) ).

cnf(i_0_19807,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,[],[18006]) ).

cnf(i_0_19808,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,[],[18008]) ).

cnf(i_0_19809,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,[],[18009]) ).

cnf(i_0_19810,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1) = X1,
    inference(equality_inference,[],[18020]) ).

cnf(i_0_19811,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Int_OPls,
    inference(equality_inference,[],[18049]) ).

cnf(i_0_19812,plain,
    c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls),
    inference(equality_inference,[],[18050]) ).

cnf(i_0_19813,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,[],[18077]) ).

cnf(i_0_19814,plain,
    X1 = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),
    inference(equality_inference,[],[18082]) ).

cnf(i_0_19815,plain,
    X1 = X1,
    inference(equality_inference,[],[18088]) ).

cnf(i_0_19816,plain,
    X1 = X1,
    inference(equality_inference,[],[18089]) ).

cnf(i_0_19817,plain,
    X1 = X1,
    inference(equality_inference,[],[18090]) ).

cnf(i_0_19818,plain,
    X1 = X1,
    inference(equality_inference,[],[18092]) ).

cnf(i_0_19819,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,[],[18101]) ).

cnf(i_0_19820,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,[],[18102]) ).

cnf(i_0_19821,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,[],[18103]) ).

cnf(i_0_19822,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,[],[18130]) ).

cnf(i_0_19823,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,[],[18131]) ).

cnf(i_0_19824,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,[],[18132]) ).

cnf(i_0_19825,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,[],[18146]) ).

cnf(i_0_19826,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,[],[18147]) ).

cnf(i_0_19827,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,[],[18163]) ).

cnf(i_0_19828,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,[],[18164]) ).

cnf(i_0_19829,plain,
    hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18166]) ).

cnf(i_0_19830,plain,
    hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18167]) ).

cnf(i_0_19831,plain,
    c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[18168]) ).

cnf(i_0_19832,plain,
    ( ~ class_Orderings_Olinorder(X1)
    | c_List_Olinorder__class_Osorted(X1,c_List_Olist_ONil(X1)) ),
    inference(equality_inference,[],[18184]) ).

cnf(i_0_19833,plain,
    ( ~ class_Rings_Osemiring__1(X1)
    | c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1)) ),
    inference(equality_inference,[],[18185]) ).

cnf(i_0_19834,plain,
    c_List_Oremdups(X1,c_List_Olist_ONil(X1)) = c_List_Olist_ONil(X1),
    inference(equality_inference,[],[18191]) ).

cnf(i_0_19835,plain,
    c_List_Olist_ONil(X1) = c_List_Oremdups(X1,c_List_Olist_ONil(X1)),
    inference(equality_inference,[],[18192]) ).

cnf(i_0_19836,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,[],[18193]) ).

cnf(i_0_19837,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,[],[18218]) ).

cnf(i_0_19838,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,[],[18219]) ).

cnf(i_0_19839,plain,
    c_Nitpick_Onat__gcd(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
    inference(equality_inference,[],[18220]) ).

cnf(i_0_19840,plain,
    c_Random_Oinc__shift(X1,X1) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral),
    inference(equality_inference,[],[18224]) ).

cnf(i_0_19841,plain,
    $false,
    inference(scs_inference,[],[i_0_13020,i_0_17246,i_0_15603,i_0_13665]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWW365+1 : TPTP v9.2.1. Released v5.2.0.
% 0.00/0.12  % Command    : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33  % Computer : n017.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit   : 300
% 0.14/0.33  % WCLimit    : 300
% 0.14/0.33  % DateTime   : Tue May  5 06:40:27 EDT 2026
% 0.14/0.33  % CPUTime    : 
% 0.14/0.34  % start to proof: theBenchmark
% 38.70/22.39  % Version  : CSE_E---1.7
% 38.70/22.39  % Problem  : theBenchmark.p
% 38.70/22.39  % SZS status Theorem for theBenchmark.p
% 38.70/22.39  % SZS output start CNFRefutation
% See solution above
% 39.63/22.84  % Total time : 22.022s
%------------------------------------------------------------------------------